Organic/inorganic hybrid synaptic transistors gated by proton conducting methylcellulose films

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wan, Chang Jin; Wan, Qing, E-mail: wanqing@nju.edu.cn, E-mail: yshi@nju.edu.cn; Ningbo Institute of Material Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201

The idea of building a brain-inspired cognitive system has been around for several decades. Recently, electric-double-layer transistors gated by ion conducting electrolytes were reported as the promising candidates for synaptic electronics and neuromorphic system. In this letter, indium-zinc-oxide transistors gated by proton conducting methylcellulose electrolyte films were experimentally demonstrated with synaptic plasticity including paired-pulse facilitation and spatiotemporal-correlated dynamic logic. More importantly, a model based on proton-related electric-double-layer modulation and stretched-exponential decay function was proposed, and the theoretical results are in good agreement with the experimentally measured synaptic behaviors.

Dynamic modeling of sludge compaction and consolidation processes in wastewater secondary settling tanks.

PubMed

Abusam, A; Keesman, K J

2009-01-01

The double exponential settling model is the widely accepted model for wastewater secondary settling tanks. However, this model does not estimate accurately solids concentrations in the settler underflow stream, mainly because sludge compression and consolidation processes are not considered. In activated sludge systems, accurate estimation of the solids in the underflow stream will facilitate the calibration process and can lead to correct estimates of particularly kinetic parameters related to biomass growth. Using principles of compaction and consolidation, as in soil mechanics, a dynamic model of the sludge consolidation processes taking place in the secondary settling tanks is developed and incorporated to the commonly used double exponential settling model. The modified double exponential model is calibrated and validated using data obtained from a full-scale wastewater treatment plant. Good agreement between predicted and measured data confirmed the validity of the modified model.

Very slow lava extrusion continued for more than five years after the 2011 Shinmoedake eruption observed from SAR interferometry

NASA Astrophysics Data System (ADS)

Ozawa, T.; Miyagi, Y.

2017-12-01

Shinmoe-dake located to SW Japan erupted in January 2011 and lava accumulated in the crater (e.g., Ozawa and Kozono, EPS, 2013). Last Vulcanian eruption occurred in September 2011, and after that, no eruption has occurred until now. Miyagi et al. (GRL, 2014) analyzed TerraSAR-X and Radarsat-2 SAR data acquired after the last eruption and found continuous inflation in the crater. Its inflation decayed with time, but had not terminated in May 2013. Since the time-series of inflation volume change rate fitted well to the exponential function with the constant term, we suggested that lava extrusion had continued in long-term due to deflation of shallow magma source and to magma supply from deeper source. To investigate its deformation after that, we applied InSAR to Sentinel-1 and ALOS-2 SAR data. Inflation decayed further, and almost terminated in the end of 2016. It means that this deformation has continued more than five years from the last eruption. We have found that the time series of inflation volume change rate fits better to the double-exponential function than single-exponential function with the constant term. The exponential component with the short time constant has almost settled in one year from the last eruption. Although InSAR result from TerraSAR-X data of November 2011 and May 2013 indicated deflation of shallow source under the crater, such deformation has not been obtained from recent SAR data. It suggests that this component has been due to deflation of shallow magma source with excess pressure. In this study, we found the possibility that long-term component also decayed exponentially. Then this factor may be deflation of deep source or delayed vesiculation.

Generating functions for weighted Hurwitz numbers

NASA Astrophysics Data System (ADS)

Guay-Paquet, Mathieu; Harnad, J.

2017-08-01

Double Hurwitz numbers enumerating weighted n-sheeted branched coverings of the Riemann sphere or, equivalently, weighted paths in the Cayley graph of Sn generated by transpositions are determined by an associated weight generating function. A uniquely determined 1-parameter family of 2D Toda τ -functions of hypergeometric type is shown to consist of generating functions for such weighted Hurwitz numbers. Four classical cases are detailed, in which the weighting is uniform: Okounkov's double Hurwitz numbers for which the ramification is simple at all but two specified branch points; the case of Belyi curves, with three branch points, two with specified profiles; the general case, with a specified number of branch points, two with fixed profiles, the rest constrained only by the genus; and the signed enumeration case, with sign determined by the parity of the number of branch points. Using the exponentiated quantum dilogarithm function as a weight generator, three new types of weighted enumerations are introduced. These determine quantum Hurwitz numbers depending on a deformation parameter q. By suitable interpretation of q, the statistical mechanics of quantum weighted branched covers may be related to that of Bosonic gases. The standard double Hurwitz numbers are recovered in the classical limit.

Characteristics of a Linearly Tapered Slot Antenna (LTSA) Conformed Longitudinally Around a Cylinder

NASA Technical Reports Server (NTRS)

Jordan, Jennifer L.; Ponchak, George E.; Tavassolian, Negar; Tentzeris, Manos M.

2007-01-01

The family of tapered slot antennas (TSA s) is suitable for numerous applications. Their ease of fabrication, wide bandwidth, and high gain make them desirable for military and commercial systems. Fabrication on thin, flexible substrates allows the TSA to be conformed over a given body, such as an aircraft wing or a piece of clothing for wearable networks. Previously, a Double Exponentially Tapered Slot Antenna (DETSA) was conformed around an exponential curvature, which showed that the main beam skewed towards the direction of curvature. This paper presents a Linearly Tapered Slot Antenna (LTSA) conformed longitudinally around a cylinder. Measured and simulated radiation patterns and the direction of maximum H co-polarization (Hco) as a function of the cylinder radius are presented.

dPotFit: A computer program to fit diatomic molecule spectral data to potential energy functions

NASA Astrophysics Data System (ADS)

Le Roy, Robert J.

2017-01-01

This paper describes program dPotFit, which performs least-squares fits of diatomic molecule spectroscopic data consisting of any combination of microwave, infrared or electronic vibrational bands, fluorescence series, and tunneling predissociation level widths, involving one or more electronic states and one or more isotopologs, and for appropriate systems, second virial coefficient data, to determine analytic potential energy functions defining the observed levels and other properties of each state. Four families of analytical potential functions are available for fitting in the current version of dPotFit: the Expanded Morse Oscillator (EMO) function, the Morse/Long-Range (MLR) function, the Double-Exponential/Long-Range (DELR) function, and the 'Generalized Potential Energy Function' (GPEF) of Šurkus, which incorporates a variety of polynomial functional forms. In addition, dPotFit allows sets of experimental data to be tested against predictions generated from three other families of analytic functions, namely, the 'Hannover Polynomial' (or "X-expansion") function, and the 'Tang-Toennies' and Scoles-Aziz 'HFD', exponential-plus-van der Waals functions, and from interpolation-smoothed pointwise potential energies, such as those obtained from ab initio or RKR calculations. dPotFit also allows the fits to determine atomic-mass-dependent Born-Oppenheimer breakdown functions, and singlet-state Λ-doubling, or 2Σ splitting radial strength functions for one or more electronic states. dPotFit always reports both the 95% confidence limit uncertainty and the "sensitivity" of each fitted parameter; the latter indicates the number of significant digits that must be retained when rounding fitted parameters, in order to ensure that predictions remain in full agreement with experiment. It will also, if requested, apply a "sequential rounding and refitting" procedure to yield a final parameter set defined by a minimum number of significant digits, while ensuring no significant loss of accuracy in the predictions yielded by those parameters.

Impact of inhomogeneity on SH-type wave propagation in an initially stressed composite structure

NASA Astrophysics Data System (ADS)

Saha, S.; Chattopadhyay, A.; Singh, A. K.

2018-02-01

The present analysis has been made on the influence of distinct form of inhomogeneity in a composite structure comprised of double superficial layers lying over a half-space, on the phase velocity of SH-type wave propagating through it. Propagation of SH-type wave in the said structure has been examined in four distinct cases of inhomogeneity viz. when inhomogeneity in double superficial layer is due to exponential variation in density only (Case I); when inhomogeneity in double superficial layers is due to exponential variation in rigidity only (Case II); when inhomogeneity in double superficial layer is due to exponential variation in rigidity, density and initial stress (Case III) and when inhomogeneity in double superficial layer is due to linear variation in rigidity, density and initial stress (Case IV). Closed-form expression of dispersion relation has been accomplished for all four aforementioned cases through extensive application of Debye asymptotic analysis. Deduced dispersion relations for all the cases are found in well-agreement to the classical Love-wave equation. Numerical computation has been carried out to graphically demonstrate the effect of inhomogeneity parameters, initial stress parameters as well as width ratio associated with double superficial layers in the composite structure for each of the four aforesaid cases on dispersion curve. Meticulous examination of distinct cases of inhomogeneity and initial stress in context of considered problem has been carried out with detailed analysis in a comparative approach.

Understanding Exponential Growth: As Simple as a Drop in a Bucket.

ERIC Educational Resources Information Center

Goldberg, Fred; Shuman, James

1984-01-01

Provides procedures for a simple laboratory activity on exponential growth and its characteristic doubling time. The equipment needed consists of a large plastic bucket, an eyedropper, a stopwatch, an assortment of containers and graduated cylinders, and a supply of water. (JN)

15-digit accuracy calculations of Ambartsumian-Chandrasekhar's H-functions for four-term phase functions with the double-exponential formula

NASA Astrophysics Data System (ADS)

Kawabata, Kiyoshi

2018-01-01

We have established an iterative scheme to calculate with 15-digit accuracy the numerical values of Ambartsumian-Chandrasekhar's H-functions for anisotropic scattering characterized by the four-term phase function: the method incorporates some advantageous features of the iterative procedure of Kawabata (Astrophys. Space Sci. 358:32, 2015) and the double-exponential integration formula (DE-formula) of Takahashi and Mori (Publ. Res. Inst. Math. Sci. Kyoto Univ. 9:721, 1974), which proved highly effective in Kawabata (Astrophys. Space Sci. 361:373, 2016). Actual calculations of the H-functions have been carried out employing 27 selected cases of the phase function, 56 values of the single scattering albedo π0, and 36 values of an angular variable μ(= cosθ), with θ being the zenith angle specifying the direction of incidence and/or emergence of radiation. Partial results obtained for conservative isotropic scattering, Rayleigh scattering, and anisotropic scattering due to a full four-term phase function are presented. They indicate that it is important to simultaneously verify accuracy of the numerical values of the H-functions for μ<0.05, the domain often neglected in tabulation. As a sample application of the isotropic scattering H-function, an attempt is made in Appendix to simulate by iteratively solving the Ambartsumian equation the values of the plane and spherical albedos of a semi-infinite, homogeneous atmosphere calculated by Rogovtsov and Borovik (J. Quant. Spectrosc. Radiat. Transf. 183:128, 2016), who employed their analytical representations for these quantities and the single-term and two-term Henyey-Greenstein phase functions of appreciably high degrees of anisotropy. While our results are in satisfactory agreement with theirs, our procedure is in need of a faster algorithm to routinely deal with problems involving highly anisotropic phase functions giving rise to near-conservative scattering.

Unfolding of Ubiquitin Studied by Picosecond Time-Resolved Fluorescence of the Tyrosine Residue

PubMed Central

Noronha, Melinda; Lima, João C.; Bastos, Margarida; Santos, Helena; Maçanita, António L.

2004-01-01

The photophysics of the single tyrosine in bovine ubiquitin (UBQ) was studied by picosecond time-resolved fluorescence spectroscopy, as a function of pH and along thermal and chemical unfolding, with the following results: First, at room temperature (25°C) and below pH 1.5, native UBQ shows single-exponential decays. From pH 2 to 7, triple-exponential decays were observed and the three decay times were attributed to the presence of tyrosine, a tyrosine-carboxylate hydrogen-bonded complex, and excited-state tyrosinate. Second, at pH 1.5, the water-exposed tyrosine of either thermally or chemically unfolded UBQ decays as a sum of two exponentials. The double-exponential decays were interpreted and analyzed in terms of excited-state intramolecular electron transfer from the phenol to the amide moiety, occurring in one of the three rotamers of tyrosine in UBQ. The values of the rate constants indicate the presence of different unfolded states and an increase in the mobility of the tyrosine residue during unfolding. Finally, from the pre-exponential coefficients of the fluorescence decays, the unfolding equilibrium constants (KU) were calculated, as a function of temperature or denaturant concentration. Despite the presence of different unfolded states, both thermal and chemical unfolding data of UBQ could be fitted to a two-state model. The thermodynamic parameters Tm = 54.6°C, ΔHTm = 56.5 kcal/mol, and ΔCp = 890 cal/mol//K, were determined from the unfolding equilibrium constants calculated accordingly, and compared to values obtained by differential scanning calorimetry also under the assumption of a two-state transition, Tm = 57.0°C, ΔHm= 51.4 kcal/mol, and ΔCp = 730 cal/mol//K. PMID:15454455

Inferring metabolic networks using the Bayesian adaptive graphical lasso with informative priors.

PubMed

Peterson, Christine; Vannucci, Marina; Karakas, Cemal; Choi, William; Ma, Lihua; Maletić-Savatić, Mirjana

2013-10-01

Metabolic processes are essential for cellular function and survival. We are interested in inferring a metabolic network in activated microglia, a major neuroimmune cell in the brain responsible for the neuroinflammation associated with neurological diseases, based on a set of quantified metabolites. To achieve this, we apply the Bayesian adaptive graphical lasso with informative priors that incorporate known relationships between covariates. To encourage sparsity, the Bayesian graphical lasso places double exponential priors on the off-diagonal entries of the precision matrix. The Bayesian adaptive graphical lasso allows each double exponential prior to have a unique shrinkage parameter. These shrinkage parameters share a common gamma hyperprior. We extend this model to create an informative prior structure by formulating tailored hyperpriors on the shrinkage parameters. By choosing parameter values for each hyperprior that shift probability mass toward zero for nodes that are close together in a reference network, we encourage edges between covariates with known relationships. This approach can improve the reliability of network inference when the sample size is small relative to the number of parameters to be estimated. When applied to the data on activated microglia, the inferred network includes both known relationships and associations of potential interest for further investigation.

Inferring metabolic networks using the Bayesian adaptive graphical lasso with informative priors

PubMed Central

PETERSON, CHRISTINE; VANNUCCI, MARINA; KARAKAS, CEMAL; CHOI, WILLIAM; MA, LIHUA; MALETIĆ-SAVATIĆ, MIRJANA

2014-01-01

Metabolic processes are essential for cellular function and survival. We are interested in inferring a metabolic network in activated microglia, a major neuroimmune cell in the brain responsible for the neuroinflammation associated with neurological diseases, based on a set of quantified metabolites. To achieve this, we apply the Bayesian adaptive graphical lasso with informative priors that incorporate known relationships between covariates. To encourage sparsity, the Bayesian graphical lasso places double exponential priors on the off-diagonal entries of the precision matrix. The Bayesian adaptive graphical lasso allows each double exponential prior to have a unique shrinkage parameter. These shrinkage parameters share a common gamma hyperprior. We extend this model to create an informative prior structure by formulating tailored hyperpriors on the shrinkage parameters. By choosing parameter values for each hyperprior that shift probability mass toward zero for nodes that are close together in a reference network, we encourage edges between covariates with known relationships. This approach can improve the reliability of network inference when the sample size is small relative to the number of parameters to be estimated. When applied to the data on activated microglia, the inferred network includes both known relationships and associations of potential interest for further investigation. PMID:24533172

An Optimization of Inventory Demand Forecasting in University Healthcare Centre

NASA Astrophysics Data System (ADS)

Bon, A. T.; Ng, T. K.

2017-01-01

Healthcare industry becomes an important field for human beings nowadays as it concerns about one’s health. With that, forecasting demand for health services is an important step in managerial decision making for all healthcare organizations. Hence, a case study was conducted in University Health Centre to collect historical demand data of Panadol 650mg for 68 months from January 2009 until August 2014. The aim of the research is to optimize the overall inventory demand through forecasting techniques. Quantitative forecasting or time series forecasting model was used in the case study to forecast future data as a function of past data. Furthermore, the data pattern needs to be identified first before applying the forecasting techniques. Trend is the data pattern and then ten forecasting techniques are applied using Risk Simulator Software. Lastly, the best forecasting techniques will be find out with the least forecasting error. Among the ten forecasting techniques include single moving average, single exponential smoothing, double moving average, double exponential smoothing, regression, Holt-Winter’s additive, Seasonal additive, Holt-Winter’s multiplicative, seasonal multiplicative and Autoregressive Integrated Moving Average (ARIMA). According to the forecasting accuracy measurement, the best forecasting technique is regression analysis.

Topological Defects in Double Exchange Materials and Anomalous Hall Resistance.

NASA Astrophysics Data System (ADS)

Calderón, M. J.; Brey, L.

2000-03-01

Recently it has been proposed that the anomalous Hall effect observed in Double Exchange materials is due to Berry phase effects caused by carrier hopping in a nontrivial spins background (J.Ye et al.) Phys.Rev.Lett. 83, 3737 1999.In order to study this possibility we have performed Monte Carlo simulations of the Double Exchange model and we have computed, as a function of the temperature, the number of topological defects in the system and the internal gauge magnetic field associated with these defects. In the simplest Double Exchange model the gauge magnetic field is random, and its average value is zero. The inclusion in the problem of spin-orbit coupling privileges the opposite direction of the magnetization and an anomalous Hall resistance (AHR) effect arises. We have computed the AHR, and we have obtained its temperature dependence. In agreement with previous experiments we obtain that AHR increases exponentially at low temperature and presents a maximum at a temperature slightly higher than the critical temperature.

Double slip effects of Magnetohydrodynamic (MHD) boundary layer flow over an exponentially stretching sheet with radiation, heat source and chemical reaction

NASA Astrophysics Data System (ADS)

Shaharuz Zaman, Azmanira; Aziz, Ahmad Sukri Abd; Ali, Zaileha Md

2017-09-01

The double slips effect on the magnetohydrodynamic boundary layer flow over an exponentially stretching sheet with suction/blowing, radiation, chemical reaction and heat source is presented in this analysis. By using the similarity transformation, the governing partial differential equations of momentum, energy and concentration are transformed into the non-linear ordinary equations. These equations are solved using Runge-Kutta-Fehlberg method with shooting technique in MAPLE software environment. The effects of the various parameter on the velocity, temperature and concentration profiles are graphically presented and discussed.

Cross-Conjugated Nanoarchitectures

DTIC Science & Technology

2013-08-23

compounds were further evaluated by Lippert –Mataga analysis of the fluorescence solvatochromism and measurement of quantum yields and fluorescence...1.9 1.1 A(mP)2A Cy 0.49 5.5 0.90 0.93 D(Th)2D Cy 0.008 1.1 0.07 9 A(Th)2A Tol 0.014 2.1f 0.07 4.7 a Calculated from Lippert –Mataga plots for...Δfʹ region of the Lippert –Mataga plot. d Double exponential fit: τ1 = 21.5 ns (73%) and τ2 = 3.7 ns (27%). e Double exponential fit: τ1 = 0.85 ns

Cyberinfrastructure for the NSF Ocean Observatories Initiative

NASA Astrophysics Data System (ADS)

Orcutt, J. A.; Vernon, F. L.; Arrott, M.; Chave, A.; Krueger, I.; Schofield, O.; Glenn, S.; Peach, C.; Nayak, A.

2007-12-01

The Internet today is vastly different than the Internet that we knew even five years ago and the changes that will be evident five years from now, when the NSF Ocean Observatories Initiative (OOI) prototype has been installed, are nearly unpredictable. Much of this progress is based on the exponential growth in capabilities of consumer electronics and information technology; the reality of this exponential behavior is rarely appreciated. For example, the number of transistors on a square cm of silicon will continue to double every 18 months, the density of disk storage will double every year, and network bandwidth will double every eight months. Today's desktop 2TB RAID will be 64TB and the 10Gbps Regional Scale Network fiber optical connection will be running at 1.8Tbps. The same exponential behavior characterizes the future of genome sequencing. The first two sequences of composites of individuals' genes cost tens of millions of dollars in 2001. Dr. Craig Venter just published a more accurate complete human genome (his own) at a cost on the order of 100,000. The J. Craig Venter Institute has provided support for the X Prize for Genomics offering 10M to the first successful sequencing of a human genome for $1,000. It's anticipated that the prize will be won within five years. Major advances in technology that are broadly viewed as disruptive or revolutionary rather than evolutionary will often depend upon the exploitation of exponential expansions in capability. Applications of these ideas to the OOI will be discussed. Specifically, the agile ability to scale cyberinfrastructure commensurate with the exponential growth of sensors, networks and computational capability and demand will be described.

Discrete sudden perturbation theory for inelastic scattering. I. Quantum and semiclassical treatment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cross, R.J.

1985-12-01

A double perturbation theory is constructed to treat rotationally and vibrationally inelastic scattering. It uses both the elastic scattering from the spherically averaged potential and the infinite-order sudden (IOS) approximation as the unperturbed solutions. First, a standard perturbation expansion is done to express the radial wave functions in terms of the elastic wave functions. The resulting coupled equations are transformed to the discrete-variable representation where the IOS equations are diagonal. Then, the IOS solutions are removed from the equations which are solved by an exponential perturbation approximation. The results for Ar+N/sub 2/ are very much more accurate than the IOSmore » and somewhat more accurate than a straight first-order exponential perturbation theory. The theory is then converted into a semiclassical, time-dependent form by using the WKB approximation. The result is an integral of the potential times a slowly oscillating factor over the classical trajectory. A method of interpolating the result is given so that the calculation is done at the average velocity for a given transition. With this procedure, the semiclassical version of the theory is more accurate than the quantum version and very much faster. Calculations on Ar+N/sub 2/ show the theory to be much more accurate than the infinite-order sudden (IOS) approximation and the exponential time-dependent perturbation theory.« less

Superionic state in double-layer capacitors with nanoporous electrodes.

PubMed

Kondrat, S; Kornyshev, A

2011-01-19

In recent experiments (Chmiola et al 2006 Science 313 1760; Largeot et al 2008 J. Am. Chem. Soc. 130 2730) an anomalous increase of the capacitance with a decrease of the pore size of a carbon-based porous electric double-layer capacitor has been observed. We explain this effect by image forces which exponentially screen out the electrostatic interactions of ions in the interior of a pore. Packing of ions of the same sign becomes easier and is mainly limited by steric interactions. We call this state 'superionic' and suggest a simple model to describe it. The model reveals the possibility of a voltage-induced first order transition between a cation(anion)-deficient phase and a cation(anion)-rich phase which manifests itself in a jump of capacitance as a function of voltage.

SU-E-T-259: Particle Swarm Optimization in Radial Dose Function Fitting for a Novel Iodine-125 Seed

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, X; Duan, J; Popple, R

2014-06-01

Purpose: To determine the coefficients of bi- and tri-exponential functions for the best fit of radial dose functions of the new iodine brachytherapy source: Iodine-125 Seed AgX-100. Methods: The particle swarm optimization (PSO) method was used to search for the coefficients of the biand tri-exponential functions that yield the best fit to data published for a few selected radial distances from the source. The coefficients were encoded into particles, and these particles move through the search space by following their local and global best-known positions. In each generation, particles were evaluated through their fitness function and their positions were changedmore » through their velocities. This procedure was repeated until the convergence criterion was met or the maximum generation was reached. All best particles were found in less than 1,500 generations. Results: For the I-125 seed AgX-100 considered as a point source, the maximum deviation from the published data is less than 2.9% for bi-exponential fitting function and 0.2% for tri-exponential fitting function. For its line source, the maximum deviation is less than 1.1% for bi-exponential fitting function and 0.08% for tri-exponential fitting function. Conclusion: PSO is a powerful method in searching coefficients for bi-exponential and tri-exponential fitting functions. The bi- and tri-exponential models of Iodine-125 seed AgX-100 point and line sources obtained with PSO optimization provide accurate analytical forms of the radial dose function. The tri-exponential fitting function is more accurate than the bi-exponential function.« less

On the Prony series representation of stretched exponential relaxation

NASA Astrophysics Data System (ADS)

Mauro, John C.; Mauro, Yihong Z.

2018-09-01

Stretched exponential relaxation is a ubiquitous feature of homogeneous glasses. The stretched exponential decay function can be derived from the diffusion-trap model, which predicts certain critical values of the fractional stretching exponent, β. In practical implementations of glass relaxation models, it is computationally convenient to represent the stretched exponential function as a Prony series of simple exponentials. Here, we perform a comprehensive mathematical analysis of the Prony series approximation of the stretched exponential relaxation, including optimized coefficients for certain critical values of β. The fitting quality of the Prony series is analyzed as a function of the number of terms in the series. With a sufficient number of terms, the Prony series can accurately capture the time evolution of the stretched exponential function, including its "fat tail" at long times. However, it is unable to capture the divergence of the first-derivative of the stretched exponential function in the limit of zero time. We also present a frequency-domain analysis of the Prony series representation of the stretched exponential function and discuss its physical implications for the modeling of glass relaxation behavior.

Polynomial Similarity Transformation Theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian

DOE Office of Scientific and Technical Information (OSTI.GOV)

Degroote, M.; Henderson, T. M.; Zhao, J.

We present a similarity transformation theory based on a polynomial form of a particle-hole pair excitation operator. In the weakly correlated limit, this polynomial becomes an exponential, leading to coupled cluster doubles. In the opposite strongly correlated limit, the polynomial becomes an extended Bessel expansion and yields the projected BCS wavefunction. In between, we interpolate using a single parameter. The e ective Hamiltonian is non-hermitian and this Polynomial Similarity Transformation Theory follows the philosophy of traditional coupled cluster, left projecting the transformed Hamiltonian onto subspaces of the Hilbert space in which the wave function variance is forced to be zero.more » Similarly, the interpolation parameter is obtained through minimizing the next residual in the projective hierarchy. We rationalize and demonstrate how and why coupled cluster doubles is ill suited to the strongly correlated limit whereas the Bessel expansion remains well behaved. The model provides accurate wave functions with energy errors that in its best variant are smaller than 1% across all interaction stengths. The numerical cost is polynomial in system size and the theory can be straightforwardly applied to any realistic Hamiltonian.« less

Dramatic changes in muscle contractile and structural properties after 2 botulinum toxin injections.

PubMed

Minamoto, Viviane B; Suzuki, Kentaro P; Bremner, Shannon N; Lieber, Richard L; Ward, Samuel R

2015-10-01

Botulinum toxin is frequently administered serially to maintain therapeutic muscle paralysis, but the effect of repeated doses on muscle function are largely unknown. This study characterized the muscle response to 2 onabotulinum toxin (BoNT) injections separated by 3 months. Animal subjects received a single toxin injection (n = 8), 2 BoNT injections separated by 3 months (n = 14), or 1 BoNT and 1 saline injection separated by 3 months (n = 8). The functional effect of 2 serial injections was exponentially greater than the effect of a single injection. While both groups treated with a single BoNT injection had decreased torque in the injected leg by approximately 50% relative to contralateral legs, the double BoNT injected group had decreased torque by over 95% relative to the preinjection level. Both single and double BoNT injections produced clear signs of fiber-type grouping. These experiments demonstrate a disproportionately greater effect of repeated BoNT injections. © 2015 Wiley Periodicals, Inc.

Individuality and universality in the growth-division laws of single E. coli cells

NASA Astrophysics Data System (ADS)

Kennard, Andrew S.; Osella, Matteo; Javer, Avelino; Grilli, Jacopo; Nghe, Philippe; Tans, Sander J.; Cicuta, Pietro; Cosentino Lagomarsino, Marco

2016-01-01

The mean size of exponentially dividing Escherichia coli cells in different nutrient conditions is known to depend on the mean growth rate only. However, the joint fluctuations relating cell size, doubling time, and individual growth rate are only starting to be characterized. Recent studies in bacteria reported a universal trend where the spread in both size and doubling times is a linear function of the population means of these variables. Here we combine experiments and theory and use scaling concepts to elucidate the constraints posed by the second observation on the division control mechanism and on the joint fluctuations of sizes and doubling times. We found that scaling relations based on the means collapse both size and doubling-time distributions across different conditions and explain how the shape of their joint fluctuations deviates from the means. Our data on these joint fluctuations highlight the importance of cell individuality: Single cells do not follow the dependence observed for the means between size and either growth rate or inverse doubling time. Our calculations show that these results emerge from a broad class of division control mechanisms requiring a certain scaling form of the "division hazard rate function," which defines the probability rate of dividing as a function of measurable parameters. This "model free" approach gives a rationale for the universal body-size distributions observed in microbial ecosystems across many microbial species, presumably dividing with multiple mechanisms. Additionally, our experiments show a crossover between fast and slow growth in the relation between individual-cell growth rate and division time, which can be understood in terms of different regimes of genome replication control.

TH-EF-207A-04: A Dynamic Contrast Enhanced Cone Beam CT Technique for Evaluation of Renal Functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Z; Shi, J; Yang, Y

Purpose: To develop a simple but robust method for the early detection and evaluation of renal functions using dynamic contrast enhanced cone beam CT technique. Methods: Experiments were performed on an integrated imaging and radiation research platform developed by our lab. Animals (n=3) were anesthetized with 20uL Ketamine/Xylazine cocktail, and then received 200uL injection of iodinated contrast agent Iopamidol via tail vein. Cone beam CT was acquired following contrast injection once per minute and up to 25 minutes. The cone beam CT was reconstructed with a dimension of 300×300×800 voxels of 130×130×130um voxel resolution. The middle kidney slices in themore » transvers and coronal planes were selected for image analysis. A double exponential function was used to fit the contrast enhanced signal intensity versus the time after contrast injection. Both pixel-based and region of interest (ROI)-based curve fitting were performed. Four parameters obtained from the curve fitting, namely the amplitude and flow constant for both contrast wash in and wash out phases, were investigated for further analysis. Results: Robust curve fitting was demonstrated for both pixel based (with R{sup 2}>0.8 for >85% pixels within the kidney contour) and ROI based (R{sup 2}>0.9 for all regions) analysis. Three different functional regions: renal pelvis, medulla and cortex, were clearly differentiated in the functional parameter map in the pixel based analysis. ROI based analysis showed the half-life T1/2 for contrast wash in and wash out phases were 0.98±0.15 and 17.04±7.16, 0.63±0.07 and 17.88±4.51, and 1.48±0.40 and 10.79±3.88 minutes for the renal pelvis, medulla and cortex, respectively. Conclusion: A robust method based on dynamic contrast enhanced cone beam CT and double exponential curve fitting has been developed to analyze the renal functions for different functional regions. Future study will be performed to investigate the sensitivity of this technique in the detection of radiation induced kidney dysfunction.« less

Profiler - A Fast and Versatile New Program for Decomposing Galaxy Light Profiles

NASA Astrophysics Data System (ADS)

Ciambur, Bogdan C.

2016-12-01

I introduce Profiler, a user-friendly program designed to analyse the radial surface brightness profiles of galaxies. With an intuitive graphical user interface, Profiler can accurately model galaxies of a broad range of morphological types, with various parametric functions routinely employed in the field (Sérsic, core-Sérsic, exponential, Gaussian, Moffat, and Ferrers). In addition to these, Profiler can employ the broken exponential model for disc truncations or anti-truncations, and two special cases of the edge-on disc model: along the disc's major or minor axis. The convolution of (circular or elliptical) models with the point spread function is performed in 2D, and offers a choice between Gaussian, Moffat or a user-provided profile for the point spread function. Profiler is optimised to work with galaxy light profiles obtained from isophotal measurements, which allow for radial gradients in the geometric parameters of the isophotes, and are thus often better at capturing the total light than 2D image-fitting programs. Additionally, the 1D approach is generally less computationally expensive and more stable. I demonstrate Profiler's features by decomposing three case-study galaxies: the cored elliptical galaxy NGC 3348, the nucleated dwarf Seyfert I galaxy Pox 52, and NGC 2549, a double-barred galaxy with an edge-on, truncated disc.

A note on large gauge transformations in double field theory

DOE PAGES

Naseer, Usman

2015-06-03

Here, we give a detailed proof of the conjecture by Hohm and Zwiebach in double field theory. Our result implies that their proposal for large gauge transformations in terms of the Jacobian matrix for coordinate transformations is, as required, equivalent to the standard exponential map associated with the generalized Lie derivative along a suitable parameter.

Scattering of acoustic evanescent waves by circular cylinders: Partial wave series solution

NASA Astrophysics Data System (ADS)

Marston, Philip L.

2002-05-01

Evanescent acoustical waves occur in a variety of situations such as when sound is incident on a fluid interface beyond the critical angle and when flexural waves on a plate are subsonic with respect to the surrounding fluid. The scattering by circular cylinders at normal incidence was calculated to give insight into the consequences on the scattering of the evanescence of the incident wave. To analyze the scattering, it is necessary to express the incident wave using a modified expansion involving cylindrical functions. For plane evanescent waves, the expansion becomes a double summation with products of modified and ordinary Bessel functions. The resulting modified series is found for the scattering by a fluid cylinder in an unbounded medium. The perfectly soft and rigid cases are also examined. Unlike the case of an ordinary incident wave, the counterpropagating partial waves of the same angular order have unequal magnitudes when the incident wave is evanescent. This is a consequence of the exponential dependence of the incident wave amplitude on the transverse coordinate. The associated exponential dependence of the scattering on the location of a scatterer was previously demonstrated [T. J. Matula and P. L. Marston, J. Acoust. Soc. Am. 93, 1192-1195 (1993)].

A study on industrial accident rate forecasting and program development of estimated zero accident time in Korea.

PubMed

Kim, Tae-gu; Kang, Young-sig; Lee, Hyung-won

2011-01-01

To begin a zero accident campaign for industry, the first thing is to estimate the industrial accident rate and the zero accident time systematically. This paper considers the social and technical change of the business environment after beginning the zero accident campaign through quantitative time series analysis methods. These methods include sum of squared errors (SSE), regression analysis method (RAM), exponential smoothing method (ESM), double exponential smoothing method (DESM), auto-regressive integrated moving average (ARIMA) model, and the proposed analytic function method (AFM). The program is developed to estimate the accident rate, zero accident time and achievement probability of an efficient industrial environment. In this paper, MFC (Microsoft Foundation Class) software of Visual Studio 2008 was used to develop a zero accident program. The results of this paper will provide major information for industrial accident prevention and be an important part of stimulating the zero accident campaign within all industrial environments.

Ammonium Removal from Aqueous Solutions by Clinoptilolite: Determination of Isotherm and Thermodynamic Parameters and Comparison of Kinetics by the Double Exponential Model and Conventional Kinetic Models

PubMed Central

Tosun, İsmail

2012-01-01

The adsorption isotherm, the adsorption kinetics, and the thermodynamic parameters of ammonium removal from aqueous solution by using clinoptilolite in aqueous solution was investigated in this study. Experimental data obtained from batch equilibrium tests have been analyzed by four two-parameter (Freundlich, Langmuir, Tempkin and Dubinin-Radushkevich (D-R)) and four three-parameter (Redlich-Peterson (R-P), Sips, Toth and Khan) isotherm models. D-R and R-P isotherms were the models that best fitted to experimental data over the other two- and three-parameter models applied. The adsorption energy (E) from the D-R isotherm was found to be approximately 7 kJ/mol for the ammonium-clinoptilolite system, thereby indicating that ammonium is adsorbed on clinoptilolite by physisorption. Kinetic parameters were determined by analyzing the nth-order kinetic model, the modified second-order model and the double exponential model, and each model resulted in a coefficient of determination (R2) of above 0.989 with an average relative error lower than 5%. A Double Exponential Model (DEM) showed that the adsorption process develops in two stages as rapid and slow phase. Changes in standard free energy (∆G°), enthalpy (∆H°) and entropy (∆S°) of ammonium-clinoptilolite system were estimated by using the thermodynamic equilibrium coefficients. PMID:22690177

Double closed-loop control of integrated optical resonance gyroscope with mean-square exponential stability.

PubMed

Li, Hui; Liu, Liying; Lin, Zhili; Wang, Qiwei; Wang, Xiao; Feng, Lishuang

2018-01-22

A new double closed-loop control system with mean-square exponential stability is firstly proposed to optimize the detection accuracy and dynamic response characteristic of the integrated optical resonance gyroscope (IORG). The influence mechanism of optical nonlinear effects on system detection sensitivity is investigated to optimize the demodulation gain, the maximum sensitivity and the linear work region of a gyro system. Especially, we analyze the effect of optical parameter fluctuation on the parameter uncertainty of system, and investigate the influence principle of laser locking-frequency noise on the closed-loop detection accuracy of angular velocity. The stochastic disturbance model of double closed-loop IORG is established that takes the unfavorable factors such as optical effect nonlinearity, disturbed disturbance, optical parameter fluctuation and unavoidable system noise into consideration. A robust control algorithm is also designed to guarantee the mean-square exponential stability of system with a prescribed H ∞ performance in order to improve the detection accuracy and dynamic performance of IORG. The conducted experiment results demonstrate that the IORG has a dynamic response time less than 76us, a long-term bias stability 7.04°/h with an integration time of 10s over one-hour test, and the corresponding bias stability 1.841°/h based on Allan deviation, which validate the effectiveness and usefulness of the proposed detection scheme.

Ammonium removal from aqueous solutions by clinoptilolite: determination of isotherm and thermodynamic parameters and comparison of kinetics by the double exponential model and conventional kinetic models.

PubMed

Tosun, Ismail

2012-03-01

The adsorption isotherm, the adsorption kinetics, and the thermodynamic parameters of ammonium removal from aqueous solution by using clinoptilolite in aqueous solution was investigated in this study. Experimental data obtained from batch equilibrium tests have been analyzed by four two-parameter (Freundlich, Langmuir, Tempkin and Dubinin-Radushkevich (D-R)) and four three-parameter (Redlich-Peterson (R-P), Sips, Toth and Khan) isotherm models. D-R and R-P isotherms were the models that best fitted to experimental data over the other two- and three-parameter models applied. The adsorption energy (E) from the D-R isotherm was found to be approximately 7 kJ/mol for the ammonium-clinoptilolite system, thereby indicating that ammonium is adsorbed on clinoptilolite by physisorption. Kinetic parameters were determined by analyzing the nth-order kinetic model, the modified second-order model and the double exponential model, and each model resulted in a coefficient of determination (R(2)) of above 0.989 with an average relative error lower than 5%. A Double Exponential Model (DEM) showed that the adsorption process develops in two stages as rapid and slow phase. Changes in standard free energy (∆G°), enthalpy (∆H°) and entropy (∆S°) of ammonium-clinoptilolite system were estimated by using the thermodynamic equilibrium coefficients.

Generalization of the event-based Carnevale-Hines integration scheme for integrate-and-fire models.

PubMed

van Elburg, Ronald A J; van Ooyen, Arjen

2009-07-01

An event-based integration scheme for an integrate-and-fire neuron model with exponentially decaying excitatory synaptic currents and double exponential inhibitory synaptic currents has been introduced by Carnevale and Hines. However, the integration scheme imposes nonphysiological constraints on the time constants of the synaptic currents, which hamper its general applicability. This letter addresses this problem in two ways. First, we provide physical arguments demonstrating why these constraints on the time constants can be relaxed. Second, we give a formal proof showing which constraints can be abolished. As part of our formal proof, we introduce the generalized Carnevale-Hines lemma, a new tool for comparing double exponentials as they naturally occur in many cascaded decay systems, including receptor-neurotransmitter dissociation followed by channel closing. Through repeated application of the generalized lemma, we lift most of the original constraints on the time constants. Thus, we show that the Carnevale-Hines integration scheme for the integrate-and-fire model can be employed for simulating a much wider range of neuron and synapse types than was previously thought.

Numerical Calculation of the Spectrum of the Severe (1%) Lighting Current and Its First Derivative

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, C G; Ong, M M; Perkins, M P

2010-02-12

Recently, the direct-strike lighting environment for the stockpile-to-target sequence was updated [1]. In [1], the severe (1%) lightning current waveforms for first and subsequent return strokes are defined based on Heidler's waveform. This report presents numerical calculations of the spectra of those 1% lightning current waveforms and their first derivatives. First, the 1% lightning current models are repeated here for convenience. Then, the numerical method for calculating the spectra is presented and tested. The test uses a double-exponential waveform and its first derivative, which we fit to the previous 1% direct-strike lighting environment from [2]. Finally, the resulting spectra aremore » given and are compared with those of the double-exponential waveform and its first derivative.« less

Characteristic length of the knotting probability revisited

NASA Astrophysics Data System (ADS)

Uehara, Erica; Deguchi, Tetsuo

2015-09-01

We present a self-avoiding polygon (SAP) model for circular DNA in which the radius of impermeable cylindrical segments corresponds to the screening length of double-stranded DNA surrounded by counter ions. For the model we evaluate the probability for a generated SAP with N segments having a given knot K through simulation. We call it the knotting probability of a knot K with N segments for the SAP model. We show that when N is large the most significant factor in the knotting probability is given by the exponentially decaying part exp(-N/NK), where the estimates of parameter NK are consistent with the same value for all the different knots we investigated. We thus call it the characteristic length of the knotting probability. We give formulae expressing the characteristic length as a function of the cylindrical radius rex, i.e. the screening length of double-stranded DNA.

Observational constraints on varying neutrino-mass cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Geng, Chao-Qiang; Lee, Chung-Chi; Myrzakulov, R.

We consider generic models of quintessence and we investigate the influence of massive neutrino matter with field-dependent masses on the matter power spectrum. In case of minimally coupled neutrino matter, we examine the effect in tracker models with inverse power-law and double exponential potentials. We present detailed investigations for the scaling field with a steep exponential potential, non-minimally coupled to massive neutrino matter, and we derive constraints on field-dependent neutrino masses from the observational data.

Equivalences between nonuniform exponential dichotomy and admissibility

NASA Astrophysics Data System (ADS)

Zhou, Linfeng; Lu, Kening; Zhang, Weinian

2017-01-01

Relationship between exponential dichotomies and admissibility of function classes is a significant problem for hyperbolic dynamical systems. It was proved that a nonuniform exponential dichotomy implies several admissible pairs of function classes and conversely some admissible pairs were found to imply a nonuniform exponential dichotomy. In this paper we find an appropriate admissible pair of classes of Lyapunov bounded functions which is equivalent to the existence of nonuniform exponential dichotomy on half-lines R± separately, on both half-lines R± simultaneously, and on the whole line R. Additionally, the maximal admissibility is proved in the case on both half-lines R± simultaneously.

Graphical analysis for gel morphology II. New mathematical approach for stretched exponential function with β>1

NASA Astrophysics Data System (ADS)

Hashimoto, Chihiro; Panizza, Pascal; Rouch, Jacques; Ushiki, Hideharu

2005-10-01

A new analytical concept is applied to the kinetics of the shrinking process of poly(N-isopropylacrylamide) (PNIPA) gels. When PNIPA gels are put into hot water above the critical temperature, two-step shrinking is observed and the secondary shrinking of gels is fitted well by a stretched exponential function. The exponent β characterizing the stretched exponential is always higher than one, although there are few analytical concepts for the stretched exponential function with β>1. As a new interpretation for this function, we propose a superposition of step (Heaviside) function and a new distribution function of characteristic time is deduced.

Exponential Increase in Relative Biological Effectiveness Along Distal Edge of a Proton Bragg Peak as Measured by Deoxyribonucleic Acid Double-Strand Breaks

PubMed Central

Cuaron, John J.; Chang, Chang; Lovelock, Michael; Higginson, Daniel S.; Mah, Dennis; Cahlon, Oren; Powell, Simon

2016-01-01

Purpose To quantify the relative biological effectiveness (RBE) of the distal edge of the proton Bragg peak, using an in vitro assay of DNA double-strand breaks (DSBs). Methods and Materials U2OS cells were irradiated within the plateau of a spread-out Bragg peak and at each millimeter position along the distal edge using a custom slide holder, allowing for simultaneous measurement of physical dose. A reference radiation signal was generated using photons. The DNA DSBs at 3 hours (to assess for early damage) and at 24 hours (to assess for residual damage and repair) after irradiation were measured using the γH2AX assay and quantified via flow cytometry. Results were confirmed with clonogenic survival assays. A detailed map of the RBE as a function of depth along the Bragg peak was generated using γH2AX measurements as a biological endpoint. Results At 3 hours after irradiation, DNA DSBs were higher with protons at every point along the distal edge compared with samples irradiated with photons to similar doses. This effect was even more pronounced after 24 hours, indicating that the impact of DNA repair is less after proton irradiation relative to photons. The RBE demonstrated an exponential increase as a function of depth and was measured to be as high as 4.0 after 3 hours and as high as 6.0 after 24 hours. When the RBE-corrected dose was plotted as a function of depth, the peak effective dose was extended 2-3 mm beyond what would be expected with physical measurement. Conclusions We generated a highly comprehensive map of the RBE of the distal edge of the Bragg peak, using a direct assay of DNA DSBs in vitro. Our data show that the RBE of the distal edge increases with depth and is significantly higher than previously reported estimates. PMID:27084629

Exponential Increase in Relative Biological Effectiveness Along Distal Edge of a Proton Bragg Peak as Measured by Deoxyribonucleic Acid Double-Strand Breaks.

PubMed

Cuaron, John J; Chang, Chang; Lovelock, Michael; Higginson, Daniel S; Mah, Dennis; Cahlon, Oren; Powell, Simon

2016-05-01

To quantify the relative biological effectiveness (RBE) of the distal edge of the proton Bragg peak, using an in vitro assay of DNA double-strand breaks (DSBs). U2OS cells were irradiated within the plateau of a spread-out Bragg peak and at each millimeter position along the distal edge using a custom slide holder, allowing for simultaneous measurement of physical dose. A reference radiation signal was generated using photons. The DNA DSBs at 3 hours (to assess for early damage) and at 24 hours (to assess for residual damage and repair) after irradiation were measured using the γH2AX assay and quantified via flow cytometry. Results were confirmed with clonogenic survival assays. A detailed map of the RBE as a function of depth along the Bragg peak was generated using γH2AX measurements as a biological endpoint. At 3 hours after irradiation, DNA DSBs were higher with protons at every point along the distal edge compared with samples irradiated with photons to similar doses. This effect was even more pronounced after 24 hours, indicating that the impact of DNA repair is less after proton irradiation relative to photons. The RBE demonstrated an exponential increase as a function of depth and was measured to be as high as 4.0 after 3 hours and as high as 6.0 after 24 hours. When the RBE-corrected dose was plotted as a function of depth, the peak effective dose was extended 2-3 mm beyond what would be expected with physical measurement. We generated a highly comprehensive map of the RBE of the distal edge of the Bragg peak, using a direct assay of DNA DSBs in vitro. Our data show that the RBE of the distal edge increases with depth and is significantly higher than previously reported estimates. Copyright © 2016 Elsevier Inc. All rights reserved.

Exponential propagators for the Schrödinger equation with a time-dependent potential.

PubMed

Bader, Philipp; Blanes, Sergio; Kopylov, Nikita

2018-06-28

We consider the numerical integration of the Schrödinger equation with a time-dependent Hamiltonian given as the sum of the kinetic energy and a time-dependent potential. Commutator-free (CF) propagators are exponential propagators that have shown to be highly efficient for general time-dependent Hamiltonians. We propose new CF propagators that are tailored for Hamiltonians of the said structure, showing a considerably improved performance. We obtain new fourth- and sixth-order CF propagators as well as a novel sixth-order propagator that incorporates a double commutator that only depends on coordinates, so this term can be considered as cost-free. The algorithms require the computation of the action of exponentials on a vector similar to the well-known exponential midpoint propagator, and this is carried out using the Lanczos method. We illustrate the performance of the new methods on several numerical examples.

In vivo growth of 60 non-screening detected lung cancers: a computed tomography study.

PubMed

Mets, Onno M; Chung, Kaman; Zanen, Pieter; Scholten, Ernst T; Veldhuis, Wouter B; van Ginneken, Bram; Prokop, Mathias; Schaefer-Prokop, Cornelia M; de Jong, Pim A

2018-04-01

Current pulmonary nodule management guidelines are based on nodule volume doubling time, which assumes exponential growth behaviour. However, this is a theory that has never been validated in vivo in the routine-care target population. This study evaluates growth patterns of untreated solid and subsolid lung cancers of various histologies in a non-screening setting.Growth behaviour of pathology-proven lung cancers from two academic centres that were imaged at least three times before diagnosis (n=60) was analysed using dedicated software. Random-intercept random-slope mixed-models analysis was applied to test which growth pattern most accurately described lung cancer growth. Individual growth curves were plotted per pathology subgroup and nodule type.We confirmed that growth in both subsolid and solid lung cancers is best explained by an exponential model. However, subsolid lesions generally progress slower than solid ones. Baseline lesion volume was not related to growth, indicating that smaller lesions do not grow slower compared to larger ones.By showing that lung cancer conforms to exponential growth we provide the first experimental basis in the routine-care setting for the assumption made in volume doubling time analysis. Copyright ©ERS 2018.

Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays.

PubMed

Rakkiyappan, R; Sakthivel, N; Cao, Jinde

2015-06-01

This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-data controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen's inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen's inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-data controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods. Copyright © 2015 Elsevier Ltd. All rights reserved.

Systematic strategies for the third industrial accident prevention plan in Korea.

PubMed

Kang, Young-sig; Yang, Sung-hwan; Kim, Tae-gu; Kim, Day-sung

2012-01-01

To minimize industrial accidents, it's critical to evaluate a firm's priorities for prevention factors and strategies since such evaluation provides decisive information for preventing industrial accidents and maintaining safety management. Therefore, this paper proposes the evaluation of priorities through statistical testing of prevention factors with a cause analysis in a cause and effect model. A priority matrix criterion is proposed to apply the ranking and for the objectivity of questionnaire results. This paper used regression method (RA), exponential smoothing method (ESM), double exponential smoothing method (DESM), autoregressive integrated moving average (ARIMA) model and proposed analytical function method (PAFM) to analyze trends of accident data that will lead to an accurate prediction. This paper standardized the questionnaire results of workers and managers in manufacturing and construction companies with less than 300 employees, located in the central Korean metropolitan areas where fatal accidents have occurred. Finally, a strategy was provided to construct safety management for the third industrial accident prevention plan and a forecasting method for occupational accident rates and fatality rates for occupational accidents per 10,000 people.

NMR investigation of the short-chain ionic surfactant-water systems.

PubMed

Popova, M V; Tchernyshev, Y S; Michel, D

2004-02-03

The structure and dynamics of surfactant molecules [CH3(CH2)7COOK] in heavy water solutions were investigated by 1H and 2H NMR. A double-exponential attenuation of the spin-echo amplitude in a Carr-Purcell-Meiboom-Gill experiment was found. We expect correspondence to both bounded and monomeric states. At high concentrations in the NMR self-diffusion measurements also a double-exponential decay of the spin-echo signal versus the square of the dc magnetic gradient was observed. The slow component of the diffusion process is caused by micellar aggregates, while the fast component is the result of the self-diffusion of the monomers through the micelles. The self-diffusion studies indicate that the form of micelles changes with increasing total surfactant concentration. The critical temperature range for self-association is reflected in the 1H transverse relaxation.

Nuclear counting filter based on a centered Skellam test and a double exponential smoothing

DOE Office of Scientific and Technical Information (OSTI.GOV)

Coulon, Romain; Kondrasovs, Vladimir; Dumazert, Jonathan

2015-07-01

Online nuclear counting represents a challenge due to the stochastic nature of radioactivity. The count data have to be filtered in order to provide a precise and accurate estimation of the count rate, this with a response time compatible with the application in view. An innovative filter is presented in this paper addressing this issue. It is a nonlinear filter based on a Centered Skellam Test (CST) giving a local maximum likelihood estimation of the signal based on a Poisson distribution assumption. This nonlinear approach allows to smooth the counting signal while maintaining a fast response when brutal change activitymore » occur. The filter has been improved by the implementation of a Brown's double Exponential Smoothing (BES). The filter has been validated and compared to other state of the art smoothing filters. The CST-BES filter shows a significant improvement compared to all tested smoothing filters. (authors)« less

A U-shaped linear ultrasonic motor using longitudinal vibration transducers with double feet.

PubMed

Liu, Yingxiang; Liu, Junkao; Chen, Weishan; Shi, Shengjun

2012-05-01

A U-shaped linear ultrasonic motor using longitudinal vibration transducers with double feet was proposed in this paper. The proposed motor contains a horizontal transducer and two vertical transducers. The horizontal transducer includes two exponential shape horns located at the leading ends, and each vertical transducer contains one exponential shape horn. The horns of the horizontal transducer and the vertical transducer intersect at the tip ends where the driving feet are located. Longitudinal vibrations are superimposed in the motor and generate elliptical motions at the driving feet. The two vibration modes of the motor are discussed, and the motion trajectories of driving feet are deduced. By adjusting the structural parameters, the resonance frequencies of two vibration modes were degenerated. A prototype motor was fabricated and measured. Typical output of the prototype is no-load speed of 854 mm/s and maximum thrust force of 40 N at a voltage of 200 V(rms).

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

NASA Technical Reports Server (NTRS)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Exponential localization of Wannier functions in insulators.

PubMed

Brouder, Christian; Panati, Gianluca; Calandra, Matteo; Mourougane, Christophe; Marzari, Nicola

2007-01-26

The exponential localization of Wannier functions in two or three dimensions is proven for all insulators that display time-reversal symmetry, settling a long-standing conjecture. Our proof relies on the equivalence between the existence of analytic quasi-Bloch functions and the nullity of the Chern numbers (or of the Hall current) for the system under consideration. The same equivalence implies that Chern insulators cannot display exponentially localized Wannier functions. An explicit condition for the reality of the Wannier functions is identified.

Integral definition of the logarithmic function and the derivative of the exponential function in calculus

NASA Astrophysics Data System (ADS)

Vaninsky, Alexander

2015-04-01

Defining the logarithmic function as a definite integral with a variable upper limit, an approach used by some popular calculus textbooks, is problematic. We discuss the disadvantages of such a definition and provide a way to fix the problem. We also consider a definition-based, rigorous derivation of the derivative of the exponential function that is easier, more intuitive, and complies with the standard definitions of the number e, the logarithmic, and the exponential functions.

DOUBLE code simulations of emissivities of fast neutrals for different plasma observation view-lines of neutral particle analyzers on the COMPASS tokamak

NASA Astrophysics Data System (ADS)

Mitosinkova, K.; Tomes, M.; Stockel, J.; Varju, J.; Stano, M.

2018-03-01

Neutral particle analyzers (NPA) measure line-integrated energy spectra of fast neutral atoms escaping the tokamak plasma, which are a product of charge-exchange (CX) collisions of plasma ions with background neutrals. They can observe variations in the ion temperature T i of non-thermal fast ions created by additional plasma heating. However, the plasma column which a fast atom has to pass through must be sufficiently short in comparison with the fast atom’s mean-free-path. Tokamak COMPASS is currently equipped with one NPA installed at a tangential mid-plane port. This orientation is optimal for observing non-thermal fast ions. However, in this configuration the signal at energies useful for T i derivation is lost in noise due to the too long fast atoms’ trajectories. Thus, a second NPA is planned to be connected for the purpose of measuring T i. We analyzed different possible view-lines (perpendicular mid-plane, tangential mid-plane, and top view) for the second NPA using the DOUBLE Monte-Carlo code and compared the results with the performance of the present NPA with tangential orientation. The DOUBLE code provides fast-atoms’ emissivity functions along the NPA view-line. The position of the median of these emissivity functions is related to the location from where the measured signal originates. Further, we compared the difference between the real central T i used as a DOUBLE code input and the T iCX derived from the exponential decay of simulated energy spectra. The advantages and disadvantages of each NPA location are discussed.

Design and implementation of the NaI(Tl)/CsI(Na) detectors output signal generator

NASA Astrophysics Data System (ADS)

Zhou, Xu; Liu, Cong-Zhan; Zhao, Jian-Ling; Zhang, Fei; Zhang, Yi-Fei; Li, Zheng-Wei; Zhang, Shuo; Li, Xu-Fang; Lu, Xue-Feng; Xu, Zhen-Ling; Lu, Fang-Jun

2014-02-01

We designed and implemented a signal generator that can simulate the output of the NaI(Tl)/CsI(Na) detectors' pre-amplifier onboard the Hard X-ray Modulation Telescope (HXMT). Using the development of the FPGA (Field Programmable Gate Array) with VHDL language and adding a random constituent, we have finally produced the double exponential random pulse signal generator. The statistical distribution of the signal amplitude is programmable. The occurrence time intervals of the adjacent signals contain negative exponential distribution statistically.

Effect of Coulomb friction on orientational correlation and velocity distribution functions in a sheared dilute granular gas.

PubMed

Gayen, Bishakhdatta; Alam, Meheboob

2011-08-01

From particle simulations of a sheared frictional granular gas, we show that the Coulomb friction can have dramatic effects on orientational correlation as well as on both the translational and angular velocity distribution functions even in the Boltzmann (dilute) limit. The dependence of orientational correlation on friction coefficient (μ) is found to be nonmonotonic, and the Coulomb friction plays a dual role of enhancing or diminishing the orientational correlation, depending on the value of the tangential restitution coefficient (which characterizes the roughness of particles). From the sticking limit (i.e., with no sliding contact) of rough particles, decreasing the Coulomb friction is found to reduce the density and spatial velocity correlations which, together with diminished orientational correlation for small enough μ, are responsible for the transition from non-gaussian to gaussian distribution functions in the double limit of small friction (μ→0) and nearly elastic particles (e→1). This double limit in fact corresponds to perfectly smooth particles, and hence the maxwellian (gaussian) is indeed a solution of the Boltzmann equation for a frictional granular gas in the limit of elastic collisions and zero Coulomb friction at any roughness. The high-velocity tails of both distribution functions seem to follow stretched exponentials even in the presence of Coulomb friction, and the related velocity exponents deviate strongly from a gaussian with increasing friction.

Quasiclassical treatment of the Auger effect in slow ion-atom collisions

NASA Astrophysics Data System (ADS)

Frémont, F.

2017-09-01

A quasiclassical model based on the resolution of Hamilton equations of motion is used to get evidence for Auger electron emission following double-electron capture in 150-keV N e10 ++He collisions. Electron-electron interaction is taken into account during the collision by using pure Coulombic potential. To make sure that the helium target is stable before the collision, phenomenological potentials for the electron-nucleus interactions that simulate the Heisenberg principle are included in addition to the Coulombic potential. First, single- and double-electron captures are determined and compared with previous experiments and theories. Then, integration time evolution is calculated for autoionizing and nonautoionizing double capture. In contrast with single capture, the number of electrons originating from autoionization slowly increases with integration time. A fit of the calculated cross sections by means of an exponential function indicates that the average lifetime is 4.4 ×10-3a .u . , in very good agreement with the average lifetime deduced from experiments and a classical model introduced to calculate individual angular momentum distributions. The present calculation demonstrates the ability of classical models to treat the Auger effect, which is a pure quantum effect.

(q,{mu}) and (p,q,{zeta})-exponential functions: Rogers-Szego'' polynomials and Fourier-Gauss transform

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hounkonnou, Mahouton Norbert; Nkouankam, Elvis Benzo Ngompe

2010-10-15

From the realization of q-oscillator algebra in terms of generalized derivative, we compute the matrix elements from deformed exponential functions and deduce generating functions associated with Rogers-Szego polynomials as well as their relevant properties. We also compute the matrix elements associated with the (p,q)-oscillator algebra (a generalization of the q-one) and perform the Fourier-Gauss transform of a generalization of the deformed exponential functions.

The dynamics of photoinduced defect creation in amorphous chalcogenides: The origin of the stretched exponential function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Freitas, R. J.; Shimakawa, K.; Department of Electrical and Electronic Engineering, Gifu University, Gifu 501-1193

The article discusses the dynamics of photoinduced defect creations (PDC) in amorphous chalcogenides, which is described by the stretched exponential function (SEF), while the well known photodarkening (PD) and photoinduced volume expansion (PVE) are governed only by the exponential function. It is shown that the exponential distribution of the thermal activation barrier produces the SEF in PDC, suggesting that thermal energy, as well as photon energy, is incorporated in PDC mechanisms. The differences in dynamics among three major photoinduced effects (PD, PVE, and PDC) in amorphous chalcogenides are now well understood.

On the Matrix Exponential Function

ERIC Educational Resources Information Center

Hou, Shui-Hung; Hou, Edwin; Pang, Wan-Kai

2006-01-01

A novel and simple formula for computing the matrix exponential function is presented. Specifically, it can be used to derive explicit formulas for the matrix exponential of a general matrix A satisfying p(A) = 0 for a polynomial p(s). It is ready for use in a classroom and suitable for both hand as well as symbolic computation.

betaFIT: A computer program to fit pointwise potentials to selected analytic functions

NASA Astrophysics Data System (ADS)

Le Roy, Robert J.; Pashov, Asen

2017-01-01

This paper describes program betaFIT, which performs least-squares fits of sets of one-dimensional (or radial) potential function values to four different types of sophisticated analytic potential energy functional forms. These families of potential energy functions are: the Expanded Morse Oscillator (EMO) potential [J Mol Spectrosc 1999;194:197], the Morse/Long-Range (MLR) potential [Mol Phys 2007;105:663], the Double Exponential/Long-Range (DELR) potential [J Chem Phys 2003;119:7398], and the "Generalized Potential Energy Function (GPEF)" form introduced by Šurkus et al. [Chem Phys Lett 1984;105:291], which includes a wide variety of polynomial potentials, such as the Dunham [Phys Rev 1932;41:713], Simons-Parr-Finlan [J Chem Phys 1973;59:3229], and Ogilvie-Tipping [Proc R Soc A 1991;378:287] polynomials, as special cases. This code will be useful for providing the realistic sets of potential function shape parameters that are required to initiate direct fits of selected analytic potential functions to experimental data, and for providing better analytical representations of sets of ab initio results.

On the Gibbs phenomenon 1: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang; Solomonoff, Alex; Vandeven, Herve

1992-01-01

It is well known that the Fourier series of an analytic or periodic function, truncated after 2N+1 terms, converges exponentially with N, even in the maximum norm, although the function is still analytic. This is known as the Gibbs phenomenon. Here, we show that the first 2N+1 Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed.

Alternative definition of excitation amplitudes in multi-reference state-specific coupled cluster

NASA Astrophysics Data System (ADS)

Garniron, Yann; Giner, Emmanuel; Malrieu, Jean-Paul; Scemama, Anthony

2017-04-01

A central difficulty of state-specific Multi-Reference Coupled Cluster (MR-CC) in the multi-exponential Jeziorski-Monkhorst formalism concerns the definition of the amplitudes of the single and double excitation operators appearing in the exponential wave operators. If the reference space is a complete active space (CAS), the number of these amplitudes is larger than the number of singly and doubly excited determinants on which one may project the eigenequation, and one must impose additional conditions. The present work first defines a state-specific reference-independent operator T˜ ^ m which acting on the CAS component of the wave function |Ψ0m⟩ maximizes the overlap between (1 +T˜ ^ m ) |Ψ0m⟩ and the eigenvector of the CAS-SD (Singles and Doubles) Configuration Interaction (CI) matrix |ΨCAS-SDm⟩ . This operator may be used to generate approximate coefficients of the triples and quadruples, and a dressing of the CAS-SD CI matrix, according to the intermediate Hamiltonian formalism. The process may be iterated to convergence. As a refinement towards a strict coupled cluster formalism, one may exploit reference-independent amplitudes provided by (1 +T˜ ^ m ) |Ψ0m⟩ to define a reference-dependent operator T^ m by fitting the eigenvector of the (dressed) CAS-SD CI matrix. The two variants, which are internally uncontracted, give rather similar results. The new MR-CC version has been tested on the ground state potential energy curves of 6 molecules (up to triple-bond breaking) and two excited states. The non-parallelism error with respect to the full-CI curves is of the order of 1 mEh.

Effects of resonant magnetic perturbation on the triggering and the evolution of double-tearing mode

NASA Astrophysics Data System (ADS)

Wang, L.; Lin, W. B.; Wang, X. Q.

2018-02-01

The effects of resonant magnetic perturbation on the triggering and the evolution of the double-tearing mode are investigated by using nonlinear magnetohydrodynamics simulations in a slab geometry. It is found that the double-tearing mode can be destabilized by boundary magnetic perturbation. Moreover, the mode has three typical development stages before it reaches saturation: the linear stable stage, the linear-growth stage, and the exponential-growth stage. The onset and growth of the double-tearing mode significantly depend on the boundary magnetic perturbations, particularly in the early development stage of the mode. The influences of the magnetic perturbation amplitude on the mode for different separations of the two rational surfaces are also discussed.

On the modeling of breath-by-breath oxygen uptake kinetics at the onset of high-intensity exercises: simulated annealing vs. GRG2 method.

PubMed

Bernard, Olivier; Alata, Olivier; Francaux, Marc

2006-03-01

Modeling in the time domain, the non-steady-state O2 uptake on-kinetics of high-intensity exercises with empirical models is commonly performed with gradient-descent-based methods. However, these procedures may impair the confidence of the parameter estimation when the modeling functions are not continuously differentiable and when the estimation corresponds to an ill-posed problem. To cope with these problems, an implementation of simulated annealing (SA) methods was compared with the GRG2 algorithm (a gradient-descent method known for its robustness). Forty simulated Vo2 on-responses were generated to mimic the real time course for transitions from light- to high-intensity exercises, with a signal-to-noise ratio equal to 20 dB. They were modeled twice with a discontinuous double-exponential function using both estimation methods. GRG2 significantly biased two estimated kinetic parameters of the first exponential (the time delay td1 and the time constant tau1) and impaired the precision (i.e., standard deviation) of the baseline A0, td1, and tau1 compared with SA. SA significantly improved the precision of the three parameters of the second exponential (the asymptotic increment A2, the time delay td2, and the time constant tau2). Nevertheless, td2 was significantly biased by both procedures, and the large confidence intervals of the whole second component parameters limit their interpretation. To compare both algorithms on experimental data, 26 subjects each performed two transitions from 80 W to 80% maximal O2 uptake on a cycle ergometer and O2 uptake was measured breath by breath. More than 88% of the kinetic parameter estimations done with the SA algorithm produced the lowest residual sum of squares between the experimental data points and the model. Repeatability coefficients were better with GRG2 for A1 although better with SA for A2 and tau2. Our results demonstrate that the implementation of SA improves significantly the estimation of most of these kinetic parameters, but a large inaccuracy remains in estimating the parameter values of the second exponential.

Saturation capability of short phase modulated pulses facilitates the measurement of longitudinal relaxation times of quadrupolar nuclei.

PubMed

Makrinich, Maria; Gupta, Rupal; Polenova, Tatyana; Goldbourt, Amir

The ability of various pulse types, which are commonly applied for distance measurements, to saturate or invert quadrupolar spin polarization has been compared by observing their effect on magnetization recovery curves under magic-angle spinning. A selective central transition inversion pulse yields a bi-exponential recovery for a diamagnetic sample with a spin-3/2, consistent with the existence of two processes: the fluctuations of the electric field gradients with identical single (W 1 ) and double (W 2 ) quantum quadrupolar-driven relaxation rates, and spin exchange between the central transition of one spin and satellite transitions of a dipolar-coupled similar spin. Using a phase modulated pulse, developed for distance measurements in quadrupolar spins (Nimerovsky et al., JMR 244, 2014, 107-113) and suggested for achieving the complete saturation of all quadrupolar spin energy levels, a mono-exponential relaxation model fits the data, compatible with elimination of the spin exchange processes. Other pulses such as an adiabatic pulse lasting one-third of a rotor period, and a two-rotor-period long continuous-wave pulse, both used for distance measurements under special experimental conditions, yield good fits to bi-exponential functions with varying coefficients and time constants due to variations in initial conditions. Those values are a measure of the extent of saturation obtained from these pulses. An empirical fit of the recovery curves to a stretched exponential function can provide general recovery times. A stretching parameter very close to unity, as obtained for a phase modulated pulse but not for other cases, suggests that in this case recovery times and longitudinal relaxation times are similar. The results are experimentally demonstrated for compounds containing 11 B (spin-3/2) and 51 V (spin-7/2). We propose that accurate spin lattice relaxation rates can be measured by a short phase modulated pulse (<1-2ms), similarly to the "true T 1 " measured by saturation with an asynchronous pulse train (Yesinowski, JMR 252, 2015, 135-144). Copyright © 2017 Elsevier Inc. All rights reserved.

Using Differentials to Differentiate Trigonometric and Exponential Functions

ERIC Educational Resources Information Center

Dray, Tevian

2013-01-01

Starting from geometric definitions, we show how differentials can be used to differentiate trigonometric and exponential functions without limits, numerical estimates, solutions of differential equations, or integration.

How bootstrap can help in forecasting time series with more than one seasonal pattern

NASA Astrophysics Data System (ADS)

Cordeiro, Clara; Neves, M. Manuela

2012-09-01

The search for the future is an appealing challenge in time series analysis. The diversity of forecasting methodologies is inevitable and is still in expansion. Exponential smoothing methods are the launch platform for modelling and forecasting in time series analysis. Recently this methodology has been combined with bootstrapping revealing a good performance. The algorithm (Boot. EXPOS) using exponential smoothing and bootstrap methodologies, has showed promising results for forecasting time series with one seasonal pattern. In case of more than one seasonal pattern, the double seasonal Holt-Winters methods and the exponential smoothing methods were developed. A new challenge was now to combine these seasonal methods with bootstrap and carry over a similar resampling scheme used in Boot. EXPOS procedure. The performance of such partnership will be illustrated for some well-know data sets existing in software.

Exponential Increase in Relative Biological Effectiveness Along Distal Edge of a Proton Bragg Peak as Measured by Deoxyribonucleic Acid Double-Strand Breaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cuaron, John J., E-mail: cuaronj@mskcc.org; Chang, Chang; Lovelock, Michael

2016-05-01

Purpose: To quantify the relative biological effectiveness (RBE) of the distal edge of the proton Bragg peak, using an in vitro assay of DNA double-strand breaks (DSBs). Methods and Materials: U2OS cells were irradiated within the plateau of a spread-out Bragg peak and at each millimeter position along the distal edge using a custom slide holder, allowing for simultaneous measurement of physical dose. A reference radiation signal was generated using photons. The DNA DSBs at 3 hours (to assess for early damage) and at 24 hours (to assess for residual damage and repair) after irradiation were measured using the γH2AX assay and quantifiedmore » via flow cytometry. Results were confirmed with clonogenic survival assays. A detailed map of the RBE as a function of depth along the Bragg peak was generated using γH2AX measurements as a biological endpoint. Results: At 3 hours after irradiation, DNA DSBs were higher with protons at every point along the distal edge compared with samples irradiated with photons to similar doses. This effect was even more pronounced after 24 hours, indicating that the impact of DNA repair is less after proton irradiation relative to photons. The RBE demonstrated an exponential increase as a function of depth and was measured to be as high as 4.0 after 3 hours and as high as 6.0 after 24 hours. When the RBE-corrected dose was plotted as a function of depth, the peak effective dose was extended 2-3 mm beyond what would be expected with physical measurement. Conclusions: We generated a highly comprehensive map of the RBE of the distal edge of the Bragg peak, using a direct assay of DNA DSBs in vitro. Our data show that the RBE of the distal edge increases with depth and is significantly higher than previously reported estimates.« less

An Unusual Exponential Graph

ERIC Educational Resources Information Center

Syed, M. Qasim; Lovatt, Ian

2014-01-01

This paper is an addition to the series of papers on the exponential function begun by Albert Bartlett. In particular, we ask how the graph of the exponential function y = e[superscript -t/t] would appear if y were plotted versus ln t rather than the normal practice of plotting ln y versus t. In answering this question, we find a new way to…

Investigation of the double exponential in the current-voltage characteristics of silicon solar cells. [proton irradiation effects on ATS 1 cells

NASA Technical Reports Server (NTRS)

Wolf, M.; Noel, G. T.; Stirn, R. J.

1977-01-01

Difficulties in relating observed current-voltage characteristics of individual silicon solar cells to their physical and material parameters were underscored by the unexpected large changes in the current-voltage characteristics telemetered back from solar cells on the ATS-1 spacecraft during their first year in synchronous orbit. Depletion region recombination was studied in cells exhibiting a clear double-exponential dark characteristic by subjecting the cells to proton irradiation. A significant change in the saturation current, an effect included in the Sah, Noyce, Shockley formulation of diode current resulting from recombination in the depletion region, was caused by the introduction of shallow levels in the depletion region by the proton irradiation. This saturation current is not attributable only to diffusion current from outside the depletion region and only its temperature dependence can clarify its origin. The current associated with the introduction of deep-lying levels did not change significantly in these experiments.

Compact exponential product formulas and operator functional derivative

NASA Astrophysics Data System (ADS)

Suzuki, Masuo

1997-02-01

A new scheme for deriving compact expressions of the logarithm of the exponential product is proposed and it is applied to several exponential product formulas. A generalization of the Dynkin-Specht-Wever (DSW) theorem on free Lie elements is given, and it is used to study the relation between the traditional method (based on the DSW theorem) and the present new scheme. The concept of the operator functional derivative is also proposed, and it is applied to ordered exponentials, such as time-evolution operators for time-dependent Hamiltonians.

R-Function Relationships for Application in the Fractional Calculus

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.

2000-01-01

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, e(t), and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, el, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

R-function relationships for application in the fractional calculus.

PubMed

Lorenzo, Carl F; Hartley, Tom T

2008-01-01

The F-function, and its generalization the R-function, are of fundamental importance in the fractional calculus. It has been shown that the solution of the fundamental linear fractional differential equation may be expressed in terms of these functions. These functions serve as generalizations of the exponential function in the solution of fractional differential equations. Because of this central role in the fractional calculus, this paper explores various intrarelationships of the R-function, which will be useful in further analysis. Relationships of the R-function to the common exponential function, et, and its fractional derivatives are shown. From the relationships developed, some important approximations are observed. Further, the inverse relationships of the exponential function, et, in terms of the R-function are developed. Also, some approximations for the R-function are developed.

Exact semiclassical expansions for one-dimensional quantum oscillators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Delabaere, E.; Dillinger, H.; Pham, F.

1997-12-01

A set of rules is given for dealing with WKB expansions in the one-dimensional analytic case, whereby such expansions are not considered as approximations but as exact encodings of wave functions, thus allowing for analytic continuation with respect to whichever parameters the potential function depends on, with an exact control of small exponential effects. These rules, which include also the case when there are double turning points, are illustrated on various examples, and applied to the study of bound state or resonance spectra. In the case of simple oscillators, it is thus shown that the Rayleigh{endash}Schr{umlt o}dinger series is Borelmore » resummable, yielding the exact energy levels. In the case of the symmetrical anharmonic oscillator, one gets a simple and rigorous justification of the Zinn-Justin quantization condition, and of its solution in terms of {open_quotes}multi-instanton expansions.{close_quotes} {copyright} {ital 1997 American Institute of Physics.}« less

Interaction quantum quenches in the one-dimensional Fermi-Hubbard model

NASA Astrophysics Data System (ADS)

Heidrich-Meisner, Fabian; Bauer, Andreas; Dorfner, Florian; Riegger, Luis; Orso, Giuliano

2016-05-01

We discuss the nonequilibrium dynamics in two interaction quantum quenches in the one-dimensional Fermi-Hubbard model. First, we study the decay of the Néel state as a function of interaction strength. We observe a fast charge dynamics over which double occupancies are built up, while the long-time decay of the staggered moment is controlled by spin excitations, corroborated by the analysis of the entanglement dynamics. Second, we investigate the formation of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations in a spin-imbalanced system in quenches from the noninteracting case to attractive interactions. Even though the quench puts the system at a finite energy density, peaks at the characteristic FFLO quasimomenta are visible in the quasi-momentum distribution function, albeit with an exponential decay of s-wave pairing correlations. We also discuss the imprinting of FFLO correlations onto repulsively bound pairs and their rapid decay in ramps. Supported by the DFG (Deutsche Forschungsgemeinschaft) via FOR 1807.

Finite-time singularity signature of hyperinflation

NASA Astrophysics Data System (ADS)

Sornette, D.; Takayasu, H.; Zhou, W.-X.

2003-07-01

We present a novel analysis extending the recent work of Mizuno et al. (Physica A 308 (2002) 411) on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a generalization of Cagan's model of inflation based on the mechanism of “inflationary expectation” of positive feedbacks between realized growth rate and people's expected growth rate, we find that hyperinflations can be characterized by a power law singularity culminating at a critical time tc. Mizuno et al.'s double-exponential function can be seen as a discrete time-step approximation of our more general non-linear ODE formulation of the price dynamics which exhibits a finite-time singular behavior. This extension of Cagan's model, which makes natural the appearance of a critical time tc, has the advantage of providing a well-defined end of the clearly unsustainable hyperinflation regime. We find an excellent and reliable agreement between theory and data for Germany, Hungary, Peru and Bolivia. For Brazil, Israel and Nicaragua, the super-exponential growth seems to be already contaminated significantly by the existence of a cross-over to a stationary regime.

Reciprocal capacitance transients?

NASA Astrophysics Data System (ADS)

Gfroerer, Tim; Simov, Peter; Wanlass, Mark

2007-03-01

When the reverse bias across a semiconductor diode is changed, charge carriers move to accommodate the appropriate depletion thickness, producing a simultaneous change in the device capacitance. Transient capacitance measurements can reveal inhibited carrier motion due to trapping, where the depth of the trap can be evaluated using the temperature-dependent escape rate. However, when we employ this technique on a GaAs0.72P0.28 n+/p diode (which is a candidate for incorporation in multi-junction solar cells), we observe a highly non-exponential response under a broad range of experimental conditions. Double exponential functions give good fits, but lead to non-physical results. The deduced rates depend on the observation time window and fast and slow rates, which presumably correspond to deep and shallow levels, have identical activation energies. Meanwhile, we have discovered a universal linear relationship between the inverse of the capacitance and time. An Arrhenius plot of the slope of the reciprocal of the transient yields an activation energy of approximately 0.4 eV, independent of the observation window and other experimental conditions. The reciprocal behavior leads us to hypothesize that hopping, rather than escape into high-mobility bands, may govern the transport of trapped holes in this system.

Analytical model for release calculations in solid thin-foils ISOL targets

NASA Astrophysics Data System (ADS)

Egoriti, L.; Boeckx, S.; Ghys, L.; Houngbo, D.; Popescu, L.

2016-10-01

A detailed analytical model has been developed to simulate isotope-release curves from thin-foils ISOL targets. It involves the separate modeling of diffusion and effusion inside the target. The former has been modeled using both first and second Fick's law. The latter, effusion from the surface of the target material to the end of the ionizer, was simulated with the Monte Carlo code MolFlow+. The calculated delay-time distribution for this process was then fitted using a double-exponential function. The release curve obtained from the convolution of diffusion and effusion shows good agreement with experimental data from two different target geometries used at ISOLDE. Moreover, the experimental yields are well reproduced when combining the release fraction with calculated in-target production.

Multiple relaxations of the cluster surface diffusion in a homoepitaxial SrTiO3 layer

NASA Astrophysics Data System (ADS)

Woo, Chang-Su; Chu, Kanghyun; Song, Jong-Hyun; Yang, Chan-Ho

2018-03-01

We examine the surface diffusion process of adatomic clusters on a (001)-oriented SrTiO3 single crystal using reflection high energy electron diffraction (RHEED). We find that the recovery curve of the RHEED intensity acquired after a homoepitaxial half-layer growth can be accurately fit into a double exponential function, indicating the existence of two dominant relaxation mechanisms. The characteristic relaxation times at selected growth temperatures are investigated to determine the diffusion activation barriers of 0.67 eV and 0.91 eV, respectively. The Monte Carlo simulation of the cluster hopping model suggests that the decrease in the number of dimeric and trimeric clusters during surface diffusion is the origin of the observed relaxation phenomena.

Quantum group structure and local fields in the algebraic approach to 2D gravity

NASA Astrophysics Data System (ADS)

Schnittger, J.

1995-07-01

This review contains a summary of the work by J.-L. Gervais and the author on the operator approach to 2d gravity. Special emphasis is placed on the construction of local observables — the Liouville exponentials and the Liouville field itself — and the underlying algebra of chiral vertex operators. The double quantum group structure arising from the presence of two screening charges is discussed and the generalized algebra and field operators are derived. In the last part, we show that our construction gives rise to a natural definition of a quantum tau function, which is a noncommutative version of the classical group-theoretic representation of the Liouville fields by Leznov and Saveliev.

Exponential quantum spreading in a class of kicked rotor systems near high-order resonances

NASA Astrophysics Data System (ADS)

Wang, Hailong; Wang, Jiao; Guarneri, Italo; Casati, Giulio; Gong, Jiangbin

2013-11-01

Long-lasting exponential quantum spreading was recently found in a simple but very rich dynamical model, namely, an on-resonance double-kicked rotor model [J. Wang, I. Guarneri, G. Casati, and J. B. Gong, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.234104 107, 234104 (2011)]. The underlying mechanism, unrelated to the chaotic motion in the classical limit but resting on quasi-integrable motion in a pseudoclassical limit, is identified for one special case. By presenting a detailed study of the same model, this work offers a framework to explain long-lasting exponential quantum spreading under much more general conditions. In particular, we adopt the so-called “spinor” representation to treat the kicked-rotor dynamics under high-order resonance conditions and then exploit the Born-Oppenheimer approximation to understand the dynamical evolution. It is found that the existence of a flat band (or an effectively flat band) is one important feature behind why and how the exponential dynamics emerges. It is also found that a quantitative prediction of the exponential spreading rate based on an interesting and simple pseudoclassical map may be inaccurate. In addition to general interests regarding the question of how exponential behavior in quantum systems may persist for a long time scale, our results should motivate further studies toward a better understanding of high-order resonance behavior in δ-kicked quantum systems.

Parameter estimation and order selection for an empirical model of VO2 on-kinetics.

PubMed

Alata, O; Bernard, O

2007-04-27

In humans, VO2 on-kinetics are noisy numerical signals that reflect the pulmonary oxygen exchange kinetics at the onset of exercise. They are empirically modelled as a sum of an offset and delayed exponentials. The number of delayed exponentials; i.e. the order of the model, is commonly supposed to be 1 for low-intensity exercises and 2 for high-intensity exercises. As no ground truth has ever been provided to validate these postulates, physiologists still need statistical methods to verify their hypothesis about the number of exponentials of the VO2 on-kinetics especially in the case of high-intensity exercises. Our objectives are first to develop accurate methods for estimating the parameters of the model at a fixed order, and then, to propose statistical tests for selecting the appropriate order. In this paper, we provide, on simulated Data, performances of Simulated Annealing for estimating model parameters and performances of Information Criteria for selecting the order. These simulated Data are generated with both single-exponential and double-exponential models, and noised by white and Gaussian noise. The performances are given at various Signal to Noise Ratio (SNR). Considering parameter estimation, results show that the confidences of estimated parameters are improved by increasing the SNR of the response to be fitted. Considering model selection, results show that Information Criteria are adapted statistical criteria to select the number of exponentials.

Wide variation of prostate-specific antigen doubling time of untreated, clinically localized, low-to-intermediate grade, prostate carcinoma.

PubMed

Choo, Richard; Klotz, Laurence; Deboer, Gerrit; Danjoux, Cyril; Morton, Gerard C

2004-08-01

To assess the prostate specific antigen (PSA) doubling time of untreated, clinically localized, low-to-intermediate grade prostate carcinoma. A prospective single-arm cohort study has been in progress since November 1995 to assess the feasibility of a watchful-observation protocol with selective delayed intervention for clinically localized, low-to-intermediate grade prostate adenocarcinoma. The PSA doubling time was estimated from a linear regression of ln(PSA) against time, assuming a simple exponential growth model. As of March 2003, 231 patients had at least 6 months of follow-up (median 45) and at least three PSA measurements (median 8, range 3-21). The distribution of the doubling time was: < 2 years, 26 patients; 2-5 years, 65; 5-10 years, 42; 10-20 years, 26; 20-50 years, 16; >50 years, 56. The median doubling time was 7.0 years; 42% of men had a doubling time of >10 years. The doubling time of untreated clinically localized, low-to-intermediate grade prostate cancer varies widely.

Non-extensive quantum statistics with particle-hole symmetry

NASA Astrophysics Data System (ADS)

Biró, T. S.; Shen, K. M.; Zhang, B. W.

2015-06-01

Based on Tsallis entropy (1988) and the corresponding deformed exponential function, generalized distribution functions for bosons and fermions have been used since a while Teweldeberhan et al. (2003) and Silva et al. (2010). However, aiming at a non-extensive quantum statistics further requirements arise from the symmetric handling of particles and holes (excitations above and below the Fermi level). Naive replacements of the exponential function or "cut and paste" solutions fail to satisfy this symmetry and to be smooth at the Fermi level at the same time. We solve this problem by a general ansatz dividing the deformed exponential to odd and even terms and demonstrate that how earlier suggestions, like the κ- and q-exponential behave in this respect.

Exponential decline of deep-sea ecosystem functioning linked to benthic biodiversity loss.

PubMed

Danovaro, Roberto; Gambi, Cristina; Dell'Anno, Antonio; Corinaldesi, Cinzia; Fraschetti, Simonetta; Vanreusel, Ann; Vincx, Magda; Gooday, Andrew J

2008-01-08

Recent investigations suggest that biodiversity loss might impair the functioning and sustainability of ecosystems. Although deep-sea ecosystems are the most extensive on Earth, represent the largest reservoir of biomass, and host a large proportion of undiscovered biodiversity, the data needed to evaluate the consequences of biodiversity loss on the ocean floor are completely lacking. Here, we present a global-scale study based on 116 deep-sea sites that relates benthic biodiversity to several independent indicators of ecosystem functioning and efficiency. We show that deep-sea ecosystem functioning is exponentially related to deep-sea biodiversity and that ecosystem efficiency is also exponentially linked to functional biodiversity. These results suggest that a higher biodiversity supports higher rates of ecosystem processes and an increased efficiency with which these processes are performed. The exponential relationships presented here, being consistent across a wide range of deep-sea ecosystems, suggest that mutually positive functional interactions (ecological facilitation) can be common in the largest biome of our biosphere. Our results suggest that a biodiversity loss in deep-sea ecosystems might be associated with exponential reductions of their functions. Because the deep sea plays a key role in ecological and biogeochemical processes at a global scale, this study provides scientific evidence that the conservation of deep-sea biodiversity is a priority for a sustainable functioning of the worlds' oceans.

Compact exponential product formulas and operator functional derivative

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suzuki, M.

1997-02-01

A new scheme for deriving compact expressions of the logarithm of the exponential product is proposed and it is applied to several exponential product formulas. A generalization of the Dynkin{endash}Specht{endash}Wever (DSW) theorem on free Lie elements is given, and it is used to study the relation between the traditional method (based on the DSW theorem) and the present new scheme. The concept of the operator functional derivative is also proposed, and it is applied to ordered exponentials, such as time-evolution operators for time-dependent Hamiltonians. {copyright} {ital 1997 American Institute of Physics.}

Investigation of the double exponential in the current-voltage characteristics of silicon solar cells

NASA Technical Reports Server (NTRS)

Wolf, M.; Noel, G. T.; Stirn, R. J.

1976-01-01

A theoretical analysis is presented of certain peculiarities of the current-voltage characteristics of silicon solar cells, involving high values of the empirical constant A in the diode equation for a p-n junction. An attempt was made in a lab experiment to demonstrate that the saturation current which is associated with the exponential term qV/A2kT of the I-V characteristic, with A2 roughly equal to 2, originates in the space charge region and that it can be increased, as observed on ATS-1 cells, by the introduction of additional defects through low energy proton irradiation. It was shown that the proton irradiation introduces defects into the space charge region which give rise to a recombination current from this region, although the I-V characteristic is, in this case, dominated by an exponential term which has A = 1.

The Exponential Function--Part VIII

ERIC Educational Resources Information Center

Bartlett, Albert A.

1978-01-01

Presents part eight of a continuing series on the exponential function in which, given the current population of the Earth and assuming a constant growth rate of 1.9 percent backward looks at world population are made. (SL)

Ill-posed problem and regularization in reconstruction of radiobiological parameters from serial tumor imaging data

NASA Astrophysics Data System (ADS)

Chvetsov, Alevei V.; Sandison, George A.; Schwartz, Jeffrey L.; Rengan, Ramesh

2015-11-01

The main objective of this article is to improve the stability of reconstruction algorithms for estimation of radiobiological parameters using serial tumor imaging data acquired during radiation therapy. Serial images of tumor response to radiation therapy represent a complex summation of several exponential processes as treatment induced cell inactivation, tumor growth rates, and the rate of cell loss. Accurate assessment of treatment response would require separation of these processes because they define radiobiological determinants of treatment response and, correspondingly, tumor control probability. However, the estimation of radiobiological parameters using imaging data can be considered an inverse ill-posed problem because a sum of several exponentials would produce the Fredholm integral equation of the first kind which is ill posed. Therefore, the stability of reconstruction of radiobiological parameters presents a problem even for the simplest models of tumor response. To study stability of the parameter reconstruction problem, we used a set of serial CT imaging data for head and neck cancer and a simplest case of a two-level cell population model of tumor response. Inverse reconstruction was performed using a simulated annealing algorithm to minimize a least squared objective function. Results show that the reconstructed values of cell surviving fractions and cell doubling time exhibit significant nonphysical fluctuations if no stabilization algorithms are applied. However, after applying a stabilization algorithm based on variational regularization, the reconstruction produces statistical distributions for survival fractions and doubling time that are comparable to published in vitro data. This algorithm is an advance over our previous work where only cell surviving fractions were reconstructed. We conclude that variational regularization allows for an increase in the number of free parameters in our model which enables development of more-advanced parameter reconstruction algorithms.

A mechanism producing power law etc. distributions

NASA Astrophysics Data System (ADS)

Li, Heling; Shen, Hongjun; Yang, Bin

2017-07-01

Power law distribution is playing an increasingly important role in the complex system study. Based on the insolvability of complex systems, the idea of incomplete statistics is utilized and expanded, three different exponential factors are introduced in equations about the normalization condition, statistical average and Shannon entropy, with probability distribution function deduced about exponential function, power function and the product form between power function and exponential function derived from Shannon entropy and maximal entropy principle. So it is shown that maximum entropy principle can totally replace equal probability hypothesis. Owing to the fact that power and probability distribution in the product form between power function and exponential function, which cannot be derived via equal probability hypothesis, can be derived by the aid of maximal entropy principle, it also can be concluded that maximal entropy principle is a basic principle which embodies concepts more extensively and reveals basic principles on motion laws of objects more fundamentally. At the same time, this principle also reveals the intrinsic link between Nature and different objects in human society and principles complied by all.

Power and Roots by Recursion.

ERIC Educational Resources Information Center

Aieta, Joseph F.

1987-01-01

This article illustrates how questions from elementary finance can serve as motivation for studying high order powers, roots, and exponential functions using Logo procedures. A second discussion addresses a relatively unknown algorithm for the trigonometric exponential and hyperbolic functions. (PK)

Controllability of a multichannel system

NASA Astrophysics Data System (ADS)

Ivanov, Sergei A.; Wang, Jun Min

2018-02-01

We consider the system consisting of K coupled acoustic channels with the different sound velocities cj. Channels are interacting at any point via the pressure and its time derivatives. Using the moment approach and the theory of exponential families with vector coefficients we establish two controllability results: the system is exactly controllable if (i) the control uj in the jth channel acts longer than the double travel time of a wave from the start to the end of the j-th channel; (ii) all controls uj act more than or equal to the maximal double travel time.

Fundamentals of Tribology; Proceedings of the International Conference on the Fundamentals of Tribology held at The Massachusetts Institute of Technology, Cambridge, MA

DTIC Science & Technology

1978-06-01

HDL). The locus of electrical centers of hydrated ions in contact with the electrode surface is known as the outer Helmholtz plane ( OHP ) while the...and then a more Crdual exponential decay in the diffuse double layer. The difference in potential between the OHP and the bulk electrolyte, i.e., the...rnntribution of the diffuse double layer, is called the electrokinetic or iC 275 (a) Wc IHP OHP GCL- BULK + + ELECTRO YTE + + + + +G+ + eS+ J f -A -A

Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation

ERIC Educational Resources Information Center

Gordon, Sheldon P.; Yang, Yajun

2017-01-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

Caustics, counting maps and semi-classical asymptotics

NASA Astrophysics Data System (ADS)

Ercolani, N. M.

2011-02-01

This paper develops a deeper understanding of the structure and combinatorial significance of the partition function for Hermitian random matrices. The coefficients of the large N expansion of the logarithm of this partition function, also known as the genus expansion (and its derivatives), are generating functions for a variety of graphical enumeration problems. The main results are to prove that these generating functions are, in fact, specific rational functions of a distinguished irrational (algebraic) function, z0(t). This distinguished function is itself the generating function for the Catalan numbers (or generalized Catalan numbers, depending on the choice of weight of the parameter t). It is also a solution of the inviscid Burgers equation for certain initial data. The shock formation, or caustic, of the Burgers characteristic solution is directly related to the poles of the rational forms of the generating functions. As an intriguing application, one gains new insights into the relation between certain derivatives of the genus expansion, in a double-scaling limit, and the asymptotic expansion of the first Painlevé transcendent. This provides a precise expression of the Painlevé asymptotic coefficients directly in terms of the coefficients of the partial fractions expansion of the rational form of the generating functions established in this paper. Moreover, these insights point towards a more general program relating the first Painlevé hierarchy to the higher order structure of the double-scaling limit through the specific rational structure of generating functions in the genus expansion. The paper closes with a discussion of the relation of this work to recent developments in understanding the asymptotics of graphical enumeration. As a by-product, these results also yield new information about the asymptotics of recurrence coefficients for orthogonal polynomials with respect to exponential weights, the calculation of correlation functions for certain tied random walks on a 1D lattice, and the large time asymptotics of random matrix partition functions.

On the origin of stretched exponential (Kohlrausch) relaxation kinetics in the room temperature luminescence decay of colloidal quantum dots.

PubMed

Bodunov, E N; Antonov, Yu A; Simões Gamboa, A L

2017-03-21

The non-exponential room temperature luminescence decay of colloidal quantum dots is often well described by a stretched exponential function. However, the physical meaning of the parameters of the function is not clear in the majority of cases reported in the literature. In this work, the room temperature stretched exponential luminescence decay of colloidal quantum dots is investigated theoretically in an attempt to identify the underlying physical mechanisms associated with the parameters of the function. Three classes of non-radiative transition processes between the excited and ground states of colloidal quantum dots are discussed: long-range resonance energy transfer, multiphonon relaxation, and contact quenching without diffusion. It is shown that multiphonon relaxation cannot explain a stretched exponential functional form of the luminescence decay while such dynamics of relaxation can be understood in terms of long-range resonance energy transfer to acceptors (molecules, quantum dots, or anharmonic molecular vibrations) in the environment of the quantum dots acting as energy-donors or by contact quenching by acceptors (surface traps or molecules) distributed statistically on the surface of the quantum dots. These non-radiative transition processes are assigned to different ranges of the stretching parameter β.

Skills for the Future.

ERIC Educational Resources Information Center

Smith, Gary R.

This publication contains two miniunits to help students in grades 7-12 build skills for the future. The exercises can also be adapted for use in grades 4-6. Each of the miniunits contains several exercises to build specific skills. Miniunit One, "The Arithmetic of Growth," deals with two concepts--exponential growth and doubling time. These two…

Ultraviolet laser-induced voltage in anisotropic shale

NASA Astrophysics Data System (ADS)

Miao, Xinyang; Zhu, Jing; Li, Yizhang; Zhao, Kun; Zhan, Honglei; Yue, Wenzheng

2018-01-01

The anisotropy of shales plays a significant role in oil and gas exploration and engineering. Owing to various problems and limitations, anisotropic properties were seldom investigated by direct current resistivity methods. Here in this work, a 248 nm ultraviolet laser was employed to assess the anisotropic electrical response of a dielectric shale. Angular dependence of laser-induced voltages (V p) were obtained, with a data symmetry at the location of 180° and a ~62.2% V p anisotropy of the sample. The double-exponential functions have provided an explanation for the electrical field controlled carrier transportation process in horizontal and vertical directions. The results demonstrate that the combination of optics and electrical logging analysis (Opti-electrical Logging) is a promising technology for the investigation of unconventional reservoirs.

Ray-theory approach to electrical-double-layer interactions.

PubMed

Schnitzer, Ory

2015-02-01

A novel approach is presented for analyzing the double-layer interaction force between charged particles in electrolyte solution, in the limit where the Debye length is small compared with both interparticle separation and particle size. The method, developed here for two planar convex particles of otherwise arbitrary geometry, yields a simple asymptotic approximation limited to neither small zeta potentials nor the "close-proximity" assumption underlying Derjaguin's approximation. Starting from the nonlinear Poisson-Boltzmann formulation, boundary-layer solutions describing the thin diffuse-charge layers are asymptotically matched to a WKBJ expansion valid in the bulk, where the potential is exponentially small. The latter expansion describes the bulk potential as superposed contributions conveyed by "rays" emanating normally from the boundary layers. On a special curve generated by the centers of all circles maximally inscribed between the two particles, the bulk stress-associated with the ray contributions interacting nonlinearly-decays exponentially with distance from the center of the smallest of these circles. The force is then obtained by integrating the traction along this curve using Laplace's method. We illustrate the usefulness of our theory by comparing it, alongside Derjaguin's approximation, with numerical simulations in the case of two parallel cylinders at low potentials. By combining our result and Derjaguin's approximation, the interaction force is provided at arbitrary interparticle separations. Our theory can be generalized to arbitrary three-dimensional geometries, nonideal electrolyte models, and other physical scenarios where exponentially decaying fields give rise to forces.

A Simulation of the ECSS Help Desk with the Erlang a Model

DTIC Science & Technology

2011-03-01

a popular distribution is the exponential distribution as shown in Figure 3. Figure 3: Exponential Distribution ( Bourke , 2001) Exponential...System Sciences, Vol 8, 235B. Bourke , P. (2001, January). Miscellaneous Functions. Retrieved January 22, 2011, from http://local.wasp.uwa.edu.au

[A modification of the Gompertz plot resulting from the age index by Ries and an approximation of the survivorship curve (author's transl)].

PubMed

Lohmann, W

1978-01-01

The shape of the survivorship curve can easily be interpreted on condition that the probability of death is proportional to an exponentially rising function of ageing. According to the formation of a sum for determining of the age index by Ries it was investigated to what extent the survivorship curve may be approximated by a sum of exponentials. It follows that the difference between the pure exponential function and a sum of exponentials by using possible values is lying within the random variation. Because the probability of death for different diseases is variable, the new statement is a better one.

Force Measurements of Single and Double Barrier DBD Plasma Actuators in Quiescent Air

NASA Technical Reports Server (NTRS)

Hoskinson, Alan R.; Hershkowitz, Noah; Ashpis, David E.

2008-01-01

We have performed measurements of the force induced by both single (one electrode insulated) and double (both electrodes insulated) dielectric barrier discharge plasma actuators in quiescent air. We have shown that, for single barrier actuators, as the electrode diameter decreased below those values previously studied the induced Force increases exponentially rather than linearly. This behavior has been experimentally verified using two different measurement techniques: stagnation probe measurements of the induced flow velocity and direct measurement of the force using an electronic balance. In addition, we have shown the the induced force is independent of the material used for the exposed electrode. The same techniques have shown that the induced force of a double barrier actuator increases with decreasing narrow electrode diameter.

U-shaped, double-tapered, fiber-optic sensor for effective biofilm growth monitoring.

PubMed

Zhong, Nianbing; Zhao, Mingfu; Li, Yishan

2016-02-01

To monitor biofilm growth on polydimethylsiloxane in a photobioreactor effectively, the biofilm cells and liquids were separated and measured using a sensor with two U-shaped, double-tapered, fiber-optic probes (Sen. and Ref. probes). The probes' Au-coated hemispherical tips enabled double-pass evanescent field absorption. The Sen. probe sensed the cells and liquids inside the biofilm. The polyimide-silica hybrid-film-coated Ref. probe separated the liquids from the biofilm cells and analyzed the liquid concentration. The biofilm structure and active biomass were also examined to confirm the effectiveness of the measurement using a simulation model. The sensor was found to effectively respond to the biofilm growth in the adsorption through exponential phases at thicknesses of 0-536 μm.

First off-time treatment prostate-specific antigen kinetics predicts survival in intermittent androgen deprivation for prostate cancer.

PubMed

Sanchez-Salas, Rafael; Olivier, Fabien; Prapotnich, Dominique; Dancausa, José; Fhima, Mehdi; David, Stéphane; Secin, Fernando P; Ingels, Alexandre; Barret, Eric; Galiano, Marc; Rozet, François; Cathelineau, Xavier

2016-01-01

Prostate-specific antigen (PSA) doubling time is relying on an exponential kinetic pattern. This pattern has never been validated in the setting of intermittent androgen deprivation (IAD). Objective is to analyze the prognostic significance for PCa of recurrent patterns in PSA kinetics in patients undergoing IAD. A retrospective study was conducted on 377 patients treated with IAD. On-treatment period (ONTP) consisted of gonadotropin-releasing hormone agonist injections combined with oral androgen receptor antagonist. Off-treatment period (OFTP) began when PSA was lower than 4 ng/ml. ONTP resumed when PSA was higher than 20 ng/ml. PSA values of each OFTP were fitted with three basic patterns: exponential (PSA(t) = λ.e(αt)), linear (PSA(t) = a.t), and power law (PSA(t) = a.t(c)). Univariate and multivariate Cox regression model analyzed predictive factors for oncologic outcomes. Only 45% of the analyzed OFTPs were exponential. Linear and power law PSA kinetics represented 7.5% and 7.7%, respectively. Remaining fraction of analyzed OFTPs (40%) exhibited complex kinetics. Exponential PSA kinetics during the first OFTP was significantly associated with worse oncologic outcome. The estimated 10-year cancer-specific survival (CSS) was 46% for exponential versus 80% for nonexponential PSA kinetics patterns. The corresponding 10-year probability of castration-resistant prostate cancer (CRPC) was 69% and 31% for the two patterns, respectively. Limitations include retrospective design and mixed indications for IAD. PSA kinetic fitted with exponential pattern in approximately half of the OFTPs. First OFTP exponential PSA kinetic was associated with a shorter time to CRPC and worse CSS. © 2015 Wiley Periodicals, Inc.

Heuristic lipophilicity potential for computer-aided rational drug design: Optimizations of screening functions and parameters

NASA Astrophysics Data System (ADS)

Du, Qishi; Mezey, Paul G.

1998-09-01

In this research we test and compare three possible atom-basedscreening functions used in the heuristic molecular lipophilicity potential(HMLP). Screening function 1 is a power distance-dependent function, b_{{i}} /| {R_{{i}}- r} |^γ, screening function 2is an exponential distance-dependent function, biexp(-| {R_i- r} |/d_0 , and screening function 3 is aweighted distance-dependent function, {{sign}}( {b_i } ){{exp}}ξ ( {| {R_i- r} |/| {b_i } |} )For every screening function, the parameters (γ ,d0, and ξ are optimized using 41 common organic molecules of 4 types of compounds:aliphatic alcohols, aliphatic carboxylic acids, aliphatic amines, andaliphatic alkanes. The results of calculations show that screening function3 cannot give chemically reasonable results, however, both the powerscreening function and the exponential screening function give chemicallysatisfactory results. There are two notable differences between screeningfunctions 1 and 2. First, the exponential screening function has largervalues in the short distance than the power screening function, thereforemore influence from the nearest neighbors is involved using screeningfunction 2 than screening function 1. Second, the power screening functionhas larger values in the long distance than the exponential screeningfunction, therefore screening function 1 is effected by atoms at longdistance more than screening function 2. For screening function 1, thesuitable range of parameter d0 is 1.5 < d0 < 3.0, and d0 = 2.0 is recommended. HMLP developed in this researchprovides a potential tool for computer-aided three-dimensional drugdesign.

Understanding quantum tunneling using diffusion Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Inack, E. M.; Giudici, G.; Parolini, T.; Santoro, G.; Pilati, S.

2018-03-01

In simple ferromagnetic quantum Ising models characterized by an effective double-well energy landscape the characteristic tunneling time of path-integral Monte Carlo (PIMC) simulations has been shown to scale as the incoherent quantum-tunneling time, i.e., as 1 /Δ2 , where Δ is the tunneling gap. Since incoherent quantum tunneling is employed by quantum annealers (QAs) to solve optimization problems, this result suggests that there is no quantum advantage in using QAs with respect to quantum Monte Carlo (QMC) simulations. A counterexample is the recently introduced shamrock model (Andriyash and Amin, arXiv:1703.09277), where topological obstructions cause an exponential slowdown of the PIMC tunneling dynamics with respect to incoherent quantum tunneling, leaving open the possibility for potential quantum speedup, even for stoquastic models. In this work we investigate the tunneling time of projective QMC simulations based on the diffusion Monte Carlo (DMC) algorithm without guiding functions, showing that it scales as 1 /Δ , i.e., even more favorably than the incoherent quantum-tunneling time, both in a simple ferromagnetic system and in the more challenging shamrock model. However, a careful comparison between the DMC ground-state energies and the exact solution available for the transverse-field Ising chain indicates an exponential scaling of the computational cost required to keep a fixed relative error as the system size increases.

Scattering of plane evanescent waves by buried cylinders: Modeling the coupling to guided waves and resonances

NASA Astrophysics Data System (ADS)

Marston, Philip L.

2003-04-01

The coupling of sound to buried targets can be associated with acoustic evanescent waves when the sea bottom is smooth. To understand the excitation of guided waves on buried fluid cylinders and shells by acoustic evanescent waves and the associated target resonances, the two-dimensional partial wave series for the scattering is found for normal incidence in an unbounded medium. The shell formulation uses the simplifications of thin-shell dynamics. The expansion of the incident wave becomes a double summation with products of modified and ordinary Bessel functions [P. L. Marston, J. Acoust. Soc. Am. 111, 2378 (2002)]. Unlike the case of an ordinary incident wave, the counterpropagating partial waves of the same angular order have unequal magnitudes when the incident wave is evanescent. This is a consequence of the exponential dependence of the incident wave amplitude on depth. Some consequences of this imbalance of partial-wave amplitudes are given by modifying previous ray theory for the scattering [P. L. Marston and N. H. Sun, J. Acoust. Soc. Am. 97, 777-783 (1995)]. The exponential dependence of the scattering on the location of a scatterer was previously demonstrated in air [T. J. Matula and P. L. Marston, J. Acoust. Soc. Am. 93, 1192-1195 (1993)].

Adaptation in the auditory midbrain of the barn owl (Tyto alba) induced by tonal double stimulation.

PubMed

Singheiser, Martin; Ferger, Roland; von Campenhausen, Mark; Wagner, Hermann

2012-02-01

During hunting, the barn owl typically listens to several successive sounds as generated, for example, by rustling mice. As auditory cells exhibit adaptive coding, the earlier stimuli may influence the detection of the later stimuli. This situation was mimicked with two double-stimulus paradigms, and adaptation was investigated in neurons of the barn owl's central nucleus of the inferior colliculus. Each double-stimulus paradigm consisted of a first or reference stimulus and a second stimulus (probe). In one paradigm (second level tuning), the probe level was varied, whereas in the other paradigm (inter-stimulus interval tuning), the stimulus interval between the first and second stimulus was changed systematically. Neurons were stimulated with monaural pure tones at the best frequency, while the response was recorded extracellularly. The responses to the probe were significantly reduced when the reference stimulus and probe had the same level and the inter-stimulus interval was short. This indicated response adaptation, which could be compensated for by an increase of the probe level of 5-7 dB over the reference level, if the latter was in the lower half of the dynamic range of a neuron's rate-level function. Recovery from adaptation could be best fitted with a double exponential showing a fast (1.25 ms) and a slow (800 ms) component. These results suggest that neurons in the auditory system show dynamic coding properties to tonal double stimulation that might be relevant for faithful upstream signal propagation. Furthermore, the overall stimulus level of the masker also seems to affect the recovery capabilities of auditory neurons. © 2012 The Authors. European Journal of Neuroscience © 2012 Federation of European Neuroscience Societies and Blackwell Publishing Ltd.

A Test of the Exponential Distribution for Stand Structure Definition in Uneven-aged Loblolly-Shortleaf Pine Stands

Treesearch

Paul A. Murphy; Robert M. Farrar

1981-01-01

In this study, 588 before-cut and 381 after-cut diameter distributions of uneven-aged loblolly-shortleaf pinestands were fitted to two different forms of the exponential probability density function. The left truncated and doubly truncated forms of the exponential were used.

On the Gibbs phenomenon 3: Recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1993-01-01

The investigation of overcoming Gibbs phenomenon was continued, i.e., obtaining exponential accuracy at all points including at the discontinuities themselves, from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. It was shown that if we are given the first N expansion coefficients of an L(sub 2) function f(x) in terms of either the trigonometrical polynomials or the Chebyshev or Legendre polynomials, an exponentially convergent approximation to the point values of f(x) in any sub-interval in which it is analytic can be constructed.

Temperature-dependent microindentation data of an epoxy composition in the glassy region

NASA Astrophysics Data System (ADS)

Minster, Jiří; Králík, Vlastimil

2015-02-01

The short-term instrumented microindentation technique was applied for assessing the influence of temperature in the glassy region on the time-dependent mechanical properties of an average epoxy resin mix near to its native state. Linear viscoelasticity theory with the assumption of time-independent Poisson ratio value forms the basis for processing the experimental results. The sharp standard Berkovich indenter was used to measure the local mechanical properties at temperatures 20, 24, 28, and 35 °C. The short-term viscoelastic compliance histories were defined by the Kohlrausch-Williams-Watts double exponential function. The findings suggest that depth-sensing indentation data of thermorheologically simple materials influenced by different temperatures in the glassy region can also be used, through the time-temperature superposition, to extract viscoelastic response functions accurately. This statement is supported by the comparison of the viscoelastic compliance master curve of the tested material with data derived from standard macro creep measurements under pressure on the material in a conformable state.

Historical Patterns of Change: The Lessons of the 1980s.

ERIC Educational Resources Information Center

Geiger, Roger L.

This paper seeks to assess the current state of academic research in light of long-term trends in the development of science. It presents three perspectives on the growth of scientific research: (1) Derek de Solla Price's (1963) hypothesis that science has exhibited exponential growth, roughly doubling every 15 years since the 17th century; (2)…

In vivo measurement of human skin absorption of topically applied substances by a photoacoustic technique.

PubMed

Gutiérrez-Juárez, G; Vargas-Luna, M; Córdova, T; Varela, J B; Bernal-Alvarado, J J; Sosa, M

2002-08-01

A photoacoustic technique is used for studying topically applied substance absorption in human skin. The proposed method utilizes a double-chamber PA cell. The absorption determination was obtained through the measurement of the thermal effusivity of the binary system substance-skin. The theoretical model assumes that the effective thermal effusivity of the binary system corresponds to that of a two-phase system. Experimental applications of the method employed different substances of topical application in different parts of the body of a volunteer. The method is demonstrated to be an easily used non-invasive technique for dermatology research. The relative concentrations as a function of time of substances such as ketoconazol and sunscreen were determined by fitting a sigmoidal function to the data, while an exponential function corresponds to the best fit for the set of data for nitrofurazona, vaseline and vaporub. The time constants associated with the rates of absorption, were found to vary in the range between 10 and 58 min, depending on the substance and the part of the body.

Initial mass function of planetesimals formed by the streaming instability

NASA Astrophysics Data System (ADS)

Schäfer, Urs; Yang, Chao-Chin; Johansen, Anders

2017-01-01

The streaming instability is a mechanism to concentrate solid particles into overdense filaments that undergo gravitational collapse and form planetesimals. However, it remains unclear how the initial mass function of these planetesimals depends on the box dimensions of numerical simulations. To resolve this, we perform simulations of planetesimal formation with the largest box dimensions to date, allowing planetesimals to form simultaneously in multiple filaments that can only emerge within such large simulation boxes. In our simulations, planetesimals with sizes between 80 km and several hundred kilometers form. We find that a power law with a rather shallow exponential cutoff at the high-mass end represents the cumulative birth mass function better than an integrated power law. The steepness of the exponential cutoff is largely independent of box dimensions and resolution, while the exponent of the power law is not constrained at the resolutions we employ. Moreover, we find that the characteristic mass scale of the exponential cutoff correlates with the mass budget in each filament. Together with previous studies of high-resolution simulations with small box domains, our results therefore imply that the cumulative birth mass function of planetesimals is consistent with an exponentially tapered power law with a power-law exponent of approximately -1.6 and a steepness of the exponential cutoff in the range of 0.3-0.4.

Geometry of the q-exponential distribution with dependent competing risks and accelerated life testing

NASA Astrophysics Data System (ADS)

Zhang, Fode; Shi, Yimin; Wang, Ruibing

2017-02-01

In the information geometry suggested by Amari (1985) and Amari et al. (1987), a parametric statistical model can be regarded as a differentiable manifold with the parameter space as a coordinate system. Note that the q-exponential distribution plays an important role in Tsallis statistics (see Tsallis, 2009), this paper investigates the geometry of the q-exponential distribution with dependent competing risks and accelerated life testing (ALT). A copula function based on the q-exponential function, which can be considered as the generalized Gumbel copula, is discussed to illustrate the structure of the dependent random variable. Employing two iterative algorithms, simulation results are given to compare the performance of estimations and levels of association under different hybrid progressively censoring schemes (HPCSs).

Microcomputer Calculation of Theoretical Pre-Exponential Factors for Bimolecular Reactions.

ERIC Educational Resources Information Center

Venugopalan, Mundiyath

1991-01-01

Described is the application of microcomputers to predict reaction rates based on theoretical atomic and molecular properties taught in undergraduate physical chemistry. Listed is the BASIC program which computes the partition functions for any specific bimolecular reactants. These functions are then used to calculate the pre-exponential factor of…

A Comparison of Two Algorithms for the Simulation of Non-Homogeneous Poisson Processes with Degree-Two Exponential Polynomial Intensity Function.

DTIC Science & Technology

1977-09-01

process with an event streaa intensity (rate) function that is of degree-two exponential pclyncaial foru. (The use of exponential pclynoaials is...4 \\v 01 ^3 C \\ \\ •r- S_ \\ \\ O \\ \\ a \\ \\ V IA C 4-> \\ \\ •«- c \\ 1 <— 3 • o \\ \\ Ol (J \\ \\ O U —1 <o \\ I...would serve as a good initial approxiaation t* , f-r the Newton-Raphson aethod. However, for the purpose of this implementation, the end point which

Bayesian inference based on dual generalized order statistics from the exponentiated Weibull model

NASA Astrophysics Data System (ADS)

Al Sobhi, Mashail M.

2015-02-01

Bayesian estimation for the two parameters and the reliability function of the exponentiated Weibull model are obtained based on dual generalized order statistics (DGOS). Also, Bayesian prediction bounds for future DGOS from exponentiated Weibull model are obtained. The symmetric and asymmetric loss functions are considered for Bayesian computations. The Markov chain Monte Carlo (MCMC) methods are used for computing the Bayes estimates and prediction bounds. The results have been specialized to the lower record values. Comparisons are made between Bayesian and maximum likelihood estimators via Monte Carlo simulation.

Avalanche Analysis from Multielectrode Ensemble Recordings in Cat, Monkey, and Human Cerebral Cortex during Wakefulness and Sleep

PubMed Central

Dehghani, Nima; Hatsopoulos, Nicholas G.; Haga, Zach D.; Parker, Rebecca A.; Greger, Bradley; Halgren, Eric; Cash, Sydney S.; Destexhe, Alain

2012-01-01

Self-organized critical states are found in many natural systems, from earthquakes to forest fires, they have also been observed in neural systems, particularly, in neuronal cultures. However, the presence of critical states in the awake brain remains controversial. Here, we compared avalanche analyses performed on different in vivo preparations during wakefulness, slow-wave sleep, and REM sleep, using high density electrode arrays in cat motor cortex (96 electrodes), monkey motor cortex and premotor cortex and human temporal cortex (96 electrodes) in epileptic patients. In neuronal avalanches defined from units (up to 160 single units), the size of avalanches never clearly scaled as power-law, but rather scaled exponentially or displayed intermediate scaling. We also analyzed the dynamics of local field potentials (LFPs) and in particular LFP negative peaks (nLFPs) among the different electrodes (up to 96 sites in temporal cortex or up to 128 sites in adjacent motor and premotor cortices). In this case, the avalanches defined from nLFPs displayed power-law scaling in double logarithmic representations, as reported previously in monkey. However, avalanche defined as positive LFP (pLFP) peaks, which are less directly related to neuronal firing, also displayed apparent power-law scaling. Closer examination of this scaling using the more reliable cumulative distribution function (CDF) and other rigorous statistical measures, did not confirm power-law scaling. The same pattern was seen for cats, monkey, and human, as well as for different brain states of wakefulness and sleep. We also tested other alternative distributions. Multiple exponential fitting yielded optimal fits of the avalanche dynamics with bi-exponential distributions. Collectively, these results show no clear evidence for power-law scaling or self-organized critical states in the awake and sleeping brain of mammals, from cat to man. PMID:22934053

AN EMPIRICAL FORMULA FOR THE DISTRIBUTION FUNCTION OF A THIN EXPONENTIAL DISC

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sharma, Sanjib; Bland-Hawthorn, Joss

2013-08-20

An empirical formula for a Shu distribution function that reproduces a thin disc with exponential surface density to good accuracy is presented. The formula has two free parameters that specify the functional form of the velocity dispersion. Conventionally, this requires the use of an iterative algorithm to produce the correct solution, which is computationally taxing for applications like Markov Chain Monte Carlo model fitting. The formula has been shown to work for flat, rising, and falling rotation curves. Application of this methodology to one of the Dehnen distribution functions is also shown. Finally, an extension of this formula to reproducemore » velocity dispersion profiles that are an exponential function of radius is also presented. Our empirical formula should greatly aid the efficient comparison of disc models with large stellar surveys or N-body simulations.« less

The First Derivative of an Exponential Function with the "White Box/Black Box" Didactical Principle and Observations with GeoGebra

ERIC Educational Resources Information Center

Budinski, Natalija; Subramaniam, Stephanie

2013-01-01

This paper shows how GeoGebra--a dynamic mathematics software--can be used to experiment, visualize and connect various concepts such as function, first derivative, slope, and tangent line. Students were given an assignment to determine the first derivative of the exponential function that they solved while experimenting with GeoGebra. GeoGebra…

Approximating exponential and logarithmic functions using polynomial interpolation

NASA Astrophysics Data System (ADS)

Gordon, Sheldon P.; Yang, Yajun

2017-04-01

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is analysed. The results of interpolating polynomials are compared with those of Taylor polynomials.

U-shaped, double-tapered, fiber-optic sensor for effective biofilm growth monitoring

PubMed Central

Zhong, Nianbing; Zhao, Mingfu; Li, Yishan

2016-01-01

To monitor biofilm growth on polydimethylsiloxane in a photobioreactor effectively, the biofilm cells and liquids were separated and measured using a sensor with two U-shaped, double-tapered, fiber-optic probes (Sen. and Ref. probes). The probes’ Au-coated hemispherical tips enabled double-pass evanescent field absorption. The Sen. probe sensed the cells and liquids inside the biofilm. The polyimide–silica hybrid-film-coated Ref. probe separated the liquids from the biofilm cells and analyzed the liquid concentration. The biofilm structure and active biomass were also examined to confirm the effectiveness of the measurement using a simulation model. The sensor was found to effectively respond to the biofilm growth in the adsorption through exponential phases at thicknesses of 0–536 μm. PMID:26977344

Average BER analysis of SCM-based free-space optical systems by considering the effect of IM3 with OSSB signals under turbulence channels.

PubMed

Lim, Wansu; Cho, Tae-Sik; Yun, Changho; Kim, Kiseon

2009-11-09

In this paper, we derive the average bit error rate (BER) of subcarrier multiplexing (SCM)-based free space optics (FSO) systems using a dual-drive Mach-Zehnder modulator (DD-MZM) for optical single-sideband (OSSB) signals under atmospheric turbulence channels. In particular, we consider the third-order intermodulation (IM3), a significant performance degradation factor, in the case of high input signal power systems. The derived average BER, as a function of the input signal power and the scintillation index, is employed to determine the optimum number of SCM users upon the designing FSO systems. For instance, when the user number doubles, the input signal power decreases by almost 2 dBm under the log-normal and exponential turbulence channels at a given average BER.

Effect of grain-alignment on the levitation force of melt-processed YBCO bulk superconductors

NASA Astrophysics Data System (ADS)

Yang, Wan-min; Zhou, Lian; Feng, Yong; Zhang, Ping-xiang; Wu, Min-zhi; Wu, Xiao-zu; Gawalek, W.

1999-07-01

Single-domain YBCO bulk superconductors have been fabricated by Top Seeded Melt Slow Cooling Growth(TSSCG) process. Two typical YBCO cylinder samples with differential grain-alignment were selected for the investigation of the relationship between the grain-alignment and the levitation force under the same testing condition at liquid nitrogen temperature. It is found that the levitation force values is much different for the two samples, the levitation force of the sample with H par c-axis is more than two times higher than that of the samples with H ⊥ c-axis. So it is necessary to take account of this anisotropy in practical applications. The relationship between a magnet and a superconductor can be well described with a double exponential function. All the results are discussed in details.

Double path integral method for obtaining the mobility of the one-dimensional charge transport in molecular chain.

PubMed

Yoo-Kong, Sikarin; Liewrian, Watchara

2015-12-01

We report on a theoretical investigation concerning the polaronic effect on the transport properties of a charge carrier in a one-dimensional molecular chain. Our technique is based on the Feynman's path integral approach. Analytical expressions for the frequency-dependent mobility and effective mass of the carrier are obtained as functions of electron-phonon coupling. The result exhibits the crossover from a nearly free particle to a heavily trapped particle. We find that the mobility depends on temperature and decreases exponentially with increasing temperature at low temperature. It exhibits large polaronic-like behaviour in the case of weak electron-phonon coupling. These results agree with the phase transition (A.S. Mishchenko et al., Phys. Rev. Lett. 114, 146401 (2015)) of transport phenomena related to polaron motion in the molecular chain.

A hybrid MD-kMC algorithm for folding proteins in explicit solvent.

PubMed

Peter, Emanuel Karl; Shea, Joan-Emma

2014-04-14

We present a novel hybrid MD-kMC algorithm that is capable of efficiently folding proteins in explicit solvent. We apply this algorithm to the folding of a small protein, Trp-Cage. Different kMC move sets that capture different possible rate limiting steps are implemented. The first uses secondary structure formation as a relevant rate event (a combination of dihedral rotations and hydrogen-bonding formation and breakage). The second uses tertiary structure formation events through formation of contacts via translational moves. Both methods fold the protein, but via different mechanisms and with different folding kinetics. The first method leads to folding via a structured helical state, with kinetics fit by a single exponential. The second method leads to folding via a collapsed loop, with kinetics poorly fit by single or double exponentials. In both cases, folding times are faster than experimentally reported values, The secondary and tertiary move sets are integrated in a third MD-kMC implementation, which now leads to folding of the protein via both pathways, with single and double-exponential fits to the rates, and to folding rates in good agreement with experimental values. The competition between secondary and tertiary structure leads to a longer search for the helix-rich intermediate in the case of the first pathway, and to the emergence of a kinetically trapped long-lived molten-globule collapsed state in the case of the second pathway. The algorithm presented not only captures experimentally observed folding intermediates and kinetics, but yields insights into the relative roles of local and global interactions in determining folding mechanisms and rates.

M. Riesz-Schur-type inequalities for entire functions of exponential type

NASA Astrophysics Data System (ADS)

Ganzburg, M. I.; Nevai, P.; Erdélyi, T.

2015-01-01

We prove a general M. Riesz-Schur-type inequality for entire functions of exponential type. If f and Q are two functions of exponential types σ > 0 and τ ≥ 0, respectively, and if Q is real-valued and the real zeros of Q, not counting multiplicities, are bounded away from each other, then \\displaystyle \\vert f(x)\\vert≤ (σ+τ) (Aσ+τ(Q))-1/2\\Vert Q f\\Vert C( R),\\qquad x\\in R, where \\displaystyle A_s(Q) \\stackrel{{def}}{=}\\infx\\in R \\bigl( \\lbrack Q'(x) \\rbrack ^2+s2 [Q(x)]^2\\bigr). We apply this inequality to the weights Q(x)\\stackrel{{def}}{=} \\sin (τ x) and Q(x) \\stackrel{{def}}{=} x and describe the extremal functions in the corresponding inequalities. Bibliography: 7 titles.

Escape driven by alpha-stable white noises.

PubMed

Dybiec, B; Gudowska-Nowak, E; Hänggi, P

2007-02-01

We explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the Brownian particle is driven by white Lévy noise in a dynamical regime where inertial effects can safely be neglected. The behavior of escaping trajectories from one well to another is investigated by pointing to the special character that underpins the noise-induced discontinuity which is caused by the generalized Brownian paths that jump beyond the barrier location without actually hitting it. This fact implies that the boundary conditions for the mean first passage time (MFPT) are no longer determined by the well-known local boundary conditions that characterize the case with normal diffusion. By numerically implementing properly the set up boundary conditions, we investigate the survival probability and the average escape time as a function of the corresponding Lévy white noise parameters. Depending on the value of the skewness beta of the Lévy noise, the escape can either become enhanced or suppressed: a negative asymmetry parameter beta typically yields a decrease for the escape rate while the rate itself depicts a non-monotonic behavior as a function of the stability index alpha that characterizes the jump length distribution of Lévy noise, exhibiting a marked discontinuity at alpha=1. We find that the typical factor of 2 that characterizes for normal diffusion the ratio between the MFPT for well-bottom-to-well-bottom and well-bottom-to-barrier-top no longer holds true. For sufficiently high barriers the survival probabilities assume an exponential behavior versus time. Distinct non-exponential deviations occur, however, for low barrier heights.

Objective-function hybridization in adjoint seismic tomography

NASA Astrophysics Data System (ADS)

Yuan, Yanhua O.; Bozdaǧ, Ebru; Simons, Frederik J.; Gao, Fuchun

2017-04-01

Seismic tomography is at the threshold of a new era of massive data sets. Improving the resolution and accuracy of the estimated Earth structure by assimilating as much information as possible from every seismogram, remains a challenge. We propose the use of the "exponentiated phase'', a type of measurement that robustly captures the information contained in the variation of phase with time in the seismogram. We explore its performance in both conventional and double-difference (Yuan, Simons & Tromp, Geophys. J. Intern, 2016) adjoint seismic tomography. We introduce a hybrid approach to combine different objective functions, taking advantage of both conventional and our new measurements. We initially focus on phase measurements in global tomography. Cross-correlation measurements are generally tailored by window selection algorithms, such as FLEXWIN, to balance amplitude differences between seismic phases. However, within selection windows, such measurements still favor the larger-amplitude phases. It is also difficult to select all usable portions of the seismogram in an optimal way, such that much information may be lost, particularly the scattered waves. Time-continuous phase measurements, which associate a time shift with each point in time, have the potential to extract information from every wiggle in the seismogram without cutting it into small pieces. One such type of measurement is the instantaneous phase (Bozdaǧ, Trampert & Tromp, Geophys. J. Intern, 2011), which thus far has not been implemented in realistic seismic-tomography experiments, given how difficult the computation of phase can sometimes be. The exponentiated phase, on the other hand, is computed on the basis of the normalized analytic signal, does not need an explicit measure of phase, and is thus much easier to implement, and more practical for real-world applications. Both types of measurements carry comparable structural information when direct measurements of the phase are not wrapped. To deal with cycle skips, we use the exponentiated phase to take into account relatively small-magnitude scattered waves at long periods, while using cross-correlation measurements on windows determined by FLEXWIN to select distinct body-wave arrivals without complicating measurements due to non-linearities at short periods. We present synthetic experiments to show how exponentiated-phase, cross-correlation measurements, and their hybridization affect tomographic results. We demonstrate the use of hybrid measurements on teleseismic seismograms, in which surface waves are prominent, for continental and global seismic imaging. It is clear that the exponentiated-phase measurements behave well and provide a better representation of the smaller phases in the adjoint sources required for the computation of the misfit gradient. The combination of two different types of phase measurements in a hybrid approach moves us towards using all of the available information in a data set, addressing data quality and measurement challenges simultaneously, while negligibly affecting computation time.

Exponential Correlation of IQ and the Wealth of Nations

ERIC Educational Resources Information Center

Dickerson, Richard E.

2006-01-01

Plots of mean IQ and per capita real Gross Domestic Product for groups of 81 and 185 nations, as collected by Lynn and Vanhanen, are best fitted by an exponential function of the form: GDP = "a" * 10["b"*(IQ)], where "a" and "b" are empirical constants. Exponential fitting yields markedly higher correlation coefficients than either linear or…

A coupled cluster theory with iterative inclusion of triple excitations and associated equation of motion formulation for excitation energy and ionization potential

NASA Astrophysics Data System (ADS)

Maitra, Rahul; Akinaga, Yoshinobu; Nakajima, Takahito

2017-08-01

A single reference coupled cluster theory that is capable of including the effect of connected triple excitations has been developed and implemented. This is achieved by regrouping the terms appearing in perturbation theory and parametrizing through two different sets of exponential operators: while one of the exponentials, involving general substitution operators, annihilates the ground state but has a non-vanishing effect when it acts on the excited determinant, the other is the regular single and double excitation operator in the sense of conventional coupled cluster theory, which acts on the Hartree-Fock ground state. The two sets of operators are solved as coupled non-linear equations in an iterative manner without significant increase in computational cost than the conventional coupled cluster theory with singles and doubles excitations. A number of physically motivated and computationally advantageous sufficiency conditions are invoked to arrive at the working equations and have been applied to determine the ground state energies of a number of small prototypical systems having weak multi-reference character. With the knowledge of the correlated ground state, we have reconstructed the triple excitation operator and have performed equation of motion with coupled cluster singles, doubles, and triples to obtain the ionization potential and excitation energies of these molecules as well. Our results suggest that this is quite a reasonable scheme to capture the effect of connected triple excitations as long as the ground state remains weakly multi-reference.

Bridging the Gap between Curriculum Planning Policies and Pre-Service Teachers' Needs

ERIC Educational Resources Information Center

Castro-Garces, Angela Yicely; Arboleda, Argemiro Arboleda

2017-01-01

The challenge and satisfaction of being a teacher is doubled when one has the precious task of being a teacher trainer, as our practices replicate exponentially, touching the lives of people we do not even get to meet. Accordingly, this article presents the analysis of a process that brought tensions to a teacher training program because of the…

The Exponential Growth of Mathematics and Technology at the University of Portsmouth

ERIC Educational Resources Information Center

McCabe, Michael

2009-01-01

The number of students studying university mathematics in the UK has been increasing gradually and linearly since 2002. At the University of Portsmouth, number of students studying mathematics doubled from 30 to 60 between 2002 and 2007, then increased by 240% in just 1 year to over 140 in 2008. This article explains how learning technology has…

Competing risk models in reliability systems, an exponential distribution model with Bayesian analysis approach

NASA Astrophysics Data System (ADS)

Iskandar, I.

2018-03-01

The exponential distribution is the most widely used reliability analysis. This distribution is very suitable for representing the lengths of life of many cases and is available in a simple statistical form. The characteristic of this distribution is a constant hazard rate. The exponential distribution is the lower rank of the Weibull distributions. In this paper our effort is to introduce the basic notions that constitute an exponential competing risks model in reliability analysis using Bayesian analysis approach and presenting their analytic methods. The cases are limited to the models with independent causes of failure. A non-informative prior distribution is used in our analysis. This model describes the likelihood function and follows with the description of the posterior function and the estimations of the point, interval, hazard function, and reliability. The net probability of failure if only one specific risk is present, crude probability of failure due to a specific risk in the presence of other causes, and partial crude probabilities are also included.

On the Gibbs phenomenon 4: Recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1994-01-01

We continue our investigation of overcoming Gibbs phenomenon, i.e., to obtain exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of a spectral partial sum of a discontinuous but piecewise analytic function. We show that if we are given the first N Gegenbauer expansion coefficients, based on the Gegenbauer polynomials C(sub k)(sup mu)(x) with the weight function (1 - x(exp 2))(exp mu - 1/2) for any constant mu is greater than or equal to 0, of an L(sub 1) function f(x), we can construct an exponentially convergent approximation to the point values of f(x) in any subinterval in which the function is analytic. The proof covers the cases of Chebyshev or Legendre partial sums, which are most common in applications.

On the Gibbs phenomenon 5: Recovering exponential accuracy from collocation point values of a piecewise analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang

1994-01-01

The paper presents a method to recover exponential accuracy at all points (including at the discontinuities themselves), from the knowledge of an approximation to the interpolation polynomial (or trigonometrical polynomial). We show that if we are given the collocation point values (or a highly accurate approximation) at the Gauss or Gauss-Lobatto points, we can reconstruct a uniform exponentially convergent approximation to the function f(x) in any sub-interval of analyticity. The proof covers the cases of Fourier, Chebyshev, Legendre, and more general Gegenbauer collocation methods.

Development and evaluation of a biomedical search engine using a predicate-based vector space model.

PubMed

Kwak, Myungjae; Leroy, Gondy; Martinez, Jesse D; Harwell, Jeffrey

2013-10-01

Although biomedical information available in articles and patents is increasing exponentially, we continue to rely on the same information retrieval methods and use very few keywords to search millions of documents. We are developing a fundamentally different approach for finding much more precise and complete information with a single query using predicates instead of keywords for both query and document representation. Predicates are triples that are more complex datastructures than keywords and contain more structured information. To make optimal use of them, we developed a new predicate-based vector space model and query-document similarity function with adjusted tf-idf and boost function. Using a test bed of 107,367 PubMed abstracts, we evaluated the first essential function: retrieving information. Cancer researchers provided 20 realistic queries, for which the top 15 abstracts were retrieved using a predicate-based (new) and keyword-based (baseline) approach. Each abstract was evaluated, double-blind, by cancer researchers on a 0-5 point scale to calculate precision (0 versus higher) and relevance (0-5 score). Precision was significantly higher (p<.001) for the predicate-based (80%) than for the keyword-based (71%) approach. Relevance was almost doubled with the predicate-based approach-2.1 versus 1.6 without rank order adjustment (p<.001) and 1.34 versus 0.98 with rank order adjustment (p<.001) for predicate--versus keyword-based approach respectively. Predicates can support more precise searching than keywords, laying the foundation for rich and sophisticated information search. Copyright © 2013 Elsevier Inc. All rights reserved.

Exponential approximations in optimal design

NASA Technical Reports Server (NTRS)

Belegundu, A. D.; Rajan, S. D.; Rajgopal, J.

1990-01-01

One-point and two-point exponential functions have been developed and proved to be very effective approximations of structural response. The exponential has been compared to the linear, reciprocal and quadratic fit methods. Four test problems in structural analysis have been selected. The use of such approximations is attractive in structural optimization to reduce the numbers of exact analyses which involve computationally expensive finite element analysis.

Dynamic heterogeneity and conditional statistics of non-Gaussian temperature fluctuations in turbulent thermal convection

NASA Astrophysics Data System (ADS)

He, Xiaozhou; Wang, Yin; Tong, Penger

2018-05-01

Non-Gaussian fluctuations with an exponential tail in their probability density function (PDF) are often observed in nonequilibrium steady states (NESSs) and one does not understand why they appear so often. Turbulent Rayleigh-Bénard convection (RBC) is an example of such a NESS, in which the measured PDF P (δ T ) of temperature fluctuations δ T in the central region of the flow has a long exponential tail. Here we show that because of the dynamic heterogeneity in RBC, the exponential PDF is generated by a convolution of a set of dynamics modes conditioned on a constant local thermal dissipation rate ɛ . The conditional PDF G (δ T |ɛ ) of δ T under a constant ɛ is found to be of Gaussian form and its variance σT2 for different values of ɛ follows an exponential distribution. The convolution of the two distribution functions gives rise to the exponential PDF P (δ T ) . This work thus provides a physical mechanism of the observed exponential distribution of δ T in RBC and also sheds light on the origin of non-Gaussian fluctuations in other NESSs.

Static versus Dynamic Disposition: The Role of GeoGebra in Representing Polynomial-Rational Inequalities and Exponential-Logarithmic Functions

ERIC Educational Resources Information Center

Caglayan, Günhan

2014-01-01

This study investigates prospective secondary mathematics teachers' visual representations of polynomial and rational inequalities, and graphs of exponential and logarithmic functions with GeoGebra Dynamic Software. Five prospective teachers in a university in the United States participated in this research study, which was situated within a…

Global exponential stability of bidirectional associative memory neural networks with distributed delays

NASA Astrophysics Data System (ADS)

Song, Qiankun; Cao, Jinde

2007-05-01

A bidirectional associative memory neural network model with distributed delays is considered. By constructing a new Lyapunov functional, employing the homeomorphism theory, M-matrix theory and the inequality (a[greater-or-equal, slanted]0,bk[greater-or-equal, slanted]0,qk>0 with , and r>1), a sufficient condition is obtained to ensure the existence, uniqueness and global exponential stability of the equilibrium point for the model. Moreover, the exponential converging velocity index is estimated, which depends on the delay kernel functions and the system parameters. The results generalize and improve the earlier publications, and remove the usual assumption that the activation functions are bounded . Two numerical examples are given to show the effectiveness of the obtained results.

New exponential stability criteria for stochastic BAM neural networks with impulses

NASA Astrophysics Data System (ADS)

Sakthivel, R.; Samidurai, R.; Anthoni, S. M.

2010-10-01

In this paper, we study the global exponential stability of time-delayed stochastic bidirectional associative memory neural networks with impulses and Markovian jumping parameters. A generalized activation function is considered, and traditional assumptions on the boundedness, monotony and differentiability of activation functions are removed. We obtain a new set of sufficient conditions in terms of linear matrix inequalities, which ensures the global exponential stability of the unique equilibrium point for stochastic BAM neural networks with impulses. The Lyapunov function method with the Itô differential rule is employed for achieving the required result. Moreover, a numerical example is provided to show that the proposed result improves the allowable upper bound of delays over some existing results in the literature.

A Simulation To Model Exponential Growth.

ERIC Educational Resources Information Center

Appelbaum, Elizabeth Berman

2000-01-01

Describes a simulation using dice-tossing students in a population cluster to model the growth of cancer cells. This growth is recorded in a scatterplot and compared to an exponential function graph. (KHR)

Power function decay of hydraulic conductivity for a TOPMODEL-based infiltration routine

NASA Astrophysics Data System (ADS)

Wang, Jun; Endreny, Theodore A.; Hassett, James M.

2006-11-01

TOPMODEL rainfall-runoff hydrologic concepts are based on soil saturation processes, where soil controls on hydrograph recession have been represented by linear, exponential, and power function decay with soil depth. Although these decay formulations have been incorporated into baseflow decay and topographic index computations, only the linear and exponential forms have been incorporated into infiltration subroutines. This study develops a power function formulation of the Green and Ampt infiltration equation for the case where the power n = 1 and 2. This new function was created to represent field measurements in the New York City, USA, Ward Pound Ridge drinking water supply area, and provide support for similar sites reported by other researchers. Derivation of the power-function-based Green and Ampt model begins with the Green and Ampt formulation used by Beven in deriving an exponential decay model. Differences between the linear, exponential, and power function infiltration scenarios are sensitive to the relative difference between rainfall rates and hydraulic conductivity. Using a low-frequency 30 min design storm with 4.8 cm h-1 rain, the n = 2 power function formulation allows for a faster decay of infiltration and more rapid generation of runoff. Infiltration excess runoff is rare in most forested watersheds, and advantages of the power function infiltration routine may primarily include replication of field-observed processes in urbanized areas and numerical consistency with power function decay of baseflow and topographic index distributions. Equation development is presented within a TOPMODEL-based Ward Pound Ridge rainfall-runoff simulation. Copyright

Fourier Transforms of Pulses Containing Exponential Leading and Trailing Profiles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Warshaw, S I

2001-07-15

In this monograph we discuss a class of pulse shapes that have exponential rise and fall profiles, and evaluate their Fourier transforms. Such pulses can be used as models for time-varying processes that produce an initial exponential rise and end with the exponential decay of a specified physical quantity. Unipolar examples of such processes include the voltage record of an increasingly rapid charge followed by a damped discharge of a capacitor bank, and the amplitude of an electromagnetic pulse produced by a nuclear explosion. Bipolar examples include acoustic N waves propagating for long distances in the atmosphere that have resultedmore » from explosions in the air, and sonic booms generated by supersonic aircraft. These bipolar pulses have leading and trailing edges that appear to be exponential in character. To the author's knowledge the Fourier transforms of such pulses are not generally well-known or tabulated in Fourier transform compendia, and it is the purpose of this monograph to derive and present these transforms. These Fourier transforms are related to a definite integral of a ratio of exponential functions, whose evaluation we carry out in considerable detail. From this result we derive the Fourier transforms of other related functions. In all Figures showing plots of calculated curves, the actual numbers used for the function parameter values and dependent variables are arbitrary and non-dimensional, and are not identified with any particular physical phenomenon or model.« less

Processing of DNA double strand breaks by alternative non-homologous end-joining in hyperacetylated chromatin.

PubMed

Manova, Vasilissa; Singh, Satyendra K; Iliakis, George

2012-08-22

Mammalian cells employ at least two subpathways of non-homologous end-joining for the repair of ionizing radiation induced DNA double strand breaks: The canonical DNA-PK-dependent form of non-homologous end-joining (D-NHEJ) and an alternative, slowly operating, error-prone backup pathway (B-NHEJ). In contrast to D-NHEJ, which operates with similar efficiency throughout the cell cycle, B-NHEJ operates more efficiently in G2-phase. Notably, B-NHEJ also shows strong and as of yet unexplained dependency on growth activity and is markedly compromised in serum-deprived cells, or in cells that enter the plateau-phase of growth. The molecular mechanisms underpinning this response remain unknown. Since chromatin structure or changes in chromatin structure are prime candidate-B-NHEJ-modulators, we study here the role of chromatin hyperacetylation, either by HDAC2 knockdown or treatment with the HDAC inhibitor TSA, on the repair by B-NHEJ of IR-induced DSBs. siRNA-mediated knockdown of HDAC2 fails to provoke histone hyperacetylation in Lig4-/- MEFs and has no detectable effect on B-NHEJ function. Treatment with TSA that inhibits multiple HDACs causes efficient, reversible chromatin hyperacetylation in Lig4-/- MEFs, as well as in human HCT116 Lig4-/- cells and the human glioma cell line M059K. The IR yield of DSBs in TSA-treated cells remains similar to that of untreated cells despite the expected chromatin relaxation. In addition, chromatin hyperacetylation leaves unchanged repair of DSBs by B-NHEJ in irradiated exponentially growing, or plateau-phase cells. Notably, under the experimental conditions employed here, chromatin hyperacetylation fails to detectably modulate B-NHEJ in M059K cells as well. In summary, the results show that chromatin acetylation or deacetylation does not affect the kinetics of alternative NHEJ in all types of cells examined both in exponentially growing and serum deprived cultures. We conclude that parameters beyond chromatin acetylation determine B-NHEJ efficiency in the plateau-phase of growth.

Preparation of an exponentially rising optical pulse for efficient excitation of single atoms in free space.

PubMed

Dao, Hoang Lan; Aljunid, Syed Abdullah; Maslennikov, Gleb; Kurtsiefer, Christian

2012-08-01

We report on a simple method to prepare optical pulses with exponentially rising envelope on the time scale of a few ns. The scheme is based on the exponential transfer function of a fast transistor, which generates an exponentially rising envelope that is transferred first on a radio frequency carrier, and then on a coherent cw laser beam with an electro-optical phase modulator. The temporally shaped sideband is then extracted with an optical resonator and can be used to efficiently excite a single (87)Rb atom.

Double-exponential decay of orientational correlations in semiflexible polyelectrolytes.

PubMed

Bačová, P; Košovan, P; Uhlík, F; Kuldová, J; Limpouchová, Z; Procházka, K

2012-06-01

In this paper we revisited the problem of persistence length of polyelectrolytes. We performed a series of Molecular Dynamics simulations using the Debye-Hückel approximation for electrostatics to test several equations which go beyond the classical description of Odijk, Skolnick and Fixman (OSF). The data confirm earlier observations that in the limit of large contour separations the decay of orientational correlations can be described by a single-exponential function and the decay length can be described by the OSF relation. However, at short countour separations the behaviour is more complex. Recent equations which introduce more complicated expressions and an additional length scale could describe the results very well on both the short and the long length scale. The equation of Manghi and Netz when used without adjustable parameters could capture the qualitative trend but deviated in a quantitative comparison. Better quantitative agreement within the estimated error could be obtained using three equations with one adjustable parameter: 1) the equation of Manghi and Netz; 2) the equation proposed by us in this paper; 3) the equation proposed by Cannavacciuolo and Pedersen. Two characteristic length scales can be identified in the data: the intrinsic or bare persistence length and the electrostatic persistence length. All three equations use a single parameter to describe a smooth crossover from the short-range behaviour dominated by the intrinsic stiffness of the chain to the long-range OSF-like behaviour.

Vibrational energies for HFCO using a neural network sum of exponentials potential energy surface

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pradhan, Ekadashi; Brown, Alex, E-mail: alex.brown@ualberta.ca

2016-05-07

A six-dimensional potential energy surface (PES) for formyl fluoride (HFCO) is fit in a sum-of-products form using neural network exponential fitting functions. The ab initio data upon which the fit is based were computed at the explicitly correlated coupled cluster with single, double, and perturbative triple excitations [CCSD(T)-F12]/cc-pVTZ-F12 level of theory. The PES fit is accurate (RMSE = 10 cm{sup −1}) up to 10 000 cm{sup −1} above the zero point energy and covers most of the experimentally measured IR data. The PES is validated by computing vibrational energies for both HFCO and deuterated formyl fluoride (DFCO) using block improved relaxationmore » with the multi-configuration time dependent Hartree approach. The frequencies of the fundamental modes, and all other vibrational states up to 5000 cm{sup −1} above the zero-point energy, are more accurate than those obtained from the previous MP2-based PES. The vibrational frequencies obtained on the PES are compared to anharmonic frequencies at the MP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels of theory obtained using second-order vibrational perturbation theory. The new PES will be useful for quantum dynamics simulations for both HFCO and DFCO, e.g., studies of intramolecular vibrational redistribution leading to unimolecular dissociation and its laser control.« less

Small-Scale, Local Area, and Transitional Millimeter Wave Propagation for 5G Communications

NASA Astrophysics Data System (ADS)

Rappaport, Theodore S.; MacCartney, George R.; Sun, Shu; Yan, Hangsong; Deng, Sijia

2017-12-01

This paper studies radio propagation mechanisms that impact handoffs, air interface design, beam steering, and MIMO for 5G mobile communication systems. Knife edge diffraction (KED) and a creeping wave linear model are shown to predict diffraction loss around typical building objects from 10 to 26 GHz, and human blockage measurements at 73 GHz are shown to fit a double knife-edge diffraction (DKED) model which incorporates antenna gains. Small-scale spatial fading of millimeter wave received signal voltage amplitude is generally Ricean-distributed for both omnidirectional and directional receive antenna patterns under both line-of-sight (LOS) and non-line-of-sight (NLOS) conditions in most cases, although the log-normal distribution fits measured data better for the omnidirectional receive antenna pattern in the NLOS environment. Small-scale spatial autocorrelations of received voltage amplitudes are shown to fit sinusoidal exponential and exponential functions for LOS and NLOS environments, respectively, with small decorrelation distances of 0.27 cm to 13.6 cm (smaller than the size of a handset) that are favorable for spatial multiplexing. Local area measurements using cluster and route scenarios show how the received signal changes as the mobile moves and transitions from LOS to NLOS locations, with reasonably stationary signal levels within clusters. Wideband mmWave power levels are shown to fade from 0.4 dB/ms to 40 dB/s, depending on travel speed and surroundings.

Exponentially accurate approximations to piece-wise smooth periodic functions

NASA Technical Reports Server (NTRS)

Greer, James; Banerjee, Saheb

1995-01-01

A family of simple, periodic basis functions with 'built-in' discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representations of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.

Possible stretched exponential parametrization for humidity absorption in polymers.

PubMed

Hacinliyan, A; Skarlatos, Y; Sahin, G; Atak, K; Aybar, O O

2009-04-01

Polymer thin films have irregular transient current characteristics under constant voltage. In hydrophilic and hydrophobic polymers, the irregularity is also known to depend on the humidity absorbed by the polymer sample. Different stretched exponential models are studied and it is shown that the absorption of humidity as a function of time can be adequately modelled by a class of these stretched exponential absorption models.

Accurate computation of gravitational field of a tesseroid

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2018-02-01

We developed an accurate method to compute the gravitational field of a tesseroid. The method numerically integrates a surface integral representation of the gravitational potential of the tesseroid by conditionally splitting its line integration intervals and by using the double exponential quadrature rule. Then, it evaluates the gravitational acceleration vector and the gravity gradient tensor by numerically differentiating the numerically integrated potential. The numerical differentiation is conducted by appropriately switching the central and the single-sided second-order difference formulas with a suitable choice of the test argument displacement. If necessary, the new method is extended to the case of a general tesseroid with the variable density profile, the variable surface height functions, and/or the variable intervals in longitude or in latitude. The new method is capable of computing the gravitational field of the tesseroid independently on the location of the evaluation point, namely whether outside, near the surface of, on the surface of, or inside the tesseroid. The achievable precision is 14-15 digits for the potential, 9-11 digits for the acceleration vector, and 6-8 digits for the gradient tensor in the double precision environment. The correct digits are roughly doubled if employing the quadruple precision computation. The new method provides a reliable procedure to compute the topographic gravitational field, especially that near, on, and below the surface. Also, it could potentially serve as a sure reference to complement and elaborate the existing approaches using the Gauss-Legendre quadrature or other standard methods of numerical integration.

An improved parameter estimation and comparison for soft tissue constitutive models containing an exponential function.

PubMed

Aggarwal, Ankush

2017-08-01

Motivated by the well-known result that stiffness of soft tissue is proportional to the stress, many of the constitutive laws for soft tissues contain an exponential function. In this work, we analyze properties of the exponential function and how it affects the estimation and comparison of elastic parameters for soft tissues. In particular, we find that as a consequence of the exponential function there are lines of high covariance in the elastic parameter space. As a result, one can have widely varying mechanical parameters defining the tissue stiffness but similar effective stress-strain responses. Drawing from elementary algebra, we propose simple changes in the norm and the parameter space, which significantly improve the convergence of parameter estimation and robustness in the presence of noise. More importantly, we demonstrate that these changes improve the conditioning of the problem and provide a more robust solution in the case of heterogeneous material by reducing the chances of getting trapped in a local minima. Based upon the new insight, we also propose a transformed parameter space which will allow for rational parameter comparison and avoid misleading conclusions regarding soft tissue mechanics.

Transfer potentials shape and equilibrate monetary systems

NASA Astrophysics Data System (ADS)

Fischer, Robert; Braun, Dieter

2003-04-01

We analyze a monetary system of random money transfer on the basis of double entry bookkeeping. Without boundary conditions, we do not reach a price equilibrium and violate text-book formulas of economist's quantity theory ( MV= PQ). To match the resulting quantity of money with the model assumption of a constant price, we have to impose boundary conditions. They either restrict specific transfers globally or impose transfers locally. Both connect through a general framework of transfer potentials. We show that either restricted or imposed transfers can shape Gaussian, tent-shape exponential, Boltzmann-exponential, pareto or periodic equilibrium distributions. We derive the master equation and find its general time-dependent approximate solution. An equivalent of quantity theory for random money transfer under the boundary conditions of transfer potentials is given.

Spectral Study of Measles Epidemics: The Dependence of Spectral Gradient on the Population Size of the Community

NASA Astrophysics Data System (ADS)

Sumi, Ayako; Olsen, Lars Folke; Ohtomo, Norio; Tanaka, Yukio; Sawamura, Sadashi

2003-02-01

We have carried out spectral analysis of measles notifications in several communities in Denmark, UK and USA. The results confirm that each power spectral density (PSD) shows exponential characteristics, which are universally observed in the PSD for time series generated from nonlinear dynamical system. The exponential gradient increases with the population size. For almost all communities, many spectral lines observed in each PSD can be fully assigned to linear combinations of several fundamental periods, suggesting that the measles data are substantially noise-free. The optimum least squares fitting curve calculated using these fundamental periods essentially reproduces an underlying variation of the measles data, and an extension of the curve can be used to predict measles epidemics. For the communities with large population sizes, some PSD patterns obtained from segment time series analysis show a close resemblance to the PSD patterns at the initial stages of a period-doubling bifurcation process for the so-called susceptible/exposed/infectious/recovered (SEIR) model with seasonal forcing. The meaning of the relationship between the exponential gradient and the population size is discussed.

Dynamic topography and gravity anomalies for fluid layers whose viscosity varies exponentially with depth

NASA Technical Reports Server (NTRS)

Revenaugh, Justin; Parsons, Barry

1987-01-01

Adopting the formalism of Parsons and Daly (1983), analytical integral equations (Green's function integrals) are derived which relate gravity anomalies and dynamic boundary topography with temperature as a function of wavenumber for a fluid layer whose viscosity varies exponentially with depth. In the earth, such a viscosity profile may be found in the asthenosphere, where the large thermal gradient leads to exponential decrease of viscosity with depth, the effects of a pressure increase being small in comparison. It is shown that, when viscosity varies rapidly, topography kernels for both the surface and bottom boundaries (and hence the gravity kernel) are strongly affected at all wavelengths.

Exponential approximation for daily average solar heating or photolysis. [of stratospheric ozone layer

NASA Technical Reports Server (NTRS)

Cogley, A. C.; Borucki, W. J.

1976-01-01

When incorporating formulations of instantaneous solar heating or photolytic rates as functions of altitude and sun angle into long range forecasting models, it may be desirable to replace the time integrals by daily average rates that are simple functions of latitude and season. This replacement is accomplished by approximating the integral over the solar day by a pure exponential. This gives a daily average rate as a multiplication factor times the instantaneous rate evaluated at an appropriate sun angle. The accuracy of the exponential approximation is investigated by a sample calculation using an instantaneous ozone heating formulation available in the literature.

A generalized exponential link function to map a conflict indicator into severity index within safety continuum framework.

PubMed

Zheng, Lai; Ismail, Karim

2017-05-01

Traffic conflict indicators measure the temporal and spatial proximity of conflict-involved road users. These indicators can reflect the severity of traffic conflicts to a reliable extent. Instead of using the indicator value directly as a severity index, many link functions have been developed to map the conflict indicator to a severity index. However, little information is available about the choice of a particular link function. To guard against link misspecification or subjectivity, a generalized exponential link function was developed. The severity index generated by this link was introduced to a parametric safety continuum model which objectively models the centre and tail regions. An empirical method, together with full Bayesian estimation method was adopted to estimate model parameters. The safety implication of return level was calculated based on the model parameters. The proposed approach was applied to the conflict and crash data collected from 21 segments from three freeways located in Guangdong province, China. The Pearson's correlation test between return levels and observed crashes showed that a θ value of 1.2 was the best choice of the generalized parameter for current data set. This provides statistical support for using the generalized exponential link function. With the determined generalized exponential link function, the visualization of parametric safety continuum was found to be a gyroscope-shaped hierarchy. Copyright © 2017 Elsevier Ltd. All rights reserved.

Joint analysis of air pollution in street canyons in St. Petersburg and Copenhagen

NASA Astrophysics Data System (ADS)

Genikhovich, E. L.; Ziv, A. D.; Iakovleva, E. A.; Palmgren, F.; Berkowicz, R.

The bi-annual data set of concentrations of several traffic-related air pollutants, measured continuously in street canyons in St. Petersburg and Copenhagen, is analysed jointly using different statistical techniques. Annual mean concentrations of NO 2, NO x and, especially, benzene are found systematically higher in St. Petersburg than in Copenhagen but for ozone the situation is opposite. In both cities probability distribution functions (PDFs) of concentrations and their daily or weekly extrema are fitted with the Weibull and double exponential distributions, respectively. Sample estimates of bi-variate distributions of concentrations, concentration roses, and probabilities of concentration of one pollutant being extreme given that another one reaches its extremum are presented in this paper as well as auto- and co-spectra. It is demonstrated that there is a reasonably high correlation between seasonally averaged concentrations of pollutants in St. Petersburg and Copenhagen.

Spectral and temporal characteristics of target current and electromagnetic pulse induced by nanosecond laser ablation

NASA Astrophysics Data System (ADS)

Krása, J.; De Marco, M.; Cikhardt, J.; Pfeifer, M.; Velyhan, A.; Klír, D.; Řezáč, K.; Limpouch, J.; Krouský, E.; Dostál, J.; Ullschmied, J.; Dudžák, R.

2017-06-01

The current balancing the target charging and the emission of transient electromagnetic pulses (EMP) driven by the interaction of a focused 1.315 μm iodine 300 ps PALS laser with metallic and plastic targets were measured with the use of inductive probes. It is experimentally proven that the duration of return target currents and EMPs is much longer than the duration of laser-target interaction. The laser-produced plasma is active after the laser-target interaction. During this phase, the target acts as a virtual cathode and the plasma-target interface expands. A double exponential function is used in order to obtain the temporal characteristics of EMP. The rise time of EMPs fluctuates in the range up to a few tens of nanoseconds. Frequency spectra of EMP and target currents are modified by resonant frequencies of the interaction chamber.

Exchange bias training relaxation in spin glass/ferromagnet bilayers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chi, Xiaodan; Du, An; Rui, Wenbin

2016-04-25

A canonical spin glass (SG) FeAu layer is fabricated to couple to a soft ferromagnet (FM) FeNi layer. Below the SG freezing temperature, exchange bias (EB) and training are observed. Training in SG/FM bilayers is insensitive to cooling field and may suppress the EB or change the sign of the EB field from negative to positive at specific temperatures, violating from the simple power-law or the single exponential function derived from the antiferromagnet based systems. In view of the SG nature, we employ a double decay model to distinguish the contributions from the SG bulk and the SG/FM interface tomore » training. Dynamical properties during training under different cooling fields and at different temperatures are discussed, and the nonzero shifting coefficient in the time index as a signature of slowing-down decay for SG based systems is interpreted by means of a modified Monte Carlo Metropolis algorithm.« less

a Unified Matrix Polynomial Approach to Modal Identification

NASA Astrophysics Data System (ADS)

Allemang, R. J.; Brown, D. L.

1998-04-01

One important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single, consistent mathematical formulation with a corresponding set of definitions and unifying concepts. Particularly, a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least-squares complex exponential (LSCE), the polyreference time domain (PTD), Ibrahim time domain (ITD), eigensystem realization algorithm (ERA), rational fraction polynomial (RFP), polyreference frequency domain (PFD) and the complex mode indication function (CMIF) methods. Using this unified matrix polynomial approach (UMPA) allows a discussion of the similarities and differences of the commonly used methods. the use of least squares (LS), total least squares (TLS), double least squares (DLS) and singular value decomposition (SVD) methods is discussed in order to take advantage of redundant measurement data. Eigenvalue and SVD transformation methods are utilized to reduce the effective size of the resulting eigenvalue-eigenvector problem as well.

Megawatt level electric propulsion perspectives

NASA Technical Reports Server (NTRS)

Jahn, Robert G.; Kelly, Arnold J.

1987-01-01

For long range space missions, deliverable payload fraction is an inverse exponential function of the propellant exhaust velocity or specific impulse of the propulsion system. The exhaust velocity of chemical systems are limited by their combustion chemistry and heat transfer to a few km/s. Nuclear rockets may achieve double this range, but are still heat transfer limited and ponderous to develop. Various electric propulsion systems can achieve exhaust velocities in the 10 km/s range, at considerably lower thrust densities, but require an external electrical power source. A general overview is provided of the currently available electric propulsion systems from the perspective of their characteristics as a terminal load for space nuclear systems. A summary of the available electric propulsion options is shown and generally characterized in the power vs. exhaust velocity plot. There are 3 general classes of electric thruster devices: neutral gas heaters, plasma devices, and space charge limited electrostatic or ion thrusters.

Heuristic lipophilicity potential for computer-aided rational drug design: optimizations of screening functions and parameters.

PubMed

Du, Q; Mezey, P G

1998-09-01

In this research we test and compare three possible atom-based screening functions used in the heuristic molecular lipophilicity potential (HMLP). Screening function 1 is a power distance-dependent function, bi/[formula: see text] Ri-r [formula: see text] gamma, screening function 2 is an exponential distance-dependent function, bi exp(-[formula: see text] Ri-r [formula: see text]/d0), and screening function 3 is a weighted distance-dependent function, sign(bi) exp[-xi [formula: see text] Ri-r [formula: see text]/magnitude of bi)]. For every screening function, the parameters (gamma, d0, and xi) are optimized using 41 common organic molecules of 4 types of compounds: aliphatic alcohols, aliphatic carboxylic acids, aliphatic amines, and aliphatic alkanes. The results of calculations show that screening function 3 cannot give chemically reasonable results, however, both the power screening function and the exponential screening function give chemically satisfactory results. There are two notable differences between screening functions 1 and 2. First, the exponential screening function has larger values in the short distance than the power screening function, therefore more influence from the nearest neighbors is involved using screening function 2 than screening function 1. Second, the power screening function has larger values in the long distance than the exponential screening function, therefore screening function 1 is effected by atoms at long distance more than screening function 2. For screening function 1, the suitable range of parameter gamma is 1.0 < gamma < 3.0, gamma = 2.3 is recommended, and gamma = 2.0 is the nearest integral value. For screening function 2, the suitable range of parameter d0 is 1.5 < d0 < 3.0, and d0 = 2.0 is recommended. HMLP developed in this research provides a potential tool for computer-aided three-dimensional drug design.

Interaction phenomenon to dimensionally reduced p-gBKP equation

NASA Astrophysics Data System (ADS)

Zhang, Runfa; Bilige, Sudao; Bai, Yuexing; Lü, Jianqing; Gao, Xiaoqing

2018-02-01

Based on searching the combining of quadratic function and exponential (or hyperbolic cosine) function from the Hirota bilinear form of the dimensionally reduced p-gBKP equation, eight class of interaction solutions are derived via symbolic computation with Mathematica. The submergence phenomenon, presented to illustrate the dynamical features concerning these obtained solutions, is observed by three-dimensional plots and density plots with particular choices of the involved parameters between the exponential (or hyperbolic cosine) function and the quadratic function. It is proved that the interference between the two solitary waves is inelastic.

Coupled-cluster Green's function: Analysis of properties originating in the exponential parametrization of the ground-state wave function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Peng, Bo; Kowalski, Karol

In this paper we derive basic properties of the Green’s function matrix elements stemming from the exponential coupled cluster (CC) parametrization of the ground-state wave function. We demon- strate that all intermediates used to express retarded (or equivalently, ionized) part of the Green’s function in the ω-representation can be expressed through connected diagrams only. Similar proper- ties are also shared by the first order ω-derivatives of the retarded part of the CC Green’s function. This property can be extended to any order ω-derivatives of the Green’s function. Through the Dyson equation of CC Green’s function, the derivatives of corresponding CCmore » self-energy can be evaluated analytically. In analogy to the CC Green’s function, the corresponding CC self-energy is expressed in terms of connected diagrams only. Moreover, the ionized part of the CC Green’s func- tion satisfies the non-homogeneous linear system of ordinary differential equations, whose solution may be represented in the exponential form. Our analysis can be easily generalized to the advanced part of the CC Green’s function.« less

Deadline rush: a time management phenomenon and its mathematical description.

PubMed

König, Cornelius J; Kleinmann, Martin

2005-01-01

A typical time management phenomenon is the rush before a deadline. Behavioral decision making research can be used to predict how behavior changes before a deadline. People are likely not to work on a project with a deadline in the far future because they generally discount future outcomes. Only when the deadline is close are people likely to work. On the basis of recent intertemporal choice experiments, the authors argue that a hyperbolic function should provide a more accurate description of the deadline rush than an exponential function predicted by an economic model of discounted utility. To show this, the fit of the hyperbolic and the exponential function were compared with data sets that describe when students study for exams. As predicted, the hyperbolic function fit the data significantly better than the exponential function. The implication for time management decisions is that they are most likely to be inconsistent over time (i.e., people make a plan how to use their time but do not follow it).

Using Solution Strategies to Examine and Promote High-School Students' Understanding of Exponential Functions: One Teacher's Attempt

ERIC Educational Resources Information Center

Brendefur, Jonathan

2014-01-01

Much research has been conducted on how elementary students develop mathematical understanding and subsequently how teachers might use this information. This article builds on this type of work by investigating how one high-school algebra teacher designs and conducts a lesson on exponential functions. Through a lesson study format she studies with…

A Spectral Lyapunov Function for Exponentially Stable LTV Systems

NASA Technical Reports Server (NTRS)

Zhu, J. Jim; Liu, Yong; Hang, Rui

2010-01-01

This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.

Statistical assessment of bi-exponential diffusion weighted imaging signal characteristics induced by intravoxel incoherent motion in malignant breast tumors

PubMed Central

Wong, Oi Lei; Lo, Gladys G.; Chan, Helen H. L.; Wong, Ting Ting; Cheung, Polly S. Y.

2016-01-01

Background The purpose of this study is to statistically assess whether bi-exponential intravoxel incoherent motion (IVIM) model better characterizes diffusion weighted imaging (DWI) signal of malignant breast tumor than mono-exponential Gaussian diffusion model. Methods 3 T DWI data of 29 malignant breast tumors were retrospectively included. Linear least-square mono-exponential fitting and segmented least-square bi-exponential fitting were used for apparent diffusion coefficient (ADC) and IVIM parameter quantification, respectively. F-test and Akaike Information Criterion (AIC) were used to statistically assess the preference of mono-exponential and bi-exponential model using region-of-interests (ROI)-averaged and voxel-wise analysis. Results For ROI-averaged analysis, 15 tumors were significantly better fitted by bi-exponential function and 14 tumors exhibited mono-exponential behavior. The calculated ADC, D (true diffusion coefficient) and f (pseudo-diffusion fraction) showed no significant differences between mono-exponential and bi-exponential preferable tumors. Voxel-wise analysis revealed that 27 tumors contained more voxels exhibiting mono-exponential DWI decay while only 2 tumors presented more bi-exponential decay voxels. ADC was consistently and significantly larger than D for both ROI-averaged and voxel-wise analysis. Conclusions Although the presence of IVIM effect in malignant breast tumors could be suggested, statistical assessment shows that bi-exponential fitting does not necessarily better represent the DWI signal decay in breast cancer under clinically typical acquisition protocol and signal-to-noise ratio (SNR). Our study indicates the importance to statistically examine the breast cancer DWI signal characteristics in practice. PMID:27709078

Exponential stability of impulsive stochastic genetic regulatory networks with time-varying delays and reaction-diffusion

DOE PAGES

Cao, Boqiang; Zhang, Qimin; Ye, Ming

2016-11-29

We present a mean-square exponential stability analysis for impulsive stochastic genetic regulatory networks (GRNs) with time-varying delays and reaction-diffusion driven by fractional Brownian motion (fBm). By constructing a Lyapunov functional and using linear matrix inequality for stochastic analysis we derive sufficient conditions to guarantee the exponential stability of the stochastic model of impulsive GRNs in the mean-square sense. Meanwhile, the corresponding results are obtained for the GRNs with constant time delays and standard Brownian motion. Finally, an example is presented to illustrate our results of the mean-square exponential stability analysis.

Exponential model normalization for electrical capacitance tomography with external electrodes under gap permittivity conditions

NASA Astrophysics Data System (ADS)

Baidillah, Marlin R.; Takei, Masahiro

2017-06-01

A nonlinear normalization model which is called exponential model for electrical capacitance tomography (ECT) with external electrodes under gap permittivity conditions has been developed. The exponential model normalization is proposed based on the inherently nonlinear relationship characteristic between the mixture permittivity and the measured capacitance due to the gap permittivity of inner wall. The parameters of exponential equation are derived by using an exponential fitting curve based on the simulation and a scaling function is added to adjust the experiment system condition. The exponential model normalization was applied to two dimensional low and high contrast dielectric distribution phantoms by using simulation and experimental studies. The proposed normalization model has been compared with other normalization models i.e. Parallel, Series, Maxwell and Böttcher models. Based on the comparison of image reconstruction results, the exponential model is reliable to predict the nonlinear normalization of measured capacitance in term of low and high contrast dielectric distribution.

Convergence and stability of the exponential Euler method for semi-linear stochastic delay differential equations.

PubMed

Zhang, Ling

2017-01-01

The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the strong order [Formula: see text] to SLSDDEs. On the one hand, the classical stability theorem to SLSDDEs is given by the Lyapunov functions. However, in this paper we study the exponential stability in mean square of the exact solution to SLSDDEs by using the definition of logarithmic norm. On the other hand, the implicit Euler scheme to SLSDDEs is known to be exponentially stable in mean square for any step size. However, in this article we propose an explicit method to show that the exponential Euler method to SLSDDEs is proved to share the same stability for any step size by the property of logarithmic norm.

Nanoindentation creep behavior of human enamel.

PubMed

He, Li-Hong; Swain, Michael V

2009-11-01

In this study, the indentation creep behavior of human enamel was investigated with a nanoindentation system and a Berkovich indenter at a force of 250 mN with one-step loading and unloading method. A constant hold period of 900 s was incorporated into each test at the maximum load as well at 5 mN minimum load during unloading. The indentation creep at the maximum load and creep recovery at the minimum load was described with a double exponential function and compared with other classic viscoelastic models (Debye/Maxwell and Kohlrausch-Williams-Watts). Indentation creep rate sensitivity, m, of human enamel was measured for the first time with a value of approximately 0.012. Enamel displayed both viscoelastic and viscoplastic behavior similar to that of bone. These results indicate that, associated with entrapment of particulates between teeth under functional loading and sliding wear conditions, the enamel may inelastically deform but recover upon its release. This behavior may be important in explaining the excellent wear resistance, antifatigue, and crack resistant abilities of natural tooth structure. (c) 2008 Wiley Periodicals, Inc.

Predator prey oscillations in a simple cascade model of drift wave turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berionni, V.; Guercan, Oe. D.

2011-11-15

A reduced three shell limit of a simple cascade model of drift wave turbulence, which emphasizes nonlocal interactions with a large scale mode, is considered. It is shown to describe both the well known predator prey dynamics between the drift waves and zonal flows and to reduce to the standard three wave interaction equations. Here, this model is considered as a dynamical system whose characteristics are investigated. The analytical solutions for the purely nonlinear limit are given in terms of the Jacobi elliptic functions. An approximate analytical solution involving Jacobi elliptic functions and exponential growth is computed using scale separationmore » for the case of unstable solutions that are observed when the energy injection rate is high. The fixed points of the system are determined, and the behavior around these fixed points is studied. The system is shown to display periodic solutions corresponding to limit cycle oscillations, apparently chaotic phase space orbits, as well as unstable solutions that grow slowly while oscillating rapidly. The period doubling route to transition to chaos is examined.« less

Atmospheric Transmittance/Radiance: Computer Code LOWTRAN 6

DTIC Science & Technology

1983-08-01

1966) The refractive index of air, Metrologia 2:12, ൞ -1...sight. For an optical path traversing N layers in an upward or downward direction this process gives N [ 7 A+M A -SCAT --SUN I e,ps+op > AIV < La ... a...for cirrus normal transmittance, r, of the form = exp - (0. 14 LA ) (49) This expression closely duplicates the double exponential model of Davis 4 0 for

Kinetics of DNA Tile Dimerization

PubMed Central

2015-01-01

Investigating how individual molecular components interact with one another within DNA nanoarchitectures, both in terms of their spatial and temporal interactions, is fundamentally important for a better understanding of their physical behaviors. This will provide researchers with valuable insight for designing more complex higher-order structures that can be assembled more efficiently. In this report, we examined several spatial factors that affect the kinetics of bivalent, double-helical (DH) tile dimerization, including the orientation and number of sticky ends (SEs), the flexibility of the double helical domains, and the size of the tiles. The rate constants we obtained confirm our hypothesis that increased nucleation opportunities and well-aligned SEs accelerate tile–tile dimerization. Increased flexibility in the tiles causes slower dimerization rates, an effect that can be reversed by introducing restrictions to the tile flexibility. The higher dimerization rates of more rigid tiles results from the opposing effects of higher activation energies and higher pre-exponential factors from the Arrhenius equation, where the pre-exponential factor dominates. We believe that the results presented here will assist in improved implementation of DNA tile based algorithmic self-assembly, DNA based molecular robotics, and other specific nucleic acid systems, and will provide guidance to design and assembly processes to improve overall yield and efficiency. PMID:24794259

Kinetics of DNA tile dimerization.

PubMed

Jiang, Shuoxing; Yan, Hao; Liu, Yan

2014-06-24

Investigating how individual molecular components interact with one another within DNA nanoarchitectures, both in terms of their spatial and temporal interactions, is fundamentally important for a better understanding of their physical behaviors. This will provide researchers with valuable insight for designing more complex higher-order structures that can be assembled more efficiently. In this report, we examined several spatial factors that affect the kinetics of bivalent, double-helical (DH) tile dimerization, including the orientation and number of sticky ends (SEs), the flexibility of the double helical domains, and the size of the tiles. The rate constants we obtained confirm our hypothesis that increased nucleation opportunities and well-aligned SEs accelerate tile-tile dimerization. Increased flexibility in the tiles causes slower dimerization rates, an effect that can be reversed by introducing restrictions to the tile flexibility. The higher dimerization rates of more rigid tiles results from the opposing effects of higher activation energies and higher pre-exponential factors from the Arrhenius equation, where the pre-exponential factor dominates. We believe that the results presented here will assist in improved implementation of DNA tile based algorithmic self-assembly, DNA based molecular robotics, and other specific nucleic acid systems, and will provide guidance to design and assembly processes to improve overall yield and efficiency.

The Use of Modeling Approach for Teaching Exponential Functions

NASA Astrophysics Data System (ADS)

Nunes, L. F.; Prates, D. B.; da Silva, J. M.

2017-12-01

This work presents a discussion related to the teaching and learning of mathematical contents related to the study of exponential functions in a freshman students group enrolled in the first semester of the Science and Technology Bachelor’s (STB of the Federal University of Jequitinhonha and Mucuri Valleys (UFVJM). As a contextualization tool strongly mentioned in the literature, the modelling approach was used as an educational teaching tool to produce contextualization in the teaching-learning process of exponential functions to these students. In this sense, were used some simple models elaborated with the GeoGebra software and, to have a qualitative evaluation of the investigation and the results, was used Didactic Engineering as a methodology research. As a consequence of this detailed research, some interesting details about the teaching and learning process were observed, discussed and described.

Decay of random correlation functions for unimodal maps

NASA Astrophysics Data System (ADS)

Baladi, Viviane; Benedicks, Michael; Maume-Deschamps, Véronique

2000-10-01

Since the pioneering results of Jakobson and subsequent work by Benedicks-Carleson and others, it is known that quadratic maps tfa( χ) = a - χ2 admit a unique absolutely continuous invariant measure for a positive measure set of parameters a. For topologically mixing tfa, Young and Keller-Nowicki independently proved exponential decay of correlation functions for this a.c.i.m. and smooth observables. We consider random compositions of small perturbations tf + ωt, with tf = tfa or another unimodal map satisfying certain nonuniform hyperbolicity axioms, and ωt chosen independently and identically in [-ɛ, ɛ]. Baladi-Viana showed exponential mixing of the associated Markov chain, i.e., averaging over all random itineraries. We obtain stretched exponential bounds for the random correlation functions of Lipschitz observables for the sample measure μωof almost every itinerary.

Some exact solutions for maximally symmetric topological defects in Anti de Sitter space

NASA Astrophysics Data System (ADS)

Alvarez, Orlando; Haddad, Matthew

2018-03-01

We obtain exact analytical solutions for a class of SO( l) Higgs field theories in a non-dynamic background n-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric p-dimensional topological defects where n = ( p + 1) + l. The radius of curvature of anti de Sitter space provides an extra length scale that allows us to study the equations of motion in a limit where the masses of the Higgs field and the massive vector bosons are both vanishing. We call this the double BPS limit. In anti de Sitter space, the equations of motion depend on both p and l. The exact analytical solutions are expressed in terms of standard special functions. The known exact analytical solutions are for kink-like defects ( p = 0 , 1 , 2 , . . . ; l = 1), vortex-like defects ( p = 1 , 2 , 3; l = 2), and the 't Hooft-Polyakov monopole ( p = 0; l = 3). A bonus is that the double BPS limit automatically gives a maximally symmetric classical glueball type solution. In certain cases where we did not find an analytic solution, we present numerical solutions to the equations of motion. The asymptotically exponentially increasing volume with distance of anti de Sitter space imposes different constraints than those found in the study of defects in Minkowski space.

Exponential Family Functional data analysis via a low-rank model.

PubMed

Li, Gen; Huang, Jianhua Z; Shen, Haipeng

2018-05-08

In many applications, non-Gaussian data such as binary or count are observed over a continuous domain and there exists a smooth underlying structure for describing such data. We develop a new functional data method to deal with this kind of data when the data are regularly spaced on the continuous domain. Our method, referred to as Exponential Family Functional Principal Component Analysis (EFPCA), assumes the data are generated from an exponential family distribution, and the matrix of the canonical parameters has a low-rank structure. The proposed method flexibly accommodates not only the standard one-way functional data, but also two-way (or bivariate) functional data. In addition, we introduce a new cross validation method for estimating the latent rank of a generalized data matrix. We demonstrate the efficacy of the proposed methods using a comprehensive simulation study. The proposed method is also applied to a real application of the UK mortality study, where data are binomially distributed and two-way functional across age groups and calendar years. The results offer novel insights into the underlying mortality pattern. © 2018, The International Biometric Society.

Hardware accelerator of convolution with exponential function for image processing applications

NASA Astrophysics Data System (ADS)

Panchenko, Ivan; Bucha, Victor

2015-12-01

In this paper we describe a Hardware Accelerator (HWA) for fast recursive approximation of separable convolution with exponential function. This filter can be used in many Image Processing (IP) applications, e.g. depth-dependent image blur, image enhancement and disparity estimation. We have adopted this filter RTL implementation to provide maximum throughput in constrains of required memory bandwidth and hardware resources to provide a power-efficient VLSI implementation.

Compensation of strong thermal lensing in high-optical-power cavities.

PubMed

Zhao, C; Degallaix, J; Ju, L; Fan, Y; Blair, D G; Slagmolen, B J J; Gray, M B; Lowry, C M Mow; McClelland, D E; Hosken, D J; Mudge, D; Brooks, A; Munch, J; Veitch, P J; Barton, M A; Billingsley, G

2006-06-16

In an experiment to simulate the conditions in high optical power advanced gravitational wave detectors, we show for the first time that the time evolution of strong thermal lenses follows the predicted infinite sum of exponentials (approximated by a double exponential), and that such lenses can be compensated using an intracavity compensation plate heated on its cylindrical surface. We show that high finesse approximately 1400 can be achieved in cavities with internal compensation plates, and that mode matching can be maintained. The experiment achieves a wave front distortion similar to that expected for the input test mass substrate in the Advanced Laser Interferometer Gravitational Wave Observatory, and shows that thermal compensation schemes are viable. It is also shown that the measurements allow a direct measurement of substrate optical absorption in the test mass and the compensation plate.

Non-equilibrium STLS approach to transport properties of single impurity Anderson model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rezai, Raheleh, E-mail: R_Rezai@sbu.ac.ir; Ebrahimi, Farshad, E-mail: Ebrahimi@sbu.ac.ir

In this work, using the non-equilibrium Keldysh formalism, we study the effects of the electron–electron interaction and the electron-spin correlation on the non-equilibrium Kondo effect and the transport properties of the symmetric single impurity Anderson model (SIAM) at zero temperature by generalizing the self-consistent method of Singwi, Tosi, Land, and Sjolander (STLS) for a single-band tight-binding model with Hubbard type interaction to out of equilibrium steady-states. We at first determine in a self-consistent manner the non-equilibrium spin correlation function, the effective Hubbard interaction, and the double-occupancy at the impurity site. Then, using the non-equilibrium STLS spin polarization function in themore » non-equilibrium formalism of the iterative perturbation theory (IPT) of Yosida and Yamada, and Horvatic and Zlatic, we compute the spectral density, the current–voltage characteristics and the differential conductance as functions of the applied bias and the strength of on-site Hubbard interaction. We compare our spectral densities at zero bias with the results of numerical renormalization group (NRG) and depict the effects of the electron–electron interaction and electron-spin correlation at the impurity site on the aforementioned properties by comparing our numerical result with the order U{sup 2} IPT. Finally, we show that the obtained numerical results on the differential conductance have a quadratic universal scaling behavior and the resulting Kondo temperature shows an exponential behavior. -- Highlights: •We introduce for the first time the non-equilibrium method of STLS for Hubbard type models. •We determine the transport properties of SIAM using the non-equilibrium STLS method. •We compare our results with order-U2 IPT and NRG. •We show that non-equilibrium STLS, contrary to the GW and self-consistent RPA, produces the two Hubbard peaks in DOS. •We show that the method keeps the universal scaling behavior and correct exponential behavior of Kondo temperature.« less

The Spatial Structure of Planform Migration - Curvature Relation of Meandering Rivers

NASA Astrophysics Data System (ADS)

Guneralp, I.; Rhoads, B. L.

2005-12-01

Planform dynamics of meandering rivers have been of fundamental interest to fluvial geomorphologists and engineers because of the intriguing complexity of these dynamics, the role of planform change in floodplain development and landscape evolution, and the economic and social consequences of bank erosion and channel migration. Improved understanding of the complex spatial structure of planform change and capacity to predict these changes are important for effective stream management, engineering and restoration. The planform characteristics of a meandering river channel are integral to its planform dynamics. Active meandering rivers continually change their positions and shapes as a consequence of hydraulic forces exerted on the channel banks and bed, but as the banks and bed change through sediment transport, so do the hydraulic forces. Thus far, this complex feedback between form and process is incompletely understood, despite the fact that the characteristics and the dynamics of meandering rivers have been studied extensively. Current theoretical models aimed at predicting planform dynamics relate rates of meander migration to local and upstream planform curvature where weighting of the influence of curvature on migration rate decays exponentially over distance. This theoretical relation, however, has not been rigorously evaluated empirically. Furthermore, although models based on exponential-weighting of curvature effects yield fairly realistic predictions of meander migration, such models are incapable of reproducing complex forms of bend development, such as double heading or compound looping. This study presents the development of a new methodology based on parametric cubic spline interpolation for the characterization of channel planform and the planform curvature of meandering rivers. The use of continuous mathematical functions overcomes the reliance on bend-averaged values or piece-wise discrete approximations of planform curvature - a major limitation of previous studies. Continuous curvature series can be related to measured rates of lateral migration to explore empirically the relationship between spatially extended curvature and local bend migration. The methodology is applied to a study reach along a highly sinuous section of the Embarras River in Illinois, USA, which contains double-headed asymmetrical loops. To identify patterns of channel planform and rates of lateral migration for a study reach along Embarrass River in central Illinois, geographical information systems analysis of historical aerial photography over a period from 1936 to 1998 was conducted. Results indicate that parametric cubic spline interpolation provides excellent characterization of the complex planforms and planform curvatures of meandering rivers. The findings also indicate that the spatial structure of migration rate-curvature relation may be more complex than a simple exponential distance-decay function. The study represents a first step toward unraveling the spatial structure of planform evolution of meandering rivers and for developing models of planform dynamics that accurately relate spatially extended patterns of channel curvature to local rates of lateral migration. Such knowledge is vital for improving the capacity to accurately predict planform change of meandering rivers.

Recursive least squares estimation and its application to shallow trench isolation

NASA Astrophysics Data System (ADS)

Wang, Jin; Qin, S. Joe; Bode, Christopher A.; Purdy, Matthew A.

2003-06-01

In recent years, run-to-run (R2R) control technology has received tremendous interest in semiconductor manufacturing. One class of widely used run-to-run controllers is based on the exponentially weighted moving average (EWMA) statistics to estimate process deviations. Using an EWMA filter to smooth the control action on a linear process has been shown to provide good results in a number of applications. However, for a process with severe drifts, the EWMA controller is insufficient even when large weights are used. This problem becomes more severe when there is measurement delay, which is almost inevitable in semiconductor industry. In order to control drifting processes, a predictor-corrector controller (PCC) and a double EWMA controller have been developed. Chen and Guo (2001) show that both PCC and double-EWMA controller are in effect Integral-double-Integral (I-II) controllers, which are able to control drifting processes. However, since offset is often within the noise of the process, the second integrator can actually cause jittering. Besides, tuning the second filter is not as intuitive as a single EWMA filter. In this work, we look at an alternative way Recursive Least Squares (RLS), to estimate and control the drifting process. EWMA and double-EWMA are shown to be the least squares estimate for locally constant mean model and locally constant linear trend model. Then the recursive least squares with exponential factor is applied to shallow trench isolation etch process to predict the future etch rate. The etch process, which is a critical process in the flash memory manufacturing, is known to suffer from significant etch rate drift due to chamber seasoning. In order to handle the metrology delay, we propose a new time update scheme. RLS with the new time update method gives very good result. The estimate error variance is smaller than that from EWMA, and mean square error decrease more than 10% compared to that from EWMA.

A review of the matrix-exponential formalism in radiative transfer

NASA Astrophysics Data System (ADS)

Efremenko, Dmitry S.; Molina García, Víctor; Gimeno García, Sebastián; Doicu, Adrian

2017-07-01

This paper outlines the matrix exponential description of radiative transfer. The eigendecomposition method which serves as a basis for computing the matrix exponential and for representing the solution in a discrete ordinate setting is considered. The mathematical equivalence of the discrete ordinate method, the matrix operator method, and the matrix Riccati equations method is proved rigorously by means of the matrix exponential formalism. For optically thin layers, approximate solution methods relying on the Padé and Taylor series approximations to the matrix exponential, as well as on the matrix Riccati equations, are presented. For optically thick layers, the asymptotic theory with higher-order corrections is derived, and parameterizations of the asymptotic functions and constants for a water-cloud model with a Gamma size distribution are obtained.

Exponential integrators in time-dependent density-functional calculations

NASA Astrophysics Data System (ADS)

Kidd, Daniel; Covington, Cody; Varga, Kálmán

2017-12-01

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn-Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.

New results on global exponential dissipativity analysis of memristive inertial neural networks with distributed time-varying delays.

PubMed

Zhang, Guodong; Zeng, Zhigang; Hu, Junhao

2018-01-01

This paper is concerned with the global exponential dissipativity of memristive inertial neural networks with discrete and distributed time-varying delays. By constructing appropriate Lyapunov-Krasovskii functionals, some new sufficient conditions ensuring global exponential dissipativity of memristive inertial neural networks are derived. Moreover, the globally exponential attractive sets and positive invariant sets are also presented here. In addition, the new proposed results here complement and extend the earlier publications on conventional or memristive neural network dynamical systems. Finally, numerical simulations are given to illustrate the effectiveness of obtained results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Anomalous NMR Relaxation in Cartilage Matrix Components and Native Cartilage: Fractional-Order Models

PubMed Central

Magin, Richard L.; Li, Weiguo; Velasco, M. Pilar; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-01-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for microstructural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues. PMID:21498095

Anomalous NMR relaxation in cartilage matrix components and native cartilage: Fractional-order models

NASA Astrophysics Data System (ADS)

Magin, Richard L.; Li, Weiguo; Pilar Velasco, M.; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.

2011-06-01

We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena ( T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter ( α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for micro-structural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues.

Calculating Formulae of Proportion Factor and Mean Neutron Exposure in the Exponential Expression of Neutron Exposure Distribution

NASA Astrophysics Data System (ADS)

Feng-Hua, Zhang; Gui-De, Zhou; Kun, Ma; Wen-Juan, Ma; Wen-Yuan, Cui; Bo, Zhang

2016-07-01

Previous studies have shown that, for the three main stages of the development and evolution of asymptotic giant branch (AGB) star s-process models, the neutron exposure distribution (DNE) in the nucleosynthesis region can always be considered as an exponential function, i.e., ρAGB(τ) = C/τ0 exp(-τ/τ0) in an effective range of the neutron exposure values. However, the specific expressions of the proportion factor C and the mean neutron exposure τ0 in the exponential distribution function for different models are not completely determined in the related literature. Through dissecting the basic method to obtain the exponential DNE, and systematically analyzing the solution procedures of neutron exposure distribution functions in different stellar models, the general formulae, as well as their auxiliary equations, for calculating C and τ0 are derived. Given the discrete neutron exposure distribution Pk, the relationships of C and τ0 with the model parameters can be determined. The result of this study has effectively solved the problem to analytically calculate the DNE in the current low-mass AGB star s-process nucleosynthesis model of 13C-pocket radiative burning.

Approximation of the exponential integral (well function) using sampling methods

NASA Astrophysics Data System (ADS)

Baalousha, Husam Musa

2015-04-01

Exponential integral (also known as well function) is often used in hydrogeology to solve Theis and Hantush equations. Many methods have been developed to approximate the exponential integral. Most of these methods are based on numerical approximations and are valid for a certain range of the argument value. This paper presents a new approach to approximate the exponential integral. The new approach is based on sampling methods. Three different sampling methods; Latin Hypercube Sampling (LHS), Orthogonal Array (OA), and Orthogonal Array-based Latin Hypercube (OA-LH) have been used to approximate the function. Different argument values, covering a wide range, have been used. The results of sampling methods were compared with results obtained by Mathematica software, which was used as a benchmark. All three sampling methods converge to the result obtained by Mathematica, at different rates. It was found that the orthogonal array (OA) method has the fastest convergence rate compared with LHS and OA-LH. The root mean square error RMSE of OA was in the order of 1E-08. This method can be used with any argument value, and can be used to solve other integrals in hydrogeology such as the leaky aquifer integral.

Learning curves in highly skilled chess players: a test of the generality of the power law of practice.

PubMed

Howard, Robert W

2014-09-01

The power law of practice holds that a power function best interrelates skill performance and amount of practice. However, the law's validity and generality are moot. Some researchers argue that it is an artifact of averaging individual exponential curves while others question whether the law generalizes to complex skills and to performance measures other than response time. The present study tested the power law's generality to development over many years of a very complex cognitive skill, chess playing, with 387 skilled participants, most of whom were grandmasters. A power or logarithmic function best fit grouped data but individuals showed much variability. An exponential function usually was the worst fit to individual data. Groups differing in chess talent were compared and a power function best fit the group curve for the more talented players while a quadratic function best fit that for the less talented. After extreme amounts of practice, a logarithmic function best fit grouped data but a quadratic function best fit most individual curves. Individual variability is great and the power law or an exponential law are not the best descriptions of individual chess skill development. Copyright © 2014 Elsevier B.V. All rights reserved.

Discrete-time BAM neural networks with variable delays

NASA Astrophysics Data System (ADS)

Liu, Xin-Ge; Tang, Mei-Lan; Martin, Ralph; Liu, Xin-Bi

2007-07-01

This Letter deals with the global exponential stability of discrete-time bidirectional associative memory (BAM) neural networks with variable delays. Using a Lyapunov functional, and linear matrix inequality techniques (LMI), we derive a new delay-dependent exponential stability criterion for BAM neural networks with variable delays. As this criterion has no extra constraints on the variable delay functions, it can be applied to quite general BAM neural networks with a broad range of time delay functions. It is also easy to use in practice. An example is provided to illustrate the theoretical development.

New results for global exponential synchronization in neural networks via functional differential inclusions.

PubMed

Wang, Dongshu; Huang, Lihong; Tang, Longkun

2015-08-01

This paper is concerned with the synchronization dynamical behaviors for a class of delayed neural networks with discontinuous neuron activations. Continuous and discontinuous state feedback controller are designed such that the neural networks model can realize exponential complete synchronization in view of functional differential inclusions theory, Lyapunov functional method and inequality technique. The new proposed results here are very easy to verify and also applicable to neural networks with continuous activations. Finally, some numerical examples show the applicability and effectiveness of our main results.

Exponential operations and aggregation operators of interval neutrosophic sets and their decision making methods.

PubMed

Ye, Jun

2016-01-01

An interval neutrosophic set (INS) is a subclass of a neutrosophic set and a generalization of an interval-valued intuitionistic fuzzy set, and then the characteristics of INS are independently described by the interval numbers of its truth-membership, indeterminacy-membership, and falsity-membership degrees. However, the exponential parameters (weights) of all the existing exponential operational laws of INSs and the corresponding exponential aggregation operators are crisp values in interval neutrosophic decision making problems. As a supplement, this paper firstly introduces new exponential operational laws of INSs, where the bases are crisp values or interval numbers and the exponents are interval neutrosophic numbers (INNs), which are basic elements in INSs. Then, we propose an interval neutrosophic weighted exponential aggregation (INWEA) operator and a dual interval neutrosophic weighted exponential aggregation (DINWEA) operator based on these exponential operational laws and introduce comparative methods based on cosine measure functions for INNs and dual INNs. Further, we develop decision-making methods based on the INWEA and DINWEA operators. Finally, a practical example on the selecting problem of global suppliers is provided to illustrate the applicability and rationality of the proposed methods.

Multistability of second-order competitive neural networks with nondecreasing saturated activation functions.

PubMed

Nie, Xiaobing; Cao, Jinde

2011-11-01

In this paper, second-order interactions are introduced into competitive neural networks (NNs) and the multistability is discussed for second-order competitive NNs (SOCNNs) with nondecreasing saturated activation functions. Firstly, based on decomposition of state space, Cauchy convergence principle, and inequality technique, some sufficient conditions ensuring the local exponential stability of 2N equilibrium points are derived. Secondly, some conditions are obtained for ascertaining equilibrium points to be locally exponentially stable and to be located in any designated region. Thirdly, the theory is extended to more general saturated activation functions with 2r corner points and a sufficient criterion is given under which the SOCNNs can have (r+1)N locally exponentially stable equilibrium points. Even if there is no second-order interactions, the obtained results are less restrictive than those in some recent works. Finally, three examples with their simulations are presented to verify the theoretical analysis.

Fast and accurate fitting and filtering of noisy exponentials in Legendre space.

PubMed

Bao, Guobin; Schild, Detlev

2014-01-01

The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a novel method where the noisy data are represented and analyzed in the space of Legendre polynomials. This is advantageous in several respects. First, parameter retrieval in the Legendre domain is typically two orders of magnitude faster than direct fitting in the time domain. Second, data fitting in a low-dimensional Legendre space yields estimates for amplitudes and time constants which are, on the average, more precise compared to least-squares-fitting with equal weights in the time domain. Third, the Legendre analysis of two exponentials gives satisfactory estimates in parameter ranges where least-squares-fitting in the time domain typically fails. Finally, filtering exponentials in the domain of Legendre polynomials leads to marked noise removal without the phase shift characteristic for conventional lowpass filters.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-01

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters.

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-14

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

A General Exponential Framework for Dimensionality Reduction.

PubMed

Wang, Su-Jing; Yan, Shuicheng; Yang, Jian; Zhou, Chun-Guang; Fu, Xiaolan

2014-02-01

As a general framework, Laplacian embedding, based on a pairwise similarity matrix, infers low dimensional representations from high dimensional data. However, it generally suffers from three issues: 1) algorithmic performance is sensitive to the size of neighbors; 2) the algorithm encounters the well known small sample size (SSS) problem; and 3) the algorithm de-emphasizes small distance pairs. To address these issues, here we propose exponential embedding using matrix exponential and provide a general framework for dimensionality reduction. In the framework, the matrix exponential can be roughly interpreted by the random walk over the feature similarity matrix, and thus is more robust. The positive definite property of matrix exponential deals with the SSS problem. The behavior of the decay function of exponential embedding is more significant in emphasizing small distance pairs. Under this framework, we apply matrix exponential to extend many popular Laplacian embedding algorithms, e.g., locality preserving projections, unsupervised discriminant projections, and marginal fisher analysis. Experiments conducted on the synthesized data, UCI, and the Georgia Tech face database show that the proposed new framework can well address the issues mentioned above.

Spectral Analyses and Radiation Exposures from Several Ground-Level Enhancement (GLE) Solar Proton Events: A Comparison of Methodologies

NASA Technical Reports Server (NTRS)

Atwell, William; Tylka, Allan; Dietrich, William; Badavi, Francis; Rojdev, Kristina

2011-01-01

Several methods for analyzing the particle spectra from extremely large solar proton events, called Ground-Level Enhancements (GLEs), have been developed and utilized by the scientific community to describe the solar proton energy spectra and have been further applied to ascertain the radiation exposures to humans and radio-sensitive systems, namely electronics. In this paper 12 GLEs dating back to 1956 are discussed, and the three methods for describing the solar proton energy spectra are reviewed. The three spectral fitting methodologies are EXP [an exponential in proton rigidity (R)], WEIB [Weibull fit: an exponential in proton energy], and the Band function (BAND) [a double power law in proton rigidity]. The EXP and WEIB methods use low energy (MeV) GLE solar proton data and make extrapolations out to approx.1 GeV. On the other hand, the BAND method utilizes low- and medium-energy satellite solar proton data combined with high-energy solar proton data deduced from high-latitude neutron monitoring stations. Thus, the BAND method completely describes the entire proton energy spectrum based on actual solar proton observations out to 10 GeV. Using the differential spectra produced from each of the 12 selected GLEs for each of the three methods, radiation exposures are presented and discussed in detail. These radiation exposures are then compared with the current 30-day and annual crew exposure limits and the radiation effects to electronics.

Determination of the direction to a source of antineutrinos via inverse beta decay in Double Chooz

NASA Astrophysics Data System (ADS)

Nikitenko, Ya.

2016-11-01

To determine the direction to a source of neutrinos (and antineutrinos) is an important problem for the physics of supernovae and of the Earth. The direction to a source of antineutrinos can be estimated through the reaction of inverse beta decay. We show that the reactor neutrino experiment Double Chooz has unique capabilities to study antineutrino signal from point-like sources. Contemporary experimental data on antineutrino directionality is given. A rigorous mathematical approach for neutrino direction studies has been developed. Exact expressions for the precision of the simple mean estimator of neutrinos' direction for normal and exponential distributions for a finite sample and for the limiting case of many events have been obtained.

Numerical analysis of spectral properties of coupled oscillator Schroedinger operators. I - Single and double well anharmonic oscillators

NASA Technical Reports Server (NTRS)

Isaacson, D.; Isaacson, E. L.; Paes-Leme, P. J.; Marchesin, D.

1981-01-01

Several methods for computing many eigenvalues and eigenfunctions of a single anharmonic oscillator Schroedinger operator whose potential may have one or two minima are described. One of the methods requires the solution of an ill-conditioned generalized eigenvalue problem. This method has the virtue of using a bounded amount of work to achieve a given accuracy in both the single and double well regions. Rigorous bounds are given, and it is proved that the approximations converge faster than any inverse power of the size of the matrices needed to compute them. The results of computations for the g:phi(4):1 theory are presented. These results indicate that the methods actually converge exponentially fast.

BORAX V EXPONENTIAL EXPERIMENT

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kirn, F.S.; Hagen, J.I.

1963-04-01

The cadmium ratio was measured in an exponential mockup of Borax V as a function of the void fraction. The extent of voids, simulated by lengths of closed polyethylene tubes, ranged from 0 to 40%. The corresponding cadmium ratios ranged from 6.1 to 4.6. The exponential was also used to determine the radial flux pattern across a Borax-type fuel assembly and the fine flux detail in and around fuel rods. For a normal loading the maximum-to-average power generation across an assembly was 1.24. (auth)

Computer Diagnostics.

ERIC Educational Resources Information Center

Tondow, Murray

The report deals with the influence of computer technology on education, particularly guidance. The need for computers is a result of increasing complexity which is defined as: (1) an exponential increase of information; (2) an exponential increase in dissemination capabilities; and (3) an accelerating curve of change. Listed are five functions of…

Bacterial genomes lacking long-range correlations may not be modeled by low-order Markov chains: the role of mixing statistics and frame shift of neighboring genes.

PubMed

Cocho, Germinal; Miramontes, Pedro; Mansilla, Ricardo; Li, Wentian

2014-12-01

We examine the relationship between exponential correlation functions and Markov models in a bacterial genome in detail. Despite the well known fact that Markov models generate sequences with correlation function that decays exponentially, simply constructed Markov models based on nearest-neighbor dimer (first-order), trimer (second-order), up to hexamer (fifth-order), and treating the DNA sequence as being homogeneous all fail to predict the value of exponential decay rate. Even reading-frame-specific Markov models (both first- and fifth-order) could not explain the fact that the exponential decay is very slow. Starting with the in-phase coding-DNA-sequence (CDS), we investigated correlation within a fixed-codon-position subsequence, and in artificially constructed sequences by packing CDSs with out-of-phase spacers, as well as altering CDS length distribution by imposing an upper limit. From these targeted analyses, we conclude that the correlation in the bacterial genomic sequence is mainly due to a mixing of heterogeneous statistics at different codon positions, and the decay of correlation is due to the possible out-of-phase between neighboring CDSs. There are also small contributions to the correlation from bases at the same codon position, as well as by non-coding sequences. These show that the seemingly simple exponential correlation functions in bacterial genome hide a complexity in correlation structure which is not suitable for a modeling by Markov chain in a homogeneous sequence. Other results include: use of the (absolute value) second largest eigenvalue to represent the 16 correlation functions and the prediction of a 10-11 base periodicity from the hexamer frequencies. Copyright © 2014 Elsevier Ltd. All rights reserved.

Exhaustive Versus Randomized Searchers for Nonlinear Optimization in 21st Century Computing: Solar Application

NASA Technical Reports Server (NTRS)

Sen, Syamal K.; AliShaykhian, Gholam

2010-01-01

We present a simple multi-dimensional exhaustive search method to obtain, in a reasonable time, the optimal solution of a nonlinear programming problem. It is more relevant in the present day non-mainframe computing scenario where an estimated 95% computing resources remains unutilized and computing speed touches petaflops. While the processor speed is doubling every 18 months, the band width is doubling every 12 months, and the hard disk space is doubling every 9 months. A randomized search algorithm or, equivalently, an evolutionary search method is often used instead of an exhaustive search algorithm. The reason is that a randomized approach is usually polynomial-time, i.e., fast while an exhaustive search method is exponential-time i.e., slow. We discuss the increasing importance of exhaustive search in optimization with the steady increase of computing power for solving many real-world problems of reasonable size. We also discuss the computational error and complexity of the search algorithm focusing on the fact that no measuring device can usually measure a quantity with an accuracy greater than 0.005%. We stress the fact that the quality of solution of the exhaustive search - a deterministic method - is better than that of randomized search. In 21 st century computing environment, exhaustive search cannot be left aside as an untouchable and it is not always exponential. We also describe a possible application of these algorithms in improving the efficiency of solar cells - a real hot topic - in the current energy crisis. These algorithms could be excellent tools in the hands of experimentalists and could save not only large amount of time needed for experiments but also could validate the theory against experimental results fast.

Quantifying Uncertainties in N2O Emission Due to N Fertilizer Application in Cultivated Areas

PubMed Central

Philibert, Aurore; Loyce, Chantal; Makowski, David

2012-01-01

Nitrous oxide (N2O) is a greenhouse gas with a global warming potential approximately 298 times greater than that of CO2. In 2006, the Intergovernmental Panel on Climate Change (IPCC) estimated N2O emission due to synthetic and organic nitrogen (N) fertilization at 1% of applied N. We investigated the uncertainty on this estimated value, by fitting 13 different models to a published dataset including 985 N2O measurements. These models were characterized by (i) the presence or absence of the explanatory variable “applied N”, (ii) the function relating N2O emission to applied N (exponential or linear function), (iii) fixed or random background (i.e. in the absence of N application) N2O emission and (iv) fixed or random applied N effect. We calculated ranges of uncertainty on N2O emissions from a subset of these models, and compared them with the uncertainty ranges currently used in the IPCC-Tier 1 method. The exponential models outperformed the linear models, and models including one or two random effects outperformed those including fixed effects only. The use of an exponential function rather than a linear function has an important practical consequence: the emission factor is not constant and increases as a function of applied N. Emission factors estimated using the exponential function were lower than 1% when the amount of N applied was below 160 kg N ha−1. Our uncertainty analysis shows that the uncertainty range currently used by the IPCC-Tier 1 method could be reduced. PMID:23226430

Lump solutions and interaction phenomenon to the third-order nonlinear evolution equation

NASA Astrophysics Data System (ADS)

Kofane, T. C.; Fokou, M.; Mohamadou, A.; Yomba, E.

2017-11-01

In this work, the lump solution and the kink solitary wave solution from the (2 + 1) -dimensional third-order evolution equation, using the Hirota bilinear method are obtained through symbolic computation with Maple. We have assumed that the lump solution is centered at the origin, when t = 0 . By considering a mixing positive quadratic function with exponential function, as well as a mixing positive quadratic function with hyperbolic cosine function, interaction solutions like lump-exponential and lump-hyperbolic cosine are presented. A completely non-elastic interaction between a lump and kink soliton is observed, showing that a lump solution can be swallowed by a kink soliton.

An accurate method for evaluating the kernel of the integral equation relating lift to downwash in unsteady potential flow

NASA Technical Reports Server (NTRS)

Desmarais, R. N.

1982-01-01

The method is capable of generating approximations of arbitrary accuracy. It is based on approximating the algebraic part of the nonelementary integrals in the kernel by exponential functions and then integrating termwise. The exponent spacing in the approximation is a geometric sequence. The coefficients and exponent multiplier of the exponential approximation are computed by least squares so the method is completely automated. Exponential approximates generated in this manner are two orders of magnitude more accurate than the exponential approximation that is currently most often used for this purpose. The method can be used to generate approximations to attain any desired trade-off between accuracy and computing cost.

Combining Orthogonal Chain-End Deprotections and Thiol-Maleimide Michael Coupling: Engineering Discrete Oligomers by an Iterative Growth Strategy.

PubMed

Huang, Zhihao; Zhao, Junfei; Wang, Zimu; Meng, Fanying; Ding, Kunshan; Pan, Xiangqiang; Zhou, Nianchen; Li, Xiaopeng; Zhang, Zhengbiao; Zhu, Xiulin

2017-10-23

Orthogonal maleimide and thiol deprotections were combined with thiol-maleimide coupling to synthesize discrete oligomers/macromolecules on a gram scale with molecular weights up to 27.4 kDa (128mer, 7.9 g) using an iterative exponential growth strategy with a degree of polymerization (DP) of 2 n -1. Using the same chemistry, a "readable" sequence-defined oligomer and a discrete cyclic topology were also created. Furthermore, uniform dendrons were fabricated using sequential growth (DP=2 n -1) or double exponential dendrimer growth approaches (DP=22n -1) with significantly accelerated growth rates. A versatile, efficient, and metal-free method for construction of discrete oligomers with tailored structures and a high growth rate would greatly facilitate research into the structure-property relationships of sophisticated polymeric materials. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Ultrafast hole carrier relaxation dynamics in p-type CuO nanowires

PubMed Central

2011-01-01

Ultrafast hole carrier relaxation dynamics in CuO nanowires have been investigated using transient absorption spectroscopy. Following femtosecond pulse excitation in a non-collinear pump-probe configuration, a combination of non-degenerate transmission and reflection measurements reveal initial ultrafast state filling dynamics independent of the probing photon energy. This behavior is attributed to the occupation of states by photo-generated carriers in the intrinsic hole region of the p-type CuO nanowires located near the top of the valence band. Intensity measurements indicate an upper fluence threshold of 40 μJ/cm2 where carrier relaxation is mainly governed by the hole dynamics. The fast relaxation of the photo-generated carriers was determined to follow a double exponential decay with time constants of 0.4 ps and 2.1 ps. Furthermore, time-correlated single photon counting measurements provide evidence of three exponential relaxation channels on the nanosecond timescale. PMID:22151927

Scalable synthesis of sequence-defined, unimolecular macromolecules by Flow-IEG

PubMed Central

Leibfarth, Frank A.; Johnson, Jeremiah A.; Jamison, Timothy F.

2015-01-01

We report a semiautomated synthesis of sequence and architecturally defined, unimolecular macromolecules through a marriage of multistep flow synthesis and iterative exponential growth (Flow-IEG). The Flow-IEG system performs three reactions and an in-line purification in a total residence time of under 10 min, effectively doubling the molecular weight of an oligomeric species in an uninterrupted reaction sequence. Further iterations using the Flow-IEG system enable an exponential increase in molecular weight. Incorporating a variety of monomer structures and branching units provides control over polymer sequence and architecture. The synthesis of a uniform macromolecule with a molecular weight of 4,023 g/mol is demonstrated. The user-friendly nature, scalability, and modularity of Flow-IEG provide a general strategy for the automated synthesis of sequence-defined, unimolecular macromolecules. Flow-IEG is thus an enabling tool for theory validation, structure–property studies, and advanced applications in biotechnology and materials science. PMID:26269573

Simplifying the Mathematical Treatment of Radioactive Decay

ERIC Educational Resources Information Center

Auty, Geoff

2011-01-01

Derivation of the law of radioactive decay is considered without prior knowledge of calculus or the exponential series. Calculus notation and exponential functions are used because ultimately they cannot be avoided, but they are introduced in a simple way and explained as needed. (Contains 10 figures, 1 box, and 1 table.)

How exponential are FREDs?

NASA Astrophysics Data System (ADS)

Schaefer, Bradley E.; Dyson, Samuel E.

1996-08-01

A common Gamma-Ray Burst-light curve shape is the ``FRED'' or ``fast-rise exponential-decay.'' But how exponential is the tail? Are they merely decaying with some smoothly decreasing decline rate, or is the functional form an exponential to within the uncertainties? If the shape really is an exponential, then it would be reasonable to assign some physically significant time scale to the burst. That is, there would have to be some specific mechanism that produces the characteristic decay profile. So if an exponential is found, then we will know that the decay light curve profile is governed by one mechanism (at least for simple FREDs) instead of by complex/multiple mechanisms. As such, a specific number amenable to theory can be derived for each FRED. We report on the fitting of exponentials (and two other shapes) to the tails of ten bright BATSE bursts. The BATSE trigger numbers are 105, 257, 451, 907, 1406, 1578, 1883, 1885, 1989, and 2193. Our technique was to perform a least square fit to the tail from some time after peak until the light curve approaches background. We find that most FREDs are not exponentials, although a few come close. But since the other candidate shapes come close just as often, we conclude that the FREDs are misnamed.

Splines and control theory

NASA Technical Reports Server (NTRS)

Zhang, Zhimin; Tomlinson, John; Martin, Clyde

1994-01-01

In this work, the relationship between splines and the control theory has been analyzed. We show that spline functions can be constructed naturally from the control theory. By establishing a framework based on control theory, we provide a simple and systematic way to construct splines. We have constructed the traditional spline functions including the polynomial splines and the classical exponential spline. We have also discovered some new spline functions such as trigonometric splines and the combination of polynomial, exponential and trigonometric splines. The method proposed in this paper is easy to implement. Some numerical experiments are performed to investigate properties of different spline approximations.

The Translated Dowling Polynomials and Numbers.

PubMed

Mangontarum, Mahid M; Macodi-Ringia, Amila P; Abdulcarim, Normalah S

2014-01-01

More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers.

Verification of mutagen function of Zeocin in Nannochloropsis oceanica through transcriptome analysis

NASA Astrophysics Data System (ADS)

Lin, Genmei; Wang, Yamei; Guo, Li; Ding, Haiyan; Hu, Yongmei; Liang, Sijie; Zhang, Zhongyi; Yang, Guanpin

2017-06-01

Zeocin can cause double strand breaks of DNA and thus is frequently used as a selective antibiotic of eukaryotic Sh ble transformants. In non-transformation system, Zeocin may function as a mutagen if not totally lethal. To verify such function of Zeocin, we mutated Nannochloropsis oceanica by increasing the concentration of Zeocin in medium gradually, and isolated a N. oceanica strain (single cell culture) which survived Zeocin up to 10.0 μg mL-1. The Zeocin-tolerant strain entered the exponential growth phase later and grew slower than the wild strain. Transcriptome profiling showed that the Zeocin-tolerant N. oceanica strain survived Zeocin mainly by adapting (heritable), rather than acclimating (plastic) to Zeocin. Hence mutating N. oceanica with Zeocin was approved effective. Meanwhile, the physiological characteristics of this Zeocin-tolerant strain were demonstrated. As we proposed, N. oceanica tolerated Zeocin by strengthening its protein degradation and antioxidation. The genes controlling cell division and cellular response to stimuli may also have played important roles in the reduction of growth and the tolerance to Zeocin. Our findings evidenced that Zeocin can serve as an appropriate mutagen of microalgae. Creating variations through mutation with Zeocin may help to study the genetic basis of the traits of this monoploidy and asexual microalga, as well as improve its production.

Enhanced Response Time of Electrowetting Lenses with Shaped Input Voltage Functions.

PubMed

Supekar, Omkar D; Zohrabi, Mo; Gopinath, Juliet T; Bright, Victor M

2017-05-16

Adaptive optical lenses based on the electrowetting principle are being rapidly implemented in many applications, such as microscopy, remote sensing, displays, and optical communication. To characterize the response of these electrowetting lenses, the dependence upon direct current (DC) driving voltage functions was investigated in a low-viscosity liquid system. Cylindrical lenses with inner diameters of 2.45 and 3.95 mm were used to characterize the dynamic behavior of the liquids under DC voltage electrowetting actuation. With the increase of the rise time of the input exponential driving voltage, the originally underdamped system response can be damped, enabling a smooth response from the lens. We experimentally determined the optimal rise times for the fastest response from the lenses. We have also performed numerical simulations of the lens actuation with input exponential driving voltage to understand the variation in the dynamics of the liquid-liquid interface with various input rise times. We further enhanced the response time of the devices by shaping the input voltage function with multiple exponential rise times. For the 3.95 mm inner diameter lens, we achieved a response time improvement of 29% when compared to the fastest response obtained using single-exponential driving voltage. The technique shows great promise for applications that require fast response times.

Processing of DNA double strand breaks by alternative non-homologous end-joining in hyperacetylated chromatin

PubMed Central

2012-01-01

Background Mammalian cells employ at least two subpathways of non-homologous end-joining for the repair of ionizing radiation induced DNA double strand breaks: The canonical DNA-PK-dependent form of non-homologous end-joining (D-NHEJ) and an alternative, slowly operating, error-prone backup pathway (B-NHEJ). In contrast to D-NHEJ, which operates with similar efficiency throughout the cell cycle, B-NHEJ operates more efficiently in G2-phase. Notably, B-NHEJ also shows strong and as of yet unexplained dependency on growth activity and is markedly compromised in serum-deprived cells, or in cells that enter the plateau-phase of growth. The molecular mechanisms underpinning this response remain unknown. Since chromatin structure or changes in chromatin structure are prime candidate-B-NHEJ-modulators, we study here the role of chromatin hyperacetylation, either by HDAC2 knockdown or treatment with the HDAC inhibitor TSA, on the repair by B-NHEJ of IR-induced DSBs. Results siRNA-mediated knockdown of HDAC2 fails to provoke histone hyperacetylation in Lig4-/- MEFs and has no detectable effect on B-NHEJ function. Treatment with TSA that inhibits multiple HDACs causes efficient, reversible chromatin hyperacetylation in Lig4-/- MEFs, as well as in human HCT116 Lig4-/- cells and the human glioma cell line M059K. The IR yield of DSBs in TSA-treated cells remains similar to that of untreated cells despite the expected chromatin relaxation. In addition, chromatin hyperacetylation leaves unchanged repair of DSBs by B-NHEJ in irradiated exponentially growing, or plateau-phase cells. Notably, under the experimental conditions employed here, chromatin hyperacetylation fails to detectably modulate B-NHEJ in M059K cells as well. Conclusions In summary, the results show that chromatin acetylation or deacetylation does not affect the kinetics of alternative NHEJ in all types of cells examined both in exponentially growing and serum deprived cultures. We conclude that parameters beyond chromatin acetylation determine B-NHEJ efficiency in the plateau-phase of growth. PMID:22908892

State of charge modeling of lithium-ion batteries using dual exponential functions

NASA Astrophysics Data System (ADS)

Kuo, Ting-Jung; Lee, Kung-Yen; Huang, Chien-Kang; Chen, Jau-Horng; Chiu, Wei-Li; Huang, Chih-Fang; Wu, Shuen-De

2016-05-01

A mathematical model is developed by fitting the discharging curve of LiFePO4 batteries and used to investigate the relationship between the state of charge and the closed-circuit voltage. The proposed mathematical model consists of dual exponential terms and a constant term which can fit the characteristics of dual equivalent RC circuits closely, representing a LiFePO4 battery. One exponential term presents the stable discharging behavior and the other one presents the unstable discharging behavior and the constant term presents the cut-off voltage.

Mean Excess Function as a method of identifying sub-exponential tails: Application to extreme daily rainfall

NASA Astrophysics Data System (ADS)

Nerantzaki, Sofia; Papalexiou, Simon Michael

2017-04-01

Identifying precisely the distribution tail of a geophysical variable is tough, or, even impossible. First, the tail is the part of the distribution for which we have the less empirical information available; second, a universally accepted definition of tail does not and cannot exist; and third, a tail may change over time due to long-term changes. Unfortunately, the tail is the most important part of the distribution as it dictates the estimates of exceedance probabilities or return periods. Fortunately, based on their tail behavior, probability distributions can be generally categorized into two major families, i.e., sub-exponentials (heavy-tailed) and hyper-exponentials (light-tailed). This study aims to update the Mean Excess Function (MEF), providing a useful tool in order to asses which type of tail better describes empirical data. The MEF is based on the mean value of a variable over a threshold and results in a zero slope regression line when applied for the Exponential distribution. Here, we construct slope confidence intervals for the Exponential distribution as functions of sample size. The validation of the method using Monte Carlo techniques on four theoretical distributions covering major tail cases (Pareto type II, Log-normal, Weibull and Gamma) revealed that it performs well especially for large samples. Finally, the method is used to investigate the behavior of daily rainfall extremes; thousands of rainfall records were examined, from all over the world and with sample size over 100 years, revealing that heavy-tailed distributions can describe more accurately rainfall extremes.

Development and growth of fruit bodies and crops of the button mushroom, Agaricus bisporus.

PubMed

Straatsma, Gerben; Sonnenberg, Anton S M; van Griensven, Leo J L D

2013-10-01

We studied the appearance of fruit body primordia, the growth of individual fruit bodies and the development of the consecutive flushes of the crop. Relative growth, measured as cap expansion, was not constant. It started extremely rapidly, and slowed down to an exponential rate with diameter doubling of 1.7 d until fruit bodies showed maturation by veil breaking. Initially many outgrowing primordia were arrested, indicating nutritional competition. After reaching 10 mm diameter, no growth arrest occurred; all growing individuals, whether relatively large or small, showed an exponential increase of both cap diameter and biomass, until veil breaking. Biomass doubled in 0.8 d. Exponential growth indicates the absence of competition. Apparently there exist differential nutritional requirements for early growth and for later, continuing growth. Flushing was studied applying different picking sizes. An ordinary flushing pattern occurred at an immature picking size of 8 mm diameter (picking mushrooms once a day with a diameter above 8 mm). The smallest picking size yielded the highest number of mushrooms picked, confirming the competition and arrested growth of outgrowing primordia: competition seems less if outgrowing primordia are removed early. The flush duration (i.e. between the first and last picking moments) was not affected by picking size. At small picking size, the subsequent flushes were not fully separated in time but overlapped. Within 2 d after picking the first individuals of the first flush, primordia for the second flush started outgrowth. Our work supports the view that the acquisition of nutrients by the mycelium is demand rather than supply driven. For formation and early outgrowth of primordia, indications were found for an alternation of local and global control, at least in the casing layer. All these data combined, we postulate that flushing is the consequence of the depletion of some unknown specific nutrition required by outgrowing primordia. Copyright © 2013 The British Mycological Society. Published by Elsevier Ltd. All rights reserved.

Necessary conditions for weighted mean convergence of Lagrange interpolation for exponential weights

NASA Astrophysics Data System (ADS)

Damelin, S. B.; Jung, H. S.; Kwon, K. H.

2001-07-01

Given a continuous real-valued function f which vanishes outside a fixed finite interval, we establish necessary conditions for weighted mean convergence of Lagrange interpolation for a general class of even weights w which are of exponential decay on the real line or at the endpoints of (-1,1).

Using Exponential Smoothing to Specify Intervention Models for Interrupted Time Series.

ERIC Educational Resources Information Center

Mandell, Marvin B.; Bretschneider, Stuart I.

1984-01-01

The authors demonstrate how exponential smoothing can play a role in the identification of the intervention component of an interrupted time-series design model that is analogous to the role that the sample autocorrelation and partial autocorrelation functions serve in the identification of the noise portion of such a model. (Author/BW)

Looking for Connections between Linear and Exponential Functions

ERIC Educational Resources Information Center

Lo, Jane-Jane; Kratky, James L.

2012-01-01

Students frequently have difficulty determining whether a given real-life situation is best modeled as a linear relationship or as an exponential relationship. One root of such difficulty is the lack of deep understanding of the very concept of "rate of change." The authors will provide a lesson that allows students to reveal their misconceptions…

Studies in Dialogue and Discourse: An Exponential Law of Successive Questioning

ERIC Educational Resources Information Center

Mishler, Elliot G.

1975-01-01

The structure of natural conversations in first-grade classrooms is the focus of this inquiry. Analyses of a particular type of discourse, namely, connected conversations initiated and sustained by questioning, suggest that the probability that a conversation will be continued may be expressed as a simple exponential function. (Author/RM)

Universal state-selective corrections to multireference coupled-cluster theories with single and double excitations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brabec, Jiri; van Dam, Hubertus JJ; Pittner, Jiri

2012-03-28

The recently proposed Universal State-Selective (USS) corrections [K. Kowalski, J. Chem. Phys. 134, 194107 (2011)] to approximate Multi-Reference Coupled Cluster (MRCC) energies can be commonly applied to any type of MRCC theory based on the Jeziorski-Monkhorst [B. Jeziorski, H.J. Monkhorst, Phys. Rev. A 24, 1668 (1981)] exponential Ansatz. In this letter we report on the performance of a simple USS correction to the Brillouin-Wigner MRCC (BW-MRCC) formalism employing single and double excitations (BW-MRCCSD). It is shown that the resulting formalism (USS-BW-MRCCSD), which uses the manifold of single and double excitations to construct the correction, can be related to a posteriorimore » corrections utilized in routine BW-MRCCSD calculations. In several benchmark calculations we compare the results of the USS-BW-MRCCSD method with results of the BW-MRCCSD approach employing a posteriori corrections and with results obtained with the Full Configuration Interaction (FCI) method.« less

Automatic selection of arterial input function using tri-exponential models

NASA Astrophysics Data System (ADS)

Yao, Jianhua; Chen, Jeremy; Castro, Marcelo; Thomasson, David

2009-02-01

Dynamic Contrast Enhanced MRI (DCE-MRI) is one method for drug and tumor assessment. Selecting a consistent arterial input function (AIF) is necessary to calculate tissue and tumor pharmacokinetic parameters in DCE-MRI. This paper presents an automatic and robust method to select the AIF. The first stage is artery detection and segmentation, where knowledge about artery structure and dynamic signal intensity temporal properties of DCE-MRI is employed. The second stage is AIF model fitting and selection. A tri-exponential model is fitted for every candidate AIF using the Levenberg-Marquardt method, and the best fitted AIF is selected. Our method has been applied in DCE-MRIs of four different body parts: breast, brain, liver and prostate. The success rates in artery segmentation for 19 cases are 89.6%+/-15.9%. The pharmacokinetic parameters computed from the automatically selected AIFs are highly correlated with those from manually determined AIFs (R2=0.946, P(T<=t)=0.09). Our imaging-based tri-exponential AIF model demonstrated significant improvement over a previously proposed bi-exponential model.

Fast and Accurate Fitting and Filtering of Noisy Exponentials in Legendre Space

PubMed Central

Bao, Guobin; Schild, Detlev

2014-01-01

The parameters of experimentally obtained exponentials are usually found by least-squares fitting methods. Essentially, this is done by minimizing the mean squares sum of the differences between the data, most often a function of time, and a parameter-defined model function. Here we delineate a novel method where the noisy data are represented and analyzed in the space of Legendre polynomials. This is advantageous in several respects. First, parameter retrieval in the Legendre domain is typically two orders of magnitude faster than direct fitting in the time domain. Second, data fitting in a low-dimensional Legendre space yields estimates for amplitudes and time constants which are, on the average, more precise compared to least-squares-fitting with equal weights in the time domain. Third, the Legendre analysis of two exponentials gives satisfactory estimates in parameter ranges where least-squares-fitting in the time domain typically fails. Finally, filtering exponentials in the domain of Legendre polynomials leads to marked noise removal without the phase shift characteristic for conventional lowpass filters. PMID:24603904

Multiserver Queueing Model subject to Single Exponential Vacation

NASA Astrophysics Data System (ADS)

Vijayashree, K. V.; Janani, B.

2018-04-01

A multi-server queueing model subject to single exponential vacation is considered. The arrivals are allowed to join the queue according to a Poisson distribution and services takes place according to an exponential distribution. Whenever the system becomes empty, all the servers goes for a vacation and returns back after a fixed interval of time. The servers then starts providing service if there are waiting customers otherwise they will wait to complete the busy period. The vacation times are also assumed to be exponentially distributed. In this paper, the stationary and transient probabilities for the number of customers during ideal and functional state of the server are obtained explicitly. Also, numerical illustrations are added to visualize the effect of various parameters.

Ciprofloxacin release using natural rubber latex membranes as carrier.

PubMed

Dias Murbach, Heitor; Jaques Ogawa, Guilherme; Azevedo Borges, Felipe; Romeiro Miranda, Matheus Carlos; Lopes, Rute; Roberto de Barros, Natan; Guedes Mazalli, Alexandre Vinicius; Gonçalves da Silva, Rosângela; Ferreira Cinman, José Luiz; de Camargo Drago, Bruno; Donizetti Herculano, Rondinelli

2014-01-01

Natural rubber latex (NRL) from Hevea brasiliensis is easily manipulated, low cost, is of can stimulate natural angiogenesis and cellular adhesion, is a biocompatible, material and presents high mechanical resistance. Ciprofloxacin (CIP) is a synthetic antibiotic (fluoroquinolone) used in the treatment of infection at external fixation screws sites and remote infections, and this use is increasingly frequent in medical practice. The aim of this study was to develop a novel sustained delivery system for CIP based on NRL membranes and to study its delivery system behavior. CIP was found to be adsorbed on the NRL membrane, according to results of energy dispersive X-ray spectroscopy. Results show that the membrane can release CIP for up to 59.08% in 312 hours and the mechanism is due to super case II (non-Fickian). The kinetics of the drug release could be fitted with double exponential function X-ray diffraction and Fourier transform infrared (FTIR) spectroscopy shows some interaction by hydrogen bound, which influences its mechanical behavior.

An organizational metamodel for hospital emergency departments.

PubMed

Kaptan, Kubilay

2014-10-01

I introduce an organizational model describing the response of the hospital emergency department. The hybrid simulation/analytical model (called a "metamodel") can estimate a hospital's capacity and dynamic response in real time and incorporate the influence of damage to structural and nonstructural components on the organizational ones. The waiting time is the main parameter of response and is used to evaluate the disaster resilience of health care facilities. Waiting time behavior is described by using a double exponential function and its parameters are calibrated based on simulated data. The metamodel covers a large range of hospital configurations and takes into account hospital resources in terms of staff and infrastructures, operational efficiency, and the possible existence of an emergency plan; maximum capacity; and behavior both in saturated and overcapacitated conditions. The sensitivity of the model to different arrival rates, hospital configurations, and capacities and the technical and organizational policies applied during and before a disaster were investigated. This model becomes an important tool in the decision process either for the engineering profession or for policy makers.

Role of exponential type random invexities for asymptotically sufficient efficiency conditions in semi-infinite multi-objective fractional programming.

PubMed

Verma, Ram U; Seol, Youngsoo

2016-01-01

First a new notion of the random exponential Hanson-Antczak type [Formula: see text]-V-invexity is introduced, which generalizes most of the existing notions in the literature, second a random function [Formula: see text] of the second order is defined, and finally a class of asymptotically sufficient efficiency conditions in semi-infinite multi-objective fractional programming is established. Furthermore, several sets of asymptotic sufficiency results in which various generalized exponential type [Formula: see text]-V-invexity assumptions are imposed on certain vector functions whose components are the individual as well as some combinations of the problem functions are examined and proved. To the best of our knowledge, all the established results on the semi-infinite aspects of the multi-objective fractional programming are new, which is a significantly new emerging field of the interdisciplinary research in nature. We also observed that the investigated results can be modified and applied to several special classes of nonlinear programming problems.

On E-discretization of tori of compact simple Lie groups. II

NASA Astrophysics Data System (ADS)

Hrivnák, Jiří; Juránek, Michal

2017-10-01

Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing one-dimensional cosine, sine, and exponential, each type of the Weyl orbit function represents an exponential symmetrized with respect to a subgroup of the Weyl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced, and all ten types of the corresponding discrete Hartley transforms are detailed.

Reduced Heme Levels Underlie the Exponential Growth Defect of the Shewanella oneidensis hfq Mutant

PubMed Central

Mezoian, Taylor; Hunt, Taylor M.; Keane, Meaghan L.; Leonard, Jessica N.; Scola, Shelby E.; Beer, Emma N.; Perdue, Sarah; Pellock, Brett J.

2014-01-01

The RNA chaperone Hfq fulfills important roles in small regulatory RNA (sRNA) function in many bacteria. Loss of Hfq in the dissimilatory metal reducing bacterium Shewanella oneidensis strain MR-1 results in slow exponential phase growth and a reduced terminal cell density at stationary phase. We have found that the exponential phase growth defect of the hfq mutant in LB is the result of reduced heme levels. Both heme levels and exponential phase growth of the hfq mutant can be completely restored by supplementing LB medium with 5-aminolevulinic acid (5-ALA), the first committed intermediate synthesized during heme synthesis. Increasing expression of gtrA, which encodes the enzyme that catalyzes the first step in heme biosynthesis, also restores heme levels and exponential phase growth of the hfq mutant. Taken together, our data indicate that reduced heme levels are responsible for the exponential growth defect of the S. oneidensis hfq mutant in LB medium and suggest that the S. oneidensis hfq mutant is deficient in heme production at the 5-ALA synthesis step. PMID:25356668

Exponential Boundary Observers for Pressurized Water Pipe

NASA Astrophysics Data System (ADS)

Hermine Som, Idellette Judith; Cocquempot, Vincent; Aitouche, Abdel

2015-11-01

This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.

Probability distribution functions for intermittent scrape-off layer plasma fluctuations

NASA Astrophysics Data System (ADS)

Theodorsen, A.; Garcia, O. E.

2018-03-01

A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common applications of the model, the pulse amplitudes are assumed exponentially distributed, supported by conditional averaging of large-amplitude fluctuations in experimental measurement data. This basic assumption has two potential limitations. First, statistical analysis of measurement data using conditional averaging only reveals the tail of the amplitude distribution to be exponentially distributed. Second, exponentially distributed amplitudes leads to a positive definite signal which cannot capture fluctuations in for example electric potential and radial velocity. Assuming pulse amplitudes which are not positive definite often make finding a closed form for the probability density function (PDF) difficult, even if the characteristic function remains relatively simple. Thus estimating model parameters requires an approach based on the characteristic function, not the PDF. In this contribution, the effect of changing the amplitude distribution on the moments, PDF and characteristic function of the process is investigated and a parameter estimation method using the empirical characteristic function is presented and tested on synthetically generated data. This proves valuable for describing intermittent fluctuations of all plasma parameters in the boundary region of magnetized plasmas.

Regulation of Hemopoietic Stem Cell Turnover and Population Size in Neonatal Mice

DTIC Science & Technology

1975-04-01

Following birth the hematopoietic stem cell population of the liver as measured by the in vivo spleen nodule assay (CFU) declines with a halving time...of about 48 hours. The stem cell population of the spleen grows exponentially with a doubling time of about 17 hours. In vitro incubation with high...single spleen colonies derived from neonatal liver and spleen CFU that both stem cell populations have a high self-renewal capacity. Thus, the decline in

Changing Mindsets to Transform Security: Leader Development for an Unpredictable and Complex World

DTIC Science & Technology

2013-01-01

fields of phys- ical science, the amount of information is doubling every one to two years, meaning that more than half of what a college student has...beyond a review of current events or it being at a “ informational ” level. Naval War College Professor Mackubin Owens stated in 2006, that, The new... information technology in education and training underpinned by a sta- ble and experienced academic community that can support the exponential growth

Extracting volatility signal using maximum a posteriori estimation

NASA Astrophysics Data System (ADS)

Neto, David

2016-11-01

This paper outlines a methodology to estimate a denoised volatility signal for foreign exchange rates using a hidden Markov model (HMM). For this purpose a maximum a posteriori (MAP) estimation is performed. A double exponential prior is used for the state variable (the log-volatility) in order to allow sharp jumps in realizations and then log-returns marginal distributions with heavy tails. We consider two routes to choose the regularization and we compare our MAP estimate to realized volatility measure for three exchange rates.

Clinical proteomics in kidney disease as an exponential technology: heading towards the disruptive phase.

PubMed

Sanchez-Niño, Maria Dolores; Sanz, Ana B; Ramos, Adrian M; Fernandez-Fernandez, Beatriz; Ortiz, Alberto

2017-04-01

Exponential technologies double in power or processing speed every year, whereas their cost halves. Deception and disruption are two key stages in the development of exponential technologies. Deception occurs when, after initial introduction, technologies are dismissed as irrelevant, while they continue to progress, perhaps not as fast or with so many immediate practical applications as initially thought. Twenty years after the first publications, clinical proteomics is still not available in most hospitals and some clinicians have felt deception at unfulfilled promises. However, there are indications that clinical proteomics may be entering the disruptive phase, where, once refined, technologies disrupt established industries or procedures. In this regard, recent manuscripts in CKJ illustrate how proteomics is entering the clinical realm, with applications ranging from the identification of amyloid proteins in the pathology lab, to a new generation of urinary biomarkers for chronic kidney disease (CKD) assessment and outcome prediction. Indeed, one such panel of urinary peptidomics biomarkers, CKD273, recently received a Food and Drug Administration letter of support, the first ever in the CKD field. In addition, a must-read resource providing information on kidney disease-related proteomics and systems biology databases and how to access and use them in clinical decision-making was also recently published in CKJ .

Prediction of Unsteady Aerodynamic Coefficients at High Angles of Attack

NASA Technical Reports Server (NTRS)

Pamadi, Bandu N.; Murphy, Patrick C.; Klein, Vladislav; Brandon, Jay M.

2001-01-01

The nonlinear indicial response method is used to model the unsteady aerodynamic coefficients in the low speed longitudinal oscillatory wind tunnel test data of the 0.1 scale model of the F-16XL aircraft. Exponential functions are used to approximate the deficiency function in the indicial response. Using one set of oscillatory wind tunnel data and parameter identification method, the unknown parameters in the exponential functions are estimated. The genetic algorithm is used as a least square minimizing algorithm. The assumed model structures and parameter estimates are validated by comparing the predictions with other sets of available oscillatory wind tunnel test data.

Basis convergence of range-separated density-functional theory.

PubMed

Franck, Odile; Mussard, Bastien; Luppi, Eleonora; Toulouse, Julien

2015-02-21

Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. We study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N2, and H2O) with cardinal number X of the Dunning basis sets cc - p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.

The Development of a High Speed Exponential Function Generator for Linearization of Microwave Voltage Controlled Oscillators.

DTIC Science & Technology

1985-10-01

characteristic of a p-n junction to provide exponential linearization in a simple, thermally-stable, wide band circuit. RESME Les oscillateurs A...exponentielle (fr6quence/tension) que V’on 1 retrouve chez plusieurs oscillateurs . Ce circuit, d’une grande largeur de bande, utilise la caractfiristique

Optimality of cycle time and inventory decisions in a two echelon inventory system with exponential price dependent demand under credit period

NASA Astrophysics Data System (ADS)

Krugon, Seelam; Nagaraju, Dega

2017-05-01

This work describes and proposes an two echelon inventory system under supply chain, where the manufacturer offers credit period to the retailer with exponential price dependent demand. The model is framed as demand is expressed as exponential function of retailer’s unit selling price. Mathematical model is framed to demonstrate the optimality of cycle time, retailer replenishment quantity, number of shipments, and total relevant cost of the supply chain. The major objective of the paper is to provide trade credit concept from the manufacturer to the retailer with exponential price dependent demand. The retailer would like to delay the payments of the manufacturer. At the first stage retailer and manufacturer expressions are expressed with the functions of ordering cost, carrying cost, transportation cost. In second stage combining of the manufacturer and retailer expressions are expressed. A MATLAB program is written to derive the optimality of cycle time, retailer replenishment quantity, number of shipments, and total relevant cost of the supply chain. From the optimality criteria derived managerial insights can be made. From the research findings, it is evident that the total cost of the supply chain is decreased with the increase in credit period under exponential price dependent demand. To analyse the influence of the model parameters, parametric analysis is also done by taking with help of numerical example.

Calcium Isotope Analysis with "Peak Cut" Method on Column Chemistry

NASA Astrophysics Data System (ADS)

Zhu, H.; Zhang, Z.; Liu, F.; Li, X.

2017-12-01

To eliminate isobaric interferences from elemental and molecular isobars (e.g., 40K+, 48Ti+, 88Sr2+, 24Mg16O+, 27Al16O+) on Ca isotopes during mass determination, samples should be purified through ion-exchange column chemistry before analysis. However, large Ca isotopic fractionation has been observed during column chemistry (Russell and Papanastassiou, 1978; Zhu et al., 2016). Therefore, full recovery during column chemistry is greatly needed, otherwise uncertainties would be caused by poor recovery (Zhu et al., 2016). Generally, matrix effects could be enhanced by full recovery, as other elements might overlap with Ca cut during column chemistry. Matrix effects and full recovery are difficult to balance and both need to be considered for high-precision analysis of stable Ca isotopes. Here, we investigate the influence of poor recovery on δ44/40Ca using TIMS with the double spike technique. The δ44/40Ca values of IAPSO seawater, ML3B-G and BHVO-2 in different Ca subcats (e.g., 0-20, 20-40, 40-60, 60-80, 80-100%) with 20% Ca recovery on column chemistry display limited variation after correction by the 42Ca-43Ca double spike technique with the exponential law. Notably, δ44/40Ca of each Ca subcut is quite consistent with δ44/40Ca of Ca cut with full recovery within error. Our results indicate that the 42Ca-43Ca double spike technique can simultaneously correct both of the Ca isotopic fractionation that occurred during column chemistry and thermal ionization mass spectrometry (TIMS) determination properly, because both of the isotopic fractionation occurred during analysis follow the exponential law well. Therefore, we propose the "peak cut" method on Ca column chemistry for samples with complex matrix effects. Briefly, for samples with low Ca contents, we can add the double spike before column chemistry, and only collect the middle of the Ca eluate and abandon the both sides of Ca eluate that might overlap with other elements (e.g., K, Sr). This method would eliminate matrix effects and improve efficiency for the column chemistry.

Synthesis, characterization and optical properties of NH4Dy(PO3)4

NASA Astrophysics Data System (ADS)

Chemingui, S.; Ferhi, M.; Horchani-Naifer, K.; Férid, M.

2014-09-01

Polycrystalline powders of NH4Dy(PO3)4 polyphosphate have been grown by the flux method. This compound was found to be isotopic with NH4Ce(PO3)4 and RbHo(PO3)4. It crystallizes in the monoclinic space group P21/n with unit cell parameters a=10.474(6) Å, b=9.011(4) Å, c=10.947(7) Å and β=106.64(3)°. The title compound has been transformed to triphosphate Dy(PO3)3 after calcination at 800 °C. Powder X-ray diffraction, infrared and Raman spectroscopies and the differential thermal analysis have been used to identify these materials. The spectroscopic properties have been investigated through absorption, excitation, emission spectra and decay curves of Dy3+ ion in both compounds at room temperature. The emission spectra show the characteristic emission bands of Dy3+ in the two compounds, before and after calcination. The integrated emission intensity ratios of the yellow to blue (IY/IB) transitions and the chromaticity properties have been determined from emission spectra. The decay curves are found to be double-exponential. The non-exponential behavior of the decay rates was related to the resonant energy transfer as well as cross-relaxation between the donor and acceptor Dy3+ ions. The determined properties have been discussed as function of crystal structure of both compounds. They reveal that NH4Dy(PO3)4 is promising for white light generation but Dy(PO3)3 is potential candidates in field emission display (FED) and plasma display panel (PDP) devices.

Transformations of the distribution of nuclei formed in a nucleation pulse: Interface-limited growth.

PubMed

Shneidman, Vitaly A

2009-10-28

A typical nucleation-growth process is considered: a system is quenched into a supersaturated state with a small critical radius r( *) (-) and is allowed to nucleate during a finite time interval t(n), after which the supersaturation is abruptly reduced to a fixed value with a larger critical radius r( *) (+). The size-distribution of nucleated particles f(r,t) further evolves due to their deterministic growth and decay for r larger or smaller than r( *) (+), respectively. A general analytic expressions for f(r,t) is obtained, and it is shown that after a large growth time t this distribution approaches an asymptotic shape determined by two dimensionless parameters, lambda related to t(n), and Lambda=r( *) (+)/r( *) (-). This shape is strongly asymmetric with an exponential and double-exponential cutoffs at small and large sizes, respectively, and with a broad near-flat top in case of a long pulse. Conversely, for a short pulse the distribution acquires a distinct maximum at r=r(max)(t) and approaches a universal shape exp[zeta-e(zeta)], with zeta proportional to r-r(max), independent of the pulse duration. General asymptotic predictions are examined in terms of Zeldovich-Frenkel nucleation model where the entire transient behavior can be described in terms of the Lambert W function. Modifications for the Turnbull-Fisher model are also considered, and analytics is compared with exact numerics. Results are expected to have direct implementations in analysis of two-step annealing crystallization experiments, although other applications might be anticipated due to universality of the nucleation pulse technique.

Surface properties and exponential stress relaxations of mammalian meibum films.

PubMed

Eftimov, Petar; Yokoi, Norihiko; Tonchev, Vesselin; Nencheva, Yana; Georgiev, Georgi As

2017-03-01

The surface properties of meibomian secretion (MGS), the major constituent of the tear film (TF) lipid layer, are of key importance for TF stability. The interfacial properties of canine, cMGS, and feline, fMGS, meibum films were studied using a Langmuir surface balance. These species were selected because they have blinking frequency and TF stability similar to those of humans. The sample's performance during dynamic area changes was evaluated by surface pressure (π)-area (A) isocycles and the layer structure was monitored with Brewster angle microscopy. The films' dilatational rheology was probed via the stress-relaxation technique. The animal MGS showed similar behavior both between each other and with human MGS (studied previously). They form reversible, non-collapsible, multilayer thick films. The relaxations of canine, feline, and human MGS films were well described by double exponential decay reflecting the presence of two processes: (1) fast elastic process, with characteristic time τ < 10 s and (2) slow viscous process, with τ > 100 s-emphasizing the meibum layers viscoelasticity. The temperature decrease from 35 to 25 °C resulted in decreased thickness and lateral expansion of all MGS layers accompanied with increase of the π/A hysteresis and of the elastic process contribution to π relaxation transients. Thus, MGS films of mammals with similar blinking frequency and TF stability have similar surface properties and stress relaxations unaltered by the interspecies MGS compositional variations. Such knowledge may impact the selection of animal mimics of human MGS and on a better understanding of lipid classes' impact on meibum functionality.

Rounded stretched exponential for time relaxation functions.

PubMed

Powles, J G; Heyes, D M; Rickayzen, G; Evans, W A B

2009-12-07

A rounded stretched exponential function is introduced, C(t)=exp{(tau(0)/tau(E))(beta)[1-(1+(t/tau(0))(2))(beta/2)]}, where t is time, and tau(0) and tau(E) are two relaxation times. This expression can be used to represent the relaxation function of many real dynamical processes, as at long times, t>tau(0), the function converges to a stretched exponential with normalizing relaxation time, tau(E), yet its expansion is even or symmetric in time, which is a statistical mechanical requirement. This expression fits well the shear stress relaxation function for model soft soft-sphere fluids near coexistence, with tau(E)

A nonstationary Poisson point process describes the sequence of action potentials over long time scales in lateral-superior-olive auditory neurons.

PubMed

Turcott, R G; Lowen, S B; Li, E; Johnson, D H; Tsuchitani, C; Teich, M C

1994-01-01

The behavior of lateral-superior-olive (LSO) auditory neurons over large time scales was investigated. Of particular interest was the determination as to whether LSO neurons exhibit the same type of fractal behavior as that observed in primary VIII-nerve auditory neurons. It has been suggested that this fractal behavior, apparent on long time scales, may play a role in optimally coding natural sounds. We found that a nonfractal model, the nonstationary dead-time-modified Poisson point process (DTMP), describes the LSO firing patterns well for time scales greater than a few tens of milliseconds, a region where the specific details of refractoriness are unimportant. The rate is given by the sum of two decaying exponential functions. The process is completely specified by the initial values and time constants of the two exponentials and by the dead-time relation. Specific measures of the firing patterns investigated were the interspike-interval (ISI) histogram, the Fano-factor time curve (FFC), and the serial count correlation coefficient (SCC) with the number of action potentials in successive counting times serving as the random variable. For all the data sets we examined, the latter portion of the recording was well approximated by a single exponential rate function since the initial exponential portion rapidly decreases to a negligible value. Analytical expressions available for the statistics of a DTMP with a single exponential rate function can therefore be used for this portion of the data. Good agreement was obtained among the analytical results, the computer simulation, and the experimental data on time scales where the details of refractoriness are insignificant.(ABSTRACT TRUNCATED AT 250 WORDS)

The impacts of precipitation amount simulation on hydrological modeling in Nordic watersheds

NASA Astrophysics Data System (ADS)

Li, Zhi; Brissette, Fancois; Chen, Jie

2013-04-01

Stochastic modeling of daily precipitation is very important for hydrological modeling, especially when no observed data are available. Precipitation is usually modeled by two component model: occurrence generation and amount simulation. For occurrence simulation, the most common method is the first-order two-state Markov chain due to its simplification and good performance. However, various probability distributions have been reported to simulate precipitation amount, and spatiotemporal differences exist in the applicability of different distribution models. Therefore, assessing the applicability of different distribution models is necessary in order to provide more accurate precipitation information. Six precipitation probability distributions (exponential, Gamma, Weibull, skewed normal, mixed exponential, and hybrid exponential/Pareto distributions) are directly and indirectly evaluated on their ability to reproduce the original observed time series of precipitation amount. Data from 24 weather stations and two watersheds (Chute-du-Diable and Yamaska watersheds) in the province of Quebec (Canada) are used for this assessment. Various indices or statistics, such as the mean, variance, frequency distribution and extreme values are used to quantify the performance in simulating the precipitation and discharge. Performance in reproducing key statistics of the precipitation time series is well correlated to the number of parameters of the distribution function, and the three-parameter precipitation models outperform the other models, with the mixed exponential distribution being the best at simulating daily precipitation. The advantage of using more complex precipitation distributions is not as clear-cut when the simulated time series are used to drive a hydrological model. While the advantage of using functions with more parameters is not nearly as obvious, the mixed exponential distribution appears nonetheless as the best candidate for hydrological modeling. The implications of choosing a distribution function with respect to hydrological modeling and climate change impact studies are also discussed.

Quantum mechanics of conformally and minimally coupled Friedmann-Robertson-Walker cosmology

NASA Astrophysics Data System (ADS)

Kim, Sang Pyo

1992-10-01

The expansion method by a time-dependent basis of the eigenfunctions for the space-coordinate-dependent sub-Hamiltonian is one of the most natural frameworks for quantum systems, relativistic as well as nonrelativistic. The complete set of wave functions is found in the product integral formulation, whose constants of integration are fixed by Cauchy initial data. The wave functions for the Friedmann-Robertson-Walker (FRW) cosmology conformally and minimally coupled to a scalar field with a power-law potential or a polynomial potential are expanded in terms of the eigenfunctions of the scalar field sub-Hamiltonian part. The resultant gravitational field part which is an ``intrinsic'' timelike variable-dependent matrix-valued differential equation is solved again in the product integral formulation. There are classically allowed regions for the ``intrinsic'' timelike variable depending on the scalar field quantum numbers and these regions increase accordingly as the quantum numbers increase. For a fixed large three-geometry the wave functions corresponding to the low excited (small quantum number) states of the scalar field are exponentially damped or diverging and the wave functions corresponding to the high excited (large quantum number) states are still oscillatory but become eventually exponential as the three-geometry becomes larger. Furthermore, a proposal is advanced that the wave functions exponentially damped for a large three-geometry may be interpreted as ``tunneling out'' wave functions into, and the wave functions exponentially diverging as ``tunneling in'' from, different universes with the same or different topologies, the former being interpreted as the recently proposed Hawking-Page wormhole wave functions. It is observed that there are complex as well as Euclidean actions depending on the quantum numbers of the scalar field part outside the classically allowed region both of the gravitational and scalar fields, suggesting the usefulness of complex geometry and complex trajectories. From the most general wave functions for the FRW cosmology conformally coupled to scalar field, the boundary conditions for the wormhole wave functions are modified so that the modulus of wave functions, instead of the wave functions themselves, should be exponentially damped for a large three-geometry and be regular up to some negative power of the three-geometry as the three-geometry collapses. The wave functions for the FRW cosmology minimally coupled to an inhomogeneous scalar field are similarly found in the product integral formulation. The role of a large number of the inhomogeneous modes of the scalar field is not only to increase the classically allowed regions for the gravitational part but also to provide a mechanism of the decoherence of quantum interferences between the different sizes of the universe.

Alphabet Soup

ERIC Educational Resources Information Center

Rebholz, Joachim A.

2017-01-01

Graphing functions is an important topic in algebra and precalculus high school courses. The functions that are usually discussed include polynomials, rational, exponential, and trigonometric functions along with their inverses. These functions can be used to teach different aspects of function theory: domain, range, monotonicity, inverse…

The luminosity function of quasars

NASA Technical Reports Server (NTRS)

Pei, Yichuan C.

1995-01-01

We propose a new evolutionary model for the optical luminosity function of quasars. Our analytical model is derived from fits to the empirical luminosity function estimated by Hartwick and Schade and Warren, Hewett, and Osmer on the basis of more than 1200 quasars over the range of redshifts 0 approximately less than z approximately less than 4.5. We find that the evolution of quasars over this entire redshift range can be well fitted by a Gaussian distribution, while the shape of the luminosity function can be well fitted by either a double power law or an exponential L(exp 1/4) law. The predicted number counts of quasars, as a function of either apparent magnitude or redshift, are fully consistent with the observed ones. Our model indicates that the evolution of quasars reaches its maximum at z approximately = 2.8 and declines at higher redshifts. An extrapolation of the evolution to z approximately greater than 4.5 implies that quasars may have started their cosmic fireworks at z(sub f) approximately = 5.2-5.5. Forthcoming surveys of quasars at these redshifts will be critical to constrain the epoch of quasar formation. All the results we derived are based on observed quasars and are therefore subject to the bias of obscuration by dust in damped Ly alpha systems. Future surveys of these absorption systems at z approximately greater than 3 will also be important if the formation epoch of quasars is to be known unambiguously.

Performance of mixed RF/FSO systems in exponentiated Weibull distributed channels

NASA Astrophysics Data System (ADS)

Zhao, Jing; Zhao, Shang-Hong; Zhao, Wei-Hu; Liu, Yun; Li, Xuan

2017-12-01

This paper presented the performances of asymmetric mixed radio frequency (RF)/free-space optical (FSO) system with the amplify-and-forward relaying scheme. The RF channel undergoes Nakagami- m channel, and the Exponentiated Weibull distribution is adopted for the FSO component. The mathematical formulas for cumulative distribution function (CDF), probability density function (PDF) and moment generating function (MGF) of equivalent signal-to-noise ratio (SNR) are achieved. According to the end-to-end statistical characteristics, the new analytical expressions of outage probability are obtained. Under various modulation techniques, we derive the average bit-error-rate (BER) based on the Meijer's G function. The evaluation and simulation are provided for the system performance, and the aperture average effect is discussed as well.

Concave utility, transaction costs, and risk in measuring discounting of delayed rewards.

PubMed

Kirby, Kris N; Santiesteban, Mariana

2003-01-01

Research has consistently found that the decline in the present values of delayed rewards as delay increases is better fit by hyperbolic than by exponential delay-discounting functions. However, concave utility, transaction costs, and risk each could produce hyperbolic-looking data, even when the underlying discounting function is exponential. In Experiments 1 (N = 45) and 2 (N = 103), participants placed bids indicating their present values of real future monetary rewards in computer-based 2nd-price auctions. Both experiments suggest that utility is not sufficiently concave to account for the superior fit of hyperbolic functions. Experiment 2 provided no evidence that the effects of transaction costs and risk are large enough to account for the superior fit of hyperbolic functions.

The many faces of the quantum Liouville exponentials

NASA Astrophysics Data System (ADS)

Gervais, Jean-Loup; Schnittger, Jens

1994-01-01

First, it is proven that the three main operator approaches to the quantum Liouville exponentials—that is the one of Gervais-Neveu (more recently developed further by Gervais), Braaten-Curtright-Ghandour-Thorn, and Otto-Weigt—are equivalent since they are related by simple basis transformations in the Fock space of the free field depending upon the zero-mode only. Second, the GN-G expressions for quantum Liouville exponentials, where the U q( sl(2)) quantum-group structure is manifest, are shown to be given by q-binomial sums over powers of the chiral fields in the J = {1}/{2} representation. Third, the Liouville exponentials are expressed as operator tau functions, whose chiral expansion exhibits a q Gauss decomposition, which is the direct quantum analogue of the classical solution of Leznov and Saveliev. It involves q exponentials of quantum-group generators with group "parameters" equal to chiral components of the quantum metric. Fourth, we point out that the OPE of the J = {1}/{2} Liouville exponential provides the quantum version of the Hirota bilinear equation.

Hydrodynamics-based functional forms of activity metabolism: a case for the power-law polynomial function in animal swimming energetics.

PubMed

Papadopoulos, Anthony

2009-01-01

The first-degree power-law polynomial function is frequently used to describe activity metabolism for steady swimming animals. This function has been used in hydrodynamics-based metabolic studies to evaluate important parameters of energetic costs, such as the standard metabolic rate and the drag power indices. In theory, however, the power-law polynomial function of any degree greater than one can be used to describe activity metabolism for steady swimming animals. In fact, activity metabolism has been described by the conventional exponential function and the cubic polynomial function, although only the power-law polynomial function models drag power since it conforms to hydrodynamic laws. Consequently, the first-degree power-law polynomial function yields incorrect parameter values of energetic costs if activity metabolism is governed by the power-law polynomial function of any degree greater than one. This issue is important in bioenergetics because correct comparisons of energetic costs among different steady swimming animals cannot be made unless the degree of the power-law polynomial function derives from activity metabolism. In other words, a hydrodynamics-based functional form of activity metabolism is a power-law polynomial function of any degree greater than or equal to one. Therefore, the degree of the power-law polynomial function should be treated as a parameter, not as a constant. This new treatment not only conforms to hydrodynamic laws, but also ensures correct comparisons of energetic costs among different steady swimming animals. Furthermore, the exponential power-law function, which is a new hydrodynamics-based functional form of activity metabolism, is a special case of the power-law polynomial function. Hence, the link between the hydrodynamics of steady swimming and the exponential-based metabolic model is defined.

Algebraic approach to electronic spectroscopy and dynamics.

PubMed

Toutounji, Mohamad

2008-04-28

Lie algebra, Zassenhaus, and parameter differentiation techniques are utilized to break up the exponential of a bilinear Hamiltonian operator into a product of noncommuting exponential operators by the virtue of the theory of Wei and Norman [J. Math. Phys. 4, 575 (1963); Proc. Am. Math. Soc., 15, 327 (1964)]. There are about three different ways to find the Zassenhaus exponents, namely, binomial expansion, Suzuki formula, and q-exponential transformation. A fourth, and most reliable method, is provided. Since linearly displaced and distorted (curvature change upon excitation/emission) Hamiltonian and spin-boson Hamiltonian may be classified as bilinear Hamiltonians, the presented algebraic algorithm (exponential operator disentanglement exploiting six-dimensional Lie algebra case) should be useful in spin-boson problems. The linearly displaced and distorted Hamiltonian exponential is only treated here. While the spin-boson model is used here only as a demonstration of the idea, the herein approach is more general and powerful than the specific example treated. The optical linear dipole moment correlation function is algebraically derived using the above mentioned methods and coherent states. Coherent states are eigenvectors of the bosonic lowering operator a and not of the raising operator a(+). While exp(a(+)) translates coherent states, exp(a(+)a(+)) operation on coherent states has always been a challenge, as a(+) has no eigenvectors. Three approaches, and the results, of that operation are provided. Linear absorption spectra are derived, calculated, and discussed. The linear dipole moment correlation function for the pure quadratic coupling case is expressed in terms of Legendre polynomials to better show the even vibronic transitions in the absorption spectrum. Comparison of the present line shapes to those calculated by other methods is provided. Franck-Condon factors for both linear and quadratic couplings are exactly accounted for by the herein calculated linear absorption spectra. This new methodology should easily pave the way to calculating the four-point correlation function, F(tau(1),tau(2),tau(3),tau(4)), of which the optical nonlinear response function may be procured, as evaluating F(tau(1),tau(2),tau(3),tau(4)) is only evaluating the optical linear dipole moment correlation function iteratively over different time intervals, which should allow calculating various optical nonlinear temporal/spectral signals.

Expanding pedestrian injury risk to the body region level: how to model passive safety systems in pedestrian injury risk functions.

PubMed

Niebuhr, Tobias; Junge, Mirko; Achmus, Stefanie

2015-01-01

Assessment of the effectiveness of advanced driver assistance systems (ADAS) plays a crucial role in accident research. A common way to evaluate the effectiveness of new systems is to determine the potentials for injury severity reduction. Because injury risk functions describe the probability of an injury of a given severity conditional on a technical accident severity (closing speed, delta V, barrier equivalent speed, etc.), they are predestined for such evaluations. Recent work has stated an approach on how to model the pedestrian injury risk in pedestrian-to-passenger car accidents as a family of functions. This approach gave explicit and easily interpretable formulae for the injury risk conditional on the closing speed of the car. These results are extended to injury risk functions for pedestrian body regions. Starting with a double-checked German In-depth Accident Study (GIDAS) pedestrian-to-car accident data set (N = 444) and a functional-anatomical definition of the body regions, investigations on the influence of specific body regions on the overall injury severity will be presented. As the measure of injury severity, the ISSx, a rescaled version of the well-known Injury Severity Score (ISS), was used. Though traditional ISS is computed by summation of the squares of the 3 most severe injured body regions, ISSx is computed by the summation of the exponentials of the Abbreviated Injury Scale (AIS) severities of the 3 most severely injured body regions. The exponentials used are scaled to fit the ISS range of values between 0 and 75. Three body regions (head/face/neck, thorax, hip/legs) clearly dominated abdominal and upper extremity injuries; that is, the latter 2 body regions had no influence at all on the overall injury risk over the range of technical accident severities. Thus, the ISSx is well described by use of the injury codes from the same body regions for any pedestrian injury severity. As a mathematical consequence, the ISSx becomes explicitly decomposable into the 3 body regions and so are the risk functions as body region-specific risk functions. The risk functions for each body region are stated explicitly for different injury severity levels and compared to the real-world accident data. The body region-specific risk functions can then be used to model the effect of improved passive safety systems. These modified body region-specific injury risk functions are aggregated to a new pedestrian injury risk function. Passive safety systems can therefore be modeled in injury risk functions for the first time. A short example on how the results can be used for assessing the effectiveness of new driver assistance systems concludes the article.

A Parametric Study of Fine-scale Turbulence Mixing Noise

NASA Technical Reports Server (NTRS)

Khavaran, Abbas; Bridges, James; Freund, Jonathan B.

2002-01-01

The present paper is a study of aerodynamic noise spectra from model functions that describe the source. The study is motivated by the need to improve the spectral shape of the MGBK jet noise prediction methodology at high frequency. The predicted spectral shape usually appears less broadband than measurements and faster decaying at high frequency. Theoretical representation of the source is based on Lilley's equation. Numerical simulations of high-speed subsonic jets as well as some recent turbulence measurements reveal a number of interesting statistical properties of turbulence correlation functions that may have a bearing on radiated noise. These studies indicate that an exponential spatial function may be a more appropriate representation of a two-point correlation compared to its Gaussian counterpart. The effect of source non-compactness on spectral shape is discussed. It is shown that source non-compactness could well be the differentiating factor between the Gaussian and exponential model functions. In particular, the fall-off of the noise spectra at high frequency is studied and it is shown that a non-compact source with an exponential model function results in a broader spectrum and better agreement with data. An alternate source model that represents the source as a covariance of the convective derivative of fine-scale turbulence kinetic energy is also examined.

Diagrammatic exponentiation for products of Wilson lines

NASA Astrophysics Data System (ADS)

Mitov, Alexander; Sterman, George; Sung, Ilmo

2010-11-01

We provide a recursive diagrammatic prescription for the exponentiation of gauge theory amplitudes involving products of Wilson lines and loops. This construction generalizes the concept of webs, originally developed for eikonal form factors and cross sections with two eikonal lines, to general soft functions in QCD and related gauge theories. Our coordinate space arguments apply to arbitrary paths for the lines.

Characterization of continuously distributed cortical water diffusion rates with a stretched-exponential model.

PubMed

Bennett, Kevin M; Schmainda, Kathleen M; Bennett, Raoqiong Tong; Rowe, Daniel B; Lu, Hanbing; Hyde, James S

2003-10-01

Experience with diffusion-weighted imaging (DWI) shows that signal attenuation is consistent with a multicompartmental theory of water diffusion in the brain. The source of this so-called nonexponential behavior is a topic of debate, because the cerebral cortex contains considerable microscopic heterogeneity and is therefore difficult to model. To account for this heterogeneity and understand its implications for current models of diffusion, a stretched-exponential function was developed to describe diffusion-related signal decay as a continuous distribution of sources decaying at different rates, with no assumptions made about the number of participating sources. DWI experiments were performed using a spin-echo diffusion-weighted pulse sequence with b-values of 500-6500 s/mm(2) in six rats. Signal attenuation curves were fit to a stretched-exponential function, and 20% of the voxels were better fit to the stretched-exponential model than to a biexponential model, even though the latter model had one more adjustable parameter. Based on the calculated intravoxel heterogeneity measure, the cerebral cortex contains considerable heterogeneity in diffusion. The use of a distributed diffusion coefficient (DDC) is suggested to measure mean intravoxel diffusion rates in the presence of such heterogeneity. Copyright 2003 Wiley-Liss, Inc.

Freezing of simple systems using density functional theory

NASA Astrophysics Data System (ADS)

de Kuijper, A.; Vos, W. L.; Barrat, J.-L.; Hansen, J.-P.; Schouten, J. A.

1990-10-01

Density functional theory (DFT) has been applied to the study of the fluid-solid transition in systems with realistic potentials (soft cores and attractive forces): the purely repulsive WCA Lennard-Jones reference potential (LJT), the full Lennard-Jones potential (LJ) and the exponential-6 potential appropriate for helium and hydrogen. Three different DFT formalisms were used: the formulation of Haymet and Oxtoby (HO) and the new theories of Denton and Ashcroft (MWDA) and of Baus (MELA). The results for the melting pressure are compared with recent simulation and experimental data. The results of the HO version are always too high, the deviation increasing when going from the repulsive Lennard-Jones to the exponential-6 potential of H2. The MWDA gives too low results for the repulsive Lennard-Jones potential. At low temperatures, it fails for the full LJ potential while at high temperatures it is in good agreement. Including the attraction as a mean-field correction gives good results also for low temperatures. The MWDA results are too high for the exponential-6 potentials. The MELA fails completely for the LJT potential and the hydrogen exponential-6 potential, since it does not give a stable solid phase.

Autoregressive processes with exponentially decaying probability distribution functions: applications to daily variations of a stock market index.

PubMed

Porto, Markus; Roman, H Eduardo

2002-04-01

We consider autoregressive conditional heteroskedasticity (ARCH) processes in which the variance sigma(2)(y) depends linearly on the absolute value of the random variable y as sigma(2)(y) = a+b absolute value of y. While for the standard model, where sigma(2)(y) = a + b y(2), the corresponding probability distribution function (PDF) P(y) decays as a power law for absolute value of y-->infinity, in the linear case it decays exponentially as P(y) approximately exp(-alpha absolute value of y), with alpha = 2/b. We extend these results to the more general case sigma(2)(y) = a+b absolute value of y(q), with 0 < q < 2. We find stretched exponential decay for 1 < q < 2 and stretched Gaussian behavior for 0 < q < 1. As an application, we consider the case q=1 as our starting scheme for modeling the PDF of daily (logarithmic) variations in the Dow Jones stock market index. When the history of the ARCH process is taken into account, the resulting PDF becomes a stretched exponential even for q = 1, with a stretched exponent beta = 2/3, in a much better agreement with the empirical data.

Statistical modeling of storm-level Kp occurrences

USGS Publications Warehouse

Remick, K.J.; Love, J.J.

2006-01-01

We consider the statistical modeling of the occurrence in time of large Kp magnetic storms as a Poisson process, testing whether or not relatively rare, large Kp events can be considered to arise from a stochastic, sequential, and memoryless process. For a Poisson process, the wait times between successive events occur statistically with an exponential density function. Fitting an exponential function to the durations between successive large Kp events forms the basis of our analysis. Defining these wait times by calculating the differences between times when Kp exceeds a certain value, such as Kp ??? 5, we find the wait-time distribution is not exponential. Because large storms often have several periods with large Kp values, their occurrence in time is not memoryless; short duration wait times are not independent of each other and are often clumped together in time. If we remove same-storm large Kp occurrences, the resulting wait times are very nearly exponentially distributed and the storm arrival process can be characterized as Poisson. Fittings are performed on wait time data for Kp ??? 5, 6, 7, and 8. The mean wait times between storms exceeding such Kp thresholds are 7.12, 16.55, 42.22, and 121.40 days respectively.

Electrostatic screening in classical Coulomb fluids: exponential or power-law decay or both? An investigation into the effect of dispersion interactions

NASA Astrophysics Data System (ADS)

Kjellander, Roland

2006-04-01

It is shown that the nature of the non-electrostatic part of the pair interaction potential in classical Coulomb fluids can have a profound influence on the screening behaviour. Two cases are compared: (i) when the non-electrostatic part equals an arbitrary finite-ranged interaction and (ii) when a dispersion r-6 interaction potential is included. A formal analysis is done in exact statistical mechanics, including an investigation of the bridge function. It is found that the Coulombic r-1 and the dispersion r-6 potentials are coupled in a very intricate manner as regards the screening behaviour. The classical one-component plasma (OCP) is a particularly clear example due to its simplicity and is investigated in detail. When the dispersion r-6 potential is turned on, the screened electrostatic potential from a particle goes from a monotonic exponential decay, exp(-κr)/r, to a power-law decay, r-8, for large r. The pair distribution function acquire, at the same time, an r-10 decay for large r instead of the exponential one. There still remains exponentially decaying contributions to both functions, but these contributions turn oscillatory when the r-6 interaction is switched on. When the Coulomb interaction is turned off but the dispersion r-6 pair potential is kept, the decay of the pair distribution function for large r goes over from the r-10 to an r-6 behaviour, which is the normal one for fluids of electroneutral particles with dispersion interactions. Differences and similarities compared to binary electrolytes are pointed out.

Investigation of hyperelastic models for nonlinear elastic behavior of demineralized and deproteinized bovine cortical femur bone.

PubMed

Hosseinzadeh, M; Ghoreishi, M; Narooei, K

2016-06-01

In this study, the hyperelastic models of demineralized and deproteinized bovine cortical femur bone were investigated and appropriate models were developed. Using uniaxial compression test data, the strain energy versus stretch was calculated and the appropriate hyperelastic strain energy functions were fitted on data in order to calculate the material parameters. To obtain the mechanical behavior in other loading conditions, the hyperelastic strain energy equations were investigated for pure shear and equi-biaxial tension loadings. The results showed the Mooney-Rivlin and Ogden models cannot predict the mechanical response of demineralized and deproteinized bovine cortical femur bone accurately, while the general exponential-exponential and general exponential-power law models have a good agreement with the experimental results. To investigate the sensitivity of the hyperelastic models, a variation of 10% in material parameters was performed and the results indicated an acceptable stability for the general exponential-exponential and general exponential-power law models. Finally, the uniaxial tension and compression of cortical femur bone were studied using the finite element method in VUMAT user subroutine of ABAQUS software and the computed stress-stretch curves were shown a good agreement with the experimental data. Copyright © 2016 Elsevier Ltd. All rights reserved.

Alternative analytical forms to model diatomic systems based on the deformed exponential function.

PubMed

da Fonsêca, José Erinaldo; de Oliveira, Heibbe Cristhian B; da Cunha, Wiliam Ferreira; Gargano, Ricardo

2014-07-01

Using a deformed exponential function and the molecular-orbital theory for the simplest molecular ion, two new analytical functions are proposed to represent the potential energy of ground-state diatomic systems. The quality of these new forms was tested by fitting the ab initio electronic energies of the system LiH, LiNa, NaH, RbH, KH, H2, Li2, K2, H 2 (+) , BeH(+) and Li 2 (+) . From these fits, it was verified that these new proposals are able to adequately describe homonuclear, heteronuclear and cationic diatomic systems with good accuracy. Vibrational spectroscopic constant results obtained from these two proposals are in good agreement with experimental data.

A study on some urban bus transport networks

NASA Astrophysics Data System (ADS)

Chen, Yong-Zhou; Li, Nan; He, Da-Ren

2007-03-01

In this paper, we present the empirical investigation results on the urban bus transport networks (BTNs) of four major cities in China. In BTN, nodes are bus stops. Two nodes are connected by an edge when the stops are serviced by a common bus route. The empirical results show that the degree distributions of BTNs take exponential function forms. Other two statistical properties of BTNs are also considered, and they are suggested as the distributions of so-called “the number of stops in a bus route” (represented by S) and “the number of bus routes a stop joins” (by R). The distributions of R also show exponential function forms, while the distributions of S follow asymmetric, unimodal functions. To explain these empirical results and attempt to simulate a possible evolution process of BTN, we introduce a model by which the analytic and numerical result obtained agrees well with the empirical facts. Finally, we also discuss some other possible evolution cases, where the degree distribution shows a power law or an interpolation between the power law and the exponential decay.

Effect of exponential density transition on self-focusing of q-Gaussian laser beam in collisionless plasma

NASA Astrophysics Data System (ADS)

Valkunde, Amol T.; Vhanmore, Bandopant D.; Urunkar, Trupti U.; Gavade, Kusum M.; Patil, Sandip D.; Takale, Mansing V.

2018-05-01

In this work, nonlinear aspects of a high intensity q-Gaussian laser beam propagating in collisionless plasma having upward density ramp of exponential profiles is studied. We have employed the nonlinearity in dielectric function of plasma by considering ponderomotive nonlinearity. The differential equation governing the dimensionless beam width parameter is achieved by using Wentzel-Kramers-Brillouin (WKB) and paraxial approximations and solved it numerically by using Runge-Kutta fourth order method. Effect of exponential density ramp profile on self-focusing of q-Gaussian laser beam for various values of q is systematically carried out and compared with results Gaussian laser beam propagating in collisionless plasma having uniform density. It is found that exponential plasma density ramp causes the laser beam to become more focused and gives reasonably interesting results.

Compressed exponential relaxation in liquid silicon: Universal feature of the crossover from ballistic to diffusive behavior in single-particle dynamics

NASA Astrophysics Data System (ADS)

Morishita, Tetsuya

2012-07-01

We report a first-principles molecular-dynamics study of the relaxation dynamics in liquid silicon (l-Si) over a wide temperature range (1000-2200 K). We find that the intermediate scattering function for l-Si exhibits a compressed exponential decay above 1200 K including the supercooled regime, which is in stark contrast to that for normal "dense" liquids which typically show stretched exponential decay in the supercooled regime. The coexistence of particles having ballistic-like motion and those having diffusive-like motion is demonstrated, which accounts for the compressed exponential decay in l-Si. An attempt to elucidate the crossover from the ballistic to the diffusive regime in the "time-dependent" diffusion coefficient is made and the temperature-independent universal feature of the crossover is disclosed.

Taming the runaway problem of inflationary landscapes

NASA Astrophysics Data System (ADS)

Hall, Lawrence J.; Watari, Taizan; Yanagida, T. T.

2006-05-01

A wide variety of vacua, and their cosmological realization, may provide an explanation for the apparently anthropic choices of some parameters of particle physics and cosmology. If the probability on various parameters is weighted by volume, a flat potential for slow-roll inflation is also naturally understood, since the flatter the potential the larger the volume of the subuniverse. However, such inflationary landscapes have a serious problem, predicting an environment that makes it exponentially hard for observers to exist and giving an exponentially small probability for a moderate universe like ours. A general solution to this problem is proposed, and is illustrated in the context of inflaton decay and leptogenesis, leading to an upper bound on the reheating temperature in our subuniverse. In a particular scenario of chaotic inflation and nonthermal leptogenesis, predictions can be made for the size of CP violating phases, the rate of neutrinoless double beta decay and, in the case of theories with gauge-mediated weak-scale supersymmetry, for the fundamental scale of supersymmetry breaking.

An improved cyan fluorescent protein variant useful for FRET.

PubMed

Rizzo, Mark A; Springer, Gerald H; Granada, Butch; Piston, David W

2004-04-01

Many genetically encoded biosensors use Förster resonance energy transfer (FRET) between fluorescent proteins to report biochemical phenomena in living cells. Most commonly, the enhanced cyan fluorescent protein (ECFP) is used as the donor fluorophore, coupled with one of several yellow fluorescent protein (YFP) variants as the acceptor. ECFP is used despite several spectroscopic disadvantages, namely a low quantum yield, a low extinction coefficient and a fluorescence lifetime that is best fit by a double exponential. To improve the characteristics of ECFP for FRET measurements, we used a site-directed mutagenesis approach to overcome these disadvantages. The resulting variant, which we named Cerulean (ECFP/S72A/Y145A/H148D), has a greatly improved quantum yield, a higher extinction coefficient and a fluorescence lifetime that is best fit by a single exponential. Cerulean is 2.5-fold brighter than ECFP and replacement of ECFP with Cerulean substantially improves the signal-to-noise ratio of a FRET-based sensor for glucokinase activation.

{phi} meson production in Au + Au and p + p collisions at {radical}s{sub NN}=200 GeV

DOE Office of Scientific and Technical Information (OSTI.GOV)

Adams, J.; Adler, C.; Aggarwal, M.M.

2004-06-01

We report the STAR measurement of {psi} meson production in Au + Au and p + p collisions at {radical}s{sub NN} = 200 GeV. Using the event mixing technique, the {psi} spectra and yields are obtained at midrapidity for five centrality bins in Au+Au collisions and for non-singly-diffractive p+p collisions. It is found that the {psi} transverse momentum distributions from Au+Au collisions are better fitted with a single-exponential while the p+p spectrum is better described by a double-exponential distribution. The measured nuclear modification factors indicate that {psi} production in central Au+Au collisions is suppressed relative to peripheral collisions when scaledmore » by the number of binary collisions (). The systematics of versus centrality and the constant {psi}/K{sup -} ratio versus beam species, centrality, and collision energy rule out kaon coalescence as the dominant mechanism for {psi} production.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rout, Dipak; Vijaya, R.; Centre for Lasers and Photonics, Indian Institute of Technology Kanpur, Kanpur 208016

Well-ordered opaline photonic crystals are grown by inward growing self-assembly method from Rhodamine B dye-doped polystyrene colloids. Subsequent to self-assembly, the crystals are infiltrated with gold nanoparticles of 40 nm diameter. Measurements of the stopband features and photoluminescence intensity from these crystals are supplemented by fluorescence decay time analysis. The fluorescence decay times from the dye-doped photonic crystals before and after the infiltration are dramatically different from each other. A lowered fluorescence decay time was observed for the case of gold infiltrated crystal along with an enhanced emission intensity. Double-exponential decay nature of the fluorescence from the dye-doped crystal gets convertedmore » into single-exponential decay upon the infiltration of gold nanoparticles due to the resonant radiative process resulting from the overlap of the surface plasmon resonance with the emission spectrum. The influence of localized surface plasmon due to gold nanoparticles on the increase in emission intensity and decrease in decay time of the emitters is established.« less

Building an Understanding of Functions: A Series of Activities for Pre-Calculus

ERIC Educational Resources Information Center

Carducci, Olivia M.

2008-01-01

Building block toys can be used to illustrate various concepts connected with functions including graphs and rates of change of linear and exponential functions, piecewise functions, and composition of functions. Five brief activities suitable for a pre-calculus course are described.

Basis convergence of range-separated density-functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Franck, Odile, E-mail: odile.franck@etu.upmc.fr; Mussard, Bastien, E-mail: bastien.mussard@upmc.fr; CNRS, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris

2015-02-21

Range-separated density-functional theory (DFT) is an alternative approach to Kohn-Sham density-functional theory. The strategy of range-separated density-functional theory consists in separating the Coulomb electron-electron interaction into long-range and short-range components and treating the long-range part by an explicit many-body wave-function method and the short-range part by a density-functional approximation. Among the advantages of using many-body methods for the long-range part of the electron-electron interaction is that they are much less sensitive to the one-electron atomic basis compared to the case of the standard Coulomb interaction. Here, we provide a detailed study of the basis convergence of range-separated density-functional theory. Wemore » study the convergence of the partial-wave expansion of the long-range wave function near the electron-electron coalescence. We show that the rate of convergence is exponential with respect to the maximal angular momentum L for the long-range wave function, whereas it is polynomial for the case of the Coulomb interaction. We also study the convergence of the long-range second-order Møller-Plesset correlation energy of four systems (He, Ne, N{sub 2}, and H{sub 2}O) with cardinal number X of the Dunning basis sets cc − p(C)V XZ and find that the error in the correlation energy is best fitted by an exponential in X. This leads us to propose a three-point complete-basis-set extrapolation scheme for range-separated density-functional theory based on an exponential formula.« less

Mechanical analysis of non-uniform bi-directional functionally graded intelligent micro-beams using modified couple stress theory

NASA Astrophysics Data System (ADS)

Bakhshi Khaniki, Hossein; Rajasekaran, Sundaramoorthy

2018-05-01

This study develops a comprehensive investigation on mechanical behavior of non-uniform bi-directional functionally graded beam sensors in the framework of modified couple stress theory. Material variation is modelled through both length and thickness directions using power-law, sigmoid and exponential functions. Moreover, beam is assumed with linear, exponential and parabolic cross-section variation through the length using power-law and sigmoid varying functions. Using these assumptions, a general model for microbeams is presented and formulated by employing Hamilton’s principle. Governing equations are solved using a mixed finite element method with Lagrangian interpolation technique, Gaussian quadrature method and Wilson’s Lagrangian multiplier method. It is shown that by using bi-directional functionally graded materials in nonuniform microbeams, mechanical behavior of such structures could be affected noticeably and scale parameter has a significant effect in changing the rigidity of nonuniform bi-directional functionally graded beams.

Count distribution for mixture of two exponentials as renewal process duration with applications

NASA Astrophysics Data System (ADS)

Low, Yeh Ching; Ong, Seng Huat

2016-06-01

A count distribution is presented by considering a renewal process where the distribution of the duration is a finite mixture of exponential distributions. This distribution is able to model over dispersion, a feature often found in observed count data. The computation of the probabilities and renewal function (expected number of renewals) are examined. Parameter estimation by the method of maximum likelihood is considered with applications of the count distribution to real frequency count data exhibiting over dispersion. It is shown that the mixture of exponentials count distribution fits over dispersed data better than the Poisson process and serves as an alternative to the gamma count distribution.

Determination of the functioning parameters in asymmetrical flow field-flow fractionation with an exponential channel.

PubMed

Déjardin, P

2013-08-30

The flow conditions in normal mode asymmetric flow field-flow fractionation are determined to approach the high retention limit with the requirement d≪l≪w, where d is the particle diameter, l the characteristic length of the sample exponential distribution and w the channel height. The optimal entrance velocity is determined from the solute characteristics, the channel geometry (exponential to rectangular) and the membrane properties, according to a model providing the velocity fields all over the cell length. In addition, a method is proposed for in situ determination of the channel height. Copyright © 2013 Elsevier B.V. All rights reserved.

Global exponential stability analysis on impulsive BAM neural networks with distributed delays

NASA Astrophysics Data System (ADS)

Li, Yao-Tang; Yang, Chang-Bo

2006-12-01

Using M-matrix and topological degree tool, sufficient conditions are obtained for the existence, uniqueness and global exponential stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with distributed delays and subjected to impulsive state displacements at fixed instants of time by constructing a suitable Lyapunov functional. The results remove the usual assumptions that the boundedness, monotonicity, and differentiability of the activation functions. It is shown that in some cases, the stability criteria can be easily checked. Finally, an illustrative example is given to show the effectiveness of the presented criteria.

Power law versus exponential state transition dynamics: application to sleep-wake architecture.

PubMed

Chu-Shore, Jesse; Westover, M Brandon; Bianchi, Matt T

2010-12-02

Despite the common experience that interrupted sleep has a negative impact on waking function, the features of human sleep-wake architecture that best distinguish sleep continuity versus fragmentation remain elusive. In this regard, there is growing interest in characterizing sleep architecture using models of the temporal dynamics of sleep-wake stage transitions. In humans and other mammals, the state transitions defining sleep and wake bout durations have been described with exponential and power law models, respectively. However, sleep-wake stage distributions are often complex, and distinguishing between exponential and power law processes is not always straightforward. Although mono-exponential distributions are distinct from power law distributions, multi-exponential distributions may in fact resemble power laws by appearing linear on a log-log plot. To characterize the parameters that may allow these distributions to mimic one another, we systematically fitted multi-exponential-generated distributions with a power law model, and power law-generated distributions with multi-exponential models. We used the Kolmogorov-Smirnov method to investigate goodness of fit for the "incorrect" model over a range of parameters. The "zone of mimicry" of parameters that increased the risk of mistakenly accepting power law fitting resembled empiric time constants obtained in human sleep and wake bout distributions. Recognizing this uncertainty in model distinction impacts interpretation of transition dynamics (self-organizing versus probabilistic), and the generation of predictive models for clinical classification of normal and pathological sleep architecture.

Human (13)N-ammonia PET studies: the importance of measuring (13)N-ammonia metabolites in blood.

PubMed

Keiding, Susanne; Sørensen, Michael; Munk, Ole Lajord; Bender, Dirk

2010-03-01

Dynamic (13)N-ammonia PET is used to assess ammonia metabolism in brain, liver and muscle based on kinetic modeling of metabolic pathways, using arterial blood (13)N-ammonia as input function. Rosenspire et al. (1990) introduced a solid phase extraction procedure for fractionation of (13)N-content in blood into (13)N-ammonia, (13)N-urea, (13)N-glutamine and (13)N-glutamate. Due to a radioactive half-life for (13)N of 10 min, the procedure is not suitable for blood samples taken beyond 5-7 min after tracer injection. By modifying Rosenspire's method, we established a method enabling analysis of up to 10 blood samples in the course of 30 min. The modified procedure was validated by HPLC and by 30-min reproducibility studies in humans examined by duplicate (13)N-ammonia injections with a 60-min interval. Blood data from a (13)N-ammonia brain PET study (from Keiding et al. 2006) showed: (1) time courses of (13)N-ammonia fractions could be described adequately by double exponential functions; (2) metabolic conversion of (13)N-ammonia to (13)N-metabolites were in the order: healthy subjects > cirrhotic patients without HE > cirrhotic patients with HE; (3) kinetics of initial tracer distribution in tissue can be assessed by using total (13)N-concentration in blood as input function, whereas assessment of metabolic processes requires (13)N-ammonia measurements.

Growth and differentiation of human lens epithelial cells in vitro on matrix

NASA Technical Reports Server (NTRS)

Blakely, E. A.; Bjornstad, K. A.; Chang, P. Y.; McNamara, M. P.; Chang, E.; Aragon, G.; Lin, S. P.; Lui, G.; Polansky, J. R.

2000-01-01

PURPOSE: To characterize the growth and maturation of nonimmortalized human lens epithelial (HLE) cells grown in vitro. METHODS: HLE cells, established from 18-week prenatal lenses, were maintained on bovine corneal endothelial (BCE) extracellular matrix (ECM) in medium supplemented with basic fibroblast growth factor (FGF-2). The identity, growth, and differentiation of the cultures were characterized by karyotyping, cell morphology, and growth kinetics studies, reverse transcription-polymerase chain reaction (RT-PCR), immunofluorescence, and Western blot analysis. RESULTS: HLE cells had a male, human diploid (2N = 46) karyotype. The population-doubling time of exponentially growing cells was 24 hours. After 15 days in culture, cell morphology changed, and lentoid formation was evident. Reverse transcription-polymerase chain reaction (RT-PCR) indicated expression of alphaA- and betaB2-crystallin, fibroblast growth factor receptor 1 (FGFR1), and major intrinsic protein (MIP26) in exponential growth. Western analyses of protein extracts show positive expression of three immunologically distinct classes of crystallin proteins (alphaA-, alphaB-, and betaB2-crystallin) with time in culture. By Western blot analysis, expression of p57(KIP2), a known marker of terminally differentiated fiber cells, was detectable in exponential cultures, and levels increased after confluence. MIP26 and gamma-crystallin protein expression was detected in confluent cultures, by using immunofluorescence, but not in exponentially growing cells. CONCLUSIONS: HLE cells can be maintained for up to 4 months on ECM derived from BCE cells in medium containing FGF-2. With time in culture, the cells demonstrate morphologic characteristics of, and express protein markers for, lens fiber cell differentiation. This in vitro model will be useful for investigations of radiation-induced cataractogenesis and other studies of lens toxicity.

On the origin of non-exponential fluorescence decays in enzyme-ligand complex

NASA Astrophysics Data System (ADS)

Wlodarczyk, Jakub; Kierdaszuk, Borys

2004-05-01

Complex fluorescence decays have usually been analyzed with the aid of a multi-exponential model, but interpretation of the individual exponential terms has not been adequately characterized. In such cases the intensity decays were also analyzed in terms of the continuous lifetime distribution as a consequence of an interaction of fluorophore with environment, conformational heterogeneity or their dynamical nature. We show that non-exponential fluorescence decay of the enzyme-ligand complexes may results from time dependent energy transport. The latter, to our opinion, may be accounted for by electron transport from the protein tyrosines to their neighbor residues. We introduce the time-dependent hopping rate in the form v(t)~(a+bt)-1. This in turn leads to the luminescence decay function in the form I(t)=Ioexp(-t/τ1)(1+lt/γτ2)-γ. Such a decay function provides good fits to highly complex fluorescence decays. The power-like tail implies the time hierarchy in migration energy process due to the hierarchical energy-level structure. Moreover, such a power-like term is a manifestation of so called Tsallis nonextensive statistic and is suitable for description of the systems with long-range interactions, memory effect as well as with fluctuations of characteristic lifetime of fluorescence. The proposed decay function was applied in analysis of fluorescence decays of tyrosine protein, i.e. the enzyme purine nucleoside phosphorylase from E. coli in a complex with formycin A (an inhibitor) and orthophosphate (a co-substrate).

Demand forecasting of electricity in Indonesia with limited historical data

NASA Astrophysics Data System (ADS)

Dwi Kartikasari, Mujiati; Rohmad Prayogi, Arif

2018-03-01

Demand forecasting of electricity is an important activity for electrical agents to know the description of electricity demand in future. Prediction of demand electricity can be done using time series models. In this paper, double moving average model, Holt’s exponential smoothing model, and grey model GM(1,1) are used to predict electricity demand in Indonesia under the condition of limited historical data. The result shows that grey model GM(1,1) has the smallest value of MAE (mean absolute error), MSE (mean squared error), and MAPE (mean absolute percentage error).

Milne, a routine for the numerical solution of Milne's problem

NASA Astrophysics Data System (ADS)

Rawat, Ajay; Mohankumar, N.

2010-11-01

The routine Milne provides accurate numerical values for the classical Milne's problem of neutron transport for the planar one speed and isotropic scattering case. The solution is based on the Case eigen-function formalism. The relevant X functions are evaluated accurately by the Double Exponential quadrature. The calculated quantities are the extrapolation distance and the scalar and the angular fluxes. Also, the H function needed in astrophysical calculations is evaluated as a byproduct. Program summaryProgram title: Milne Catalogue identifier: AEGS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 701 No. of bytes in distributed program, including test data, etc.: 6845 Distribution format: tar.gz Programming language: Fortran 77 Computer: PC under Linux or Windows Operating system: Ubuntu 8.04 (Kernel version 2.6.24-16-generic), Windows-XP Classification: 4.11, 21.1, 21.2 Nature of problem: The X functions are integral expressions. The convergence of these regular and Cauchy Principal Value integrals are impaired by the singularities of the integrand in the complex plane. The DE quadrature scheme tackles these singularities in a robust manner compared to the standard Gauss quadrature. Running time: The test included in the distribution takes a few seconds to run.

Dpf Analyses Yield Fully Analytic Potentials for the B ^1Πu ``BARRIER'' States of {Rb}_2 and {Li}_2 and AN Improved Ground-State Well Depth for {Rb}_2

NASA Astrophysics Data System (ADS)

Slaughter, Kai; Dattani, Nikesh S.; Amiot, Claude S.; Ross, Amanda J.; Le Roy, Robert J.

2015-06-01

Determining full model potential energy functions for molecular states that have a `natural' rotationless barrier which protrudes above the potential asymptote, such as the B ^1Π_u states of alkali dimers, is a challenging problem. The present work extends our previous Direct-Potential-Fit (DPF) analysis of data for the B ^1Π_u state of Li_2 by introducing a more sophisticated model for the long-range tail of the fully analytic `Double Exponential Long-Range' (DELR) potential function form^a that takes account of the interstate coupling that occurs near the asymptotes of nS+nP alkali dimers. This type of analysis is then applied to data for the B ^1Π_u state of Rb_2, and a concurrent extension of the DPF analysis of Seto and Le Roy yields an improved fully analytic potential energy function for its ground X ^1σ_g^+ state. The effect of taking account of the long-range inter-state coupling on the shapes of the outer walls of the B ^1Π_u state potential functions for these two species will also be examined. Y. Huang and R.J. Le Roy, J. Chem. Phys., 119, 7398 (2003) M. Aubert-Frécon and G. Hadinger and S. Magnier and S. Rousseau, J. Mol. Spectosc., 288, 182 (1998). J.Y. Seto and R.J. Le Roy, J. Chem. Phys., 113, 3067 (2000).

Temporal and spatial binning of TCSPC data to improve signal-to-noise ratio and imaging speed

NASA Astrophysics Data System (ADS)

Walsh, Alex J.; Beier, Hope T.

2016-03-01

Time-correlated single photon counting (TCSPC) is the most robust method for fluorescence lifetime imaging using laser scanning microscopes. However, TCSPC is inherently slow making it ineffective to capture rapid events due to the single photon product per laser pulse causing extensive acquisition time limitations and the requirement of low fluorescence emission efficiency to avoid bias of measurement towards short lifetimes. Furthermore, thousands of photons per pixel are required for traditional instrument response deconvolution and fluorescence lifetime exponential decay estimation. Instrument response deconvolution and fluorescence exponential decay estimation can be performed in several ways including iterative least squares minimization and Laguerre deconvolution. This paper compares the limitations and accuracy of these fluorescence decay analysis techniques to accurately estimate double exponential decays across many data characteristics including various lifetime values, lifetime component weights, signal-to-noise ratios, and number of photons detected. Furthermore, techniques to improve data fitting, including binning data temporally and spatially, are evaluated as methods to improve decay fits and reduce image acquisition time. Simulation results demonstrate that binning temporally to 36 or 42 time bins, improves accuracy of fits for low photon count data. Such a technique reduces the required number of photons for accurate component estimation if lifetime values are known, such as for commercial fluorescent dyes and FRET experiments, and improve imaging speed 10-fold.

On-top density functionals for the short-range dynamic correlation between electrons of opposite and parallel spin

NASA Astrophysics Data System (ADS)

Hollett, Joshua W.; Pegoretti, Nicholas

2018-04-01

Separate, one-parameter, on-top density functionals are derived for the short-range dynamic correlation between opposite and parallel-spin electrons, in which the electron-electron cusp is represented by an exponential function. The combination of both functionals is referred to as the Opposite-spin exponential-cusp and Fermi-hole correction (OF) functional. The two parameters of the OF functional are set by fitting the ionization energies and electron affinities, of the atoms He to Ar, predicted by ROHF in combination with the OF functional to the experimental values. For ionization energies, the overall performance of ROHF-OF is better than completely renormalized coupled-cluster [CR-CC(2,3)] and better than, or as good as, conventional density functional methods. For electron affinities, the overall performance of ROHF-OF is less impressive. However, for both ionization energies and electron affinities of third row atoms, the mean absolute error of ROHF-OF is only 3 kJ mol-1.

Beyond the usual mapping functions in GPS, VLBI and Deep Space tracking.

NASA Astrophysics Data System (ADS)

Barriot, Jean-Pierre; Serafini, Jonathan; Sichoix, Lydie

2014-05-01

We describe here a new algorithm to model the water contents of the atmosphere (including ZWD) from GPS slant wet delays relative to a single receiver. We first make the assumption that the water vapor contents are mainly governed by a scale height (exponential law), and secondly that the departures from this decaying exponential can be mapped as a set of low degree 3D Zernike functions (w.r.t. space) and Tchebyshev polynomials (w.r.t. time.) We compare this new algorithm with previous algorithms known as mapping functions in GPS, VLBI and Deep Space tracking and give an example with data acquired over a one day time span at the Geodesy Observatory of Tahiti.

On the Singularity Structure of WKB Solution of the Boosted Whittaker Equation: its Relevance to Resurgent Functions with Essential Singularities

NASA Astrophysics Data System (ADS)

Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya

2016-12-01

Inspired by the symbol calculus of linear differential operators of infinite order applied to the Borel transformed WKB solutions of simple-pole type equation [Kamimoto et al. (RIMS Kôkyûroku Bessatsu B 52:127-146, 2014)], which is summarized in Section 1, we introduce in Section 2 the space of simple resurgent functions depending on a parameter with an infra-exponential type growth order, and then we define the assigning operator A which acts on the space and produces resurgent functions with essential singularities. In Section 3, we apply the operator A to the Borel transforms of the Voros coefficient and its exponentiation for the Whittaker equation with a large parameter so that we may find the Borel transforms of the Voros coefficient and its exponentiation for the boosted Whittaker equation with a large parameter. In Section 4, we use these results to find the explicit form of the alien derivatives of the Borel transformed WKB solutions of the boosted Whittaker equation with a large parameter. The results in this paper manifest the importance of resurgent functions with essential singularities in developing the exact WKB analysis, the WKB analysis based on the resurgent function theory. It is also worth emphasizing that the concrete form of essential singularities we encounter is expressed by the linear differential operators of infinite order.

Survival Bayesian Estimation of Exponential-Gamma Under Linex Loss Function

NASA Astrophysics Data System (ADS)

Rizki, S. W.; Mara, M. N.; Sulistianingsih, E.

2017-06-01

This paper elaborates a research of the cancer patients after receiving a treatment in cencored data using Bayesian estimation under Linex Loss function for Survival Model which is assumed as an exponential distribution. By giving Gamma distribution as prior and likelihood function produces a gamma distribution as posterior distribution. The posterior distribution is used to find estimatior {\\hat{λ }}BL by using Linex approximation. After getting {\\hat{λ }}BL, the estimators of hazard function {\\hat{h}}BL and survival function {\\hat{S}}BL can be found. Finally, we compare the result of Maximum Likelihood Estimation (MLE) and Linex approximation to find the best method for this observation by finding smaller MSE. The result shows that MSE of hazard and survival under MLE are 2.91728E-07 and 0.000309004 and by using Bayesian Linex worths 2.8727E-07 and 0.000304131, respectively. It concludes that the Bayesian Linex is better than MLE.

A non-Gaussian option pricing model based on Kaniadakis exponential deformation

NASA Astrophysics Data System (ADS)

Moretto, Enrico; Pasquali, Sara; Trivellato, Barbara

2017-09-01

A way to make financial models effective is by letting them to represent the so called "fat tails", i.e., extreme changes in stock prices that are regarded as almost impossible by the standard Gaussian distribution. In this article, the Kaniadakis deformation of the usual exponential function is used to define a random noise source in the dynamics of price processes capable of capturing such real market phenomena.

Echo Statistics of Aggregations of Scatterers in a Random Waveguide: Application to Biologic Sonar Clutter

DTIC Science & Technology

2012-09-01

used in this paper to compare probability density functions, the Lilliefors test and the Kullback - Leibler distance. The Lilliefors test is a goodness ... of interest in this study are the Rayleigh distribution and the exponential distribution. The Lilliefors test is used to test goodness - of - fit for...Lilliefors test for goodness of fit with an exponential distribution. These results suggests that,

Atmospheric-radiation boundary conditions for high-frequency waves in time-distance helioseismology

NASA Astrophysics Data System (ADS)

Fournier, D.; Leguèbe, M.; Hanson, C. S.; Gizon, L.; Barucq, H.; Chabassier, J.; Duruflé, M.

2017-12-01

The temporal covariance between seismic waves measured at two locations on the solar surface is the fundamental observable in time-distance helioseismology. Above the acoustic cut-off frequency ( 5.3 mHz), waves are not trapped in the solar interior and the covariance function can be used to probe the upper atmosphere. We wish to implement appropriate radiative boundary conditions for computing the propagation of high-frequency waves in the solar atmosphere. We consider recently developed and published radiative boundary conditions for atmospheres in which sound-speed is constant and density decreases exponentially with radius. We compute the cross-covariance function using a finite element method in spherical geometry and in the frequency domain. The ratio between first- and second-skip amplitudes in the time-distance diagram is used as a diagnostic to compare boundary conditions and to compare with observations. We find that a boundary condition applied 500 km above the photosphere and derived under the approximation of small angles of incidence accurately reproduces the "infinite atmosphere" solution for high-frequency waves. When the radiative boundary condition is applied 2 Mm above the photosphere, we find that the choice of atmospheric model affects the time-distance diagram. In particular, the time-distance diagram exhibits double-ridge structure when using a Vernazza Avrett Loeser atmospheric model.

Replication Cycle and Molecular Biology of the West Nile Virus

PubMed Central

Brinton, Margo A.

2013-01-01

West Nile virus (WNV) is a member of the genus Flavivirus in the family Flaviviridae. Flaviviruses replicate in the cytoplasm of infected cells and modify the host cell environment. Although much has been learned about virion structure and virion-endosomal membrane fusion, the cell receptor(s) used have not been definitively identified and little is known about the early stages of the virus replication cycle. Members of the genus Flavivirus differ from members of the two other genera of the family by the lack of a genomic internal ribosomal entry sequence and the creation of invaginations in the ER membrane rather than double-membrane vesicles that are used as the sites of exponential genome synthesis. The WNV genome 3' and 5' sequences that form the long distance RNA-RNA interaction required for minus strand initiation have been identified and contact sites on the 5' RNA stem loop for NS5 have been mapped. Structures obtained for many of the viral proteins have provided information relevant to their functions. Viral nonstructural protein interactions are complex and some may occur only in infected cells. Although interactions between many cellular proteins and virus components have been identified, the functions of most of these interactions have not been delineated. PMID:24378320

CO₂ sorption kinetics of scaled-up polyethylenimine-functionalized mesoporous silica sorbent.

PubMed

Al-Marri, M J; Khader, M M; Tawfik, M; Qi, G; Giannelis, E P

2015-03-31

Two CO2 solid sorbents based on polyethylenimine, PEI (M(n) ∼ 423 and 10K), impregnated into mesoporous silica (MPS) foam prepared in kilogram quantities via a scale-up process were synthesized and systematically characterized by a range of analytical and surface techniques. The mesoporous silica sorbent impregnated with lower molecular weight PEI, PEI-423/MPS, showed higher capacity toward CO2 sorption than the sorbent functionalized with the higher molecular weight PEI (PEI-10K/MPS). On the other hand, PEI-10K/MPS exhibited higher thermal stability than PEI-423/MPS. The kinetics of CO2 adsorption on both PEI/MPS fitted well with a double-exponential model. According to this model CO2 adsorption can be divided into two steps: the first is fast and is attributed to CO2 adsorption on the sorbent surface; the second is slower and can be related to the diffusion of CO2 within and between the mesoporous particles. In contrast, the desorption process obeyed first-order kinetics with activation energies of 64.3 and 140.7 kJ mol(-1) for PEI-423/MPS and PEI-10K/MPS, respectively. These studies suggest that the selection of amine is critical as it affects not only sorbent capacity and stability but also the energy penalty associated with sorbent regeneration.

Effect of ethanol variation on the internal environment of sol-gel bulk and thin films with aging.

PubMed

Gupta, R; Mozumdar, S; Chaudhury, N K

2005-10-15

Sol-gel derived bulk and thin films were prepared from different compositions at low pH ( approximately 2.0) containing varying concentrations of ethanol from 15 to 60% at constant water (H(2)O)/tetraethyl-orthosilicate (TEOS) ratio (R=4). The fluorescence microscopic and spectroscopic measurements on fluorescent probe, Hoechst 33258 (H258) entrapped in these compositions were carried out at different days of storage to monitor the effects of concentration of ethanol on the internal environment of sol-gel materials. Fluorescence microscopic observations on sol-gel thin films, prepared by dip coating technique depicted uniform and cracked surface at withdrawal speed 1cm/min (high speed) and 0.1cm/min (low speed) respectively, which did not change during aging. Fluorescence spectral measurements showed emission maximum of H258 at approximately 535 nm in fresh sols at all concentrations of ethanol which depicted slight blue shift to 512 nm during aging in bulk. No such spectral shift has been observed in sol-gel thin films coated at high speed whereas thin films coated at low speed clearly showed an additional band at approximately 404 nm at 45 and 60% concentration of ethanol after about one month of storage. Analysis of the fluorescence lifetime data indicated single exponential decay (1.6-1.8 ns) in fresh sol and from third day onwards, invariably double exponential decay with a short (tau(1)) and a long (tau(2)) component were observed in sol-gel bulk with a dominant tau(1) at approximately 1.2 ns at all concentrations of ethanol. A double exponential decay consisting of a short component (tau(1)) at approximately 0.2 ns and a long component (tau(2)) at approximately 3.5 ns were observed at all ethanol concentrations in both fresh and aged sol-gel thin films. Further, distribution analysis of lifetimes of H258 showed two mean lifetimes with increased width in aged bulk and thin films. These results are likely to have strong implications in designing the internal environment for applications in biosensors.

Very low threshold-current temperature sensitivity in constricted double-heterojunction AlGaAs lasers

NASA Technical Reports Server (NTRS)

Botez, D.; Connolly, J. C.; Gilbert, D. B.; Ettenberg, M.

1981-01-01

The temperature dependence of threshold currents in constricted double-heterojunction diode lasers with strong lateral mode confinement is found to be significantly milder than for other types of lasers. The threshold-current relative variations with ambient temperature are typically two to three times less than for other devices of CW-operation capability. Over the interval 10-70 C the threshold currents fit the empirical exponential law exp/(T2-T1)/T0/ with T0 values in the 240-375 C range in pulsed operation, and in the 200-310 C range in CW operation. The external differential quantum efficiency and the mode far-field pattern near threshold are virtually invariant with temperature. The possible causes of high-T0 behavior are analyzed, and a new phenomenon - temperature-dependent current focusing - is presented to explain the results.

Applying elliptic curve cryptography to a chaotic synchronisation system: neural-network-based approach

NASA Astrophysics Data System (ADS)

Hsiao, Feng-Hsiag

2017-10-01

In order to obtain double encryption via elliptic curve cryptography (ECC) and chaotic synchronisation, this study presents a design methodology for neural-network (NN)-based secure communications in multiple time-delay chaotic systems. ECC is an asymmetric encryption and its strength is based on the difficulty of solving the elliptic curve discrete logarithm problem which is a much harder problem than factoring integers. Because it is much harder, we can get away with fewer bits to provide the same level of security. To enhance the strength of the cryptosystem, we conduct double encryption that combines chaotic synchronisation with ECC. According to the improved genetic algorithm, a fuzzy controller is synthesised to realise the exponential synchronisation and achieves optimal H∞ performance by minimising the disturbances attenuation level. Finally, a numerical example with simulations is given to demonstrate the effectiveness of the proposed approach.

Dynamical analysis for a scalar-tensor model with kinetic and nonminimal couplings

NASA Astrophysics Data System (ADS)

Granda, L. N.; Jimenez, D. F.

We study the autonomous system for a scalar-tensor model of dark energy with nonminimal coupling to curvature and nonminimal kinetic coupling to the Einstein tensor. The critical points describe important stable asymptotic scenarios including quintessence, phantom and de Sitter attractor solutions. Two functional forms for the coupling functions and the scalar potential were considered: power-law and exponential functions of the scalar field. For power-law couplings, the restrictions on stable quintessence and phantom solutions lead to asymptotic freedom regime for the gravitational interaction. For the exponential functions, the stable quintessence, phantom or de Sitter solutions allow asymptotic behaviors where the effective Newtonian coupling can reach either the asymptotic freedom regime or constant value. The phantom solutions could be realized without appealing to ghost degrees of freedom. Transient inflationary and radiation dominated phases can also be described.

Stability in Cohen Grossberg-type bidirectional associative memory neural networks with time-varying delays

NASA Astrophysics Data System (ADS)

Cao, Jinde; Song, Qiankun

2006-07-01

In this paper, the exponential stability problem is investigated for a class of Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays. By using the analysis method, inequality technique and the properties of an M-matrix, several novel sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are derived. Moreover, the exponential convergence rate is estimated. The obtained results are less restrictive than those given in the earlier literature, and the boundedness and differentiability of the activation functions and differentiability of the time-varying delays are removed. Two examples with their simulations are given to show the effectiveness of the obtained results.

Global exponential stability for switched memristive neural networks with time-varying delays.

PubMed

Xin, Youming; Li, Yuxia; Cheng, Zunshui; Huang, Xia

2016-08-01

This paper considers the problem of exponential stability for switched memristive neural networks (MNNs) with time-varying delays. Different from most of the existing papers, we model a memristor as a continuous system, and view switched MNNs as switched neural networks with uncertain time-varying parameters. Based on average dwell time technique, mode-dependent average dwell time technique and multiple Lyapunov-Krasovskii functional approach, two conditions are derived to design the switching signal and guarantee the exponential stability of the considered neural networks, which are delay-dependent and formulated by linear matrix inequalities (LMIs). Finally, the effectiveness of the theoretical results is demonstrated by two numerical examples. Copyright © 2016 Elsevier Ltd. All rights reserved.

Endotoxin inactivation via steam-heat treatment in dilute simethicone emulsions used in biopharmaceutical processes.

PubMed

Britt, Keith A; Galvin, Jeffrey; Gammell, Patrick; Nti-Gyabaah, Joseph; Boras, George; Kolwyck, David; Ramirez, José G; Presente, Esther; Naugle, Gregory

2014-01-01

Simethicone emulsion is used to regulate foaming in cell culture operations in biopharmaceutical processes. It is also a potential source of endotoxin contamination. The inactivation of endotoxins in dilute simethicone emulsions was assessed as a function of time at different steam temperatures using a Limulus amebocyte lysate kinetic chromogenic technique. Endotoxin inactivation from steam-heat treatment was fit to a four-parameter double exponential decay model, which indicated that endotoxin inactivation was biphasic, consisting of fast and slow regimes. In the fast regime, temperature-related effects were dominant. Transitioning into the slow regime, the observed temperature dependence diminished, and concentration-related effects became increasingly significant. The change in the Gibbs free energy moving through the transition state indicated that a large energy barrier must be overcome for endotoxin inactivation to occur. The corresponding Arrhenius pre-exponential factor was >10(12) s(-1) suggesting that endotoxins in aqueous solution exist as aggregates. The disorder associated with the endotoxin inactivation reaction pathway was assessed via the change in entropy moving through the transition state. This quantity was positive indicating that endotoxin inactivation may result from hydrolysis of individual endotoxin molecules, which perturbs the conformation of endotoxin aggregates, thereby modulating the biological activity observed. Steam-heat treatment decreased endotoxin levels by 1-2 logarithm (log) reduction (LRV), which may be practically relevant depending on incoming raw material endotoxin levels. Antifoam efficiency and cell culture performance were negligibly impacted following steam-heat treatment. The results from this study show that steam-heat treatment is a viable endotoxin control strategy that can be implemented to support large-scale biopharmaceutical manufacturing. © 2014 American Institute of Chemical Engineers.

Modeling the growth processes of polyelectrolyte multilayers using a quartz crystal resonator.

PubMed

Salomäki, Mikko; Kankare, Jouko

2007-07-26

The layer-by-layer buildup of chitosan/hyaluronan (CH/HA) and poly(l-lysine)/hyaluronan (PLL/HA) multilayers was followed on a quartz crystal resonator (QCR) in different ionic strengths and at different temperatures. These polyelectrolytes were chosen to demonstrate the method whereby useful information is retrieved from acoustically thick polymer layers during their buildup. Surface acoustic impedance recorded in these measurements gives a single or double spiral when plotted in the complex plane. The shape of this spiral depends on the viscoelasticity of the layer material and regularity of the growth process. The polymer layer is assumed to consist of one or two zones. A mathematical model was devised to represent the separation of the layer to two zones with different viscoelastic properties. Viscoelastic quantities of the layer material and the mode and parameters of the growth process were acquired by fitting a spiral to the experimental data. In all the cases the growth process was mainly exponential as a function of deposition cycles, the growth exponent being between 0.250 and 0.275.

Performance improvement of pentacosa-diynoic acid label dosimeter for radiation processing technology

NASA Astrophysics Data System (ADS)

Abdel-Fattah, A. A.; Soliman, Y. S.

2017-12-01

A radiation sensitive material, 10,12-pentacosa-diynoic acid (PCDA), was incorporated into polyvinyl butyral (PVB) films to develop indicators/dosimeters for blood and food irradiation. The present study aims to improve the dosimetric performance of these previously prepared dosimeters and to extend their shelf life by the combination of a radical scavenger, propyl gallate (PG), and a UV absorber, tinuvin-p (TP). The X-ray diffraction (XRD) patterns of the dosimeters were analysed and their dosimetric characteristics were investigated by specular reflectance in the visible spectrum range of 400-700 nm. Upon irradiation, the films turn blue exhibiting two main bands around 670 and 620 nm. Their dose-response functions were fitted by a double exponential growth, 5 parameters, equation. Irradiation temperature influences the dosimeter response at 670 nm without causing thermochromic transition up to 50 °C in poly-PCDA. The useful dose range is 5-4000 Gy depending on the wavelengths of analysis and PCDA content in the films. The overall uncertainty of dose measurement is less than 6% at 2σ.

Dichromatic laser radiation effects on DNA of Escherichia coli and plasmids

NASA Astrophysics Data System (ADS)

Martins, W. A.; Polignano, G. A. C.; Guimarães, O. R.; Geller, M.; Paoli, F.; Fonseca, A. S.

2015-04-01

Dichromatic and consecutive laser radiations have attracted increased attention for clinical applications as offering new tools for the treatment of dysfunctional tissues in situations where monochromatic radiation is not effective. This work evaluated the survival, filamentation and morphology of Escherichia coli cells, and the induction of DNA lesions, in plasmid DNA exposed to low-intensity consecutive dichromatic laser radiation. Exponential and stationary wild type and formamidopyrimidine DNA glycosylase/MutM protein deficient E. coli cultures were exposed to consecutive low-intensity dichromatic laser radiation (infrared laser immediately after red laser) to study the survival, filamentation and morphology of bacterial cells. Plasmid DNA samples were exposed to dichromatic radiation to study DNA lesions by electrophoretic profile. Dichromatic laser radiation affects the survival, filamentation and morphology of E. coli cultures depending on the growth phase and the functional repair mechanism of oxidizing lesions in DNA, but does not induce single/double strands breaks or alkali-labile DNA lesions. Results show that low-intensity consecutive dichromatic laser radiation induces biological effects that differ from those induced by monochromatic laser radiation, suggesting that other therapeutic effects could be obtained using dichromatic radiation.

Reliable Viscosity Calculation from Equilibrium Molecular Dynamics Simulations: A Time Decomposition Method.

PubMed

Zhang, Yong; Otani, Akihito; Maginn, Edward J

2015-08-11

Equilibrium molecular dynamics is often used in conjunction with a Green-Kubo integral of the pressure tensor autocorrelation function to compute the shear viscosity of fluids. This approach is computationally expensive and is subject to a large amount of variability because the plateau region of the Green-Kubo integral is difficult to identify unambiguously. Here, we propose a time decomposition approach for computing the shear viscosity using the Green-Kubo formalism. Instead of one long trajectory, multiple independent trajectories are run and the Green-Kubo relation is applied to each trajectory. The averaged running integral as a function of time is fit to a double-exponential function with a weighting function derived from the standard deviation of the running integrals. Such a weighting function minimizes the uncertainty of the estimated shear viscosity and provides an objective means of estimating the viscosity. While the formal Green-Kubo integral requires an integration to infinite time, we suggest an integration cutoff time tcut, which can be determined by the relative values of the running integral and the corresponding standard deviation. This approach for computing the shear viscosity can be easily automated and used in computational screening studies where human judgment and intervention in the data analysis are impractical. The method has been applied to the calculation of the shear viscosity of a relatively low-viscosity liquid, ethanol, and relatively high-viscosity ionic liquid, 1-n-butyl-3-methylimidazolium bis(trifluoromethane-sulfonyl)imide ([BMIM][Tf2N]), over a range of temperatures. These test cases show that the method is robust and yields reproducible and reliable shear viscosity values.

A new generalized exponential rational function method to find exact special solutions for the resonance nonlinear Schrödinger equation

NASA Astrophysics Data System (ADS)

Ghanbari, Behzad; Inc, Mustafa

2018-04-01

The present paper suggests a novel technique to acquire exact solutions of nonlinear partial differential equations. The main idea of the method is to generalize the exponential rational function method. In order to examine the ability of the method, we consider the resonant nonlinear Schrödinger equation (R-NLSE). Many variants of exact soliton solutions for the equation are derived by the proposed method. Physical interpretations of some obtained solutions is also included. One can easily conclude that the new proposed method is very efficient and finds the exact solutions of the equation in a relatively easy way.

New class of control laws for robotic manipulators. I - Nonadaptive case. II - Adaptive case

NASA Technical Reports Server (NTRS)

Wen, John T.; Bayard, David S.

1988-01-01

A new class of exponentially stabilizing control laws for joint level control of robot arms is discussed. Closed-loop exponential stability has been demonstrated for both the set point and tracking control problems by a slight modification of the energy Lyapunov function and the use of a lemma which handles third-order terms in the Lyapunov function derivatives. In the second part, these control laws are adapted in a simple fashion to achieve asymptotically stable adaptive control. The analysis addresses the nonlinear dynamics directly without approximation, linearization, or ad hoc assumptions, and uses a parameterization based on physical (time-invariant) quantities.

Simple robust control laws for robot manipulators. Part 1: Non-adaptive case

NASA Technical Reports Server (NTRS)

Wen, J. T.; Bayard, D. S.

1987-01-01

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has been recently recognized that the nonlinear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from the Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third order terms in the Lyapunov function derivatives, closed loop exponential stability for both the set point and tracking control problem is demonstrated. The exponential convergence property also leads to robustness with respect to frictions, bounded modeling errors and instrument noise. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on-line computation of nonlinear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing tradeoffs between robustness, computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.

Improvements to Shortwave Absorption in the GFDL General Circulation Model Radiation Code

NASA Astrophysics Data System (ADS)

Freidenreich, S.

2015-12-01

The multiple-band shortwave radiation parameterization used in the GFDL general circulation models is being revised to better simulate the disposition of the solar flux in comparison with line-by-line+doubling-adding reference calculations based on the HITRAN 2012 catalog. For clear skies, a notable deficiency in the older formulation is an underestimate of atmospheric absorption. The two main reasons for this is the neglecting of both H2O absorption for wavenumbers < 2500 cm-1 and the O2 continuum. Further contributions to this underestimate are due to neglecting the effects of CH4, N2O and stratospheric H2O absorption. These issues are addressed in the revised formulation and result in globally average shortwave absorption increasing from 74 to 78 Wm-2. The number of spectral bands considered remains the same (18), but the number of pseudomonochromatic intervals (based mainly on the exponential-sum-fit technique) for the determination of H2O absorption is increased from 38 to 74, allowing for more accuracy in its simulation. Also, CO2 absorption is now determined by the exponential-sum-fit technique, replacing an algebraic absorptivity expression in the older parameterization; this improves the simulation of the heating in the stratosphere. Improvements to the treatment of multiple scattering are currently being tested. This involves replacing the current algorithm, which consists of the two stream delta-Eddington, with a four stream algorithm. Initial results show that in most, but not all cases these produce better agreement with the reference doubling-adding results.

Complex Dynamic Development of Poliovirus Membranous Replication Complexes

PubMed Central

Nair, Vinod; Hansen, Bryan T.; Hoyt, Forrest H.; Fischer, Elizabeth R.; Ehrenfeld, Ellie

2012-01-01

Replication of all positive-strand RNA viruses is intimately associated with membranes. Here we utilize electron tomography and other methods to investigate the remodeling of membranes in poliovirus-infected cells. We found that the viral replication structures previously described as “vesicles” are in fact convoluted, branching chambers with complex and dynamic morphology. They are likely to originate from cis-Golgi membranes and are represented during the early stages of infection by single-walled connecting and branching tubular compartments. These early viral organelles gradually transform into double-membrane structures by extension of membranous walls and/or collapsing of the luminal cavity of the single-membrane structures. As the double-membrane regions develop, they enclose cytoplasmic material. At this stage, a continuous membranous structure may have double- and single-walled membrane morphology at adjacent cross-sections. In the late stages of the replication cycle, the structures are represented mostly by double-membrane vesicles. Viral replication proteins, double-stranded RNA species, and actively replicating RNA are associated with both double- and single-membrane structures. However, the exponential phase of viral RNA synthesis occurs when single-membrane formations are predominant in the cell. It has been shown previously that replication complexes of some other positive-strand RNA viruses form on membrane invaginations, which result from negative membrane curvature. Our data show that the remodeling of cellular membranes in poliovirus-infected cells produces structures with positive curvature of membranes. Thus, it is likely that there is a fundamental divergence in the requirements for the supporting cellular membrane-shaping machinery among different groups of positive-strand RNA viruses. PMID:22072780

A New Insight into the Earthquake Recurrence Studies from the Three-parameter Generalized Exponential Distributions

NASA Astrophysics Data System (ADS)

Pasari, S.; Kundu, D.; Dikshit, O.

2012-12-01

Earthquake recurrence interval is one of the important ingredients towards probabilistic seismic hazard assessment (PSHA) for any location. Exponential, gamma, Weibull and lognormal distributions are quite established probability models in this recurrence interval estimation. However, they have certain shortcomings too. Thus, it is imperative to search for some alternative sophisticated distributions. In this paper, we introduce a three-parameter (location, scale and shape) exponentiated exponential distribution and investigate the scope of this distribution as an alternative of the afore-mentioned distributions in earthquake recurrence studies. This distribution is a particular member of the exponentiated Weibull distribution. Despite of its complicated form, it is widely accepted in medical and biological applications. Furthermore, it shares many physical properties with gamma and Weibull family. Unlike gamma distribution, the hazard function of generalized exponential distribution can be easily computed even if the shape parameter is not an integer. To contemplate the plausibility of this model, a complete and homogeneous earthquake catalogue of 20 events (M ≥ 7.0) spanning for the period 1846 to 1995 from North-East Himalayan region (20-32 deg N and 87-100 deg E) has been used. The model parameters are estimated using maximum likelihood estimator (MLE) and method of moment estimator (MOME). No geological or geophysical evidences have been considered in this calculation. The estimated conditional probability reaches quite high after about a decade for an elapsed time of 17 years (i.e. 2012). Moreover, this study shows that the generalized exponential distribution fits the above data events more closely compared to the conventional models and hence it is tentatively concluded that generalized exponential distribution can be effectively considered in earthquake recurrence studies.

Long period pseudo random number sequence generator

NASA Technical Reports Server (NTRS)

Wang, Charles C. (Inventor)

1989-01-01

A circuit for generating a sequence of pseudo random numbers, (A sub K). There is an exponentiator in GF(2 sup m) for the normal basis representation of elements in a finite field GF(2 sup m) each represented by m binary digits and having two inputs and an output from which the sequence (A sub K). Of pseudo random numbers is taken. One of the two inputs is connected to receive the outputs (E sub K) of maximal length shift register of n stages. There is a switch having a pair of inputs and an output. The switch outputs is connected to the other of the two inputs of the exponentiator. One of the switch inputs is connected for initially receiving a primitive element (A sub O) in GF(2 sup m). Finally, there is a delay circuit having an input and an output. The delay circuit output is connected to the other of the switch inputs and the delay circuit input is connected to the output of the exponentiator. Whereby after the exponentiator initially receives the primitive element (A sub O) in GF(2 sup m) through the switch, the switch can be switched to cause the exponentiator to receive as its input a delayed output A(K-1) from the exponentiator thereby generating (A sub K) continuously at the output of the exponentiator. The exponentiator in GF(2 sup m) is novel and comprises a cyclic-shift circuit; a Massey-Omura multiplier; and, a control logic circuit all operably connected together to perform the function U(sub i) = 92(sup i) (for n(sub i) = 1 or 1 (for n(subi) = 0).

On exponentially suppressed corrections to BMPV black hole entropy

NASA Astrophysics Data System (ADS)

Lal, Shailesh; Narayan, Prithvi

2018-05-01

The microscopic formula for the degeneracy of BMPV black hole microstates contains a series of exponentially suppressed corrections to the leading Bekenstein Hawking expression. We identify saddle points of the quantum entropy function for the BMPV black hole which are natural counterparts to these corrections and discuss the matching of leading and next-to-leading terms from the microscopic and macroscopic sides in a limit where the black hole charges are large.

Improved result on stability analysis of discrete stochastic neural networks with time delay

NASA Astrophysics Data System (ADS)

Wu, Zhengguang; Su, Hongye; Chu, Jian; Zhou, Wuneng

2009-04-01

This Letter investigates the problem of exponential stability for discrete stochastic time-delay neural networks. By defining a novel Lyapunov functional, an improved delay-dependent exponential stability criterion is established in terms of linear matrix inequality (LMI) approach. Meanwhile, the computational complexity of the newly established stability condition is reduced because less variables are involved. Numerical example is given to illustrate the effectiveness and the benefits of the proposed method.

Integrating products of Bessel functions with an additional exponential or rational factor

NASA Astrophysics Data System (ADS)

Van Deun, Joris; Cools, Ronald

2008-04-01

We provide two MATLAB programs to compute integrals of the form ex∏i=1kJν_i(ax)dxand 0∞xr+x∏i=1kJν_i(ax)dx with Jν_i(x) the Bessel function of the first kind and (real) order ν. The parameter m is a real number such that ∑ν+m>-1 (to assure integrability near zero), r is real and the numbers c and a are all strictly positive. The program can deliver accurate error estimates. Program summaryProgram title: BESSELINTR, BESSELINTC Catalogue identifier: AEAH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1601 No. of bytes in distributed program, including test data, etc.: 13 161 Distribution format: tar.gz Programming language: Matlab (version ⩾6.5), Octave (version ⩾2.1.69) Computer: All supporting Matlab or Octave Operating system: All supporting Matlab or Octave RAM: For k Bessel functions our program needs approximately ( 500+140k) double precision variables Classification: 4.11 Nature of problem: The problem consists in integrating an arbitrary product of Bessel functions with an additional rational or exponential factor over a semi-infinite interval. Difficulties arise from the irregular oscillatory behaviour and the possible slow decay of the integrand, which prevents truncation at a finite point. Solution method: The interval of integration is split into a finite and infinite part. The integral over the finite part is computed using Gauss-Legendre quadrature. The integrand on the infinite part is approximated using asymptotic expansions and this approximation is integrated exactly with the aid of the upper incomplete gamma function. In the case where a rational factor is present, this factor is first expanded in a Taylor series around infinity. Restrictions: Some (and eventually all) numerical accuracy is lost when one or more of the parameters r,c,a or v grow very large, or when r becomes small. Running time: Less than 0.02 s for a simple problem (two Bessel functions, small parameters), a few seconds for a more complex problem (more than six Bessel functions, large parameters), in Matlab 7.4 (R2007a) on a 2.4 GHz AMD Opteron Processor 250. References:J. Van Deun, R. Cools, Algorithm 858: Computing infinite range integrals of an arbitrary product of Bessel functions, ACM Trans. Math. Software 32 (4) (2006) 580-596.

Sodium 22+ washout from cultured rat cells

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kino, M.; Nakamura, A.; Hopp, L.

1986-10-01

The washout of Na/sup +/ isotopes from tissues and cells is quite complex and not well defined. To further gain insight into this process, we have studied /sup 22/Na/sup +/ washout from cultured Wistar rat skin fibroblasts and vascular smooth muscle cells (VSMCs). In these preparations, /sup 22/Na/sup +/ washout is described by a general three-exponential function. The exponential factor of the fastest component (k1) and the initial exchange rate constant (kie) of cultured fibroblasts decrease in magnitude in response to incubation in K+-deficient medium or in the presence of ouabain and increase in magnitude when the cells are incubatedmore » in a Ca++-deficient medium. As the magnitude of the kie declines (in the presence of ouabain) to the level of the exponential factor of the middle component (k2), /sup 22/Na/sup +/ washout is adequately described by a two-exponential function. When the kie is further diminished (in the presence of both ouabain and phloretin) to the range of the exponential factor of the slowest component (k3), the washout of /sup 22/Na/sup +/ is apparently monoexponential. Calculations of the cellular Na/sup +/ concentrations, based on the /sup 22/Na/sup +/ activity in the cells at the initiation of the washout experiments, and the medium specific activity agree with atomic absorption spectrometry measurements of the cellular concentration of this ion. Thus, all three components of /sup 22/Na/sup +/ washout from cultured rat cells are of cellular origin. Using the exponential parameters, compartmental analyses of two models (in parallel and in series) with three cellular Na/sup +/ pools were performed. The results indicate that, independent of the model chosen, the relative size of the largest Na+ pool is 92-93% in fibroblasts and approximately 96% in VSMCs. This pool is most likely to represent the cytosol.« less

Development of a golden beam data set for the commissioning of a proton double-scattering system in a pencil-beam dose calculation algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slopsema, R. L., E-mail: rslopsema@floridaproton.org; Flampouri, S.; Yeung, D.

2014-09-15

Purpose: The purpose of this investigation is to determine if a single set of beam data, described by a minimal set of equations and fitting variables, can be used to commission different installations of a proton double-scattering system in a commercial pencil-beam dose calculation algorithm. Methods: The beam model parameters required to commission the pencil-beam dose calculation algorithm (virtual and effective SAD, effective source size, and pristine-peak energy spread) are determined for a commercial double-scattering system. These parameters are measured in a first room and parameterized as function of proton energy and nozzle settings by fitting four analytical equations tomore » the measured data. The combination of these equations and fitting values constitutes the golden beam data (GBD). To determine the variation in dose delivery between installations, the same dosimetric properties are measured in two additional rooms at the same facility, as well as in a single room at another facility. The difference between the room-specific measurements and the GBD is evaluated against tolerances that guarantee the 3D dose distribution in each of the rooms matches the GBD-based dose distribution within clinically reasonable limits. The pencil-beam treatment-planning algorithm is commissioned with the GBD. The three-dimensional dose distribution in water is evaluated in the four treatment rooms and compared to the treatment-planning calculated dose distribution. Results: The virtual and effective SAD measurements fall between 226 and 257 cm. The effective source size varies between 2.4 and 6.2 cm for the large-field options, and 1.0 and 2.0 cm for the small-field options. The pristine-peak energy spread decreases from 1.05% at the lowest range to 0.6% at the highest. The virtual SAD as well as the effective source size can be accurately described by a linear relationship as function of the inverse of the residual energy. An additional linear correction term as function of RM-step thickness is required for accurate parameterization of the effective SAD. The GBD energy spread is given by a linear function of the exponential of the beam energy. Except for a few outliers, the measured parameters match the GBD within the specified tolerances in all of the four rooms investigated. For a SOBP field with a range of 15 g/cm{sup 2} and an air gap of 25 cm, the maximum difference in the 80%–20% lateral penumbra between the GBD-commissioned treatment-planning system and measurements in any of the four rooms is 0.5 mm. Conclusions: The beam model parameters of the double-scattering system can be parameterized with a limited set of equations and parameters. This GBD closely matches the measured dosimetric properties in four different rooms.« less

Importance sampling large deviations in nonequilibrium steady states. I.

PubMed

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T

2018-03-28

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.

Importance sampling large deviations in nonequilibrium steady states. I

NASA Astrophysics Data System (ADS)

Ray, Ushnish; Chan, Garnet Kin-Lic; Limmer, David T.

2018-03-01

Large deviation functions contain information on the stability and response of systems driven into nonequilibrium steady states and in such a way are similar to free energies for systems at equilibrium. As with equilibrium free energies, evaluating large deviation functions numerically for all but the simplest systems is difficult because by construction they depend on exponentially rare events. In this first paper of a series, we evaluate different trajectory-based sampling methods capable of computing large deviation functions of time integrated observables within nonequilibrium steady states. We illustrate some convergence criteria and best practices using a number of different models, including a biased Brownian walker, a driven lattice gas, and a model of self-assembly. We show how two popular methods for sampling trajectory ensembles, transition path sampling and diffusion Monte Carlo, suffer from exponentially diverging correlations in trajectory space as a function of the bias parameter when estimating large deviation functions. Improving the efficiencies of these algorithms requires introducing guiding functions for the trajectories.

Bi-periodicity evoked by periodic external inputs in delayed Cohen-Grossberg-type bidirectional associative memory networks

NASA Astrophysics Data System (ADS)

Cao, Jinde; Wang, Yanyan

2010-05-01

In this paper, the bi-periodicity issue is discussed for Cohen-Grossberg-type (CG-type) bidirectional associative memory (BAM) neural networks (NNs) with time-varying delays and standard activation functions. It is shown that the model considered in this paper has two periodic orbits located in saturation regions and they are locally exponentially stable. Meanwhile, some conditions are derived to ensure that, in any designated region, the model has a locally exponentially stable or globally exponentially attractive periodic orbit located in it. As a special case of bi-periodicity, some results are also presented for the system with constant external inputs. Finally, four examples are given to illustrate the effectiveness of the obtained results.

Global exponential stability and lag synchronization for delayed memristive fuzzy Cohen-Grossberg BAM neural networks with impulses.

PubMed

Yang, Wengui; Yu, Wenwu; Cao, Jinde; Alsaadi, Fuad E; Hayat, Tasawar

2018-02-01

This paper investigates the stability and lag synchronization for memristor-based fuzzy Cohen-Grossberg bidirectional associative memory (BAM) neural networks with mixed delays (asynchronous time delays and continuously distributed delays) and impulses. By applying the inequality analysis technique, homeomorphism theory and some suitable Lyapunov-Krasovskii functionals, some new sufficient conditions for the uniqueness and global exponential stability of equilibrium point are established. Furthermore, we obtain several sufficient criteria concerning globally exponential lag synchronization for the proposed system based on the framework of Filippov solution, differential inclusion theory and control theory. In addition, some examples with numerical simulations are given to illustrate the feasibility and validity of obtained results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Metal-induced gap states in ferroelectric capacitors and its relationship with complex band structures

NASA Astrophysics Data System (ADS)

Junquera, Javier; Aguado-Puente, Pablo

2013-03-01

At metal-isulator interfaces, the metallic wave functions with an energy eigenvalue within the band gap decay exponentially inside the dielectric (metal-induced gap states, MIGS). These MIGS can be actually regarded as Bloch functions with an associated complex wave vector. Usually only real values of the wave vectors are discussed in text books, since infinite periodicity is assumed and, in that situation, wave functions growing exponentially in any direction would not be physically valid. However, localized wave functions with an exponential decay are indeed perfectly valid solution of the Schrodinger equation in the presence of defects, surfaces or interfaces. For this reason, properties of MIGS have been typically discussed in terms of the complex band structure of bulk materials. The probable dependence on the interface particulars has been rarely taken into account explicitly due to the difficulties to include them into the model or simulations. We aim to characterize from first-principles simulations the MIGS in realistic ferroelectric capacitors and their connection with the complex band structure of the ferroelectric material. We emphasize the influence of the real interface beyond the complex band structure of bulk materials. Financial support provided by MICINN Grant FIS2009-12721-C04-02, and by the European Union Grant No. CP-FP 228989-2 ``OxIDes''. Computer resources provided by the RES.

Analytical model of coincidence resolving time in TOF-PET

NASA Astrophysics Data System (ADS)

Wieczorek, H.; Thon, A.; Dey, T.; Khanin, V.; Rodnyi, P.

2016-06-01

The coincidence resolving time (CRT) of scintillation detectors is the parameter determining noise reduction in time-of-flight PET. We derive an analytical CRT model based on the statistical distribution of photons for two different prototype scintillators. For the first one, characterized by single exponential decay, CRT is proportional to the decay time and inversely proportional to the number of photons, with a square root dependence on the trigger level. For the second scintillator prototype, characterized by exponential rise and decay, CRT is proportional to the square root of the product of rise time and decay time divided by the doubled number of photons, and it is nearly independent of the trigger level. This theory is verified by measurements of scintillation time constants, light yield and CRT on scintillator sticks. Trapping effects are taken into account by defining an effective decay time. We show that in terms of signal-to-noise ratio, CRT is as important as patient dose, imaging time or PET system sensitivity. The noise reduction effect of better timing resolution is verified and visualized by Monte Carlo simulation of a NEMA image quality phantom.

Constant growth rate can be supported by decreasing energy flux and increasing aerobic glycolysis.

PubMed

Slavov, Nikolai; Budnik, Bogdan A; Schwab, David; Airoldi, Edoardo M; van Oudenaarden, Alexander

2014-05-08

Fermenting glucose in the presence of enough oxygen to support respiration, known as aerobic glycolysis, is believed to maximize growth rate. We observed increasing aerobic glycolysis during exponential growth, suggesting additional physiological roles for aerobic glycolysis. We investigated such roles in yeast batch cultures by quantifying O2 consumption, CO2 production, amino acids, mRNAs, proteins, posttranslational modifications, and stress sensitivity in the course of nine doublings at constant rate. During this course, the cells support a constant biomass-production rate with decreasing rates of respiration and ATP production but also decrease their stress resistance. As the respiration rate decreases, so do the levels of enzymes catalyzing rate-determining reactions of the tricarboxylic-acid cycle (providing NADH for respiration) and of mitochondrial folate-mediated NADPH production (required for oxidative defense). The findings demonstrate that exponential growth can represent not a single metabolic/physiological state but a continuum of changing states and that aerobic glycolysis can reduce the energy demands associated with respiratory metabolism and stress survival. Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Finite-time containment control of perturbed multi-agent systems based on sliding-mode control

NASA Astrophysics Data System (ADS)

Yu, Di; Ji, Xiang Yang

2018-01-01

Aimed at faster convergence rate, this paper investigates finite-time containment control problem for second-order multi-agent systems with norm-bounded non-linear perturbation. When topology between the followers are strongly connected, the nonsingular fast terminal sliding-mode error is defined, corresponding discontinuous control protocol is designed and the appropriate value range of control parameter is obtained by applying finite-time stability analysis, so that the followers converge to and move along the desired trajectories within the convex hull formed by the leaders in finite time. Furthermore, on the basis of the sliding-mode error defined, the corresponding distributed continuous control protocols are investigated with fast exponential reaching law and double exponential reaching law, so as to make the followers move to the small neighbourhoods of their desired locations and keep within the dynamic convex hull formed by the leaders in finite time to achieve practical finite-time containment control. Meanwhile, we develop the faster control scheme according to comparison of the convergence rate of these two different reaching laws. Simulation examples are given to verify the correctness of theoretical results.

Picosecond absorption anisotropy of polymethine and squarylium dyes in liquid and polymeric media

NASA Astrophysics Data System (ADS)

Przhonska, Olga V.; Hagan, David J.; Novikov, Evgueni; Lepkowicz, Richard; Van Stryland, Eric W.; Bondar, Mikhail V.; Slominsky, Yuriy L.; Kachkovski, Alexei D.

2001-11-01

Time-resolved excitation-probe polarization measurements are performed for polymethine and squarylium dyes in ethanol and an elastopolymer of polyurethane acrylate (PUA). These molecules exhibit strong excited-state absorption in the visible, which results in reverse saturable absorption (RSA). In pump-probe experiments, we observe a strong angular dependence of the RSA decay kinetics upon variation of the angle between pump and probe polarizations. The difference in absorption anisotropy kinetics in ethanol and PUA is detected and analyzed. Anisotropy decay curves in ethanol follow a single exponential decay leading to complete depolarization of the excited state. We also observe complete depolarization in PUA, in which case the anisotropy decay follows a double exponential behavior. Possible rotations in the PUA polymeric matrix are connected with the existence of local microcavities of free volume. We believe that the fast decay component is connected with the rotation of molecular fragments and the slower decay component is connected with the rotation of entire molecules in local microcavities, which is possible because of the elasticity of the polymeric material.

An exponential model equation for thiamin loss in irradiated ground pork as a function of dose and temperature of irradiation

NASA Astrophysics Data System (ADS)

Fox, J. B.; Thayer, D. W.; Phillips, J. G.

The effect of low dose γ-irradiation on the thiamin content of ground pork was studied in the range of 0-14 kGy at 2°C and at radiation doses from 0.5 to 7 kGy at temperatures -20, 10, 0, 10 and 20°C. The detailed study at 2°C showed that loss of thiamin was exponential down to 0kGy. An exponential expression was derived for the effect of radiation dose and temperature of irradiation on thiamin loss, and compared with a previously derived general linear expression. Both models were accurate depictions of the data, but the exponential expression showed a significant decrease in the rate of loss between 0 and -10°C. This is the range over which water in meat freezes, the decrease being due to the immobolization of reactive radiolytic products of water in ice crystals.

In vivo chlorine and sodium MRI of rat brain at 21.1 T.

PubMed

Schepkin, Victor D; Elumalai, Malathy; Kitchen, Jason A; Qian, Chunqi; Gor'kov, Peter L; Brey, William W

2014-02-01

MR imaging of low-gamma nuclei at the ultrahigh magnetic field of 21.1 T provides a new opportunity for understanding a variety of biological processes. Among these, chlorine and sodium are attracting attention for their involvement in brain function and cancer development. MRI of (35)Cl and (23)Na were performed and relaxation times were measured in vivo in normal rat (n = 3) and in rat with glioma (n = 3) at 21.1 T. The concentrations of both nuclei were evaluated using the center-out back-projection method. T 1 relaxation curve of chlorine in normal rat head was fitted by bi-exponential function (T 1a = 4.8 ms (0.7) T 1b = 24.4 ± 7 ms (0.3) and compared with sodium (T 1 = 41.4 ms). Free induction decays (FID) of chlorine and sodium in vivo were bi-exponential with similar rapidly decaying components of [Formula: see text] ms and [Formula: see text] ms, respectively. Effects of small acquisition matrix and bi-exponential FIDs were assessed for quantification of chlorine (33.2 mM) and sodium (44.4 mM) in rat brain. The study modeled a dramatic effect of the bi-exponential decay on MRI results. The revealed increased chlorine concentration in glioma (~1.5 times) relative to a normal brain correlates with the hypothesis asserting the importance of chlorine for tumor progression.

Doubly differential cross sections for galactic heavy-ion fragmentation

NASA Technical Reports Server (NTRS)

Cucinotta, Francis A.; Norbury, John W.; Khandelwal, Govind S.; Townsend, Lawrence W.

1987-01-01

An abrasion-ablation T-matrix formulation is applied to the calculation of double differential-cross sections in projectile fragmentation of 2.1 GeV/nucleon O-16 on Be-9 and 86 MeV/nucleon C-12 on C-12 and Ag-108. An exponential parameterization of the ablation T-matrix is used and the total width of the intermediate states is taken as a parameter. Fitted values of the total width to experimental results are used to predict the lifetime of the ablation stage and indicate a decay time on the order of 10 to the -19th power sec.

Introducing correlations into carrier transport simulations of disordered materials through seeded nucleation: impact on density of states, carrier mobility, and carrier statistics

NASA Astrophysics Data System (ADS)

Brown, J. S.; Shaheen, S. E.

2018-04-01

Disorder in organic semiconductors has made it challenging to achieve performance gains; this is a result of the many competing and often nuanced mechanisms effecting charge transport. In this article, we attempt to illuminate one of these mechanisms in the hopes of aiding experimentalists in exceeding current performance thresholds. Using a heuristic exponential function, energetic correlation has been added to the Gaussian disorder model (GDM). The new model is grounded in the concept that energetic correlations can arise in materials without strong dipoles or dopants, but may be a result of an incomplete crystal formation process. The proposed correlation has been used to explain the exponential tail states often observed in these materials; it is also better able to capture the carrier mobility field dependence, commonly known as the Poole-Frenkel dependence, when compared to the GDM. Investigation of simulated current transients shows that the exponential tail states do not necessitate Montroll and Scher fits. Montroll and Scher fits occur in the form of two distinct power law curves that share a common constant in their exponent; they are clearly observed as linear lines when the current transient is plotted using a log-log scale. Typically, these fits have been found appropriate for describing amorphous silicon and other disordered materials which display exponential tail states. Furthermore, we observe the proposed correlation function leads to domains of energetically similar sites separated by boundaries where the site energies exhibit stochastic deviation. These boundary sites are found to be the source of the extended exponential tail states, and are responsible for high charge visitation frequency, which may be associated with the molecular turnover number and ultimately the material stability.

Introducing correlations into carrier transport simulations of disordered materials through seeded nucleation: impact on density of states, carrier mobility, and carrier statistics.

PubMed

Brown, J S; Shaheen, S E

2018-04-04

Disorder in organic semiconductors has made it challenging to achieve performance gains; this is a result of the many competing and often nuanced mechanisms effecting charge transport. In this article, we attempt to illuminate one of these mechanisms in the hopes of aiding experimentalists in exceeding current performance thresholds. Using a heuristic exponential function, energetic correlation has been added to the Gaussian disorder model (GDM). The new model is grounded in the concept that energetic correlations can arise in materials without strong dipoles or dopants, but may be a result of an incomplete crystal formation process. The proposed correlation has been used to explain the exponential tail states often observed in these materials; it is also better able to capture the carrier mobility field dependence, commonly known as the Poole-Frenkel dependence, when compared to the GDM. Investigation of simulated current transients shows that the exponential tail states do not necessitate Montroll and Scher fits. Montroll and Scher fits occur in the form of two distinct power law curves that share a common constant in their exponent; they are clearly observed as linear lines when the current transient is plotted using a log-log scale. Typically, these fits have been found appropriate for describing amorphous silicon and other disordered materials which display exponential tail states. Furthermore, we observe the proposed correlation function leads to domains of energetically similar sites separated by boundaries where the site energies exhibit stochastic deviation. These boundary sites are found to be the source of the extended exponential tail states, and are responsible for high charge visitation frequency, which may be associated with the molecular turnover number and ultimately the material stability.

Multidimensional Extension of the Generalized Chowla-Selberg Formula

NASA Astrophysics Data System (ADS)

Elizalde, E.

After recalling the precise existence conditions of the zeta function of a pseudodifferential operator, and the concept of reflection formula, an exponentially convergent expression for the analytic continuation of a multidimensional inhomogeneous Epstein-type zeta function of the general form with A the p×p$ matrix of a quadratic form, a p vector and q a constant, is obtained. It is valid on the whole complex s-plane, is exponentially convergent and provides the residua at the poles explicitly. It reduces to the famous formula of Chowla and Selberg in the particular case p=2, , q=0. Some variations of the formula and physical applications are considered.

A note on the accuracy of spectral method applied to nonlinear conservation laws

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang; Wong, Peter S.

1994-01-01

Fourier spectral method can achieve exponential accuracy both on the approximation level and for solving partial differential equations if the solutions are analytic. For a linear partial differential equation with a discontinuous solution, Fourier spectral method produces poor point-wise accuracy without post-processing, but still maintains exponential accuracy for all moments against analytic functions. In this note we assess the accuracy of Fourier spectral method applied to nonlinear conservation laws through a numerical case study. We find that the moments with respect to analytic functions are no longer very accurate. However the numerical solution does contain accurate information which can be extracted by a post-processing based on Gegenbauer polynomials.

Laser-induced periodic surface structures on 6H-SiC single crystals using temporally delayed femtosecond laser double-pulse trains

NASA Astrophysics Data System (ADS)

Song, Juan; Tao, Wenjun; Song, Hui; Gong, Min; Ma, Guohong; Dai, Ye; Zhao, Quanzhong; Qiu, Jianrong

2016-04-01

In this paper, a time-delay-adjustable double-pulse train with 800-nm wavelength, 200-fs pulse duration and a repetition rate of 1 kHz, produced by a collinear two-beam optical system like a Mach-Zehnder interferometer, was employed for irradiation of 6H-SiC crystal. The dependence of the induced structures on time delay of double-pulse train for parallel-polarization configuration was studied. The results show that as the time delay of collinear parallel-polarization dual-pulse train increased, the induced near-subwavelength ripples (NSWRs) turn from irregular rippled pattern to regularly periodic pattern and have their grooves much deepened. The characteristics timescale for this transition is about 6.24 ps. Besides, the areas of NSWR were found to decay exponentially for time delay from 0 to 1.24 ps and then slowly increase for time delay from 1.24 to 14.24 ps. Analysis shows that multiphoton ionization effect, grating-assisted surface plasmon coupling effect, and timely intervene of second pulse in a certain physical stage experienced by 6H-SiC excited upon first pulse irradiation may contribute to the transition of morphology details.

SECULAR BEHAVIOR OF EXOPLANETS: SELF-CONSISTENCY AND COMPARISONS WITH THE PLANET-PLANET SCATTERING HYPOTHESIS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Timpe, Miles; Barnes, Rory; Kopparapu, Ravikumar

2013-09-15

If mutual gravitational scattering among exoplanets occurs, then it may produce unique orbital properties. For example, two-planet systems that lie near the boundary between circulation and libration of their periapses could result if planet-planet scattering ejected a former third planet quickly, leaving one planet on an eccentric orbit and the other on a circular orbit. We first improve upon previous work that examined the apsidal behavior of known multiplanet systems by doubling the sample size and including observational uncertainties. This analysis recovers previous results that demonstrated that many systems lay on the apsidal boundary between libration and circulation. We thenmore » performed over 12,000 three-dimensional N-body simulations of hypothetical three-body systems that are unstable, but stabilize to two-body systems after an ejection. Using these synthetic two-planet systems, we test the planet-planet scattering hypothesis by comparing their apsidal behavior, over a range of viewing angles, to that of the observed systems and find that they are statistically consistent regardless of the multiplicity of the observed systems. Finally, we combine our results with previous studies to show that, from the sampled cases, the most likely planetary mass function prior to planet-planet scattering follows a power law with index -1.1. We find that this pre-scattering mass function predicts a mutual inclination frequency distribution that follows an exponential function with an index between -0.06 and -0.1.« less

A Nonlinear Least Squares Approach to Time of Death Estimation Via Body Cooling.

PubMed

Rodrigo, Marianito R

2016-01-01

The problem of time of death (TOD) estimation by body cooling is revisited by proposing a nonlinear least squares approach that takes as input a series of temperature readings only. Using a reformulation of the Marshall-Hoare double exponential formula and a technique for reducing the dimension of the state space, an error function that depends on the two cooling rates is constructed, with the aim of minimizing this function. Standard nonlinear optimization methods that are used to minimize the bivariate error function require an initial guess for these unknown rates. Hence, a systematic procedure based on the given temperature data is also proposed to determine an initial estimate for the rates. Then, an explicit formula for the TOD is given. Results of numerical simulations using both theoretical and experimental data are presented, both yielding reasonable estimates. The proposed procedure does not require knowledge of the temperature at death nor the body mass. In fact, the method allows the estimation of the temperature at death once the cooling rates and the TOD have been calculated. The procedure requires at least three temperature readings, although more measured readings could improve the estimates. With the aid of computerized recording and thermocouple detectors, temperature readings spaced 10-15 min apart, for example, can be taken. The formulas can be straightforwardly programmed and installed on a hand-held device for field use. © 2015 American Academy of Forensic Sciences.

Two solar proton fluence models based on ground level enhancement observations

NASA Astrophysics Data System (ADS)

Raukunen, Osku; Vainio, Rami; Tylka, Allan J.; Dietrich, William F.; Jiggens, Piers; Heynderickx, Daniel; Dierckxsens, Mark; Crosby, Norma; Ganse, Urs; Siipola, Robert

2018-01-01

Solar energetic particles (SEPs) constitute an important component of the radiation environment in interplanetary space. Accurate modeling of SEP events is crucial for the mitigation of radiation hazards in spacecraft design. In this study we present two new statistical models of high energy solar proton fluences based on ground level enhancement (GLE) observations during solar cycles 19-24. As the basis of our modeling, we utilize a four parameter double power law function (known as the Band function) fits to integral GLE fluence spectra in rigidity. In the first model, the integral and differential fluences for protons with energies between 10 MeV and 1 GeV are calculated using the fits, and the distributions of the fluences at certain energies are modeled with an exponentially cut-off power law function. In the second model, we use a more advanced methodology: by investigating the distributions and relationships of the spectral fit parameters we find that they can be modeled as two independent and two dependent variables. Therefore, instead of modeling the fluences separately at different energies, we can model the shape of the fluence spectrum. We present examples of modeling results and show that the two methodologies agree well except for a short mission duration (1 year) at low confidence level. We also show that there is a reasonable agreement between our models and three well-known solar proton models (JPL, ESP and SEPEM), despite the differences in both the modeling methodologies and the data used to construct the models.

An Empirical Assessment of the Form of Utility Functions

ERIC Educational Resources Information Center

Kirby, Kris N.

2011-01-01

Utility functions, which relate subjective value to physical attributes of experience, are fundamental to most decision theories. Seven experiments were conducted to test predictions of the most widely assumed mathematical forms of utility (power, log, and negative exponential), and a function proposed by Rachlin (1992). For pairs of gambles for…

Cluster decomposition of full configuration interaction wave functions: A tool for chemical interpretation of systems with strong correlation

NASA Astrophysics Data System (ADS)

Lehtola, Susi; Tubman, Norm M.; Whaley, K. Birgitta; Head-Gordon, Martin

2017-10-01

Approximate full configuration interaction (FCI) calculations have recently become tractable for systems of unforeseen size, thanks to stochastic and adaptive approximations to the exponentially scaling FCI problem. The result of an FCI calculation is a weighted set of electronic configurations, which can also be expressed in terms of excitations from a reference configuration. The excitation amplitudes contain information on the complexity of the electronic wave function, but this information is contaminated by contributions from disconnected excitations, i.e., those excitations that are just products of independent lower-level excitations. The unwanted contributions can be removed via a cluster decomposition procedure, making it possible to examine the importance of connected excitations in complicated multireference molecules which are outside the reach of conventional algorithms. We present an implementation of the cluster decomposition analysis and apply it to both true FCI wave functions, as well as wave functions generated from the adaptive sampling CI algorithm. The cluster decomposition is useful for interpreting calculations in chemical studies, as a diagnostic for the convergence of various excitation manifolds, as well as as a guidepost for polynomially scaling electronic structure models. Applications are presented for (i) the double dissociation of water, (ii) the carbon dimer, (iii) the π space of polyacenes, and (iv) the chromium dimer. While the cluster amplitudes exhibit rapid decay with an increasing rank for the first three systems, even connected octuple excitations still appear important in Cr2, suggesting that spin-restricted single-reference coupled-cluster approaches may not be tractable for some problems in transition metal chemistry.

Analytic solutions to modelling exponential and harmonic functions using Chebyshev polynomials: fitting frequency-domain lifetime images with photobleaching.

PubMed

Malachowski, George C; Clegg, Robert M; Redford, Glen I

2007-12-01

A novel approach is introduced for modelling linear dynamic systems composed of exponentials and harmonics. The method improves the speed of current numerical techniques up to 1000-fold for problems that have solutions of multiple exponentials plus harmonics and decaying components. Such signals are common in fluorescence microscopy experiments. Selective constraints of the parameters being fitted are allowed. This method, using discrete Chebyshev transforms, will correctly fit large volumes of data using a noniterative, single-pass routine that is fast enough to analyse images in real time. The method is applied to fluorescence lifetime imaging data in the frequency domain with varying degrees of photobleaching over the time of total data acquisition. The accuracy of the Chebyshev method is compared to a simple rapid discrete Fourier transform (equivalent to least-squares fitting) that does not take the photobleaching into account. The method can be extended to other linear systems composed of different functions. Simulations are performed and applications are described showing the utility of the method, in particular in the area of fluorescence microscopy.

On the Time Scale of Nocturnal Boundary Layer Cooling in Valleys and Basins and over Plains

NASA Astrophysics Data System (ADS)

de Wekker, Stephan F. J.; Whiteman, C. David

2006-06-01

Sequences of vertical temperature soundings over flat plains and in a variety of valleys and basins of different sizes and shapes were used to determine cooling-time-scale characteristics in the nocturnal stable boundary layer under clear, undisturbed weather conditions. An exponential function predicts the cumulative boundary layer cooling well. The fitting parameter or time constant in the exponential function characterizes the cooling of the valley atmosphere and is equal to the time required for the cumulative cooling to attain 63.2% of its total nighttime value. The exponential fit finds time constants varying between 3 and 8 h. Calculated time constants are smallest in basins, are largest over plains, and are intermediate in valleys. Time constants were also calculated from air temperature measurements made at various heights on the sidewalls of a small basin. The variation with height of the time constant exhibited a characteristic parabolic shape in which the smallest time constants occurred near the basin floor and on the upper sidewalls of the basin where cooling was governed by cold-air drainage and radiative heat loss, respectively.

A non-Boltzmannian behavior of the energy distribution for quasi-stationary regimes of the Fermi–Pasta–Ulam β system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leo, Mario, E-mail: mario.leo@le.infn.it; Leo, Rosario Antonio, E-mail: leora@le.infn.it; Tempesta, Piergiulio, E-mail: p.tempesta@fis.ucm.es

2013-06-15

In a recent paper [M. Leo, R.A. Leo, P. Tempesta, C. Tsallis, Phys. Rev. E 85 (2012) 031149], the existence of quasi-stationary states for the Fermi–Pasta–Ulam β system has been shown numerically, by analyzing the stability properties of the N/4-mode exact nonlinear solution. Here we study the energy distribution of the modes N/4, N/3 and N/2, when they are unstable, as a function of N and of the initial excitation energy. We observe that the classical Boltzmann weight is replaced by a different weight, expressed by a q-exponential function. -- Highlights: ► New statistical properties of the Fermi–Pasta–Ulam beta systemmore » are found. ► The energy distribution of specific observables are studied: a deviation from the standard Boltzmann behavior is found. ► A q-exponential weight should be used instead. ► The classical exponential weight is restored in the large particle limit (mesoscopic nature of the phenomenon)« less

Estimating piecewise exponential frailty model with changing prior for baseline hazard function

NASA Astrophysics Data System (ADS)

Thamrin, Sri Astuti; Lawi, Armin

2016-02-01

Piecewise exponential models provide a very flexible framework for modelling univariate survival data. It can be used to estimate the effects of different covariates which are influenced by the survival data. Although in a strict sense it is a parametric model, a piecewise exponential hazard can approximate any shape of a parametric baseline hazard. In the parametric baseline hazard, the hazard function for each individual may depend on a set of risk factors or explanatory variables. However, it usually does not explain all such variables which are known or measurable, and these variables become interesting to be considered. This unknown and unobservable risk factor of the hazard function is often termed as the individual's heterogeneity or frailty. This paper analyses the effects of unobserved population heterogeneity in patients' survival times. The issue of model choice through variable selection is also considered. A sensitivity analysis is conducted to assess the influence of the prior for each parameter. We used the Markov Chain Monte Carlo method in computing the Bayesian estimator on kidney infection data. The results obtained show that the sex and frailty are substantially associated with survival in this study and the models are relatively quite sensitive to the choice of two different priors.

General solution of the Bagley-Torvik equation with fractional-order derivative

NASA Astrophysics Data System (ADS)

Wang, Z. H.; Wang, X.

2010-05-01

This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.

Fine Grained Chaos in AdS2 Gravity

NASA Astrophysics Data System (ADS)

Haehl, Felix M.; Rozali, Moshe

2018-03-01

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u^*. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS2 ) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2 k -point functions, characterized as being both "maximally braided" and "k -out of time order," which exhibit exponential growth until progressively longer time scales u^*(k)˜(k -1 )u^*. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

Fine Grained Chaos in AdS_{2} Gravity.

PubMed

Haehl, Felix M; Rozali, Moshe

2018-03-23

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u[over ^]_{*}. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS_{2}) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2k-point functions, characterized as being both "maximally braided" and "k-out of time order," which exhibit exponential growth until progressively longer time scales u[over ^]_{*}^{(k)}∼(k-1)u[over ^]_{*}. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

Biological growth functions describe published site index curves for Lake States timber species.

Treesearch

Allen L. Lundgren; William A. Dolid

1970-01-01

Two biological growth functions, an exponential-monomolecular function and a simple monomolecular function, have been fit to published site index curves for 11 Lake States tree species: red, jack, and white pine, balsam fir, white and black spruce, tamarack, white-cedar, aspen, red oak, and paper birch. Both functions closely fit all published curves except those for...

Large-deviation joint statistics of the finite-time Lyapunov spectrum in isotropic turbulence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Perry L., E-mail: pjohns86@jhu.edu; Meneveau, Charles

2015-08-15

One of the hallmarks of turbulent flows is the chaotic behavior of fluid particle paths with exponentially growing separation among them while their distance does not exceed the viscous range. The maximal (positive) Lyapunov exponent represents the average strength of the exponential growth rate, while fluctuations in the rate of growth are characterized by the finite-time Lyapunov exponents (FTLEs). In the last decade or so, the notion of Lagrangian coherent structures (which are often computed using FTLEs) has gained attention as a tool for visualizing coherent trajectory patterns in a flow and distinguishing regions of the flow with different mixingmore » properties. A quantitative statistical characterization of FTLEs can be accomplished using the statistical theory of large deviations, based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms and introduce a finite-size correction to the histogram-based method. We generalize the existing univariate formalism to the joint distributions of the two FTLEs needed to fully specify the Lyapunov spectrum in 3D flows. The joint Cramér function of turbulence is measured from two direct numerical simulation datasets of isotropic turbulence. Results are compared with joint statistics of FTLEs computed using only the symmetric part of the velocity gradient tensor, as well as with joint statistics of instantaneous strain-rate eigenvalues. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. The most likely ratio of the FTLEs λ{sub 1} : λ{sub 2} : λ{sub 3} is shown to be about 4:1:−5, compared to about 8:3:−11 when using only the strain-rate tensor for calculating fluid volume deformations. The results serve to characterize the fundamental statistical and geometric structure of turbulence at small scales including cumulative, time integrated effects. These are important for deformable particles such as droplets and polymers advected by turbulence.« less

Periodic bidirectional associative memory neural networks with distributed delays

NASA Astrophysics Data System (ADS)

Chen, Anping; Huang, Lihong; Liu, Zhigang; Cao, Jinde

2006-05-01

Some sufficient conditions are obtained for the existence and global exponential stability of a periodic solution to the general bidirectional associative memory (BAM) neural networks with distributed delays by using the continuation theorem of Mawhin's coincidence degree theory and the Lyapunov functional method and the Young's inequality technique. These results are helpful for designing a globally exponentially stable and periodic oscillatory BAM neural network, and the conditions can be easily verified and be applied in practice. An example is also given to illustrate our results.

Global exponential stability of BAM neural networks with time-varying delays: The discrete-time case

NASA Astrophysics Data System (ADS)

Raja, R.; Marshal Anthoni, S.

2011-02-01

This paper deals with the problem of stability analysis for a class of discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient conditions is proposed for the global exponential stability of discrete-time BAM neural networks. The proposed LMI based results can be easily checked by LMI control toolbox. Moreover, an example is also provided to demonstrate the effectiveness of the proposed method.

Global exponential stability of positive periodic solution of the n-species impulsive Gilpin-Ayala competition model with discrete and distributed time delays.

PubMed

Zhao, Kaihong

2018-12-01

In this paper, we study the n-species impulsive Gilpin-Ayala competition model with discrete and distributed time delays. The existence of positive periodic solution is proved by employing the fixed point theorem on cones. By constructing appropriate Lyapunov functional, we also obtain the global exponential stability of the positive periodic solution of this system. As an application, an interesting example is provided to illustrate the validity of our main results.

Photocounting distributions for exponentially decaying sources.

PubMed

Teich, M C; Card, H C

1979-05-01

Exact photocounting distributions are obtained for a pulse of light whose intensity is exponentially decaying in time, when the underlying photon statistics are Poisson. It is assumed that the starting time for the sampling interval (which is of arbitrary duration) is uniformly distributed. The probability of registering n counts in the fixed time T is given in terms of the incomplete gamma function for n >/= 1 and in terms of the exponential integral for n = 0. Simple closed-form expressions are obtained for the count mean and variance. The results are expected to be of interest in certain studies involving spontaneous emission, radiation damage in solids, and nuclear counting. They will also be useful in neurobiology and psychophysics, since habituation and sensitization processes may sometimes be characterized by the same stochastic model.

Radar correlated imaging for extended target by the combination of negative exponential restraint and total variation

NASA Astrophysics Data System (ADS)

Qian, Tingting; Wang, Lianlian; Lu, Guanghua

2017-07-01

Radar correlated imaging (RCI) introduces the optical correlated imaging technology to traditional microwave imaging, which has raised widespread concern recently. Conventional RCI methods neglect the structural information of complex extended target, which makes the quality of recovery result not really perfect, thus a novel combination of negative exponential restraint and total variation (NER-TV) algorithm for extended target imaging is proposed in this paper. The sparsity is measured by a sequential order one negative exponential function, then the 2D total variation technique is introduced to design a novel optimization problem for extended target imaging. And the proven alternating direction method of multipliers is applied to solve the new problem. Experimental results show that the proposed algorithm could realize high resolution imaging efficiently for extended target.

Broadband Spectral Modeling of the Extreme Gigahertz-peaked Spectrum Radio Source PKS B0008-421

NASA Astrophysics Data System (ADS)

Callingham, J. R.; Gaensler, B. M.; Ekers, R. D.; Tingay, S. J.; Wayth, R. B.; Morgan, J.; Bernardi, G.; Bell, M. E.; Bhat, R.; Bowman, J. D.; Briggs, F.; Cappallo, R. J.; Deshpande, A. A.; Ewall-Wice, A.; Feng, L.; Greenhill, L. J.; Hazelton, B. J.; Hindson, L.; Hurley-Walker, N.; Jacobs, D. C.; Johnston-Hollitt, M.; Kaplan, D. L.; Kudrayvtseva, N.; Lenc, E.; Lonsdale, C. J.; McKinley, B.; McWhirter, S. R.; Mitchell, D. A.; Morales, M. F.; Morgan, E.; Oberoi, D.; Offringa, A. R.; Ord, S. M.; Pindor, B.; Prabu, T.; Procopio, P.; Riding, J.; Srivani, K. S.; Subrahmanyan, R.; Udaya Shankar, N.; Webster, R. L.; Williams, A.; Williams, C. L.

2015-08-01

We present broadband observations and spectral modeling of PKS B0008-421 and identify it as an extreme gigahertz-peaked spectrum (GPS) source. PKS B0008-421 is characterized by the steepest known spectral slope below the turnover, close to the theoretical limit of synchrotron self-absorption, and the smallest known spectral width of any GPS source. Spectral coverage of the source spans from 0.118 to 22 GHz, which includes data from the Murchison Widefield Array and the wide bandpass receivers on the Australia Telescope Compact Array. We have implemented a Bayesian inference model fitting routine to fit the data with internal free-free absorption (FFA), single- and double-component FFA in an external homogeneous medium, FFA in an external inhomogeneous medium, or single- and double-component synchrotron self-absorption models, all with and without a high-frequency exponential break. We find that without the inclusion of a high-frequency break these models cannot accurately fit the data, with significant deviations above and below the peak in the radio spectrum. The addition of a high-frequency break provides acceptable spectral fits for the inhomogeneous FFA and double-component synchrotron self-absorption models, with the inhomogeneous FFA model statistically favored. The requirement of a high-frequency spectral break implies that the source has ceased injecting fresh particles. Additional support for the inhomogeneous FFA model as being responsible for the turnover in the spectrum is given by the consistency between the physical parameters derived from the model fit and the implications of the exponential spectral break, such as the necessity of the source being surrounded by a dense ambient medium to maintain the peak frequency near the gigahertz region. This implies that PKS B0008-421 should display an internal H i column density greater than 1020 cm-2. The discovery of PKS B0008-421 suggests that the next generation of low radio frequency surveys could reveal a large population of GPS sources that have ceased activity, and that a portion of the ultra-steep-spectrum source population could be composed of these GPS sources in a relic phase.

Estimating Age Distributions of Base Flow in Watersheds Underlain by Single and Dual Porosity Formations Using Groundwater Transport Simulation and Weighted Weibull Functions

NASA Astrophysics Data System (ADS)

Sanford, W. E.

2015-12-01

Age distributions of base flow to streams are important to estimate for predicting the timing of water-quality responses to changes in distributed inputs of nutrients or pollutants at the land surface. Simple models of shallow aquifers will predict exponential age distributions, but more realistic 3-D stream-aquifer geometries will cause deviations from an exponential curve. In addition, in fractured rock terrains the dual nature of the effective and total porosity of the system complicates the age distribution further. In this study shallow groundwater flow and advective transport were simulated in two regions in the Eastern United States—the Delmarva Peninsula and the upper Potomac River basin. The former is underlain by layers of unconsolidated sediment, while the latter consists of folded and fractured sedimentary rocks. Transport of groundwater to streams was simulated using the USGS code MODPATH within 175 and 275 watersheds, respectively. For the fractured rock terrain, calculations were also performed along flow pathlines to account for exchange between mobile and immobile flow zones. Porosities at both sites were calibrated using environmental tracer data (3H, 3He, CFCs and SF6) in wells and springs, and with a 30-year tritium record from the Potomac River. Carbonate and siliciclastic rocks were calibrated to have mobile porosity values of one and six percent, and immobile porosity values of 18 and 12 percent, respectively. The age distributions were fitted to Weibull functions. Whereas an exponential function has one parameter that controls the median age of the distribution, a Weibull function has an extra parameter that controls the slope of the curve. A weighted Weibull function was also developed that potentially allows for four parameters, two that control the median age and two that control the slope, one of each weighted toward early or late arrival times. For both systems the two-parameter Weibull function nearly always produced a substantially better fit to the data than the one-parameter exponential function. For the single porosity system it was found that the use of three parameters was often optimal for accurately describing the base-flow age distribution, whereas for the dual porosity system the fourth parameter was often required to fit the more complicated response curves.

On the Nature and History of Blue Amorphous Galaxies

NASA Astrophysics Data System (ADS)

Marlowe, Amanda True

1998-07-01

Dwarf galaxies play an important role in our understanding of galaxy formation and evolution. We have embarked on a systematic study of 12 blue amorphous galaxies (BAGs) whose properties suggest that they are dwarf galaxies in a starburst or post-burst state. It seems likely that BAGs are related to other 'starburst' dwarfs such as blue compact dwarfs (BCDs) and HII galaxies. The BAGs in our sample, however, are considerably closer than BCDs and HII galaxies in other samples, and therefore easier to study. These galaxies may offer important insights into dwarf galaxy evolution. In an effort to clarify the role of BAGs in evolutionary scenarios for dwarf galaxies, we present and analyze Hα and UBVI data for our sample. BAGs, like BCDs and HII galaxies, have surface brightness profiles that are exponential in the outer regions but have a predominantly blue central blue excess, suggesting a young burst in an older, redder galaxy. Seven of the galaxies have the bubble or filamentary Hα morphology and double peaked emission lines that are the signature of superbubbles or superwind activity. These galaxies are typically the ones with the strongest central excesses. The starbursting regions are young events compared to the older underlying galaxy, which follow an exponential surface brightness law. Not all of the galaxies develop superwinds: the appearance of superwinds is most sensitive to the concentration and rate of star formation in the starbursting core. The underlying exponential galaxies are very similar to those found in BCDs and HII galaxies, though the 'burst' colors are slightly redder than those found in HII galaxies. BAGs are structurally similar to BCDs and HII galaxies. How BAGs fit into the dwarf galaxy evolutionary debate is less clear. While some compact dIs have properties similar to those of the underlying exponential galaxy in our sample, issues such as mass loss from superwinds, the impact of the starbursting core on the underlying galaxy, and fading complicate the search for BAG progenitor and evolved or faded BAG galaxy classes.

Mathematical modelling of the growth of human fetus anatomical structures.

PubMed

Dudek, Krzysztof; Kędzia, Wojciech; Kędzia, Emilia; Kędzia, Alicja; Derkowski, Wojciech

2017-09-01

The goal of this study was to present a procedure that would enable mathematical analysis of the increase of linear sizes of human anatomical structures, estimate mathematical model parameters and evaluate their adequacy. Section material consisted of 67 foetuses-rectus abdominis muscle and 75 foetuses- biceps femoris muscle. The following methods were incorporated to the study: preparation and anthropologic methods, image digital acquisition, Image J computer system measurements and statistical analysis method. We used an anthropologic method based on age determination with the use of crown-rump length-CRL (V-TUB) by Scammon and Calkins. The choice of mathematical function should be based on a real course of the curve presenting growth of anatomical structure linear size Ύ in subsequent weeks t of pregnancy. Size changes can be described with a segmental-linear model or one-function model with accuracy adequate enough for clinical purposes. The interdependence of size-age is described with many functions. However, the following functions are most often considered: linear, polynomial, spline, logarithmic, power, exponential, power-exponential, log-logistic I and II, Gompertz's I and II and von Bertalanffy's function. With the use of the procedures described above, mathematical models parameters were assessed for V-PL (the total length of body) and CRL body length increases, rectus abdominis total length h, its segments hI, hII, hIII, hIV, as well as biceps femoris length and width of long head (LHL and LHW) and of short head (SHL and SHW). The best adjustments to measurement results were observed in the exponential and Gompertz's models.

Manufacturing of a novel double-function ssDNA aptamer for sensitive diagnosis and efficient neutralization of SEA.

PubMed

Sedighian, Hamid; Halabian, Raheleh; Amani, Jafar; Heiat, Mohammad; Taheri, Ramezan Ali; Imani Fooladi, Abbas Ali

2018-05-01

Staphylococcal enterotoxin A (SEA) is an enterotoxin produced mainly by Staphylococcus aureus. In recent years, it has become the most prevalent compound for staphylococcal food poisoning (SFP) around the world. In this study, we isolate new dual-function single-stranded DNA (ssDNA) aptamers by using some new methods, such as the Taguchi method, by focusing on the detection and neutralization of SEA enterotoxin in food and clinical samples. For the asymmetric polymerase chain reaction (PCR) optimization of each round of systematic evolution of ligands by exponential enrichment (SELEX), we use Taguchi L9 orthogonal arrays, and the aptamer mobility shift assay (AMSA) is used for initial evaluation of the protein-DNA interactions on the last SELEX round. In our investigation the dissociation constant (K D ) value and the limit of detection (LOD) of the candidate aptamer were found to be 8.5 ± 0.91 of nM and 5 ng/ml using surface plasmon resonance (SPR). In the current study, the Taguchi and mobility shift assay methods were innovatively harnessed to improve the selection process and evaluate the protein-aptamer interactions. To the best of our knowledge, this is the first report on employing these two methods in aptamer technology especially against bacterial toxin. Copyright © 2018 Elsevier Inc. All rights reserved.

Stable organic thin-film transistors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jia, Xiaojia; Fuentes-Hernandez, Canek; Wang, Cheng-Yin

Organic thin-film transistors (OTFTs) can be fabricated at moderate temperatures and through cost-effective solution-based processes on a wide range of low-cost flexible and deformable substrates. Although the charge mobility of state-of-the-art OTFTs is superior to that of amorphous silicon and approaches that of amorphous oxide thin-film transistors (TFTs), their operational stability generally remains inferior and a point of concern for their commercial deployment. We report on an exhaustive characterization of OTFTs with an ultrathin bilayer gate dielectric comprising the amorphous fluoropolymer CYTOP and an Al2O3:HfO2 nanolaminate. Threshold voltage shifts measured at room temperatureovertimeperiods upto5.9×105 s do not vary monotonically andmore » remain below 0.2 V in microcrystalline OTFTs (mc-OTFTs) with field-effect carrier mobility values up to 1.6 cm2 V-1 s-1. Modeling of these shifts as a function of time with a double stretched-exponential (DSE) function suggests that two compensating aging mechanisms are at play and responsible for this high stability. The measured threshold voltage shifts at temperatures up to 75°C represent at least a one-order-of-magnitude improvement in the operational stability over previous reports, bringing OTFT technologies to a performance level comparable to that reported in the scientific literature for other commercial TFTs technologies.« less

A computational study of bulk porous two-dimensional polymers related to graphyne.

PubMed

Sánchez-González, A; Dobado, J A; Torneiro, M

2016-08-03

Over the last twelve years there has been an explosion in the area of reticular chemistry with several classes of carbonaceous or carbon-rich reticular compounds coming into the scene and/or suffering an exponential growth in the number of related studies. Examples are MOFs, COFs, graphene and 2D polymers. π-Conjugated reticular compounds in particular are of great interest due to their optoelectronic properties. In this study we use density functional theory methods with periodic boundary conditions to investigate the stacking arrangements of bulk 2D polymer multilayer porous graphyne A, the related carbon allotrope multilayer graphyne B, and the analog bulk 2D polymer C in which the triple bonds of A are substituted by double bonds. The results show that for the three materials the eclipsed stacking arrangements are considerably less stable than staggered and slipped arrangements, with the more stable structures being slipped, staggered and off-centered-staggered arrangements for A, B and C, respectively. To shed light on the π-π interactions responsible for the geometry and relative energies of the different stacking modes we analyze the topology of the electron density using the electron localization function. In addition, simulated patterns for powder X-ray diffraction have been obtained from the optimized systems, which can be used for identification of the bulk 2D reticular compounds in future syntheses.

Stable organic thin-film transistors

DOE PAGES

Jia, Xiaojia; Fuentes-Hernandez, Canek; Wang, Cheng-Yin; ...

2018-01-12

Organic thin-film transistors (OTFTs) can be fabricated at moderate temperatures and through cost-effective solution-based processes on a wide range of low-cost flexible and deformable substrates. Although the charge mobility of state-of-the-art OTFTs is superior to that of amorphous silicon and approaches that of amorphous oxide thin-film transistors (TFTs), their operational stability generally remains inferior and a point of concern for their commercial deployment. We report on an exhaustive characterization of OTFTs with an ultrathin bilayer gate dielectric comprising the amorphous fluoropolymer CYTOP and an Al2O3:HfO2 nanolaminate. Threshold voltage shifts measured at room temperatureovertimeperiods upto5.9×105 s do not vary monotonically andmore » remain below 0.2 V in microcrystalline OTFTs (mc-OTFTs) with field-effect carrier mobility values up to 1.6 cm2 V-1 s-1. Modeling of these shifts as a function of time with a double stretched-exponential (DSE) function suggests that two compensating aging mechanisms are at play and responsible for this high stability. The measured threshold voltage shifts at temperatures up to 75°C represent at least a one-order-of-magnitude improvement in the operational stability over previous reports, bringing OTFT technologies to a performance level comparable to that reported in the scientific literature for other commercial TFTs technologies.« less

Stable organic thin-film transistors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jia, Xiaojia; Fuentes-Hernandez, Canek; Wang, Cheng-Yin

2018-01-01

Organic thin-film transistors (OTFTs) can be fabricated at moderate temperatures and through cost-effective solution-based processes on a wide range of low-cost flexible and deformable substrates. Although the charge mobility of state-of-the-art OTFTs is superior to that of amorphous silicon and approaches that of amorphous oxide thin-film transistors (TFTs), their operational stability generally remains inferior and a point of concern for their commercial deployment. We report on an exhaustive characterization of OTFTs with an ultrathin bilayer gate dielectric comprising the amorphous fluoropolymer CYTOP and an Al2O3:HfO2 nanolaminate. Threshold voltage shifts measured at room temperatureovertimeperiods upto5.9×105 s do not vary monotonically andmore » remain below 0.2 V in microcrystalline OTFTs (mc-OTFTs) with field-effect carrier mobility values up to 1.6 cm2 V−1 s−1. Modeling of these shifts as a function of time with a double stretched-exponential (DSE) function suggests that two compensating aging mechanisms are at play and responsible for this high stability. The measured threshold voltage shifts at temperatures up to 75°C represent at least a one-order-of-magnitude improvement in the operational stability over previous reports, bringing OTFT technologies to a performance level comparable to that reported in the scientific literature for other commercial TFTs technologies.« less

Stable organic thin-film transistors

PubMed Central

Jia, Xiaojia; Fuentes-Hernandez, Canek; Wang, Cheng-Yin; Park, Youngrak; Kippelen, Bernard

2018-01-01

Organic thin-film transistors (OTFTs) can be fabricated at moderate temperatures and through cost-effective solution-based processes on a wide range of low-cost flexible and deformable substrates. Although the charge mobility of state-of-the-art OTFTs is superior to that of amorphous silicon and approaches that of amorphous oxide thin-film transistors (TFTs), their operational stability generally remains inferior and a point of concern for their commercial deployment. We report on an exhaustive characterization of OTFTs with an ultrathin bilayer gate dielectric comprising the amorphous fluoropolymer CYTOP and an Al2O3:HfO2 nanolaminate. Threshold voltage shifts measured at room temperature over time periods up to 5.9 × 105 s do not vary monotonically and remain below 0.2 V in microcrystalline OTFTs (μc-OTFTs) with field-effect carrier mobility values up to 1.6 cm2 V−1 s−1. Modeling of these shifts as a function of time with a double stretched-exponential (DSE) function suggests that two compensating aging mechanisms are at play and responsible for this high stability. The measured threshold voltage shifts at temperatures up to 75°C represent at least a one-order-of-magnitude improvement in the operational stability over previous reports, bringing OTFT technologies to a performance level comparable to that reported in the scientific literature for other commercial TFTs technologies. PMID:29340301

H∞ control problem of linear periodic piecewise time-delay systems

NASA Astrophysics Data System (ADS)

Xie, Xiaochen; Lam, James; Li, Panshuo

2018-04-01

This paper investigates the H∞ control problem based on exponential stability and weighted L2-gain analyses for a class of continuous-time linear periodic piecewise systems with time delay. A periodic piecewise Lyapunov-Krasovskii functional is developed by integrating a discontinuous time-varying matrix function with two global terms. By applying the improved constraints to the stability and L2-gain analyses, sufficient delay-dependent exponential stability and weighted L2-gain criteria are proposed for the periodic piecewise time-delay system. Based on these analyses, an H∞ control scheme is designed under the considerations of periodic state feedback control input and iterative optimisation. Finally, numerical examples are presented to illustrate the effectiveness of our proposed conditions.

Exponential lag function projective synchronization of memristor-based multidirectional associative memory neural networks via hybrid control

NASA Astrophysics Data System (ADS)

Yuan, Manman; Wang, Weiping; Luo, Xiong; Li, Lixiang; Kurths, Jürgen; Wang, Xiao

2018-03-01

This paper is concerned with the exponential lag function projective synchronization of memristive multidirectional associative memory neural networks (MMAMNNs). First, we propose a new model of MMAMNNs with mixed time-varying delays. In the proposed approach, the mixed delays include time-varying discrete delays and distributed time delays. Second, we design two kinds of hybrid controllers. Traditional control methods lack the capability of reflecting variable synaptic weights. In this paper, the controllers are carefully designed to confirm the process of different types of synchronization in the MMAMNNs. Third, sufficient criteria guaranteeing the synchronization of system are derived based on the derive-response concept. Finally, the effectiveness of the proposed mechanism is validated with numerical experiments.

Design data for radars based on 13.9 GHz Skylab scattering coefficient measurements

NASA Technical Reports Server (NTRS)

Moore, R. K. (Principal Investigator)

1974-01-01

The author has identified the following significant results. Measurements made at 13.9 GHz with the radar scatterometer on Skylab have been combined to produce median curves of the variation of scattering coefficient with angle of incidence out to 45 deg. Because of the large number of observations, and the large area averaged for each measured data point, these curves may be used as a new design base for radars. A reasonably good fit at larger angles is obtained using the theoretical expression based on an exponential height correlation function and also using Lambert's law. For angles under 10 deg, a different fit based on the exponential correlation function, and a fit based on geometric optics expressions are both reasonably valid.

An understanding of human dynamics in urban subway traffic from the Maximum Entropy Principle

NASA Astrophysics Data System (ADS)

Yong, Nuo; Ni, Shunjiang; Shen, Shifei; Ji, Xuewei

2016-08-01

We studied the distribution of entry time interval in Beijing subway traffic by analyzing the smart card transaction data, and then deduced the probability distribution function of entry time interval based on the Maximum Entropy Principle. Both theoretical derivation and data statistics indicated that the entry time interval obeys power-law distribution with an exponential cutoff. In addition, we pointed out the constraint conditions for the distribution form and discussed how the constraints affect the distribution function. It is speculated that for bursts and heavy tails in human dynamics, when the fitted power exponent is less than 1.0, it cannot be a pure power-law distribution, but with an exponential cutoff, which may be ignored in the previous studies.

Velocity and stress autocorrelation decay in isothermal dissipative particle dynamics

NASA Astrophysics Data System (ADS)

Chaudhri, Anuj; Lukes, Jennifer R.

2010-02-01

The velocity and stress autocorrelation decay in a dissipative particle dynamics ideal fluid model is analyzed in this paper. The autocorrelation functions are calculated at three different friction parameters and three different time steps using the well-known Groot/Warren algorithm and newer algorithms including self-consistent leap-frog, self-consistent velocity Verlet and Shardlow first and second order integrators. At low friction values, the velocity autocorrelation function decays exponentially at short times, shows slower-than exponential decay at intermediate times, and approaches zero at long times for all five integrators. As friction value increases, the deviation from exponential behavior occurs earlier and is more pronounced. At small time steps, all the integrators give identical decay profiles. As time step increases, there are qualitative and quantitative differences between the integrators. The stress correlation behavior is markedly different for the algorithms. The self-consistent velocity Verlet and the Shardlow algorithms show very similar stress autocorrelation decay with change in friction parameter, whereas the Groot/Warren and leap-frog schemes show variations at higher friction factors. Diffusion coefficients and shear viscosities are calculated using Green-Kubo integration of the velocity and stress autocorrelation functions. The diffusion coefficients match well-known theoretical results at low friction limits. Although the stress autocorrelation function is different for each integrator, fluctuates rapidly, and gives poor statistics for most of the cases, the calculated shear viscosities still fall within range of theoretical predictions and nonequilibrium studies.

Redox protein noncovalent functionalization of double-wall carbon nanotubes: electrochemical binder-less glucose biosensor.

PubMed

Pumera, Martin; Smíd, Bretislav

2007-10-01

Double wall carbon nanotubes are noncovalently functionalized with redox protein and such assembly is used for construction of electrochemical binder-less glucose biosensor. Redox protein glucose oxidase performs as biorecognition element and double wall carbon nanotubes act both as immobilization platform for redox enzyme and as signal transducer. The double carbon nanotubes are characterized by cyclic voltammetry and specific surface area measurements; the redox protein noncovalently functionalized double wall carbon nanotubes are characterized in detail by X-ray photoelectron spectroscopy, cyclic voltammetry, amperometry, and transmission electron microscopy.

A Study of the Thermal Environment Developed by a Traveling Slipper at High Velocity

DTIC Science & Technology

2013-03-01

Power Partition Function The next partition function takes the same formulation as the powered function but now the exponent is squared. The...function and note the squared term in the exponent . 66 Equation 4.27 (4.36) Thus far the three partition functions each give a predicted...hypothesized that the function would fall somewhere between the first exponential decay function and the power function. However, by squaring the exponent

In vivo chlorine and sodium MRI of rat brain at 21.1 T

PubMed Central

Elumalai, Malathy; Kitchen, Jason A.; Qian, Chunqi; Gor’kov, Peter L.; Brey, William W.

2017-01-01

Object MR imaging of low-gamma nuclei at the ultrahigh magnetic field of 21.1 T provides a new opportunity for understanding a variety of biological processes. Among these, chlorine and sodium are attracting attention for their involvement in brain function and cancer development. Materials and methods MRI of 35Cl and 23Na were performed and relaxation times were measured in vivo in normal rat (n = 3) and in rat with glioma (n = 3) at 21.1 T. The concentrations of both nuclei were evaluated using the center-out back-projection method. Results T1 relaxation curve of chlorine in normal rat head was fitted by bi-exponential function (T1a = 4.8 ms (0.7) T1b = 24.4 ± 7 ms (0.3) and compared with sodium (T1 = 41.4 ms). Free induction decays (FID) of chlorine and sodium in vivo were bi-exponential with similar rapidly decaying components of T2a∗=0.4 ms and T2a∗=0.53 ms, respectively. Effects of small acquisition matrix and bi-exponential FIDs were assessed for quantification of chlorine (33.2 mM) and sodium (44.4 mM) in rat brain. Conclusion The study modeled a dramatic effect of the bi-exponential decay on MRI results. The revealed increased chlorine concentration in glioma (~1.5 times) relative to a normal brain correlates with the hypothesis asserting the importance of chlorine for tumor progression. PMID:23748497

Monotonicity and Logarithmic Concavity of Two Functions Involving Exponential Function

ERIC Educational Resources Information Center

Liu, Ai-Qi; Li, Guo-Fu; Guo, Bai-Ni; Qi, Feng

2008-01-01

The function 1 divided by "x"[superscript 2] minus "e"[superscript"-x"] divided by (1 minus "e"[superscript"-x"])[superscript 2] for "x" greater than 0 is proved to be strictly decreasing. As an application of this monotonicity, the logarithmic concavity of the function "t" divided by "e"[superscript "at"] minus "e"[superscript"(a-1)""t"] for "a"…

Reliability analysis using an exponential power model with bathtub-shaped failure rate function: a Bayes study.

PubMed

Shehla, Romana; Khan, Athar Ali

2016-01-01

Models with bathtub-shaped hazard function have been widely accepted in the field of reliability and medicine and are particularly useful in reliability related decision making and cost analysis. In this paper, the exponential power model capable of assuming increasing as well as bathtub-shape, is studied. This article makes a Bayesian study of the same model and simultaneously shows how posterior simulations based on Markov chain Monte Carlo algorithms can be straightforward and routine in R. The study is carried out for complete as well as censored data, under the assumption of weakly-informative priors for the parameters. In addition to this, inference interest focuses on the posterior distribution of non-linear functions of the parameters. Also, the model has been extended to include continuous explanatory variables and R-codes are well illustrated. Two real data sets are considered for illustrative purposes.

Trigonometric Integration without Trigonometric Functions

ERIC Educational Resources Information Center

Quinlan, James; Kolibal, Joseph

2016-01-01

Teaching techniques of integration can be tedious and often uninspired. We present an obvious but underutilized approach for finding antiderivatives of various trigonometric functions using the complex exponential representation of the sine and cosine. The purpose goes beyond providing students an alternative approach to trigonometric integrals.…

Time prediction of failure a type of lamps by using general composite hazard rate model

NASA Astrophysics Data System (ADS)

Riaman; Lesmana, E.; Subartini, B.; Supian, S.

2018-03-01

This paper discusses the basic survival model estimates to obtain the average predictive value of lamp failure time. This estimate is for the parametric model, General Composite Hazard Level Model. The random time variable model used is the exponential distribution model, as the basis, which has a constant hazard function. In this case, we discuss an example of survival model estimation for a composite hazard function, using an exponential model as its basis. To estimate this model is done by estimating model parameters, through the construction of survival function and empirical cumulative function. The model obtained, will then be used to predict the average failure time of the model, for the type of lamp. By grouping the data into several intervals and the average value of failure at each interval, then calculate the average failure time of a model based on each interval, the p value obtained from the tes result is 0.3296.

Linear prediction and single-channel recording.

PubMed

Carter, A A; Oswald, R E

1995-08-01

The measurement of individual single-channel events arising from the gating of ion channels provides a detailed data set from which the kinetic mechanism of a channel can be deduced. In many cases, the pattern of dwells in the open and closed states is very complex, and the kinetic mechanism and parameters are not easily determined. Assuming a Markov model for channel kinetics, the probability density function for open and closed time dwells should consist of a sum of decaying exponentials. One method of approaching the kinetic analysis of such a system is to determine the number of exponentials and the corresponding parameters which comprise the open and closed dwell time distributions. These can then be compared to the relaxations predicted from the kinetic model to determine, where possible, the kinetic constants. We report here the use of a linear technique, linear prediction/singular value decomposition, to determine the number of exponentials and the exponential parameters. Using simulated distributions and comparing with standard maximum-likelihood analysis, the singular value decomposition techniques provide advantages in some situations and are a useful adjunct to other single-channel analysis techniques.

A new variation of the Buckingham exponential-6 potential with a tunable, singularity-free short-range repulsion and an adjustable long-range attraction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Werhahn, Jasper C.; Miliordos, Evangelos; Xantheas, Sotiris S.

2015-01-05

We introduce new generalized (reverting to the original) and extended (not reverting to the original) 4-parameter forms of the (B-2) Potential Energy Function (PEF) of Wang etal. (L.-P. Wang, J. Chen and T. van Voorhis, J. Chem. Theor. Comp. 9, 452 (2013)), which is itself a modification of the Buckingham exponential-6 PEF. The new forms have a tunable, singularity-free short-range repulsion and an adjustable long-range attraction. They produce fits to high quality ab initio data for the X–(H2O), X=F, Cl, Br, I and M+(H2O), M=Li, Na, K, Rb, Cs dimers that are between 1 and 2 orders of magnitude bettermore » than the original 3-parameter (B-2) and modified Buckingham exponential-6 PEFs. They are also slightly better than the 4-parameter generalized Buckingham exponential-6(gBe-6) and of comparable quality with the 4-parameter extended Morse (eM) PEFs introduced recently by us.« less

Extended q -Gaussian and q -exponential distributions from gamma random variables

NASA Astrophysics Data System (ADS)

Budini, Adrián A.

2015-05-01

The family of q -Gaussian and q -exponential probability densities fit the statistical behavior of diverse complex self-similar nonequilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis "nonextensive" entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that q -Gaussian and q -exponential random variables can always be expressed as a function of two statistically independent gamma random variables with the same scale parameter. Their shape index determines the complexity q parameter. This result also allows us to define an extended family of asymmetric q -Gaussian and modified q -exponential densities, which reduce to the standard ones when the shape parameters are the same. Furthermore, we demonstrate that a simple change of variables always allows relating any of these distributions with a beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in a fluid flow.

Cole-Davidson dynamics of simple chain models.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dotson, Taylor C.; McCoy, John Dwane; Adolf, Douglas Brian

2008-10-01

Rotational relaxation functions of the end-to-end vector of short, freely jointed and freely rotating chains were determined from molecular dynamics simulations. The associated response functions were obtained from the one-sided Fourier transform of the relaxation functions. The Cole-Davidson function was used to fit the response functions with extensive use being made of Cole-Cole plots in the fitting procedure. For the systems studied, the Cole-Davidson function provided remarkably accurate fits [as compared to the transform of the Kohlrausch-Williams-Watts (KWW) function]. The only appreciable deviations from the simulation results were in the high frequency limit and were due to ballistic or freemore » rotation effects. The accuracy of the Cole-Davidson function appears to be the result of the transition in the time domain from stretched exponential behavior at intermediate time to single exponential behavior at long time. Such a transition can be explained in terms of a distribution of relaxation times with a well-defined longest relaxation time. Since the Cole-Davidson distribution has a sharp cutoff in relaxation time (while the KWW function does not), it makes sense that the Cole-Davidson would provide a better frequency-domain description of the associated response function than the KWW function does.« less

Simplified formula for mean cycle-slip time of phase-locked loops with steady-state phase error.

NASA Technical Reports Server (NTRS)

Tausworthe, R. C.

1972-01-01

Previous work shows that the mean time from lock to a slipped cycle of a phase-locked loop is given by a certain double integral. Accurate numerical evaluation of this formula for the second-order loop is extremely vexing because the difference between exponentially large quantities is involved. The presented article demonstrates a method in which a much-reduced precision program can be used to obtain the mean first-cycle slip time for a loop of arbitrary degree tracking at a specified SNR and steady-state phase error. It also presents a simple approximate formula that is asymptotically tight at higher loop SNR.

Readout models for BaFBr0.85I0.15:Eu image plates

NASA Astrophysics Data System (ADS)

Stoeckl, M.; Solodov, A. A.

2018-06-01

The linearity of the photostimulated luminescence process makes repeated image-plate scanning a viable technique to extract a more dynamic range. In order to obtain a response estimate, two semi-empirical models for the readout fading of an image plate are introduced; they relate the depth distribution of activated photostimulated luminescence centers within an image plate to the recorded signal. Model parameters are estimated from image-plate scan series with BAS-MS image plates and the Typhoon FLA 7000 scanner for the hard x-ray image-plate diagnostic over a collection of experiments providing x-ray energy spectra whose approximate shape is a double exponential.

Interplay of Structure and Dynamics in Biomaterials

NASA Astrophysics Data System (ADS)

Vodnala, Preeti

Study of structure and dynamic behavior is essential to understand molecular motions in biological systems. In this work, two biomaterials were studied to address membrane properties and protein diffusion. For the first project, we studied the structure of liposomes, artificial vesicles that are used for drug encapsulation and administration of pharmaceuticals or cellular nutrients. Small-angle x-ray scattering (SAXS) was used to determine the structural properties of different liposomes composed of egg-PC and cholesterol bilayer. We examined the location of cholesterol by labelling cholesterol with bromine molecule and reveal that cholesterol is located one side of the leaflet adjusting itself to the curvature of a liposome. In my second project, we studied the dynamics of concentrated suspensions of alpha crystallin, one of the most abundant proteins in the human eye lens using X-ray photon correlation spectroscopy (XPCS). An improved understanding of dynamics could point the way towards treatments presbyopia and cataract. The dynamics were measured at volume fraction close to the critical volume fraction for the glass transition, where the intermediate scattering function, ƒ(q,T) could be well fit using a double exponential decay. The measured relaxation is in reasonable agreement with published molecular dynamics simulations for the relaxation times of hard-sphere colloids.

Assessment of tumor angiogenesis using fluorescence contrast agents

NASA Astrophysics Data System (ADS)

Chen, Yu; Liu, Qian; Huang, Ping; Hyman, Shay; Intes, Xavier; Lee, William; Chance, Britton

2003-12-01

Angiogenesis is an important factor for further tumor growth and thus could be an attractive therapeutic target. Optical imaging can provide a non-invasive way to measure the permeability of tumor blood vessels and assess the tumor vasculature. We have developed a dual-channel near-infrared fluorescence system for simultaneous measurement of the pharmacokinetics of tumorous and normal tissues with exogenous contrast agents. This frequency-domain system consists of the light source (780 nm laser diode), fiber optics, interference filter (830 nm) and the detector (PMT). The fluorescent contrast agent used in this study is Indocyanine Green (ICG), and the normal dosage is 100 μl at a concentration of 5 μM. In vivo animal study is performed on the K1735 melanoma-bearing mouse. The fluorescence signals both tumorous and normal tissues after the bolus injection of ICG through the tail vein are continuously recorded as a function of time. The data is fitted by a double-exponential model to reveal the wash-in and wash-out parameters of different tissues. We observed an elongated wash-out from the tumor compared with normal tissue (leg). The effect of radiation therapy on the tumor vasculature is also discussed.

Lyapunov exponents for one-dimensional aperiodic photonic bandgap structures

NASA Astrophysics Data System (ADS)

Kissel, Glen J.

2011-10-01

Existing in the "gray area" between perfectly periodic and purely randomized photonic bandgap structures are the socalled aperoidic structures whose layers are chosen according to some deterministic rule. We consider here a onedimensional photonic bandgap structure, a quarter-wave stack, with the layer thickness of one of the bilayers subject to being either thin or thick according to five deterministic sequence rules and binary random selection. To produce these aperiodic structures we examine the following sequences: Fibonacci, Thue-Morse, Period doubling, Rudin-Shapiro, as well as the triadic Cantor sequence. We model these structures numerically with a long chain (approximately 5,000,000) of transfer matrices, and then use the reliable algorithm of Wolf to calculate the (upper) Lyapunov exponent for the long product of matrices. The Lyapunov exponent is the statistically well-behaved variable used to characterize the Anderson localization effect (exponential confinement) when the layers are randomized, so its calculation allows us to more precisely compare the purely randomized structure with its aperiodic counterparts. It is found that the aperiodic photonic systems show much fine structure in their Lyapunov exponents as a function of frequency, and, in a number of cases, the exponents are quite obviously fractal.

Motor Variability Arises from a Slow Random Walk in Neural State

PubMed Central

Chaisanguanthum, Kris S.; Shen, Helen H.

2014-01-01

Even well practiced movements cannot be repeated without variability. This variability is thought to reflect “noise” in movement preparation or execution. However, we show that, for both professional baseball pitchers and macaque monkeys making reaching movements, motor variability can be decomposed into two statistical components, a slowly drifting mean and fast trial-by-trial fluctuations about the mean. The preparatory activity of dorsal premotor cortex/primary motor cortex neurons in monkey exhibits similar statistics. Although the neural and behavioral drifts appear to be correlated, neural activity does not account for trial-by-trial fluctuations in movement, which must arise elsewhere, likely downstream. The statistics of this drift are well modeled by a double-exponential autocorrelation function, with time constants similar across the neural and behavioral drifts in two monkeys, as well as the drifts observed in baseball pitching. These time constants can be explained by an error-corrective learning processes and agree with learning rates measured directly in previous experiments. Together, these results suggest that the central contributions to movement variability are not simply trial-by-trial fluctuations but are rather the result of longer-timescale processes that may arise from motor learning. PMID:25186752

Location priority for non-formal early childhood education school based on promethee method and map visualization

NASA Astrophysics Data System (ADS)

Ayu Nurul Handayani, Hemas; Waspada, Indra

2018-05-01

Non-formal Early Childhood Education (non-formal ECE) is an education that is held for children under 4 years old. The implementation in District of Banyumas, Non-formal ECE is monitored by The District Government of Banyumas and helped by Sanggar Kegiatan Belajar (SKB) Purwokerto as one of the organizer of Non-formal Education. The government itself has a program for distributing ECE to all villages in Indonesia. However, The location to construct the ECE school in several years ahead is not arranged yet. Therefore, for supporting that program, a decision support system is made to give some recommendation villages for constructing The ECE building. The data are projected based on Brown’s Double Exponential Smoothing Method and utilizing Preference Ranking Organization Method for Enrichment Evaluation (Promethee) to generate priority order. As the recommendations system, it generates map visualization which is colored according to the priority level of sub-district and village area. The system was tested with black box testing, Promethee testing, and usability testing. The results showed that the system functionality and Promethee algorithm were working properly, and the user was satisfied.

Genomics of bacteria and archaea: the emerging dynamic view of the prokaryotic world

PubMed Central

Koonin, Eugene V.; Wolf, Yuri I.

2008-01-01

The first bacterial genome was sequenced in 1995, and the first archaeal genome in 1996. Soon after these breakthroughs, an exponential rate of genome sequencing was established, with a doubling time of approximately 20 months for bacteria and approximately 34 months for archaea. Comparative analysis of the hundreds of sequenced bacterial and dozens of archaeal genomes leads to several generalizations on the principles of genome organization and evolution. A crucial finding that enables functional characterization of the sequenced genomes and evolutionary reconstruction is that the majority of archaeal and bacterial genes have conserved orthologs in other, often, distant organisms. However, comparative genomics also shows that horizontal gene transfer (HGT) is a dominant force of prokaryotic evolution, along with the loss of genetic material resulting in genome contraction. A crucial component of the prokaryotic world is the mobilome, the enormous collection of viruses, plasmids and other selfish elements, which are in constant exchange with more stable chromosomes and serve as HGT vehicles. Thus, the prokaryotic genome space is a tightly connected, although compartmentalized, network, a novel notion that undermines the ‘Tree of Life’ model of evolution and requires a new conceptual framework and tools for the study of prokaryotic evolution. PMID:18948295

Vibrational dynamics of acetate in D2O studied by infrared pump-probe spectroscopy.

PubMed

Banno, Motohiro; Ohta, Kaoru; Tominaga, Keisuke

2012-05-14

Solute-solvent interactions between acetate and D(2)O were investigated by vibrational spectroscopic methods. The vibrational dynamics of the COO asymmetric stretching mode in D(2)O was observed by time-resolved infrared (IR) pump-probe spectroscopy. The pump-probe signal contained both decay and oscillatory components. The time dependence of the decay component could be explained by a double exponential function with time constants of 200 fs and 2.6 ps, which are the same for both the COO asymmetric and symmetric stretching modes. The Fourier spectrum of the oscillatory component contained a band around 80 cm(-1), which suggests that the COO asymmetric stretching mode couples to a low-frequency vibrational mode with a wavenumber of 80 cm(-1). Based on quantum chemistry calculations, we propose that a bridged complex comprising an acetate ion and one D(2)O molecule, in which the two oxygen atoms in the acetate anion form hydrogen bonds with the two deuterium atoms in D(2)O, is the most stable structure. The 80 cm(-1) low-frequency mode was assigned to the asymmetric stretching vibration of the hydrogen bond in the bridged complex. This journal is © the Owner Societies 2012

Global synchronization of memristive neural networks subject to random disturbances via distributed pinning control.

PubMed

Guo, Zhenyuan; Yang, Shaofu; Wang, Jun

2016-12-01

This paper presents theoretical results on global exponential synchronization of multiple memristive neural networks in the presence of external noise by means of two types of distributed pinning control. The multiple memristive neural networks are coupled in a general structure via a nonlinear function, which consists of a linear diffusive term and a discontinuous sign term. A pinning impulsive control law is introduced in the coupled system to synchronize all neural networks. Sufficient conditions are derived for ascertaining global exponential synchronization in mean square. In addition, a pinning adaptive control law is developed to achieve global exponential synchronization in mean square. Both pinning control laws utilize only partial state information received from the neighborhood of the controlled neural network. Simulation results are presented to substantiate the theoretical results. Copyright © 2016 Elsevier Ltd. All rights reserved.

Stochastic exponential synchronization of memristive neural networks with time-varying delays via quantized control.

PubMed

Zhang, Wanli; Yang, Shiju; Li, Chuandong; Zhang, Wei; Yang, Xinsong

2018-08-01

This paper focuses on stochastic exponential synchronization of delayed memristive neural networks (MNNs) by the aid of systems with interval parameters which are established by using the concept of Filippov solution. New intermittent controller and adaptive controller with logarithmic quantization are structured to deal with the difficulties induced by time-varying delays, interval parameters as well as stochastic perturbations, simultaneously. Moreover, not only control cost can be reduced but also communication channels and bandwidth are saved by using these controllers. Based on novel Lyapunov functions and new analytical methods, several synchronization criteria are established to realize the exponential synchronization of MNNs with stochastic perturbations via intermittent control and adaptive control with or without logarithmic quantization. Finally, numerical simulations are offered to substantiate our theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

Master-slave exponential synchronization of delayed complex-valued memristor-based neural networks via impulsive control.

PubMed

Li, Xiaofan; Fang, Jian-An; Li, Huiyuan

2017-09-01

This paper investigates master-slave exponential synchronization for a class of complex-valued memristor-based neural networks with time-varying delays via discontinuous impulsive control. Firstly, the master and slave complex-valued memristor-based neural networks with time-varying delays are translated to two real-valued memristor-based neural networks. Secondly, an impulsive control law is constructed and utilized to guarantee master-slave exponential synchronization of the neural networks. Thirdly, the master-slave synchronization problems are transformed into the stability problems of the master-slave error system. By employing linear matrix inequality (LMI) technique and constructing an appropriate Lyapunov-Krasovskii functional, some sufficient synchronization criteria are derived. Finally, a numerical simulation is provided to illustrate the effectiveness of the obtained theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.

On the analytical determination of relaxation modulus of viscoelastic materials by Prony's interpolation method

NASA Technical Reports Server (NTRS)

Rodriguez, Pedro I.

1986-01-01

A computer implementation to Prony's curve fitting by exponential functions is presented. The method, although more than one hundred years old, has not been utilized to its fullest capabilities due to the restriction that the time range must be given in equal increments in order to obtain the best curve fit for a given set of data. The procedure used in this paper utilizes the 3-dimensional capabilities of the Interactive Graphics Design System (I.G.D.S.) in order to obtain the equal time increments. The resultant information is then input into a computer program that solves directly for the exponential constants yielding the best curve fit. Once the exponential constants are known, a simple least squares solution can be applied to obtain the final form of the equation.

Feasibility of protein turnover studies in prototroph Saccharomyces cerevisiae strains.

PubMed

Martin-Perez, Miguel; Villén, Judit

2015-04-07

Quantitative proteomics studies of yeast that use metabolic labeling with amino acids rely on auxotrophic mutations of one or more genes on the amino acid biosynthesis pathways. These mutations affect yeast metabolism and preclude the study of some biological processes. Overcoming this limitation, it has recently been described that proteins in a yeast prototrophic strain can also be metabolically labeled with heavy amino acids. However, the temporal profiles of label incorporation under the different phases of the prototroph's growth have not been examined. Labeling trajectories are important in the study of protein turnover and dynamics, in which label incorporation into proteins is monitored across many time points. Here we monitored protein labeling trajectories for 48 h after a pulse with heavy lysine in a yeast prototrophic strain and compared them with those of a lysine auxotrophic yeast. Labeling was successful in prototroph yeast during exponential growth phase but not in stationary phase. Furthermore, we were able to determine the half-lives of more than 1700 proteins during exponential phase of growth with high accuracy and reproducibility. We found a median half-life of 2 h in both strains, which corresponds with the cellular doubling time. Nucleolar and ribosomal proteins showed short half-lives, whereas mitochondrial proteins and other energy production enzymes presented longer half-lives. Except for some proteins involved in lysine biosynthesis, we observed a high correlation in protein half-lives between prototroph and auxotroph strains. Overall, our results demonstrate the feasibility of using prototrophs for proteomic turnover studies and provide a reliable data set of protein half-lives in exponentially growing yeast.

Evaluating the Use of Problem-Based Video Podcasts to Teach Mathematics in Higher Education

ERIC Educational Resources Information Center

Kay, Robin; Kletskin, Ilona

2012-01-01

Problem-based video podcasts provide short, web-based, audio-visual explanations of how to solve specific procedural problems in subject areas such as mathematics or science. A series of 59 problem-based video podcasts covering five key areas (operations with functions, solving equations, linear functions, exponential and logarithmic functions,…

Can One Take the Logarithm or the Sine of a Dimensioned Quantity or a Unit? Dimensional Analysis Involving Transcendental Functions

ERIC Educational Resources Information Center

Matta, Cherif F.; Massa, Lou; Gubskaya, Anna V.; Knoll, Eva

2011-01-01

The fate of dimensions of dimensioned quantities that are inserted into the argument of transcendental functions such as logarithms, exponentiation, trigonometric, and hyperbolic functions is discussed. Emphasis is placed on common misconceptions that are not often systematically examined in undergraduate courses of physical sciences. The argument…

Regional height-diameter equations for major tree species of southwest Oregon.

Treesearch

H. Temesgen; D.W. Hann; V.J. Monleon

2006-01-01

Selected tree height and diameter functions were evaluated for their predictive abilities for major tree species of southwest Oregon. The equations included tree diameter alone, or diameter plus alternative measures of stand density and relative position. Two of the base equations were asymptotic functions, and two were exponential functional forms. The inclusion of...

Double plasma resonance instability as a source of solar zebra emission

NASA Astrophysics Data System (ADS)

Benáček, J.; Karlický, M.

2018-03-01

Context. The double plasma resonance (DPR) instability plays a basic role in the generation of solar radio zebras. In the plasma, consisting of the loss-cone type distribution of hot electrons and much denser and colder background plasma, this instability generates the upper-hybrid waves, which are then transformed into the electromagnetic waves and observed as radio zebras. Aims: In the present paper we numerically study the double plasma resonance instability from the point of view of the zebra interpretation. Methods: We use a 3-dimensional electromagnetic particle-in-cell (3D PIC) relativistic model. We use this model in two versions: (a) a spatially extended "multi-mode" model and (b) a spatially limited "specific-mode" model. While the multi-mode model is used for detailed computations and verifications of the results obtained by the "specific-mode" model, the specific-mode model is used for computations in a broad range of model parameters, which considerably save computational time. For an analysis of the computational results, we developed software tools in Python. Results: First using the multi-mode model, we study details of the double plasma resonance instability. We show how the distribution function of hot electrons changes during this instability. Then we show that there is a very good agreement between results obtained by the multi-mode and specific-mode models, which is caused by a dominance of the wave with the maximal growth rate. Therefore, for computations in a broad range of model parameters, we use the specific-mode model. We compute the maximal growth rates of the double plasma resonance instability with a dependence on the ratio between the upper-hybrid ωUH and electron-cyclotron ωce frequency. We vary temperatures of both the hot and background plasma components and study their effects on the resulting growth rates. The results are compared with the analytical ones. We find a very good agreement between numerical and analytical growth rates. We also compute saturation energies of the upper-hybrid waves in a very broad range of parameters. We find that the saturation energies of the upper-hybrid waves show maxima and minima at almost the same values of ωUH/ωce as the growth rates, but with a higher contrast between them than the growth rate maxima and minima. The contrast between saturation energy maxima and minima increases when the temperature of hot electrons increases. Furthermore, we find that the saturation energy of the upper-hybrid waves is proportional to the density of hot electrons. The maximum saturated energy can be up to one percent of the kinetic energy of hot electrons. Finally we find that the saturation energy maxima in the interval of ωUH/ωce = 3-18 decrease according to the exponential function. All these findings can be used in the interpretation of solar radio zebras.

Analysis of crackling noise using the maximum-likelihood method: Power-law mixing and exponential damping.

PubMed

Salje, Ekhard K H; Planes, Antoni; Vives, Eduard

2017-10-01

Crackling noise can be initiated by competing or coexisting mechanisms. These mechanisms can combine to generate an approximate scale invariant distribution that contains two or more contributions. The overall distribution function can be analyzed, to a good approximation, using maximum-likelihood methods and assuming that it follows a power law although with nonuniversal exponents depending on a varying lower cutoff. We propose that such distributions are rather common and originate from a simple superposition of crackling noise distributions or exponential damping.

Quantitative photoplethysmography: Lambert-Beer law or inverse function incorporating light scatter.

PubMed

Cejnar, M; Kobler, H; Hunyor, S N

1993-03-01

Finger blood volume is commonly determined from measurement of infra-red (IR) light transmittance using the Lambert-Beer law of light absorption derived for use in non-scattering media, even when such transmission involves light scatter around the phalangeal bone. Simultaneous IR transmittance and finger volume were measured over the full dynamic range of vascular volumes in seven subjects and outcomes compared with data fitted according to the Lambert-Beer exponential function and an inverse function derived for light attenuation by scattering materials. Curves were fitted by the least-squares method and goodness of fit was compared using standard errors of estimate (SEE). The inverse function gave a better data fit in six of the subjects: mean SEE 1.9 (SD 0.7, range 0.7-2.8) and 4.6 (2.2, 2.0-8.0) respectively (p < 0.02, paired t-test). Thus, when relating IR transmittance to blood volume, as occurs in the finger during measurements of arterial compliance, an inverse function derived from a model of light attenuation by scattering media gives more accurate results than the traditional exponential fit.

Fractional Stability of Trunk Acceleration Dynamics of Daily-Life Walking: Toward a Unified Concept of Gait Stability

PubMed Central

Ihlen, Espen A. F.; van Schooten, Kimberley S.; Bruijn, Sjoerd M.; Pijnappels, Mirjam; van Dieën, Jaap H.

2017-01-01

Over the last decades, various measures have been introduced to assess stability during walking. All of these measures assume that gait stability may be equated with exponential stability, where dynamic stability is quantified by a Floquet multiplier or Lyapunov exponent. These specific constructs of dynamic stability assume that the gait dynamics are time independent and without phase transitions. In this case the temporal change in distance, d(t), between neighboring trajectories in state space is assumed to be an exponential function of time. However, results from walking models and empirical studies show that the assumptions of exponential stability break down in the vicinity of phase transitions that are present in each step cycle. Here we apply a general non-exponential construct of gait stability, called fractional stability, which can define dynamic stability in the presence of phase transitions. Fractional stability employs the fractional indices, α and β, of differential operator which allow modeling of singularities in d(t) that cannot be captured by exponential stability. The fractional stability provided an improved fit of d(t) compared to exponential stability when applied to trunk accelerations during daily-life walking in community-dwelling older adults. Moreover, using multivariate empirical mode decomposition surrogates, we found that the singularities in d(t), which were well modeled by fractional stability, are created by phase-dependent modulation of gait. The new construct of fractional stability may represent a physiologically more valid concept of stability in vicinity of phase transitions and may thus pave the way for a more unified concept of gait stability. PMID:28900400

Recurrence formulas for fully exponentially correlated four-body wave functions

NASA Astrophysics Data System (ADS)

Harris, Frank E.

2009-03-01

Formulas are presented for the recursive generation of four-body integrals in which the integrand consists of arbitrary integer powers (≥-1) of all the interparticle distances rij , multiplied by an exponential containing an arbitrary linear combination of all the rij . These integrals are generalizations of those encountered using Hylleraas basis functions and include all that are needed to make energy computations on the Li atom and other four-body systems with a fully exponentially correlated Slater-type basis of arbitrary quantum numbers. The only quantities needed to start the recursion are the basic four-body integral first evaluated by Fromm and Hill plus some easily evaluated three-body “boundary” integrals. The computational labor in constructing integral sets for practical computations is less than when the integrals are generated using explicit formulas obtained by differentiating the basic integral with respect to its parameters. Computations are facilitated by using a symbolic algebra program (MAPLE) to compute array index pointers and present syntactically correct FORTRAN source code as output; in this way it is possible to obtain error-free high-speed evaluations with minimal effort. The work can be checked by verifying sum rules the integrals must satisfy.

Rate laws of the self-induced aggregation kinetics of Brownian particles

NASA Astrophysics Data System (ADS)

Mondal, Shrabani; Sen, Monoj Kumar; Baura, Alendu; Bag, Bidhan Chandra

2016-03-01

In this paper we have studied the self induced aggregation kinetics of Brownian particles in the presence of both multiplicative and additive noises. In addition to the drift due to the self aggregation process, the environment may induce a drift term in the presence of a multiplicative noise. Then there would be an interplay between the two drift terms. It may account qualitatively the appearance of the different laws of aggregation process. At low strength of white multiplicative noise, the cluster number decreases as a Gaussian function of time. If the noise strength becomes appreciably large then the variation of cluster number with time is fitted well by the mono exponentially decaying function of time. For additive noise driven case, the decrease of cluster number can be described by the power law. But in case of multiplicative colored driven process, cluster number decays multi exponentially. However, we have explored how the rate constant (in the mono exponentially cluster number decaying case) depends on strength of interference of the noises and their intensity. We have also explored how the structure factor at long time depends on the strength of the cross correlation (CC) between the additive and the multiplicative noises.

DOUBLE POWER LAWS IN THE EVENT-INTEGRATED SOLAR ENERGETIC PARTICLE SPECTRUM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Lulu; Zhang, Ming; Rassoul, Hamid K., E-mail: lzhao@fit.edu

2016-04-10

A double power law or a power law with exponential rollover at a few to tens of MeV nucleon{sup −1} of the event-integrated differential spectra has been reported in many solar energetic particle (SEP) events. The rollover energies per nucleon of different elements correlate with a particle's charge-to-mass ratio (Q/A). The probable causes are suggested as residing in shock finite lifetimes, shock finite sizes, shock geometry, and an adiabatic cooling effect. In this work, we conduct a numerical simulation to investigate a particle's transport process in the inner heliosphere. We solve the focused transport equation using a time-backward Markov stochasticmore » approach. The convection, magnetic focusing, adiabatic cooling effect, and pitch-angle scattering are included. The effects that the interplanetary turbulence imposes on the shape of the resulting SEP spectra are examined. By assuming a pure power-law differential spectrum at the Sun, a perfect double-power-law feature with a break energy ranging from 10 to 120 MeV nucleon{sup −1} is obtained at 1 au. We found that the double power law of the differential energy spectrum is a robust result of SEP interplanetary propagation. It works for many assumptions of interplanetary turbulence spectra that give various forms of momentum dependence of a particle's mean free path. The different spectral shapes in low-energy and high-energy ends are not just a transition from the convection-dominated propagation to diffusion-dominated propagation.« less

Control of Growth Rate by Initial Substrate Concentration at Values Below Maximum Rate

PubMed Central

Gaudy, Anthony F.; Obayashi, Alan; Gaudy, Elizabeth T.

1971-01-01

The hyperbolic relationship between specific growth rate, μ, and substrate concentration, proposed by Monod and used since as the basis for the theory of steady-state growth in continuous-flow systems, was tested experimentally in batch cultures. Use of a Flavobacterium sp. exhibiting a high saturation constant for growth in glucose minimal medium allowed direct measurement of growth rate and substrate concentration throughout the growth cycle in medium containing a rate-limiting initial concentration of glucose. Specific growth rates were also measured for a wide range of initial glucose concentrations. A plot of specific growth rate versus initial substrate concentration was found to fit the hyperbolic equation. However, the instantaneous relationship between specific growth rate and substrate concentration during growth, which is stated by the equation, was not observed. Well defined exponential growth phases were developed at initial substrate concentrations below that required for support of the maximum exponential growth rate and a constant doubling time was maintained until 50% of the substrate had been used. It is suggested that the external substrate concentration initially present “sets” the specific growth rate by establishing a steady-state internal concentration of substrate, possibly through control of the number of permeation sites. PMID:5137579

Exponential growth and selection in self-replicating materials from DNA origami rafts

NASA Astrophysics Data System (ADS)

He, Xiaojin; Sha, Ruojie; Zhuo, Rebecca; Mi, Yongli; Chaikin, Paul M.; Seeman, Nadrian C.

2017-10-01

Self-replication and evolution under selective pressure are inherent phenomena in life, and but few artificial systems exhibit these phenomena. We have designed a system of DNA origami rafts that exponentially replicates a seed pattern, doubling the copies in each diurnal-like cycle of temperature and ultraviolet illumination, producing more than 7 million copies in 24 cycles. We demonstrate environmental selection in growing populations by incorporating pH-sensitive binding in two subpopulations. In one species, pH-sensitive triplex DNA bonds enable parent-daughter templating, while in the second species, triplex binding inhibits the formation of duplex DNA templating. At pH 5.3, the replication rate of species I is ~1.3-1.4 times faster than that of species II. At pH 7.8, the replication rates are reversed. When mixed together in the same vial, the progeny of species I replicate preferentially at pH 7.8 similarly at pH 5.3, the progeny of species II take over the system. This addressable selectivity should be adaptable to the selection and evolution of multi-component self-replicating materials in the nanoscopic-to-microscopic size range.

Inventory control of raw material using silver meal heuristic method in PR. Trubus Alami Malang

NASA Astrophysics Data System (ADS)

Ikasari, D. M.; Lestari, E. R.; Prastya, E.

2018-03-01

The purpose of this study was to compare the total inventory cost calculated using the method applied by PR. Trubus Alami and Silver Meal Heuristic (SMH) method. The study was started by forecasting the cigarette demand from July 2016 to June 2017 (48 weeks) using additive decomposition forecasting method. The additive decomposition was used because it has the lowest value of Mean Abosolute Deviation (MAD) and Mean Squared Deviation (MSD) compared to other methods such as multiplicative decomposition, moving average, single exponential smoothing, and double exponential smoothing. The forcasting results was then converted as a raw material needs and further calculated using SMH method to obtain inventory cost. As expected, the result shows that the order frequency of using SMH methods was smaller than that of using the method applied by Trubus Alami. This affected the total inventory cost. The result suggests that using SMH method gave a 29.41% lower inventory cost, giving the cost different of IDR 21,290,622. The findings, is therefore, indicated that the PR. Trubus Alami should apply the SMH method if the company wants to reduce the total inventory cost.

[Litter decomposition and nutrient release in Acacia mangium plantations established on degraded soils of Colombia].

PubMed

Castellanos-Barliza, Jeiner; León Peláez, Juan Diego

2011-03-01

Several factors control the decomposition in terrestrial ecosystems such as humidity, temperature, quality of litter and microbial activity. We investigated the effects of rainfall and soil plowing prior to the establishment of Acacia mangium plantations, using the litterbag technique, during a six month period, in forests plantations in Bajo Cauca region, Colombia. The annual decomposition constants (k) of simple exponential model, oscillated between 1.24 and 1.80, meanwhile k1 y k2 decomposition constants of double exponential model were 0.88-1.81 and 0.58-7.01. At the end of the study, the mean residual dry matter (RDM) was 47% of the initial value for the three sites. We found a slow N, Ca and Mg release pattern from the A. mangium leaf litter, meanwhile, phosphorus (P) showed a dominant immobilization phase, suggesting its low availability in soils. Chemical leaf litter quality parameters (e.g. N and P concentrations, C/N, N/P ratios and phenols content) showed an important influence on decomposition rates. The results of this study indicated that rainfall plays an important role on the decomposition process, but not soil plowing.

Geomorphic effectiveness of long profile shape and role of inherent geological controls, Ganga River Basin, India

NASA Astrophysics Data System (ADS)

Sonam, Sonam; Jain, Vikrant

2017-04-01

River long profile is one of the fundamental geomorphic parameters which provides a platform to study interaction of geological and geomorphic processes at different time scales. Long profile shape is governed by geological processes at 10 ^ 5 - 10 ^ 6 years' time scale and it controls the modern day (10 ^ 0 - 10 ^ 1 years' time scale) fluvial processes by controlling the spatial variability of channel slope. Identification of an appropriate model for river long profile may provide a tool to analyse the quantitative relationship between basin geology, profile shape and its geomorphic effectiveness. A systematic analysis of long profiles has been carried for the Himalayan tributaries of the Ganga River basin. Long profile shape and stream power distribution pattern is derived using SRTM DEM data (90 m spatial resolution). Peak discharge data from 34 stations is used for hydrological analysis. Lithological variability and major thrusts are marked along the river long profile. The best fit of long profile is analysed for power, logarithmic and exponential function. Second order exponential function provides the best representation of long profiles. The second order exponential equation is Z = K1*exp(-β1*L) + K2*exp(-β2*L), where Z is elevation of channel long profile, L is the length, K and β are coefficients of the exponential function. K1 and K2 are the proportion of elevation change of the long profile represented by β1 (fast) and β2 (slow) decay coefficients of the river long profile. Different values of coefficients express the variability in long profile shapes and is related with the litho-tectonic variability of the study area. Channel slope of long profile is estimated taking the derivative of exponential function. Stream power distribution pattern along long profile is estimated by superimposing the discharge and long profile slope. Sensitivity analysis of stream power distribution with decay coefficients of the second order exponential equation is evaluated for a range of coefficient values. Our analysis suggests that the amplitude of stream power peak value is dependent on K1, the proportion of elevation change coming under the fast decay exponent and the location of stream power peak is dependent of the long profile decay coefficient (β1). Different long profile shapes owing to litho-tectonic variability across the Himalayas are responsible for spatial variability of stream power distribution pattern. Most of the stream power peaks lie in the Higher Himalaya. In general, eastern rivers have higher stream power in hinterland area and low stream power in the alluvial plains. This is responsible for, 1) higher erosion rate and sediment supply in hinterland of eastern rivers, 2) the incised and stable nature of channels in the western alluvial plains and 3) aggrading channels with dynamic nature in the eastern alluvial plains. Our study shows that the spatial variability of litho-units defines the coefficients of long profile function which in turn controls the position and magnitude of stream power maxima and hence the geomorphic variability in a fluvial system.

Exercise modality effect on oxygen uptake off-transient kinetics at maximal oxygen uptake intensity.

PubMed

Sousa, Ana; Rodríguez, Ferran A; Machado, Leandro; Vilas-Boas, J Paulo; Fernandes, Ricardo J

2015-06-01

What is the central question of this study? Do the mechanical differences between swimming, rowing, running and cycling have a potential effect on the oxygen uptake (V̇O2) off-kinetics after an exercise sustained until exhaustion at 100% of maximal oxygen uptake (V̇O2max) intensity? What is the main finding and its importance? The mechanical differences between exercise modes had a potential effect and contributed to distinct amplitude of the fast component (higher in running compared with cycling) and time constant (higher in swimming compared with rowing and cycling) in the V̇O2 off-kinetic patterns at 100% of V̇O2max intensity. This suggests that swimmers, unlike rowers and cyclists, would benefit more from a longer duration of training intervals after each set of exercise performed at V̇O2max intensity. The kinetics of oxygen uptake (V̇O2) during recovery (off-transient kinetics) for different exercise modes is largely unexplored, hampering the prescription of training and recovery to enhance performance. The purpose of this study was to compare the V̇O2 off-transient kinetics response between swimmers, rowers, runners and cyclists during their specific mode of exercise at 100% of maximal oxygen uptake (V̇O2max) intensity and to examine the on-off symmetry. Groups of swimmers, rowers, runners and cyclists (n = 8 per group) performed (i) an incremental exercise protocol to assess the velocity or power associated with V̇O2max (vV̇O2max or wV̇O2max, respectively) and (ii) a square-wave exercise transition from rest to vV̇O2max/vV̇O2maxwV̇O2maxwV̇O2max until volitional exhaustion. Pulmonary exchange parameters were measured using a telemetric portable gas analyser (K4b(2) ; Cosmed, Rome, Italy), and the on- and off-transient kinetics were analysed through a double-exponential approach. For all exercise modes, both transient periods were symmetrical in shape once they had both been adequately fitted by a double-exponential model. However, differences were found in the off-kinetic parameters between exercise modes; the amplitude of the fast component of the V̇O2 off-response was higher in running compared with cycling (48 ± 5 and 36 ± 7 ml kg(-1) min(-1) , respectively; P < 0.001), and the time constant of the same phase was higher in swimming compared with rowing and cycling (63 ± 5, 56 ± 5 and 55 ± 3 s, respectively; P < 0.001). Although both phases were well described by a double-exponential model, the differences between exercise modes had a potential effect and contributed to distinct V̇O2 off-transient kinetic patterns at 100% of V̇O2max intensity. © 2015 The Authors. Experimental Physiology © 2015 The Physiological Society.

Quantum mechanical generalized phase-shift approach to atom-surface scattering: a Feshbach projection approach to dealing with closed channel effects.

PubMed

Maji, Kaushik; Kouri, Donald J

2011-03-28

We have developed a new method for solving quantum dynamical scattering problems, using the time-independent Schrödinger equation (TISE), based on a novel method to generalize a "one-way" quantum mechanical wave equation, impose correct boundary conditions, and eliminate exponentially growing closed channel solutions. The approach is readily parallelized to achieve approximate N(2) scaling, where N is the number of coupled equations. The full two-way nature of the TISE is included while propagating the wave function in the scattering variable and the full S-matrix is obtained. The new algorithm is based on a "Modified Cayley" operator splitting approach, generalizing earlier work where the method was applied to the time-dependent Schrödinger equation. All scattering variable propagation approaches to solving the TISE involve solving a Helmholtz-type equation, and for more than one degree of freedom, these are notoriously ill-behaved, due to the unavoidable presence of exponentially growing contributions to the numerical solution. Traditionally, the method used to eliminate exponential growth has posed a major obstacle to the full parallelization of such propagation algorithms. We stabilize by using the Feshbach projection operator technique to remove all the nonphysical exponentially growing closed channels, while retaining all of the propagating open channel components, as well as exponentially decaying closed channel components.

Data Modeling Using Finite Differences

ERIC Educational Resources Information Center

Rhoads, Kathryn; Mendoza Epperson, James A.

2017-01-01

The Common Core State Standards for Mathematics (CCSSM) states that high school students should be able to recognize patterns of growth in linear, quadratic, and exponential functions and construct such functions from tables of data (CCSSI 2010). In their work with practicing secondary teachers, the authors found that teachers may make some tacit…

University of Chicago School Mathematics Project (UCSMP) Algebra. WWC Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2009

2009-01-01

University of Chicago School Mathematics Project (UCSMP) Algebra is a one-year course covering three primary topics: (1) linear and quadratic expressions, sentences, and functions; (2) exponential expressions and functions; and (3) linear systems. Topics from geometry, probability, and statistics are integrated with the appropriate algebra.…

Baldcypress Height-Diamter Equations and Their Prediction Confindence Intervals

Treesearch

Bernard R. Parresol

1992-01-01

Height-diameter relationships are an important component in yield estimation, stand description, and damage appraisals. A nonlinear exponential function used extensively in the northwest United States was chosen for bald cypress (Taxodium distichum (L.) Rich.). Homogeneity and normality of residuals were examined, and the function as well as the...

Reinforcer magnitude and demand under fixed-ratio schedules with domestic hens.

PubMed

Grant, Amber A; Foster, T Mary; Temple, William; Jackson, Surrey; Kinloch, Jennifer; Poling, Alan

2014-03-01

This study compared three methods of normalizing demand functions to allow comparison of demand for different commodities and examined how varying reinforcer magnitudes affected these analyses. Hens responded under fixed-ratio schedules in 40-min sessions with response requirement doubling each session and with 2-s, 8-s, and 12-s access to wheat. Over the smaller fixed ratios overall response rates generally increased and were higher the shorter the magazine duration. The logarithms of the number of reinforcers obtained (consumption) and the fixed ratio (price) were well fitted by curvilinear demand functions (Hursh et al., 1988. Journal of the Experimental Analysis of Behavior 50, 419-440) that were inelastic (b negative) over small fixed-ratios. The fixed ratio with maximal response rate (Pmax) increased, and the rate of change of elasticity (a) and initial consumption (L) decreased with increased magazine duration. Normalizing consumption using measures of preference for various magazine durations (3-s vs. 3-s, 2-s vs. 8-s, and 2-s vs. 12-s), obtained using concurrent schedules, gave useful results as it removed the differences in L. Normalizing consumption and price (Hursh and Winger, 1995. Journal of the Experimental Analysis of Behavior 64, 373-384) unified the data functions as intended by that analysis. The exponential function (Hursh and Silberberg, 2008. Psychological Review, 115, 186-198) gave an essential value that increased (i.e., α decreased significantly) as magazine duration decreased. This was not as predicted, since α should be constant over variations in magazine duration, but is similar to previous findings using a similar procedure with different food qualities (hens) and food quantities (rats). Copyright © 2014 Elsevier B.V. All rights reserved.

On stable Pareto laws in a hierarchical model of economy

NASA Astrophysics Data System (ADS)

Chebotarev, A. M.

2007-01-01

This study considers a model of the income distribution of agents whose pairwise interaction is asymmetric and price-invariant. Asymmetric transactions are typical for chain-trading groups who arrange their business such that commodities move from senior to junior partners and money moves in the opposite direction. The price-invariance of transactions means that the probability of a pairwise interaction is a function of the ratio of incomes, which is independent of the price scale or absolute income level. These two features characterize the hierarchical model. The income distribution in this class of models is a well-defined double-Pareto function, which possesses Pareto tails for the upper and lower incomes. For gross and net upper incomes, the model predicts definite values of the Pareto exponents, agross and anet, which are stable with respect to quantitative variation of the pair-interaction. The Pareto exponents are also stable with respect to the choice of a demand function within two classes of status-dependent behavior of agents: linear demand ( agross=1, anet=2) and unlimited slowly varying demand ( agross=anet=1). For the sigmoidal demand that describes limited returns, agross=anet=1+α, with some α>0 satisfying a transcendental equation. The low-income distribution may be singular or vanishing in the neighborhood of the minimal income; in any case, it is L1-integrable and its Pareto exponent is given explicitly. The theory used in the present study is based on a simple balance equation and new results from multiplicative Markov chains and exponential moments of random geometric progressions.

Significant Figure Rules for General Arithmetic Functions.

ERIC Educational Resources Information Center

Graham, D. M.

1989-01-01

Provides some significant figure rules used in chemistry including the general theoretical basis; logarithms and antilogarithms; exponentiation (with exactly known exponents); sines and cosines; and the extreme value rule. (YP)

Continuous-Time Finance and the Waiting Time Distribution: Multiple Characteristic Times

NASA Astrophysics Data System (ADS)

Fa, Kwok Sau

2012-09-01

In this paper, we model the tick-by-tick dynamics of markets by using the continuous-time random walk (CTRW) model. We employ a sum of products of power law and stretched exponential functions for the waiting time probability distribution function; this function can fit well the waiting time distribution for BUND futures traded at LIFFE in 1997.

Third-order Douglas-Kroll Relativistic Coupled-Cluster Theory through Connected Single, Double, Triple, and Quadruple Substitutions: Applications to Diatomic and Triatomic Hydrides

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hirata, So; Yanai, Takeshi; De Jong, Wibe A.

Coupled-cluster methods including through and up to the connected single, double, triple, and quadruple substitutions (CCSD, CCSDT, and CCSDTQ) have been automatically derived and implemented for sequential and parallel executions for use in conjunction with a one-component third-order Douglas-Kroll (DK3) approximation for relativistic corrections. A combination of the converging electron-correlation methods, the accurate relativistic reference wave functions, and the use of systematic basis sets tailored to the relativistic approximation has been shown to predict the experimental singlet-triplet separations within 0.02 eV (0.5 kcal/mol) for five triatomic hydrides (CH2, NH2+, SiH2, PH2+, and AsH2+), the experimental bond lengths within 0.002 angstroms,more » rotational constants within 0.02 cm-1, vibration-rotation constants within 0.01 cm-1, centrifugal distortion constants within 2 %, harmonic vibration frequencies within 9 cm-1 (0.4 %), anharmonic vibrational constants within 2 cm-1, and dissociation energies within 0.03 eV (0.8 kcal/mol) for twenty diatomic hydrides (BH, CH, NH, OH, FH, AlH, SiH, PH, SH, ClH, GaH, GeH, AsH, SeH, BrH, InH, SnH, SbH, TeH, and IH) containing main-group elements across the second through fifth periods of the periodic table. In these calculations, spin-orbit effects on dissociation energies, which were assumed to be additive, were estimated from the measured spin-orbit coupling constants of atoms and diatomic molecules, and an electronic energy in the complete-basis-set, complete-electron-correlation limit has been extrapolated by the formula which was in turn based on the exponential-Gaussian extrapolation formula of the basis set dependence.« less

Spectrum analysis of radar life signal in the three kinds of theoretical models

NASA Astrophysics Data System (ADS)

Yang, X. F.; Ma, J. F.; Wang, D.

2017-02-01

In the single frequency continuous wave radar life detection system, based on the Doppler effect, the theory model of radar life signal is expressed by the real function, and there is a phenomenon that can't be confirmed by the experiment. When the phase generated by the distance between the measured object and the radar measuring head is л of integer times, the main frequency spectrum of life signal (respiration and heartbeat) is not existed in radar life signal. If this phase is л/2 of odd times, the main frequency spectrum of breath and heartbeat frequency is the strongest. In this paper, we use the Doppler effect as the basic theory, using three different mathematical expressions——real function, complex exponential function and Bessel's function expansion form. They are used to establish the theoretical model of radar life signal. Simulation analysis revealed that the Bessel expansion form theoretical model solve the problem of real function form. Compared with the theoretical model of the complex exponential function, the derived spectral line is greatly reduced in the theoretical model of Bessel expansion form, which is more consistent with the actual situation.

How extreme are extremes?

NASA Astrophysics Data System (ADS)

Cucchi, Marco; Petitta, Marcello; Calmanti, Sandro

2016-04-01

High temperatures have an impact on the energy balance of any living organism and on the operational capabilities of critical infrastructures. Heat-wave indicators have been mainly developed with the aim of capturing the potential impacts on specific sectors (agriculture, health, wildfires, transport, power generation and distribution). However, the ability to capture the occurrence of extreme temperature events is an essential property of a multi-hazard extreme climate indicator. Aim of this study is to develop a standardized heat-wave indicator, that can be combined with other indices in order to describe multiple hazards in a single indicator. The proposed approach can be used in order to have a quantified indicator of the strenght of a certain extreme. As a matter of fact, extremes are usually distributed in exponential or exponential-exponential functions and it is difficult to quickly asses how strong was an extreme events considering only its magnitude. The proposed approach simplify the quantitative and qualitative communication of extreme magnitude

Elastically driven intermittent microscopic dynamics in soft solids

NASA Astrophysics Data System (ADS)

Bouzid, Mehdi; Colombo, Jader; Barbosa, Lucas Vieira; Del Gado, Emanuela

2017-06-01

Soft solids with tunable mechanical response are at the core of new material technologies, but a crucial limit for applications is their progressive aging over time, which dramatically affects their functionalities. The generally accepted paradigm is that such aging is gradual and its origin is in slower than exponential microscopic dynamics, akin to the ones in supercooled liquids or glasses. Nevertheless, time- and space-resolved measurements have provided contrasting evidence: dynamics faster than exponential, intermittency and abrupt structural changes. Here we use 3D computer simulations of a microscopic model to reveal that the timescales governing stress relaxation, respectively, through thermal fluctuations and elastic recovery are key for the aging dynamics. When thermal fluctuations are too weak, stress heterogeneities frozen-in upon solidification can still partially relax through elastically driven fluctuations. Such fluctuations are intermittent, because of strong correlations that persist over the timescale of experiments or simulations, leading to faster than exponential dynamics.

Exponential Synchronization of Networked Chaotic Delayed Neural Network by a Hybrid Event Trigger Scheme.

PubMed

Fei, Zhongyang; Guan, Chaoxu; Gao, Huijun; Zhongyang Fei; Chaoxu Guan; Huijun Gao; Fei, Zhongyang; Guan, Chaoxu; Gao, Huijun

2018-06-01

This paper is concerned with the exponential synchronization for master-slave chaotic delayed neural network with event trigger control scheme. The model is established on a network control framework, where both external disturbance and network-induced delay are taken into consideration. The desired aim is to synchronize the master and slave systems with limited communication capacity and network bandwidth. In order to save the network resource, we adopt a hybrid event trigger approach, which not only reduces the data package sending out, but also gets rid of the Zeno phenomenon. By using an appropriate Lyapunov functional, a sufficient criterion for the stability is proposed for the error system with extended ( , , )-dissipativity performance index. Moreover, hybrid event trigger scheme and controller are codesigned for network-based delayed neural network to guarantee the exponential synchronization between the master and slave systems. The effectiveness and potential of the proposed results are demonstrated through a numerical example.

On the Occurrence of Mass Inflation for the Einstein-Maxwell-Scalar Field System with a Cosmological Constant and an Exponential Price Law

NASA Astrophysics Data System (ADS)

Costa, João L.; Girão, Pedro M.; Natário, José; Silva, Jorge Drumond

2018-03-01

In this paper we study the spherically symmetric characteristic initial data problem for the Einstein-Maxwell-scalar field system with a positive cosmological constant in the interior of a black hole, assuming an exponential Price law along the event horizon. More precisely, we construct open sets of characteristic data which, on the outgoing initial null hypersurface (taken to be the event horizon), converges exponentially to a reference Reissner-Nördstrom black hole at infinity. We prove the stability of the radius function at the Cauchy horizon, and show that, depending on the decay rate of the initial data, mass inflation may or may not occur. In the latter case, we find that the solution can be extended across the Cauchy horizon with continuous metric and Christoffel symbols in {L^2_{loc}} , thus violating the Christodoulou-Chruściel version of strong cosmic censorship.

Adult Age Differences and the Role of Cognitive Resources in Perceptual–Motor Skill Acquisition: Application of a Multilevel Negative Exponential Model

PubMed Central

Kennedy, Kristen M.; Rodrigue, Karen M.; Lindenberger, Ulman; Raz, Naftali

2010-01-01

The effects of advanced age and cognitive resources on the course of skill acquisition are unclear, and discrepancies among studies may reflect limitations of data analytic approaches. We applied a multilevel negative exponential model to skill acquisition data from 80 trials (four 20-trial blocks) of a pursuit rotor task administered to healthy adults (19–80 years old). The analyses conducted at the single-trial level indicated that the negative exponential function described performance well. Learning parameters correlated with measures of task-relevant cognitive resources on all blocks except the last and with age on all blocks after the second. Thus, age differences in motor skill acquisition may evolve in 2 phases: In the first, age differences are collinear with individual differences in task-relevant cognitive resources; in the second, age differences orthogonal to these resources emerge. PMID:20047985

Discharging dynamics in an electrolytic cell

NASA Astrophysics Data System (ADS)

Feicht, Sarah E.; Frankel, Alexandra E.; Khair, Aditya S.

2016-07-01

We analyze the dynamics of a discharging electrolytic cell comprised of a binary symmetric electrolyte between two planar, parallel blocking electrodes. When a voltage is initially applied, ions in the electrolyte migrate towards the electrodes, forming electrical double layers. After the system reaches steady state and the external current decays to zero, the applied voltage is switched off and the cell discharges, with the ions eventually returning to a uniform spatial concentration. At voltages on the order of the thermal voltage VT=kBT /q ≃25 mV, where kB is Boltzmann's constant, T is temperature, and q is the charge of a proton, experiments on surfactant-doped nonpolar fluids observe that the temporal evolution of the external current during charging and discharging is not symmetric [V. Novotny and M. A. Hopper, J. Electrochem. Soc. 126, 925 (1979), 10.1149/1.2129195; P. Kornilovitch and Y. Jeon, J. Appl. Phys. 109, 064509 (2011), 10.1063/1.3554445]. In fact, at sufficiently large voltages (several VT), the current during discharging is no longer monotonic: it displays a "reverse peak" before decaying in magnitude to zero. We analyze the dynamics of discharging by solving the Poisson-Nernst-Planck equations governing ion transport via asymptotic and numerical techniques in three regimes. First, in the "linear regime" when the applied voltage V is formally much less than VT, the charging and discharging currents are antisymmetric in time; however, the potential and charge density profiles during charging and discharging are asymmetric. The current evolution is on the R C timescale of the cell, λDL /D , where L is the width of the cell, D is the diffusivity of ions, and λD is the Debye length. Second, in the (experimentally relevant) thin-double-layer limit ɛ =λD/L ≪1 , there is a "weakly nonlinear" regime defined by VT≲V ≲VTln(1 /ɛ ) , where the bulk salt concentration is uniform; thus the R C timescale of the evolution of the current magnitude persists. However, nonlinear, voltage-dependent, capacitance of the double layer is responsible for a break in temporal antisymmetry of the charging and discharging currents. Third, the reverse peak in the discharging current develops in a "strongly nonlinear" regime V ≳VTln(1 /ɛ ) , driven by neutral salt adsorption into the double layers and consequent bulk depletion during charging. The strongly nonlinear regime features current evolution over three timescales. The current decays in magnitude on the double layer relaxation timescale, λD2/D ; then grows exponentially in time towards the reverse peak on the diffusion timescale, L2/D , indicating that the reverse peak is the results of fast diffusion of ions from the double layer layer to the bulk. Following the reverse peak, the current decays exponentially to zero on the R C timescale. Notably, the current at the reverse peak and the time of the reverse peak saturate at large voltages V ≫VTln(1 /ɛ ) . We provide semi-analytic expressions for the saturated reverse peak time and current, which can be used to infer charge carrier diffusivity and concentration from experiments.

Well hydraulics in pumping tests with exponentially decayed rates of abstraction in confined aquifers

NASA Astrophysics Data System (ADS)

Wen, Zhang; Zhan, Hongbin; Wang, Quanrong; Liang, Xing; Ma, Teng; Chen, Chen

2017-05-01

Actual field pumping tests often involve variable pumping rates which cannot be handled by the classical constant-rate or constant-head test models, and often require a convolution process to interpret the test data. In this study, we proposed a semi-analytical model considering an exponentially decreasing pumping rate started at a certain (higher) rate and eventually stabilized at a certain (lower) rate for cases with or without wellbore storage. A striking new feature of the pumping test with an exponentially decayed rate is that the drawdowns will decrease over a certain period of time during intermediate pumping stage, which has never been seen before in constant-rate or constant-head pumping tests. It was found that the drawdown-time curve associated with an exponentially decayed pumping rate function was bounded by two asymptotic curves of the constant-rate tests with rates equaling to the starting and stabilizing rates, respectively. The wellbore storage must be considered for a pumping test without an observation well (single-well test). Based on such characteristics of the time-drawdown curve, we developed a new method to estimate the aquifer parameters by using the genetic algorithm.

Optimal Pulse Configuration Design for Heart Stimulation. A Theoretical, Numerical and Experimental Study.

NASA Astrophysics Data System (ADS)

Hardy, Neil; Dvir, Hila; Fenton, Flavio

Existing pacemakers consider the rectangular pulse to be the optimal form of stimulation current. However, other waveforms for the use of pacemakers could save energy while still stimulating the heart. We aim to find the optimal waveform for pacemaker use, and to offer a theoretical explanation for its advantage. Since the pacemaker battery is a charge source, here we probe the stimulation current waveforms with respect to the total charge delivery. In this talk we present theoretical analysis and numerical simulations of myocyte ion-channel currents acting as an additional source of charge that adds to the external stimulating charge for stimulation purposes. Therefore, we find that as the action potential emerges, the external stimulating current can be reduced accordingly exponentially. We then performed experimental studies in rabbit and cat hearts and showed that indeed exponential truncated pulses with less total charge can still induce activation in the heart. From the experiments, we present curves showing the savings in charge as a function of exponential waveform and we calculated that the longevity of the pacemaker battery would be ten times higher for the exponential current compared to the rectangular waveforms. Thanks to Petit Undergraduate Research Scholars Program and NSF# 1413037.

The shock waves in decaying supersonic turbulence

NASA Astrophysics Data System (ADS)

Smith, M. D.; Mac Low, M.-M.; Zuev, J. M.

2000-04-01

We here analyse numerical simulations of supersonic, hypersonic and magnetohydrodynamic turbulence that is free to decay. Our goals are to understand the dynamics of the decay and the characteristic properties of the shock waves produced. This will be useful for interpretation of observations of both motions in molecular clouds and sources of non-thermal radiation. We find that decaying hypersonic turbulence possesses an exponential tail of fast shocks and an exponential decay in time, i.e. the number of shocks is proportional to t exp (-ktv) for shock velocity jump v and mean initial wavenumber k. In contrast to the velocity gradients, the velocity Probability Distribution Function remains Gaussian with a more complex decay law. The energy is dissipated not by fast shocks but by a large number of low Mach number shocks. The power loss peaks near a low-speed turn-over in an exponential distribution. An analytical extension of the mapping closure technique is able to predict the basic decay features. Our analytic description of the distribution of shock strengths should prove useful for direct modeling of observable emission. We note that an exponential distribution of shocks such as we find will, in general, generate very low excitation shock signatures.

Algebraic approach to electronic spectroscopy and dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Toutounji, Mohamad

Lie algebra, Zassenhaus, and parameter differentiation techniques are utilized to break up the exponential of a bilinear Hamiltonian operator into a product of noncommuting exponential operators by the virtue of the theory of Wei and Norman [J. Math. Phys. 4, 575 (1963); Proc. Am. Math. Soc., 15, 327 (1964)]. There are about three different ways to find the Zassenhaus exponents, namely, binomial expansion, Suzuki formula, and q-exponential transformation. A fourth, and most reliable method, is provided. Since linearly displaced and distorted (curvature change upon excitation/emission) Hamiltonian and spin-boson Hamiltonian may be classified as bilinear Hamiltonians, the presented algebraic algorithm (exponentialmore » operator disentanglement exploiting six-dimensional Lie algebra case) should be useful in spin-boson problems. The linearly displaced and distorted Hamiltonian exponential is only treated here. While the spin-boson model is used here only as a demonstration of the idea, the herein approach is more general and powerful than the specific example treated. The optical linear dipole moment correlation function is algebraically derived using the above mentioned methods and coherent states. Coherent states are eigenvectors of the bosonic lowering operator a and not of the raising operator a{sup +}. While exp(a{sup +}) translates coherent states, exp(a{sup +}a{sup +}) operation on coherent states has always been a challenge, as a{sup +} has no eigenvectors. Three approaches, and the results, of that operation are provided. Linear absorption spectra are derived, calculated, and discussed. The linear dipole moment correlation function for the pure quadratic coupling case is expressed in terms of Legendre polynomials to better show the even vibronic transitions in the absorption spectrum. Comparison of the present line shapes to those calculated by other methods is provided. Franck-Condon factors for both linear and quadratic couplings are exactly accounted for by the herein calculated linear absorption spectra. This new methodology should easily pave the way to calculating the four-point correlation function, F({tau}{sub 1},{tau}{sub 2},{tau}{sub 3},{tau}{sub 4}), of which the optical nonlinear response function may be procured, as evaluating F({tau}{sub 1},{tau}{sub 2},{tau}{sub 3},{tau}{sub 4}) is only evaluating the optical linear dipole moment correlation function iteratively over different time intervals, which should allow calculating various optical nonlinear temporal/spectral signals.« less

Existence and global exponential stability of periodic solution to BAM neural networks with periodic coefficients and continuously distributed delays

NASA Astrophysics Data System (ADS)

Zhou, distributed delays [rapid communication] T.; Chen, A.; Zhou, Y.

2005-08-01

By using the continuation theorem of coincidence degree theory and Liapunov function, we obtain some sufficient criteria to ensure the existence and global exponential stability of periodic solution to the bidirectional associative memory (BAM) neural networks with periodic coefficients and continuously distributed delays. These results improve and generalize the works of papers [J. Cao, L. Wang, Phys. Rev. E 61 (2000) 1825] and [Z. Liu, A. Chen, J. Cao, L. Huang, IEEE Trans. Circuits Systems I 50 (2003) 1162]. An example is given to illustrate that the criteria are feasible.

Observational constraints on tachyonic chameleon dark energy model

NASA Astrophysics Data System (ADS)

Banijamali, A.; Bellucci, S.; Fazlpour, B.; Solbi, M.

2018-03-01

It has been recently shown that tachyonic chameleon model of dark energy in which tachyon scalar field non-minimally coupled to the matter admits stable scaling attractor solution that could give rise to the late-time accelerated expansion of the universe and hence alleviate the coincidence problem. In the present work, we use data from Type Ia supernova (SN Ia) and Baryon Acoustic oscillations to place constraints on the model parameters. In our analysis we consider in general exponential and non-exponential forms for the non-minimal coupling function and tachyonic potential and show that the scenario is compatible with observations.

A spatial scan statistic for survival data based on Weibull distribution.

PubMed

Bhatt, Vijaya; Tiwari, Neeraj

2014-05-20

The spatial scan statistic has been developed as a geographical cluster detection analysis tool for different types of data sets such as Bernoulli, Poisson, ordinal, normal and exponential. We propose a scan statistic for survival data based on Weibull distribution. It may also be used for other survival distributions, such as exponential, gamma, and log normal. The proposed method is applied on the survival data of tuberculosis patients for the years 2004-2005 in Nainital district of Uttarakhand, India. Simulation studies reveal that the proposed method performs well for different survival distribution functions. Copyright © 2013 John Wiley & Sons, Ltd.

Synchronised firing patterns in a random network of adaptive exponential integrate-and-fire neuron model.

PubMed

Borges, F S; Protachevicz, P R; Lameu, E L; Bonetti, R C; Iarosz, K C; Caldas, I L; Baptista, M S; Batista, A M

2017-06-01

We have studied neuronal synchronisation in a random network of adaptive exponential integrate-and-fire neurons. We study how spiking or bursting synchronous behaviour appears as a function of the coupling strength and the probability of connections, by constructing parameter spaces that identify these synchronous behaviours from measurements of the inter-spike interval and the calculation of the order parameter. Moreover, we verify the robustness of synchronisation by applying an external perturbation to each neuron. The simulations show that bursting synchronisation is more robust than spike synchronisation. Copyright © 2017 Elsevier Ltd. All rights reserved.

Cosmological models with a hybrid scale factor in an extended gravity theory

NASA Astrophysics Data System (ADS)

Mishra, B.; Tripathy, S. K.; Tarai, Sankarsan

2018-03-01

A general formalism to investigate Bianchi type V Ih universes is developed in an extended theory of gravity. A minimally coupled geometry and matter field is considered with a rescaled function of f(R,T) substituted in place of the Ricci scalar R in the geometrical action. Dynamical aspects of the models are discussed by using a hybrid scale factor (HSF) that behaves as power law in an initial epoch and as an exponential form at late epoch. The power law behavior and the exponential behavior appear as two extreme cases of the present model.

Individual tree-diameter growth model for the Northeastern United States

Treesearch

Richard M. Teck; Donald E. Hilt

1991-01-01

Describes a distance-independent individual-tree diameter growth model for the Northeastern United States. Diameter growth is predicted in two steps using a two parameter, sigmoidal growth function modified by a one parameter exponential decay function with species-specific coefficients. Coefficients are presented for 28 species groups. The model accounts for...

Calculus of Elementary Functions, Part II. Student Text. Revised Edition.

ERIC Educational Resources Information Center

Herriot, Sarah T.; And Others

This course is intended for students who have a thorough knowledge of college preparatory mathematics, including algebra, axiomatic geometry, trigonometry, and analytic geometry. This text, Part II, contains material designed to follow Part I. Chapters included in this text are: (6) Derivatives of Exponential and Related Functions; (7) Area and…

Chem Ed Compacts

ERIC Educational Resources Information Center

Wolf, Walter A., Ed.

1976-01-01

Presents three activities: (1) the investigation of the purity and stability of nicotinamide and flavin coenzymes; (2) desk-computer fitting of a two-exponential function; and (3) an interesting and inexpensive solubility product experiment for introductory chemistry. (RH)

Computerized glow curve deconvolution of thermoluminescent emission from polyminerals of Jamaica Mexican flower

NASA Astrophysics Data System (ADS)

Favalli, A.; Furetta, C.; Zaragoza, E. Cruz; Reyes, A.

The aim of this work is to study the main thermoluminescence (TL) characteristics of the inorganic polyminerals extracted from dehydrated Jamaica flower or roselle (Hibiscus sabdariffa L.) belonging to Malvaceae family of Mexican origin. TL emission properties of the polymineral fraction in powder were studied using the initial rise (IR) method. The complex structure and kinetic parameters of the glow curves have been analysed accurately using the computerized glow curve deconvolution (CGCD) assuming an exponential distribution of trapping levels. The extension of the IR method to the case of a continuous and exponential distribution of traps is reported, such as the derivation of the TL glow curve deconvolution functions for continuous trap distribution. CGCD is performed both in the case of frequency factor, s, temperature independent, and in the case with the s function of temperature.

Thermal dynamics on the lattice with exponentially improved accuracy

NASA Astrophysics Data System (ADS)

Pawlowski, Jan M.; Rothkopf, Alexander

2018-03-01

We present a novel simulation prescription for thermal quantum fields on a lattice that operates directly in imaginary frequency space. By distinguishing initial conditions from quantum dynamics it provides access to correlation functions also outside of the conventional Matsubara frequencies ωn = 2 πnT. In particular it resolves their frequency dependence between ω = 0 and ω1 = 2 πT, where the thermal physics ω ∼ T of e.g. transport phenomena is dominantly encoded. Real-time spectral functions are related to these correlators via an integral transform with rational kernel, so that their unfolding from the novel simulation data is exponentially improved compared to standard Euclidean simulations. We demonstrate this improvement within a non-trivial 0 + 1-dimensional quantum mechanical toy-model and show that spectral features inaccessible in standard Euclidean simulations are quantitatively captured.

Memory feedback PID control for exponential synchronisation of chaotic Lur'e systems

NASA Astrophysics Data System (ADS)

Zhang, Ruimei; Zeng, Deqiang; Zhong, Shouming; Shi, Kaibo

2017-09-01

This paper studies the problem of exponential synchronisation of chaotic Lur'e systems (CLSs) via memory feedback proportional-integral-derivative (PID) control scheme. First, a novel augmented Lyapunov-Krasovskii functional (LKF) is constructed, which can make full use of the information on time delay and activation function. Second, improved synchronisation criteria are obtained by using new integral inequalities, which can provide much tighter bounds than what the existing integral inequalities can produce. In comparison with existing results, in which only proportional control or proportional derivative (PD) control is used, less conservative results are derived for CLSs by PID control. Third, the desired memory feedback controllers are designed in terms of the solution to linear matrix inequalities. Finally, numerical simulations of Chua's circuit and neural network are provided to show the effectiveness and advantages of the proposed results.

n-Iterative Exponential Forgetting Factor for EEG Signals Parameter Estimation

PubMed Central

Palma Orozco, Rosaura

2018-01-01

Electroencephalograms (EEG) signals are of interest because of their relationship with physiological activities, allowing a description of motion, speaking, or thinking. Important research has been developed to take advantage of EEG using classification or predictor algorithms based on parameters that help to describe the signal behavior. Thus, great importance should be taken to feature extraction which is complicated for the Parameter Estimation (PE)–System Identification (SI) process. When based on an average approximation, nonstationary characteristics are presented. For PE the comparison of three forms of iterative-recursive uses of the Exponential Forgetting Factor (EFF) combined with a linear function to identify a synthetic stochastic signal is presented. The one with best results seen through the functional error is applied to approximate an EEG signal for a simple classification example, showing the effectiveness of our proposal. PMID:29568310

The Superstatistical Nature and Interoccurrence Time of Atmospheric Mercury Concentration Fluctuations

NASA Astrophysics Data System (ADS)

Carbone, F.; Bruno, A. G.; Naccarato, A.; De Simone, F.; Gencarelli, C. N.; Sprovieri, F.; Hedgecock, I. M.; Landis, M. S.; Skov, H.; Pfaffhuber, K. A.; Read, K. A.; Martin, L.; Angot, H.; Dommergue, A.; Magand, O.; Pirrone, N.

2018-01-01

The probability density function (PDF) of the time intervals between subsequent extreme events in atmospheric Hg0 concentration data series from different latitudes has been investigated. The Hg0 dynamic possesses a long-term memory autocorrelation function. Above a fixed threshold Q in the data, the PDFs of the interoccurrence time of the Hg0 data are well described by a Tsallis q-exponential function. This PDF behavior has been explained in the framework of superstatistics, where the competition between multiple mesoscopic processes affects the macroscopic dynamics. An extensive parameter μ, encompassing all possible fluctuations related to mesoscopic phenomena, has been identified. It follows a χ2 distribution, indicative of the superstatistical nature of the overall process. Shuffling the data series destroys the long-term memory, the distributions become independent of Q, and the PDFs collapse on to the same exponential distribution. The possible central role of atmospheric turbulence on extreme events in the Hg0 data is highlighted.

The acquisition of conditioned responding.

PubMed

Harris, Justin A

2011-04-01

This report analyzes the acquisition of conditioned responses in rats trained in a magazine approach paradigm. Following the suggestion by Gallistel, Fairhurst, and Balsam (2004), Weibull functions were fitted to the trial-by-trial response rates of individual rats. These showed that the emergence of responding was often delayed, after which the response rate would increase relatively gradually across trials. The fit of the Weibull function to the behavioral data of each rat was equaled by that of a cumulative exponential function incorporating a response threshold. Thus, the growth in conditioning strength on each trial can be modeled by the derivative of the exponential--a difference term of the form used in many models of associative learning (e.g., Rescorla & Wagner, 1972). Further analyses, comparing the acquisition of responding with a continuously reinforced stimulus (CRf) and a partially reinforced stimulus (PRf), provided further evidence in support of the difference term. In conclusion, the results are consistent with conventional models that describe learning as the growth of associative strength, incremented on each trial by an error-correction process.

Communication: Evaluating non-empirical double hybrid functionals for spin-state energetics in transition-metal complexes

NASA Astrophysics Data System (ADS)

Wilbraham, Liam; Adamo, Carlo; Ciofini, Ilaria

2018-01-01

The computationally assisted, accelerated design of inorganic functional materials often relies on the ability of a given electronic structure method to return the correct electronic ground state of the material in question. Outlining difficulties with current density functionals and wave function-based approaches, we highlight why double hybrid density functionals represent promising candidates for this purpose. In turn, we show that PBE0-DH (and PBE-QIDH) offers a significant improvement over its hybrid parent functional PBE0 [as well as B3LYP* and coupled cluster singles and doubles with perturbative triples (CCSD(T))] when computing spin-state splitting energies, using high-level diffusion Monte Carlo calculations as a reference. We refer to the opposing influence of Hartree-Fock (HF) exchange and MP2, which permits higher levels of HF exchange and a concomitant reduction in electronic density error, as the reason for the improved performance of double-hybrid functionals relative to hybrid functionals. Additionally, using 16 transition metal (Fe and Co) complexes, we show that low-spin states are stabilised by increasing contributions from MP2 within the double hybrid formulation. Furthermore, this stabilisation effect is more prominent for high field strength ligands than low field strength ligands.

Ferromagnetic resonance in coupled permalloy double films separated by a Cu interlayer

NASA Astrophysics Data System (ADS)

Maksymowicz, A. Z.; Whiting, J. S. S.; Watson, M. L.; Chambers, A.

1991-03-01

Ferromagnetic resonance (FMR) at 16 GHz was used to study the magnetic coupling between two-layers of permalloy separated by a nonmagnetic Cu layer. Samples with the same thickness (600 Å) of both permalloy layers were deposited from e-gun sources onto glass substrates in UHV. The thickness d of the Cu interlayer was varied from 5 to 37 Å. The exchange coupling energy ( E = - KM1· M2) model was used to describe the interaction between the two magnetic layers. It was found from the ferromagnetic resonance data in the perpendicular configuration that K( d) follows an exponential law, K = K0e - d/ q, where q = 9.3 Å.

Instantaneous and dynamical decoherence

NASA Astrophysics Data System (ADS)

Polonyi, Janos

2018-04-01

Two manifestations of decoherence, called instantaneous and dynamical, are investigated. The former reflects the suppression of the interference between the components of the current state while the latter reflects that within the initial state. These types of decoherence are computed in the case of the Brownian motion and the harmonic and anharmonic oscillators within the semiclassical approximation. A remarkable phenomenon, namely the opposite orientation of the time arrow of the dynamical variables compared to that of the quantum fluctuations generates a double exponential time dependence of the dynamical decoherence in the presence of a harmonic force. For the weakly anharmonic oscillator the dynamical decoherence is found to depend in a singular way on the amount of the anharmonicity.

Universal renormalization-group dynamics at the onset of chaos in logistic maps and nonextensive statistical mechanics

NASA Astrophysics Data System (ADS)

Baldovin, F.; Robledo, A.

2002-10-01

We uncover the dynamics at the chaos threshold μ∞ of the logistic map and find that it consists of trajectories made of intertwined power laws that reproduce the entire period-doubling cascade that occurs for μ<μ∞. We corroborate this structure analytically via the Feigenbaum renormalization-group (RG) transformation and find that the sensitivity to initial conditions has precisely the form of a q exponential, of which we determine the q index and the q-generalized Lyapunov coefficient λq. Our results are an unequivocal validation of the applicability of the nonextensive generalization of Boltzmann-Gibbs statistical mechanics to critical points of nonlinear maps.

An Analysis of Wave Interactions in Swept-Wing Flows

NASA Technical Reports Server (NTRS)

Reed, H. L.

1984-01-01

Crossflow instabilities dominate disturbance growth in the leading-edge region of swept wings. Streamwise vortices in a boundary layer strongly influence the behavior of other disturbances. Amplification of crossflow vortices near the leading edge produces a residual spanwise nonuniformity in the mid-chord regions where Tollmien-Schlichting (T-S) waves are strongly amplified. Should the T-S wave undergo double-exponential growth because of this effect, the usual transition prediction methods would fail. The crossflow/Tollmien-Schlichting wave interaction was modeled as a secondary instability. The effects of suction are included, and different stability criteria are examined. The results are applied to laminar flow control wings characteristic of energy-efficient aircraft designs.

Plasmids as stochastic model systems

NASA Astrophysics Data System (ADS)

Paulsson, Johan

2003-05-01

Plasmids are self-replicating gene clusters present in on average 2-100 copies per bacterial cell. To reduce random fluctuations and thereby avoid extinction, they ubiquitously autoregulate their own synthesis using negative feedback loops. Here I use van Kampen's Ω-expansion for a two-dimensional model of negative feedback including plasmids and ther replication inhibitors. This analytically summarizes the standard perspective on replication control -- including the effects of sensitivity amplification, exponential time-delays and noisy signaling. I further review the two most common molecular sensitivity mechanisms: multistep control and cooperativity. Finally, I discuss more controversial sensitivity schemes, such as noise-enhanced sensitivity, the exploitation of small-number combinatorics and double-layered feedback loops to suppress noise in disordered environments.

Does double-row rotator cuff repair improve functional outcome of patients compared with single-row technique? A systematic review.

PubMed

DeHaan, Alexander M; Axelrad, Thomas W; Kaye, Elizabeth; Silvestri, Lorenzo; Puskas, Brian; Foster, Timothy E

2012-05-01

The advantage of single-row versus double-row arthroscopic rotator cuff repair techniques has been a controversial issue in sports medicine and shoulder surgery. There is biomechanical evidence that double-row techniques are superior to single-row techniques; however, there is no clinical evidence that the double-row technique provides an improved functional outcome. When compared with single-row rotator cuff repair, double-row fixation, although biomechanically superior, has no clinical benefit with respect to retear rate or improved functional outcome. Systematic review. The authors reviewed prospective studies of level I or II clinical evidence that compared the efficacy of single- and double-row rotator cuff repairs. Functional outcome scores included the American Shoulder and Elbow Surgeons (ASES) shoulder scale, the Constant shoulder score, and the University of California, Los Angeles (UCLA) shoulder rating scale. Radiographic failures and complications were also analyzed. A test of heterogeneity for patient demographics was also performed to determine if there were differences in the patient profiles across the included studies. Seven studies fulfilled our inclusion criteria. The test of heterogeneity across these studies showed no differences. The functional ASES, Constant, and UCLA outcome scores revealed no difference between single- and double-row rotator cuff repairs. The total retear rate, which included both complete and partial retears, was 43.1% for the single-row repair and 27.2% for the double-row repair (P = .057), representing a trend toward higher failures in the single-row group. Through a comprehensive literature search and meta-analysis of current arthroscopic rotator cuff repairs, we found that the single-row repairs did not differ from the double-row repairs in functional outcome scores. The double-row repairs revealed a trend toward a lower radiographic proven retear rate, although the data did not reach statistical significance. There may be a concerning trend toward higher retear rates in patients undergoing a single-row repair, but further studies are required.

The origin of replicators and reproducers

PubMed Central

Szathmáry, Eörs

2006-01-01

Replicators are fundamental to the origin of life and evolvability. Their survival depends on the accuracy of replication and the efficiency of growth relative to spontaneous decay. Infrabiological systems are built of two coupled autocatalytic systems, in contrast to minimal living systems that must comprise at least a metabolic subsystem, a hereditary subsystem and a boundary, serving respective functions. Some scenarios prefer to unite all these functions into one primordial system, as illustrated in the lipid world scenario, which is considered as a didactic example in detail. Experimentally produced chemical replicators grow parabolically owing to product inhibition. A selection consequence is survival of everybody. The chromatographized replicator model predicts that such replicators spreading on surfaces can be selected for higher replication rate because double strands are washed away slower than single strands from the surface. Analysis of real ribozymes suggests that the error threshold of replication is less severe by about one order of magnitude than thought previously. Surface-bound dynamics is predicted to play a crucial role also for exponential replicators: unlinked genes belonging to the same genome do not displace each other by competition, and efficient and accurate replicases can spread. The most efficient form of such useful population structure is encapsulation by reproducing vesicles. The stochastic corrector model shows how such a bag of genes can survive, and what the role of chromosome formation and intragenic recombination could be. Prebiotic and early evolution cannot be understood without the models of dynamics. PMID:17008217

Star Formation Rate Distribution in the Galaxy NGC 1232

NASA Astrophysics Data System (ADS)

Araújo de Souza, Alexandre; Martins, Lucimara P.; Rodríguez-Ardila, Alberto; Fraga, Luciano

2018-06-01

NGC 1232 is a face-on spiral galaxy and a great laboratory for the study of star formation due to its proximity. We obtained high spatial resolution Hα images of this galaxy, with adaptive optics, using the SAM instrument at the SOAR telescope, and used these images to study its H II regions. These observations allowed us to produce the most complete H II region catalog for it to date, with a total of 976 sources. This doubles the number of H II regions previously found for this object. We used these data to construct the H II luminosity function, and obtained a power-law index lower than the typical values found for Sc galaxies. This shallower slope is related to the presence of a significant number of high-luminosity H II regions (log L > 39 dex). We also constructed the size distribution function, verifying that, as for most galaxies, NGC 1232 follows an exponential law. We also used the Hα luminosity to calculate the star formation rate. An extremely interesting fact about this galaxy is that X-ray diffuse observations suggest that NGC 1232 recently suffered a collision with a dwarf galaxy. We found an absence of star formation around the region where the X-ray emission is more intense, which we interpret as a star formation quenching due to the collision. Along with that, we found an excess of star-forming regions in the northeast part of the galaxy, where the X-ray emission is less intense.

Piecewise exponential models to assess the influence of job-specific experience on the hazard of acute injury for hourly factory workers

PubMed Central

2013-01-01

Background An inverse relationship between experience and risk of injury has been observed in many occupations. Due to statistical challenges, however, it has been difficult to characterize the role of experience on the hazard of injury. In particular, because the time observed up to injury is equivalent to the amount of experience accumulated, the baseline hazard of injury becomes the main parameter of interest, excluding Cox proportional hazards models as applicable methods for consideration. Methods Using a data set of 81,301 hourly production workers of a global aluminum company at 207 US facilities, we compared competing parametric models for the baseline hazard to assess whether experience affected the hazard of injury at hire and after later job changes. Specific models considered included the exponential, Weibull, and two (a hypothesis-driven and a data-driven) two-piece exponential models to formally test the null hypothesis that experience does not impact the hazard of injury. Results We highlighted the advantages of our comparative approach and the interpretability of our selected model: a two-piece exponential model that allowed the baseline hazard of injury to change with experience. Our findings suggested a 30% increase in the hazard in the first year after job initiation and/or change. Conclusions Piecewise exponential models may be particularly useful in modeling risk of injury as a function of experience and have the additional benefit of interpretability over other similarly flexible models. PMID:23841648

Diffusive processes in a stochastic magnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, H.; Vlad, M.; Vanden Eijnden, E.

1995-05-01

The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing,more » in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle`s trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works.« less

μ SR studies of the extended kagome systems YBaCo4O7+δ (δ = 0 and 0.1)

NASA Astrophysics Data System (ADS)

Lee, Suheon; Lee, Wonjun; Mitchell, John; Choi, Kwang-Yong

We present a μSR study of the extended kagome systems YBaCo4O7+δ (δ = 0 and 0.1), which are made up of an alternating stacking of triangular and kagome layers. The parent material YBaCo4O7.0 undergoes a structural phase transition at 310 K, releasing geometrical frustration and thereby stabilizing an antiferromagnetically ordered state below TN = 106 K. The μSR spectra of YBaCo4O7.0 exhibit the loss of initial asymmetry and the development of a fast relaxation component below TN = 111 K. This indicates that the Co spins in the kagome planes remain in an inhomogeneous and dynamically fluctuating state down to 4 K, while the triangular spins order antiferromagnetically below TN. The nonstoichiometric YBaCo4O7.1 compound with no magnetic ordering exhibits a disparate spin dynamics between the fast cooling (10 K/min) and slow cooling (1 K/min) procedures. While the fast-cooled μSR spectra show a simple exponential decay, the slow-cooled spectra are described with a sum of a simple exponential function and a stretched exponential function. These are in agreements with the occurrence of the phase separation between interstitial oxygen-rich and poor regions in the slow-cooling measurements.

Estimation of the light field inside photosynthetic microorganism cultures through Mittag-Leffler functions at depleted light conditions

NASA Astrophysics Data System (ADS)

Fuente, David; Lizama, Carlos; Urchueguía, Javier F.; Conejero, J. Alberto

2018-01-01

Light attenuation within suspensions of photosynthetic microorganisms has been widely described by the Lambert-Beer equation. However, at depths where most of the light has been absorbed by the cells, light decay deviates from the exponential behaviour and shows a lower attenuation than the corresponding from the purely exponential fall. This discrepancy can be modelled through the Mittag-Leffler function, extending Lambert-Beer law via a tuning parameter α that takes into account the attenuation process. In this work, we describe a fractional Lambert-Beer law to estimate light attenuation within cultures of model organism Synechocystis sp. PCC 6803. Indeed, we benchmark the measured light field inside cultures of two different Synechocystis strains, namely the wild-type and the antenna mutant strain called Olive at five different cell densities, with our in silico results. The Mittag-Leffler hyper-parameter α that best fits the data is 0.995, close to the exponential case. One of the most striking results to emerge from this work is that unlike prior literature on the subject, this one provides experimental evidence on the validity of fractional calculus for determining the light field. We show that by applying the fractional Lambert-Beer law for describing light attenuation, we are able to properly model light decay in photosynthetic microorganisms suspensions.

Stellar Surface Brightness Profiles of Dwarf Galaxies

NASA Astrophysics Data System (ADS)

Herrmann, K. A.

2014-03-01

Radial stellar surface brightness profiles of spiral galaxies can be classified into three types: (I) single exponential, or the light falls off with one exponential out to a break radius and then falls off (II) more steeply (“truncated”), or (III) less steeply (“anti-truncated”). Why there are three different radial profile types is still a mystery, including why light falls off as an exponential at all. Profile breaks are also found in dwarf disks, but some dwarf Type IIs are flat or increasing (FI) out to a break before falling off. I have been re-examining the multi-wavelength stellar disk profiles of 141 dwarf galaxies, primarily from Hunter & Elmegreen (2004, 2006). Each dwarf has data in up to 11 wavelength bands: FUV and NUV from GALEX, UBVJHK and Hα from ground-based observations, and 3.6 and 4.5μm from Spitzer. Here I highlight some results from a semi-automatic fitting of this data set including: (1) statistics of break locations and other properties as a function of wavelength and profile type, (2) color trends and radial mass distribution as a function of profile type, and (3) the relationship of the break radius to the kinematics and density profiles of atomic hydrogen gas in the 40 dwarfs of the LITTLE THINGS subsample.

From Experiment to Theory: What Can We Learn from Growth Curves?

PubMed

Kareva, Irina; Karev, Georgy

2018-01-01

Finding an appropriate functional form to describe population growth based on key properties of a described system allows making justified predictions about future population development. This information can be of vital importance in all areas of research, ranging from cell growth to global demography. Here, we use this connection between theory and observation to pose the following question: what can we infer about intrinsic properties of a population (i.e., degree of heterogeneity, or dependence on external resources) based on which growth function best fits its growth dynamics? We investigate several nonstandard classes of multi-phase growth curves that capture different stages of population growth; these models include hyperbolic-exponential, exponential-linear, exponential-linear-saturation growth patterns. The constructed models account explicitly for the process of natural selection within inhomogeneous populations. Based on the underlying hypotheses for each of the models, we identify whether the population that it best fits by a particular curve is more likely to be homogeneous or heterogeneous, grow in a density-dependent or frequency-dependent manner, and whether it depends on external resources during any or all stages of its development. We apply these predictions to cancer cell growth and demographic data obtained from the literature. Our theory, if confirmed, can provide an additional biomarker and a predictive tool to complement experimental research.

Theoretical analysis of oscillatory terms in lattice heat-current time correlation functions and their contributions to thermal conductivity

NASA Astrophysics Data System (ADS)

Pereverzev, Andrey; Sewell, Tommy

2018-03-01

Lattice heat-current time correlation functions for insulators and semiconductors obtained using molecular dynamics (MD) simulations exhibit features of both pure exponential decay and oscillatory-exponential decay. For some materials the oscillatory terms contribute significantly to the lattice heat conductivity calculated from the correlation functions. However, the origin of the oscillatory terms is not well understood, and their contribution to the heat conductivity is accounted for by fitting them to empirical functions. Here, a translationally invariant expression for the heat current in terms of creation and annihilation operators is derived. By using this full phonon-picture definition of the heat current and applying the relaxation-time approximation we explain, at least in part, the origin of the oscillatory terms in the lattice heat-current correlation function. We discuss the relationship between the crystal Hamiltonian and the magnitude of the oscillatory terms. A solvable one-dimensional model is used to illustrate the potential importance of terms that are omitted in the commonly used phonon-picture expression for the heat current. While the derivations are fully quantum mechanical, classical-limit expressions are provided that enable direct contact with classical quantities obtainable from MD.

Wildfires in Siberian Mountain Forest

NASA Astrophysics Data System (ADS)

Kharuk, V.; Ponomarev, E. I.; Antamoshkina, O.

2017-12-01

The annual burned area in Russia was estimated as 0.55 to 20 Mha with >70% occurred in Siberia. We analyzed Siberian wildfires distribution with respect to elevation, slope steepness and exposure. In addition, wildfires temporal dynamic and latitudinal range were analyzed. We used daily thermal anomalies derived from NOAA/AVHRR and Terra/MODIS satellites (1990-2016). Fire return intervals were (FRI) calculated based on the dendrochronology analysis of samples taken from trees with burn marks. Spatial distribution of wildfires dependent on topo features: relative burned area increase with elevation increase (ca. 1100 m), switching to following decrease. The wildfires frequency exponentially decreased within lowlands - highlands transition. Burned area is increasing with slope steepness increase (up to 5-10°). Fire return intervals (FRI) on the southfacing slopes are about 30% longer than on the north facing. Wildfire re-occurrence is decreasing exponentially: 90% of burns were caused by single fires, 8.5% by double fires, 1% burned three times, and on about 0.05% territory wildfires occurred four times (observed period: 75 yr.). Wildfires area and number, as well as FRI, also dependent on latitude: relative burned area increasing exponentially in norward direction, whereas relative fire number is exponentially decreasing. FRI increases in the northward direction: from 80 years at 62°N to 200 years at the Arctic Circle, and to 300 years at the northern limit of closed forests ( 71+°N). Fire frequency, fire danger period and FRI are strongly correlated with incoming solar radiation (r = 0.81 - 0.95). In 21-s century, a positive trend of wildfires number and area observed in mountain areas in all Siberia. Thus, burned area and number of fires in Siberia are significantly increased since 1990th (R2 =0.47, R2 =0.69, respectively), and that increase correlated with air temperatures and climate aridity increases. However, wildfires are essential for supporting fire-resistant species (e.g., Larix sibirica, L, dahurica and Pinus silvestris) reforestation and completion with non-fire-resistant species. This work was supported by the Russian Foundation for Basic Research, the Government of the Krasnoyarsk krai, the Krasnoyarsk Fund for Support of Scientific and Technological Activities (N 17-41-240475)

A Question of Interest

ERIC Educational Resources Information Center

Holley, Ann D.

1978-01-01

Formulas are developed which answer installment-buying questions without the use of amortization, sinking funds, or annuity tables. Applications for geometric progressions, proof by induction, solution of exponential equations, and the notion of recursive functions are displayed. (MN)

Post-test probability for neonatal hyperbilirubinemia based on umbilical cord blood bilirubin, direct antiglobulin test, and ABO compatibility results.

PubMed

Peeters, Bart; Geerts, Inge; Van Mullem, Mia; Micalessi, Isabel; Saegeman, Veroniek; Moerman, Jan

2016-05-01

Many hospitals opt for early postnatal discharge of newborns with a potential risk of readmission for neonatal hyperbilirubinemia. Assays/algorithms with the possibility to improve prediction of significant neonatal hyperbilirubinemia are needed to optimize screening protocols and safe discharge of neonates. This study investigated the predictive value of umbilical cord blood (UCB) testing for significant hyperbilirubinemia. Neonatal UCB bilirubin, UCB direct antiglobulin test (DAT), and blood group were determined, as well as the maternal blood group and the red blood cell antibody status. Moreover, in newborns with clinically apparent jaundice after visual assessment, plasma total bilirubin (TB) was measured. Clinical factors positively associated with UCB bilirubin were ABO incompatibility, positive DAT, presence of maternal red cell antibodies, alarming visual assessment and significant hyperbilirubinemia in the first 6 days of life. UCB bilirubin performed clinically well with an area under the receiver-operating characteristic curve (AUC) of 0.82 (95 % CI 0.80-0.84). The combined UCB bilirubin, DAT, and blood group analysis outperformed results of these parameters considered separately to detect significant hyperbilirubinemia and correlated exponentially with hyperbilirubinemia post-test probability. Post-test probabilities for neonatal hyperbilirubinemia can be calculated using exponential functions defined by UCB bilirubin, DAT, and ABO compatibility results. • The diagnostic value of the triad umbilical cord blood bilirubin measurement, direct antiglobulin testing and blood group analysis for neonatal hyperbilirubinemia remains unclear in literature. • Currently no guideline recommends screening for hyperbilirubinemia using umbilical cord blood. What is New: • Post-test probability for hyperbilirubinemia correlated exponentially with umbilical cord blood bilirubin in different risk groups defined by direct antiglobulin test and ABO blood group compatibility results. • Exponential functions can be used to calculate hyperbilirubinemia probability.

Gene expression profiles of Vibrio parahaemolyticus in the early stationary phase.

PubMed

Meng, L; Alter, T; Aho, T; Huehn, S

2015-09-01

Vibrio (V.) parahaemolyticus is an aquatic bacterium capable of causing foodborne gastroenteritis. In the environment or the food chain, V. parahaemolyticus cells are usually forced into the stationary phase, the common phase for bacterial survival in the environment. So far, little is known about whole genomic expression of V. parahaemolyticus in the early stationary phase compared with the exponential growth phase. We performed whole transcriptomic profiling of V. parahaemolyticus cells in both phases (exponential and early stationary phase). Our data showed in total that 172 genes were induced in early stationary phase, while 61 genes were repressed in early stationary phase compared with the exponential phase. Three functional categories showed stable gene expression in the early stationary phase. Eleven functional categories showed that up-regulation of genes was dominant over down-regulation in the early stationary phase. Although genes related to endogenous metabolism were repressed in the early stationary phase, massive regulation of gene expression occurred in the early stationary phase, indicating the expressed gene set of V. parahaemolyticus in the early stationary phase impacts environmental survival. Vibrio (V.) parahaemolyticus is one of the main bacterial causes of foodborne intestinal infections. This bacterium usually is forced into stationary phase in the environment, which includes, e.g. seafood. When bacteria are in stationary phase, physiological changes can lead to a resistance to many stresses, including physical and chemical challenges during food processing. To the best of our knowledge, highlighting the whole genome expression changes in the early stationary phase compared with exponential phase, as well as the investigation of physiological changes of V. parahaemolyticus such as the survival mechanism in the stationary phase has been the very first study in this field. © 2015 The Society for Applied Microbiology.

Mixed boundary-value problem for an orthotropic rectangular strip with variable coefficients of elasticity

NASA Astrophysics Data System (ADS)

Sargsyan, M. Z.; Poghosyan, H. M.

2018-04-01

A dynamical problem for a rectangular strip with variable coefficients of elasticity is solved by an asymptotic method. It is assumed that the strip is orthotropic, the elasticity coefficients are exponential functions of y, and mixed boundary conditions are posed. The solution of the inner problem is obtained using Bessel functions.

Formative versus Reflective Measurement in Executive Functions: A Critique of Willoughby et al.

ERIC Educational Resources Information Center

Peterson, Eric; Welsh, Marilyn C.

2014-01-01

Research into executive functioning (EF) has indeed grown exponentially across the past few decades, but as the Willoughby et al. critique makes clear, there remain fundamental questions to be resolved. The crux of their argument is built upon an examination of the confirmatory factor analysis (CFA) approach to understanding executive processes.…

Quantifying the relationship between PM2.5 concentration, visibility and planetary boundary layer height for long-lasting haze and fog-haze mixed events in Beijing

NASA Astrophysics Data System (ADS)

Luan, Tian; Guo, Xueliang; Guo, Lijun; Zhang, Tianhang

2018-01-01

Air quality and visibility are strongly influenced by aerosol loading, which is driven by meteorological conditions. The quantification of their relationships is critical to understanding the physical and chemical processes and forecasting of the polluted events. We investigated and quantified the relationship between PM2.5 (particulate matter with aerodynamic diameter is 2.5 µm and less) mass concentration, visibility and planetary boundary layer (PBL) height in this study based on the data obtained from four long-lasting haze events and seven fog-haze mixed events from January 2014 to March 2015 in Beijing. The statistical results show that there was a negative exponential function between the visibility and the PM2.5 mass concentration for both haze and fog-haze mixed events (with the same R2 of 0.80). However, the fog-haze events caused a more obvious decrease of visibility than that for haze events due to the formation of fog droplets that could induce higher light extinction. The PM2.5 concentration had an inversely linear correlation with PBL height for haze events and a negative exponential correlation for fog-haze mixed events, indicating that the PM2.5 concentration is more sensitive to PBL height in fog-haze mixed events. The visibility had positively linear correlation with the PBL height with an R2 of 0.35 in haze events and positive exponential correlation with an R2 of 0.56 in fog-haze mixed events. We also investigated the physical mechanism responsible for these relationships between visibility, PM2.5 concentration and PBL height through typical haze and fog-haze mixed event and found that a double inversion layer formed in both typical events and played critical roles in maintaining and enhancing the long-lasting polluted events. The variations of the double inversion layers were closely associated with the processes of long-wave radiation cooling in the nighttime and short-wave solar radiation reduction in the daytime. The upper-level stable inversion layer was formed by the persistent warm and humid southwestern airflow, while the low-level inversion layer was initially produced by the surface long-wave radiation cooling in the nighttime and maintained by the reduction of surface solar radiation in the daytime. The obvious descending process of the upper-level inversion layer induced by the radiation process could be responsible for the enhancement of the low-level inversion layer and the lowering PBL height, as well as high aerosol loading for these polluted events. The reduction of surface solar radiation in the daytime could be around 35 % for the haze event and 94 % for the fog-haze mixed event. Therefore, the formation and subsequent descending processes of the upper-level inversion layer should be an important factor in maintaining and strengthening the long-lasting severe polluted events, which has not been revealed in previous publications. The interactions and feedbacks between PM2.5 concentration and PBL height linked by radiation process caused a more significant and long-lasting deterioration of air quality and visibility in fog-haze mixed events. The interactions and feedbacks of all processes were particularly strong when the PM2.5 mass concentration was larger than 150-200 µg m-3.

Generalized zeta function representation of groups and 2-dimensional topological Yang-Mills theory: The example of GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q})

DOE Office of Scientific and Technical Information (OSTI.GOV)

Roche, Ph., E-mail: philippe.roche@univ-montp2.fr

We recall the relation between zeta function representation of groups and two-dimensional topological Yang-Mills theory through Mednikh formula. We prove various generalisations of Mednikh formulas and define generalization of zeta function representations of groups. We compute some of these functions in the case of the finite group GL(2, #Mathematical Double-Struck Capital F#{sub q}) and PGL(2, #Mathematical Double-Struck Capital F#{sub q}). We recall the table characters of these groups for any q, compute the Frobenius-Schur indicator of their irreducible representations, and give the explicit structure of their fusion rings.

Carbon dioxide emissions from semi-arid soils amended with biochar alone or combined with mineral and organic fertilizers.

PubMed

Fernández, José M; Nieto, M Aurora; López-de-Sá, Esther G; Gascó, Gabriel; Méndez, Ana; Plaza, César

2014-06-01

Semi-arid soils cover a significant area of Earth's land surface and typically contain large amounts of inorganic C. Determining the effects of biochar additions on CO2 emissions from semi-arid soils is therefore essential for evaluating the potential of biochar as a climate change mitigation strategy. Here, we measured the CO2 that evolved from semi-arid calcareous soils amended with biochar at rates of 0 and 20tha(-1) in a full factorial combination with three different fertilizers (mineral fertilizer, municipal solid waste compost, and sewage sludge) applied at four rates (equivalent to 0, 75, 150, and 225kg potentially available Nha(-1)) during 182 days of aerobic incubation. A double exponential model, which describes cumulative CO2 emissions from two active soil C compartments with different turnover rates (one relatively stable and the other more labile), was found to fit very well all the experimental datasets. In general, the organic fertilizers increased the size and decomposition rate of the stable and labile soil C pools. In contrast, biochar addition had no effects on any of the double exponential model parameters and did not interact with the effects ascribed to the type and rate of fertilizer. After 182 days of incubation, soil organic and microbial biomass C contents tended to increase with increasing the application rates of organic fertilizer, especially of compost, whereas increasing the rate of mineral fertilizer tended to suppress microbial biomass. Biochar was found to increase both organic and inorganic C contents in soil and not to interact with the effects of type and rate of fertilizer on C fractions. As a whole, our results suggest that the use of biochar as enhancer of semi-arid soils, either alone or combined with mineral and organic fertilizers, is unlikely to increase abiotic and biotic soil CO2 emissions. Copyright © 2014 Elsevier B.V. All rights reserved.

Rectal temperature-based death time estimation in infants.

PubMed

Igari, Yui; Hosokai, Yoshiyuki; Funayama, Masato

2016-03-01

In determining the time of death in infants based on rectal temperature, the same methods used in adults are generally used. However, whether the methods for adults are suitable for infants is unclear. In this study, we examined the following 3 methods in 20 infant death cases: computer simulation of rectal temperature based on the infinite cylinder model (Ohno's method), computer-based double exponential approximation based on Marshall and Hoare's double exponential model with Henssge's parameter determination (Henssge's method), and computer-based collinear approximation based on extrapolation of the rectal temperature curve (collinear approximation). The interval between the last time the infant was seen alive and the time that he/she was found dead was defined as the death time interval and compared with the estimated time of death. In Ohno's method, 7 cases were within the death time interval, and the average deviation in the other 12 cases was approximately 80 min. The results of both Henssge's method and collinear approximation were apparently inferior to the results of Ohno's method. The corrective factor was set within the range of 0.7-1.3 in Henssge's method, and a modified program was newly developed to make it possible to change the corrective factors. Modification A, in which the upper limit of the corrective factor range was set as the maximum value in each body weight, produced the best results: 8 cases were within the death time interval, and the average deviation in the other 12 cases was approximately 80min. There was a possibility that the influence of thermal isolation on the actual infants was stronger than that previously shown by Henssge. We conclude that Ohno's method and Modification A are useful for death time estimation in infants. However, it is important to accept the estimated time of death with certain latitude considering other circumstances. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

The decline and fall of Type II error rates

Treesearch

Steve Verrill; Mark Durst

2005-01-01

For general linear models with normally distributed random errors, the probability of a Type II error decreases exponentially as a function of sample size. This potentially rapid decline reemphasizes the importance of performing power calculations.