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

Fractional compartmental models and multi-term Mittag-Leffler response functions.

PubMed

Verotta, Davide

2010-04-01

Systems of fractional differential equations (SFDE) have been increasingly used to represent physical and control system, and have been recently proposed for use in pharmacokinetics (PK) by (J Pharmacokinet Pharmacodyn 36:165-178, 2009) and (J Phamacokinet Pharmacodyn, 2010). We contribute to the development of a theory for the use of SFDE in PK by, first, further clarifying the nature of systems of FDE, and in particular point out the distinction and properties of commensurate versus non-commensurate ones. The second purpose is to show that for both types of systems, relatively simple response functions can be derived which satisfy the requirements to represent single-input/single-output PK experiments. The response functions are composed of sums of single- (for commensurate) or two-parameters (for non-commensurate) Mittag-Leffler functions, and establish a direct correspondence with the familiar sums of exponentials used in PK.

Use of Continuous Exponential Families to Link Forms via Anchor Tests. Research Report. ETS RR-11-11

ERIC Educational Resources Information Center

Haberman, Shelby J.; Yan, Duanli

2011-01-01

Continuous exponential families are applied to linking test forms via an internal anchor. This application combines work on continuous exponential families for single-group designs and work on continuous exponential families for equivalent-group designs. Results are compared to those for kernel and equipercentile equating in the case of chained…

Single- and multiple-pulse noncoherent detection statistics associated with partially developed speckle.

PubMed

Osche, G R

2000-08-20

Single- and multiple-pulse detection statistics are presented for aperture-averaged direct detection optical receivers operating against partially developed speckle fields. A partially developed speckle field arises when the probability density function of the received intensity does not follow negative exponential statistics. The case of interest here is the target surface that exhibits diffuse as well as specular components in the scattered radiation. An approximate expression is derived for the integrated intensity at the aperture, which leads to single- and multiple-pulse discrete probability density functions for the case of a Poisson signal in Poisson noise with an additive coherent component. In the absence of noise, the single-pulse discrete density function is shown to reduce to a generalized negative binomial distribution. The radar concept of integration loss is discussed in the context of direct detection optical systems where it is shown that, given an appropriate set of system parameters, multiple-pulse processing can be more efficient than single-pulse processing over a finite range of the integration parameter n.

Difference in Dwarf Galaxy Surface Brightness Profiles as a Function of Environment

NASA Astrophysics Data System (ADS)

Lee, Youngdae; Park, Hong Soo; Kim, Sang Chul; Moon, Dae-Sik; Lee, Jae-Joon; Kim, Dong-Jin; Cha, Sang-Mok

2018-05-01

We investigate surface brightness profiles (SBPs) of dwarf galaxies in field, group, and cluster environments. With deep BV I images from the Korea Microlensing Telescope Network Supernova Program, SBPs of 38 dwarfs in the NGC 2784 group are fitted by a single-exponential or double-exponential model. We find that 53% of the dwarfs are fitted with single-exponential profiles (“Type I”), while 47% of the dwarfs show double-exponential profiles; 37% of all dwarfs have smaller sizes for the outer part than the inner part (“Type II”), while 10% have a larger outer than inner part (“Type III”). We compare these results with those in the field and in the Virgo cluster, where the SBP types of 102 field dwarfs are compiled from a previous study and the SBP types of 375 cluster dwarfs are measured using SDSS r-band images. As a result, the distributions of SBP types are different in the three environments. Common SBP types for the field, the NGC 2784 group, and the Virgo cluster are Type II, Type I and II, and Type I and III profiles, respectively. After comparing the sizes of dwarfs in different environments, we suggest that since the sizes of some dwarfs are changed due to environmental effects, SBP types are capable of being transformed and the distributions of SBP types in the three environments are different. We discuss possible environmental mechanisms for the transformation of SBP types. Based on data collected at KMTNet Telescopes and SDSS.

15-digit accuracy calculations of Chandrasekhar's H-function for isotropic scattering by means of the double exponential formula

NASA Astrophysics Data System (ADS)

Kawabata, Kiyoshi

2016-12-01

This work shows that it is possible to calculate numerical values of the Chandrasekhar H-function for isotropic scattering at least with 15-digit accuracy by making use of the double exponential formula (DE-formula) of Takahashi and Mori (Publ. RIMS, Kyoto Univ. 9:721, 1974) instead of the Gauss-Legendre quadrature employed in the numerical scheme of Kawabata and Limaye (Astrophys. Space Sci. 332:365, 2011) and simultaneously taking a precautionary measure to minimize the effects due to loss of significant digits particularly in the cases of near-conservative scattering and/or errors involved in returned values of library functions supplied by compilers in use. The results of our calculations are presented for 18 selected values of single scattering albedo π0 and 22 values of an angular variable μ, the cosine of zenith angle θ specifying the direction of radiation incident on or emergent from semi-infinite media.

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

Characteristics of single Ca(2+) channel kinetics in feline hypertrophied ventricular myocytes.

PubMed

Yang, Xiangjun; Hui, Jie; Jiang, Tingbo; Song, Jianping; Liu, Zhihua; Jiang, Wenping

2002-04-01

To explore the mechanism underlying the prolongation of action potential and delayed inactivation of the L-type Ca(2+) (I(Ca, L)) current in a feline model of left ventricular system hypertension and concomitant hypertrophy. Single Ca(2+) channel properties in myocytes isolated from normal and pressure overloaded cat left ventricles were studied, using patch-clamp techniques. Left ventricular pressure overload was induced by partial ligation of the ascending aorta for 4 - 6 weeks. The amplitude of single Ca(2+) channel current evoked by depolarizing pulses from -40 mV to 0 mV was 1.02 +/- 0.03 pA in normal cells and 1.05 +/- 0.03 pA in hypertrophied cells, and there was no difference in single channel current-voltage relationships between the groups since slope conductance was 26.2 +/- 1.0 pS in normal and hypertrophied cells, respectively. Peak amplitudes of the ensemble-averaged single Ca(2+) channel currents were not different between the two groups of cells. However, the amplitude of this averaged current at the end of the clamp pulse was significantly larger in hypertrophied cells than in normal cells. Open-time histograms revealed that open-time distribution was fitted by a single exponential function in channels of normal cells and by a two exponential function in channels of hypertrophied cells. The number of long-lasting openings was increased in channels of hypertrophied cells, and therefore the calculated mean open time of the channel was significantly longer compared to normal controls. Kinetic changes in the Ca(2+) channel may underlie both hypertrophy-associated delayed inactivation of the Ca(2+) current and, in part, the pressure overload-induced action potential lengthening in this cat model of ventricular left systolic hypertension and hypertrophy.

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.

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.

Modeling of single event transients with dual double-exponential current sources: Implications for logic cell characterization

DOE PAGES

Black, Dolores Archuleta; Robinson, William H.; Wilcox, Ian Zachary; ...

2015-08-07

Single event effects (SEE) are a reliability concern for modern microelectronics. Bit corruptions can be caused by single event upsets (SEUs) in the storage cells or by sampling single event transients (SETs) from a logic path. Likewise, an accurate prediction of soft error susceptibility from SETs requires good models to convert collected charge into compact descriptions of the current injection process. This paper describes a simple, yet effective, method to model the current waveform resulting from a charge collection event for SET circuit simulations. The model uses two double-exponential current sources in parallel, and the results illustrate why a conventionalmore » model based on one double-exponential source can be incomplete. Furthermore, a small set of logic cells with varying input conditions, drive strength, and output loading are simulated to extract the parameters for the dual double-exponential current sources. As a result, the parameters are based upon both the node capacitance and the restoring current (i.e., drive strength) of the logic cell.« less

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.

Magnetic pattern at supergranulation scale: the void size distribution

NASA Astrophysics Data System (ADS)

Berrilli, F.; Scardigli, S.; Del Moro, D.

2014-08-01

The large-scale magnetic pattern observed in the photosphere of the quiet Sun is dominated by the magnetic network. This network, created by photospheric magnetic fields swept into convective downflows, delineates the boundaries of large-scale cells of overturning plasma and exhibits "voids" in magnetic organization. These voids include internetwork fields, which are mixed-polarity sparse magnetic fields that populate the inner part of network cells. To single out voids and to quantify their intrinsic pattern we applied a fast circle-packing-based algorithm to 511 SOHO/MDI high-resolution magnetograms acquired during the unusually long solar activity minimum between cycles 23 and 24. The computed void distribution function shows a quasi-exponential decay behavior in the range 10-60 Mm. The lack of distinct flow scales in this range corroborates the hypothesis of multi-scale motion flows at the solar surface. In addition to the quasi-exponential decay, we have found that the voids depart from a simple exponential decay at about 35 Mm.

Universality in stochastic exponential growth.

PubMed

Iyer-Biswas, Srividya; Crooks, Gavin E; Scherer, Norbert F; Dinner, Aaron R

2014-07-11

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Universality in Stochastic Exponential Growth

NASA Astrophysics Data System (ADS)

Iyer-Biswas, Srividya; Crooks, Gavin E.; Scherer, Norbert F.; Dinner, Aaron R.

2014-07-01

Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the division-time distributions. A model is needed to delineate the minimal requirements for these scaling behaviors. We formulate a microscopic theory of stochastic exponential growth as a Master Equation that accounts for these observations, in contrast to existing quantitative models of stochastic exponential growth (e.g., the Black-Scholes equation or geometric Brownian motion). Our model, the stochastic Hinshelwood cycle (SHC), is an autocatalytic reaction cycle in which each molecular species catalyzes the production of the next. By finding exact analytical solutions to the SHC and the corresponding first passage time problem, we uncover universal signatures of fluctuations in exponential growth and division. The model makes minimal assumptions, and we describe how more complex reaction networks can reduce to such a cycle. We thus expect similar scalings to be discovered in stochastic processes resulting in exponential growth that appear in diverse contexts such as cosmology, finance, technology, and population growth.

Semi-empirical scaling for ion-atom single charge exchange cross sections in the intermediate velocity regime

NASA Astrophysics Data System (ADS)

Friedman, B.; DuCharme, G.

2017-06-01

We present a semi-empirical scaling law for non-resonant ion-atom single charge exchange cross sections for collisions with velocities from {10}7 {{t}}{{o}} {10}9 {cm} {{{s}}}-1 and ions with positive charge q< 8. Non-resonant cross sections tend to have a velocity peak at collision velocities v≲ 1 {{a}}{{u}} with exponential decay around this peak. We construct a scaling formula for the location of this peak then choose a functional form for the cross section curve and scale it. The velocity at which the cross section peaks, v m, is proportional to the energy defect of the collision, {{Δ }}E, which we predict with the decay approximation. The value of the cross section maximum is proportional to the charge state q, inversely proportional to the target ionization energy I T, and inversely proportional to v m. For the shape of the cross section curve, we use a function that decays exponentially asymptotically at high and low velocities. We scale this function with parameters {v}{{m}},{I}{{T}},{Z}{{T}},{and} {Z}{{P}}, where the {Z}{{T},{{P}}} are the target and projectile atomic numbers. For the more than 100 cross section curves that we use to find the scaling rules, the scaling law predicts cross sections within a little over a factor of 2 on average.

Analytical optimization of demand management strategies across all urban water use sectors

NASA Astrophysics Data System (ADS)

Friedman, Kenneth; Heaney, James P.; Morales, Miguel; Palenchar, John

2014-07-01

An effective urban water demand management program can greatly influence both peak and average demand and therefore long-term water supply and infrastructure planning. Although a theoretical framework for evaluating residential indoor demand management has been well established, little has been done to evaluate other water use sectors such as residential irrigation in a compatible manner for integrating these results into an overall solution. This paper presents a systematic procedure to evaluate the optimal blend of single family residential irrigation demand management strategies to achieve a specified goal based on performance functions derived from parcel level tax assessor's data linked to customer level monthly water billing data. This framework is then generalized to apply to any urban water sector, as exponential functions can be fit to all resulting cumulative water savings functions. Two alternative formulations are presented: maximize net benefits, or minimize total costs subject to satisfying a target water savings. Explicit analytical solutions are presented for both formulations based on appropriate exponential best fits of performance functions. A direct result of this solution is the dual variable which represents the marginal cost of water saved at a specified target water savings goal. A case study of 16,303 single family irrigators in Gainesville Regional Utilities utilizing high quality tax assessor and monthly billing data along with parcel level GIS data provide an illustrative example of these techniques. Spatial clustering of targeted homes can be easily performed in GIS to identify priority demand management areas.

Two-dimensional, phase modulated lattice sums with application to the Helmholtz Green’s function

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

Linton, C. M., E-mail: C.M.Linton@lboro.ac.uk

2015-01-15

A class of two-dimensional phase modulated lattice sums in which the denominator is an indefinite quadratic polynomial Q is expressed in terms of a single, exponentially convergent series of elementary functions. This expression provides an extremely efficient method for the computation of the quasi-periodic Green’s function for the Helmholtz equation that arises in a number of physical contexts when studying wave propagation through a doubly periodic medium. For a class of sums in which Q is positive definite, our new result can be used to generate representations in terms of θ-functions which are significant generalisations of known results.

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

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.

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.

Novel use of UV broad-band excitation and stretched exponential function in the analysis of fluorescent dissolved organic matter: study of interaction between protein and humic-like components

NASA Astrophysics Data System (ADS)

Panigrahi, Suraj Kumar; Mishra, Ashok Kumar

2017-09-01

A combination of broad-band UV radiation (UV A and UV B; 250-400 nm) and a stretched exponential function (StrEF) has been utilised in efforts towards convenient and sensitive detection of fluorescent dissolved organic matter (FDOM). This approach enables accessing the gross fluorescence spectral signature of both protein-like and humic-like components in a single measurement. Commercial FDOM components are excited with the broad-band UV excitation; the variation of spectral profile as a function of varying component ratio is analysed. The underlying fluorescence dynamics and non-linear quenching of amino acid moieties are studied with the StrEF (exp(-V[Q] β )). The complex quenching pattern reflects the inner filter effect (IFE) as well as inter-component interactions. The inter-component interactions are essentially captured through the ‘sphere of action’ and ‘dark complex’ models. The broad-band UV excitation ascertains increased excitation energy, resulting in increased population density in the excited state and thereby resulting in enhanced sensitivity.

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.

Correlating the stretched-exponential and super-Arrhenius behaviors in the structural relaxation of glass-forming liquids.

PubMed

Wang, Lianwen; Li, Jiangong; Fecht, Hans-Jörg

2011-04-20

Following the report of a single-exponential activation behavior behind the super-Arrhenius structural relaxation of glass-forming liquids in our preceding paper, we find that the non-exponentiality in the structural relaxation of glass-forming liquids is straightforwardly determined by the relaxation time, and could be calculated from the measured relaxation data. Comparisons between the calculated and measured non-exponentialities for typical glass-forming liquids, from fragile to intermediate, convincingly support the present analysis. Hence the origin of the non-exponentiality and its correlation with liquid fragility become clearer.

(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.

Theoretical electrical conductivity of hydrogen-bonded benzamide-derived molecules and single DNA bases.

PubMed

Chen, Xiang

2013-09-01

A benzamide molecule is used as a "reader" molecule to form hydrogen bonds with five single DNA bases, i.e., four normal single DNA bases A,T,C,G and one for 5methylC. The whole molecule is then attached to the gold surface so that a meta-molecule junction is formed. We calculate the transmission function and conductance for the five metal-molecule systems, with the implementation of density functional theory-based non-equilibrium Green function method. Our results show that each DNA base exhibits a unique conductance and most of them are on the pS level. The distinguishable conductance of each DNA base provides a way for the fast sequencing of DNA. We also investigate the dependence of conductivity of such a metal-molecule system on the hydrogen bond length between the "reader" molecule and DNA base, which shows that conductance follows an exponential decay as the hydrogen bond length increases, i.e., the conductivity is highly sensitive to the change in hydrogen bond length.

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.

Exponential Sum-Fitting of Dwell-Time Distributions without Specifying Starting Parameters

PubMed Central

Landowne, David; Yuan, Bin; Magleby, Karl L.

2013-01-01

Fitting dwell-time distributions with sums of exponentials is widely used to characterize histograms of open- and closed-interval durations recorded from single ion channels, as well as for other physical phenomena. However, it can be difficult to identify the contributing exponential components. Here we extend previous methods of exponential sum-fitting to present a maximum-likelihood approach that consistently detects all significant exponentials without the need for user-specified starting parameters. Instead of searching for exponentials, the fitting starts with a very large number of initial exponentials with logarithmically spaced time constants, so that none are missed. Maximum-likelihood fitting then determines the areas of all the initial exponentials keeping the time constants fixed. In an iterative manner, with refitting after each step, the analysis then removes exponentials with negligible area and combines closely spaced adjacent exponentials, until only those exponentials that make significant contributions to the dwell-time distribution remain. There is no limit on the number of significant exponentials and no starting parameters need be specified. We demonstrate fully automated detection for both experimental and simulated data, as well as for classical exponential-sum-fitting problems. PMID:23746510

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.

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.

Scaling in the distribution of intertrade durations of Chinese stocks

NASA Astrophysics Data System (ADS)

Jiang, Zhi-Qiang; Chen, Wei; Zhou, Wei-Xing

2008-10-01

The distribution of intertrade durations, defined as the waiting times between two consecutive transactions, is investigated based upon the limit order book data of 23 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. A scaling pattern is observed in the distributions of intertrade durations, where the empirical density functions of the normalized intertrade durations of all 23 stocks collapse onto a single curve. The scaling pattern is also observed in the intertrade duration distributions for filled and partially filled trades and in the conditional distributions. The ensemble distributions for all stocks are modeled by the Weibull and the Tsallis q-exponential distributions. Maximum likelihood estimation shows that the Weibull distribution outperforms the q-exponential for not-too-large intertrade durations which account for more than 98.5% of the data. Alternatively, nonlinear least-squares estimation selects the q-exponential as a better model, in which the optimization is conducted on the distance between empirical and theoretical values of the logarithmic probability densities. The distribution of intertrade durations is Weibull followed by a power-law tail with an asymptotic tail exponent close to 3.

Semi-empirical scaling for ion–atom single charge exchange cross sections in the intermediate velocity regime

DOE PAGES

Friedman, B.; DuCharme, G.

2017-05-11

We present a semi-empirical scaling law for non-resonant ion–atom single charge exchange cross sections for collisions with velocities frommore » $${10}^{7}\\,{\\rm{t}}{\\rm{o}}\\,{10}^{9}\\,\\mathrm{cm}\\,{{\\rm{s}}}^{-1}$$ and ions with positive charge $$q\\lt 8$$. Non-resonant cross sections tend to have a velocity peak at collision velocities $$v\\lesssim 1\\ {\\rm{a}}{\\rm{u}}$$ with exponential decay around this peak. We construct a scaling formula for the location of this peak then choose a functional form for the cross section curve and scale it. The velocity at which the cross section peaks, v m, is proportional to the energy defect of the collision, $${\\rm{\\Delta }}E$$, which we predict with the decay approximation. The value of the cross section maximum is proportional to the charge state q, inversely proportional to the target ionization energy I T, and inversely proportional to v m. For the shape of the cross section curve, we use a function that decays exponentially asymptotically at high and low velocities. We scale this function with parameters $${v}_{{\\rm{m}}},{I}_{{\\rm{T}}},{Z}_{{\\rm{T}}},\\mathrm{and}\\ {Z}_{{\\rm{P}}}$$, where the $${Z}_{{\\rm{T}},{\\rm{P}}}$$ are the target and projectile atomic numbers. In conclusion, for the more than 100 cross section curves that we use to find the scaling rules, the scaling law predicts cross sections within a little over a factor of 2 on average.« less

The Homotopic Probability Distribution and the Partition Function for the Entangled System Around a Ribbon Segment Chain

NASA Astrophysics Data System (ADS)

Qian, Shang-Wu; Gu, Zhi-Yu

2001-12-01

Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution P_L^n for the winding number n and the partition function P_L of the entangled system around a ribbon segment chain. We find that when the width of the ribbon segment chain 2a increases,the partition function exponentially decreases, whereas the free energy increases an amount, which is proportional to the square of the width. When the width tends to zero we obtain the same results as those of a single chain with one singular point.

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.

Single-arm phase II trial design under parametric cure models.

PubMed

Wu, Jianrong

2015-01-01

The current practice of designing single-arm phase II survival trials is limited under the exponential model. Trial design under the exponential model may not be appropriate when a portion of patients are cured. There is no literature available for designing single-arm phase II trials under the parametric cure model. In this paper, a test statistic is proposed, and a sample size formula is derived for designing single-arm phase II trials under a class of parametric cure models. Extensive simulations showed that the proposed test and sample size formula perform very well under different scenarios. Copyright © 2015 John Wiley & Sons, Ltd.

Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation.

PubMed

Marcotte, Christopher D; Grigoriev, Roman O

2016-09-01

This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.

Adjoint eigenfunctions of temporally recurrent single-spiral solutions in a simple model of atrial fibrillation

NASA Astrophysics Data System (ADS)

Marcotte, Christopher D.; Grigoriev, Roman O.

2016-09-01

This paper introduces a numerical method for computing the spectrum of adjoint (left) eigenfunctions of spiral wave solutions to reaction-diffusion systems in arbitrary geometries. The method is illustrated by computing over a hundred eigenfunctions associated with an unstable time-periodic single-spiral solution of the Karma model on a square domain. We show that all leading adjoint eigenfunctions are exponentially localized in the vicinity of the spiral tip, although the marginal modes (response functions) demonstrate the strongest localization. We also discuss the implications of the localization for the dynamics and control of unstable spiral waves. In particular, the interaction with no-flux boundaries leads to a drift of spiral waves which can be understood with the help of the response functions.

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.

Stellar Surface Brightness Profiles of Dwarf Galaxies

NASA Astrophysics Data System (ADS)

Herrmann, Kimberly A.; LITTLE THINGS Team

2012-01-01

Radial stellar surface brightness profiles of spiral galaxies can be classified into three types: (I) single exponential, (II) truncated: the light falls off with one exponential out to a break radius and then falls off more steeply, and (III) anti-truncated: the light falls off with one exponential out to a break radius and then falls off less steeply. Stellar surface brightness profile breaks are also found in dwarf disk galaxies, but with an additional category: (FI) flat-inside: the light is roughly constant or increasing and then falls off beyond a break. We have been re-examining the multi-wavelength stellar disk profiles of 141 dwarf galaxies, primarily from Hunter & Elmegreen (2006, 2004). Each dwarf has data in up to 11 wavelength bands: FUV and NUV from GALEX, UBVJHK and H-alpha from ground-based observations, and 3.6 and 4.5 microns from Spitzer. In this talk, I will highlight 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 41 dwarfs of the LITTLE THINGS subsample. We gratefully acknowledge funding for this research from the National Science Foundation (AST-0707563).

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…

Correlation of conformational heterogeneity of the tryptophyl side chain and time-resolved fluorescence intensity decay kinetics

NASA Astrophysics Data System (ADS)

Laws, William R.; Ross, J. B. Alexander

1992-04-01

The time-resolved fluorescence properties of a tryptophan residue should be useful for probing protein structure, function, and dynamics. To date, however, the non-single exponential fluorescence intensity decay kinetics for numerous peptides and proteins having a single tryptophan residue have not been adequately explained. Many possibilities have been considered and include: (1) contributions from the 1La and 1Lb states of indole; (2) excited-state hydrogen exchange; and (3) environmental heterogeneity from (chi) 1 and (chi) 2 rotamers. In addition, it has been suggested that generally many factors contribute to the decay and a distribution of probabilities may be more appropriate. Two recent results support multiple species due to conformational heterogeneity as the major contributor to complex kinetics. First, a rotationally constrained tryptophan analogue has fluorescence intensity decay kinetics that can be described by the sum of two exponentials with amplitudes comparable to the relative populations of the two rotational isomers. Second, the multiple exponentials observed for tyrosine-containing model compounds and peptides correlate with the (chi) 1 rotamer populations independently determined by 1H NMR. We now report similar correlations between rotamer populations and fluorescence intensity decay kinetics for a tryptophan analogue of oxytocin. It appears for this compound that either (chi) 2 rotations do not appreciably alter the indole environment, (chi) 2 rotations are rapid enough to average the observed dependence, or only one of two possible (chi) 2 populations is associated with each (chi) 1 rotamer.

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.

Creep substructure formation in sodium chloride single crystals in the power law and exponential creep regimes

NASA Technical Reports Server (NTRS)

Raj, S. V.; Pharr, G. M.

1989-01-01

Creep tests conducted on NaCl single crystals in the temperature range from 373 to 1023 K show that true steady state creep is obtained only above 873 K when the ratio of the applied stress to the shear modulus is less than or equal to 0.0001. Under other stress and temperature conditions, corresponding to both power law and exponential creep, the creep rate decreases monotonically with increasing strain. The transition from power law to exponential creep is shown to be associated with increases in the dislocation density, the cell boundary width, and the aspect ratio of the subgrains along the primary slip planes. The relation between dislocation structure and creep behavior is also assessed.

Proceedings of the Third International Workshop on Multistrategy Learning, May 23-25 Harpers Ferry, WV.

DTIC Science & Technology

1996-09-16

approaches are: • Adaptive filtering • Single exponential smoothing (Brown, 1963) * The Box-Jenkins methodology ( ARIMA modeling ) - Linear exponential... ARIMA • Linear exponential smoothing: Holt’s two parameter modeling (Box and Jenkins, 1976). However, there are two approach (Holt et al., 1960) very...crucial disadvantages: The most important point in - Winters’ three parameter method (Winters, 1960) ARIMA modeling is model identification. As shown in

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.

Spectral Modeling of the EGRET 3EG Gamma Ray Sources Near the Galactic Plane

NASA Technical Reports Server (NTRS)

Bertsch, D. L.; Hartman, R. C.; Hunter, S. D.; Thompson, D. J.; Lin, Y. C.; Kniffen, D. A.; Kanbach, G.; Mayer-Hasselwander, H. A.; Reimer, O.; Sreekumar, P.

1999-01-01

The third EGRET catalog lists 84 sources within 10 deg of the Galactic Plane. Five of these are well-known spin-powered pulsars, 2 and possibly 3 others are blazars, and the remaining 74 are classified as unidentified, although 6 of these are likely to be artifacts of nearby strong sources. Several of the remaining 68 unidentified sources have been noted as having positional agreement with supernovae remnants and OB associations. Others may be radio-quiet pulsars like Geminga, and still others may belong to a totally new class of sources. The question of the energy spectral distributions of these sources is an important clue to their identification. In this paper, the spectra of the sources within 10 deg of Galactic Plane are fit with three different functional forms; a single power law, two power laws, and a power law with an exponential cutoff. Where possible, the best fit is selected with statistical tests. Twelve, and possibly an additional 5 sources, are found to have spectra that are fit by a breaking power law or by the power law with exponential cutoff function.

Stochastic modelling of intermittent fluctuations in the scrape-off layer: Correlations, distributions, level crossings, and moment estimation

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

Garcia, O. E., E-mail: odd.erik.garcia@uit.no; Kube, R.; Theodorsen, A.

A stochastic model is presented for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas. The fluctuations in the plasma density are modeled by a super-position of uncorrelated pulses with fixed shape and duration, describing radial motion of blob-like structures. In the case of an exponential pulse shape and exponentially distributed pulse amplitudes, predictions are given for the lowest order moments, probability density function, auto-correlation function, level crossings, and average times for periods spent above and below a given threshold level. Also, the mean squared errors on estimators of sample mean and variance for realizations of the process bymore » finite time series are obtained. These results are discussed in the context of single-point measurements of fluctuations in the scrape-off layer, broad density profiles, and implications for plasma–wall interactions due to the transient transport events in fusion grade plasmas. The results may also have wide applications for modelling fluctuations in other magnetized plasmas such as basic laboratory experiments and ionospheric irregularities.« less

Linear diffusion into a Faraday cage.

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

Warne, Larry Kevin; Lin, Yau Tang; Merewether, Kimball O.

2011-11-01

Linear lightning diffusion into a Faraday cage is studied. An early-time integral valid for large ratios of enclosure size to enclosure thickness and small relative permeability ({mu}/{mu}{sub 0} {le} 10) is used for this study. Existing solutions for nearby lightning impulse responses of electrically thick-wall enclosures are refined and extended to calculate the nearby lightning magnetic field (H) and time-derivative magnetic field (HDOT) inside enclosures of varying thickness caused by a decaying exponential excitation. For a direct strike scenario, the early-time integral for a worst-case line source outside the enclosure caused by an impulse is simplified and numerically integrated tomore » give the interior H and HDOT at the location closest to the source as well as a function of distance from the source. H and HDOT enclosure response functions for decaying exponentials are considered for an enclosure wall of any thickness. Simple formulas are derived to provide a description of enclosure interior H and HDOT as well. Direct strike voltage and current bounds for a single-turn optimally-coupled loop for all three waveforms are also given.« less

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.}

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)

Single-exponential activation behavior behind the super-Arrhenius relaxations in glass-forming liquids.

PubMed

Wang, Lianwen; Li, Jiangong; Fecht, Hans-Jörg

2010-11-17

The reported relaxation time for several typical glass-forming liquids was analyzed by using a kinetic model for liquids which invoked a new kind of atomic cooperativity--thermodynamic cooperativity. The broadly studied 'cooperative length' was recognized as the kinetic cooperativity. Both cooperativities were conveniently quantified from the measured relaxation data. A single-exponential activation behavior was uncovered behind the super-Arrhenius relaxations for the liquids investigated. Hence the mesostructure of these liquids and the atomic mechanism of the glass transition became clearer.

A mechanical model of bacteriophage DNA ejection

NASA Astrophysics Data System (ADS)

Arun, Rahul; Ghosal, Sandip

2017-08-01

Single molecule experiments on bacteriophages show an exponential scaling for the dependence of mobility on the length of DNA within the capsid. It has been suggested that this could be due to the ;capstan mechanism; - the exponential amplification of friction forces that result when a rope is wound around a cylinder as in a ship's capstan. Here we describe a desktop experiment that illustrates the effect. Though our model phage is a million times larger, it exhibits the same scaling observed in single molecule experiments.

High-Performance Clock Synchronization Algorithms for Distributed Wireless Airborne Computer Networks with Applications to Localization and Tracking of Targets

DTIC Science & Technology

2010-06-01

GMKPF represents a better and more flexible alternative to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ...accurate results relative to GML and EML when the network delays are modeled in terms of a single non-Gaussian/non-exponential distribution or as a...to the Gaussian Maximum Likelihood (GML), and Exponential Maximum Likelihood ( EML ) estimators for clock offset estimation in non-Gaussian or non

A space-efficient quantum computer simulator suitable for high-speed FPGA implementation

NASA Astrophysics Data System (ADS)

Frank, Michael P.; Oniciuc, Liviu; Meyer-Baese, Uwe H.; Chiorescu, Irinel

2009-05-01

Conventional vector-based simulators for quantum computers are quite limited in the size of the quantum circuits they can handle, due to the worst-case exponential growth of even sparse representations of the full quantum state vector as a function of the number of quantum operations applied. However, this exponential-space requirement can be avoided by using general space-time tradeoffs long known to complexity theorists, which can be appropriately optimized for this particular problem in a way that also illustrates some interesting reformulations of quantum mechanics. In this paper, we describe the design and empirical space/time complexity measurements of a working software prototype of a quantum computer simulator that avoids excessive space requirements. Due to its space-efficiency, this design is well-suited to embedding in single-chip environments, permitting especially fast execution that avoids access latencies to main memory. We plan to prototype our design on a standard FPGA development board.

Regression of altitude-produced cardiac hypertrophy.

NASA Technical Reports Server (NTRS)

Sizemore, D. A.; Mcintyre, T. W.; Van Liere, E. J.; Wilson , M. F.

1973-01-01

The rate of regression of cardiac hypertrophy with time has been determined in adult male albino rats. The hypertrophy was induced by intermittent exposure to simulated high altitude. The percentage hypertrophy was much greater (46%) in the right ventricle than in the left (16%). The regression could be adequately fitted to a single exponential function with a half-time of 6.73 plus or minus 0.71 days (90% CI). There was no significant difference in the rates of regression for the two ventricles.

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)

Characterization of x-ray framing cameras for the National Ignition Facility using single photon pulse height analysis.

PubMed

Holder, J P; Benedetti, L R; Bradley, D K

2016-11-01

Single hit pulse height analysis is applied to National Ignition Facility x-ray framing cameras to quantify gain and gain variation in a single micro-channel plate-based instrument. This method allows the separation of gain from detectability in these photon-detecting devices. While pulse heights measured by standard-DC calibration methods follow the expected exponential distribution at the limit of a compound-Poisson process, gain-gated pulse heights follow a more complex distribution that may be approximated as a weighted sum of a few exponentials. We can reproduce this behavior with a simple statistical-sampling model.

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.

LETTER TO THE EDITOR: Anti-self-dual Riemannian metrics without Killing vectors: can they be realized on K3?

NASA Astrophysics Data System (ADS)

Malykh, A. A.; Nutku, Y.; Sheftel, M. B.

2003-11-01

Explicit Riemannian metrics with Euclidean signature and anti-self-dual curvature that do not admit any Killing vectors are presented. The metric and the Riemann curvature scalars are homogeneous functions of degree zero in a single real potential and its derivatives. The solution for the potential is a sum of exponential functions which suggests that for the choice of a suitable domain of coordinates and parameters it can be the metric on a compact manifold. Then, by the theorem of Hitchin, it could be a class of metrics on K3, or on surfaces whose universal covering is K3.

Striatal dopamine in Parkinson disease: A meta-analysis of imaging studies.

PubMed

Kaasinen, Valtteri; Vahlberg, Tero

2017-12-01

A meta-analysis of 142 positron emission tomography and single photon emission computed tomography studies that have investigated striatal presynaptic dopamine function in Parkinson disease (PD) was performed. Subregional estimates of striatal dopamine metabolism are presented. The aromatic L-amino-acid decarboxylase (AADC) defect appears to be consistently smaller than the dopamine transporter and vesicular monoamine transporter 2 defects, suggesting upregulation of AADC function in PD. The correlation between disease severity and dopamine loss appears linear, but the majority of longitudinal studies point to a negative exponential progression pattern of dopamine loss in PD. Ann Neurol 2017;82:873-882. © 2017 American Neurological Association.

Measurement of the fall in the level of plasma radioactivity after intravenous administration of radiohippuran as a test of renal function

PubMed Central

Briggs, J. D.; Boyle, J. A.

1965-01-01

The level of plasma radioactivity following a single intravenous injection of 131I-labelled sodium orthoiodohippurate (radiohuppuran) falls with time in a tri-exponential fashion. The rate of fall of plasma radioactivity after an intravenous injection of radiohippuran was measured over the period 25 to 40 minutes from the time of injection and was expressed as the half-life of radiohippuran. The results suggest that this procedure may provide a valid measure of renal function which is more sensitive than the blood urea estimation but less sensitive than the creatinine clearance. PMID:14304256

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…

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

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.

Modulation of lens cell adhesion molecules by particle beams

NASA Technical Reports Server (NTRS)

McNamara, M. P.; Bjornstad, K. A.; Chang, P. Y.; Chou, W.; Lockett, S. J.; Blakely, E. A.

2001-01-01

Cell adhesion molecules (CAMs) are proteins which anchor cells to each other and to the extracellular matrix (ECM), but whose functions also include signal transduction, differentiation, and apoptosis. We are testing a hypothesis that particle radiations modulate CAM expression and this contributes to radiation-induced lens opacification. We observed dose-dependent changes in the expression of beta 1-integrin and ICAM-1 in exponentially-growing and confluent cells of a differentiating human lens epithelial cell model after exposure to particle beams. Human lens epithelial (HLE) cells, less than 10 passages after their initial culture from fetal tissue, were grown on bovine corneal endothelial cell-derived ECM in medium containing 15% fetal bovine serum and supplemented with 5 ng/ml basic fibroblast growth factor (FGF-2). Multiple cell populations at three different stages of differentiation were prepared for experiment: cells in exponential growth, and cells at 5 and 10 days post-confluence. The differentiation status of cells was characterized morphologically by digital image analysis, and biochemically by Western blotting using lens epithelial and fiber cell-specific markers. Cultures were irradiated with single doses (4, 8 or 12 Gy) of 55 MeV protons and, along with unirradiated control samples, were fixed using -20 degrees C methanol at 6 hours after exposure. Replicate experiments and similar experiments with helium ions are in progress. The intracellular localization of beta 1-integrin and ICAM-1 was detected by immunofluorescence using monoclonal antibodies specific for each CAM. Cells known to express each CAM were also processed as positive controls. Both exponentially-growing and confluent, differentiating cells demonstrated a dramatic proton-dose-dependent modulation (upregulation for exponential cells, downregulation for confluent cells) and a change in the intracellular distribution of the beta 1-integrin, compared to unirradiated controls. In contrast, there was a dose-dependent increase in ICAM-1 immunofluorescence in confluent, but not exponentially-growing cells. These results suggest that proton irradiation downregulates beta 1-integrin and upregulates ICAM-1, potentially contributing to cell death or to aberrant differentiation via modulation of anchorage and/or signal transduction functions. Quantification of the expression levels of the CAMs by Western analysis is in progress.

Smoothing Forecasting Methods for Academic Library Circulations: An Evaluation and Recommendation.

ERIC Educational Resources Information Center

Brooks, Terrence A.; Forys, John W., Jr.

1986-01-01

Circulation time-series data from 50 midwest academic libraries were used to test 110 variants of 8 smoothing forecasting methods. Data and methodologies and illustrations of two recommended methods--the single exponential smoothing method and Brown's one-parameter linear exponential smoothing method--are given. Eight references are cited. (EJS)

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.

Detecting biodiversity hotspots by species-area relationships: a case study of Mediterranean beetles.

PubMed

Fattorini, Simone

2006-08-01

Any method of identifying hotspots should take into account the effect of area on species richness. I examined the importance of the species-area relationship in determining tenebrionid (Coleoptera: Tenebrionidae) hotspots on the Aegean Islands (Greece). Thirty-two islands and 170 taxa (species and subspecies) were included in this study. I tested several species-area relationship models with linear and nonlinear regressions, including power exponential, negative exponential, logistic, Gompertz, Weibull, Lomolino, and He-Legendre functions. Islands with positive residuals were identified as hotspots. I also analyzed the values of the C parameter of the power function and the simple species-area ratios. Species richness was significantly correlated with island area for all models. The power function model was the most convenient one. Most functions, however identified certain islands as hotspots. The importance of endemics in insular biotas should be evaluated carefully because they are of high conservation concern. The simple use of the species-area relationship can be problematic when areas with no endemics are included. Therefore the importance of endemics should be evaluated according to different methods, such as percentages, to take into account different levels of endemism and different kinds of "endemics" (e.g., endemic to single islands vs. endemic to the archipelago). Because the species-area relationship is a key pattern in ecology, my findings can be applied at broader scales.

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.

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.

A new formula for normal tissue complication probability (NTCP) as a function of equivalent uniform dose (EUD).

PubMed

Luxton, Gary; Keall, Paul J; King, Christopher R

2008-01-07

To facilitate the use of biological outcome modeling for treatment planning, an exponential function is introduced as a simpler equivalent to the Lyman formula for calculating normal tissue complication probability (NTCP). The single parameter of the exponential function is chosen to reproduce the Lyman calculation to within approximately 0.3%, and thus enable easy conversion of data contained in empirical fits of Lyman parameters for organs at risk (OARs). Organ parameters for the new formula are given in terms of Lyman model m and TD(50), and conversely m and TD(50) are expressed in terms of the parameters of the new equation. The role of the Lyman volume-effect parameter n is unchanged from its role in the Lyman model. For a non-homogeneously irradiated OAR, an equation relates d(ref), n, v(eff) and the Niemierko equivalent uniform dose (EUD), where d(ref) and v(eff) are the reference dose and effective fractional volume of the Kutcher-Burman reduction algorithm (i.e. the LKB model). It follows in the LKB model that uniform EUD irradiation of an OAR results in the same NTCP as the original non-homogeneous distribution. The NTCP equation is therefore represented as a function of EUD. The inverse equation expresses EUD as a function of NTCP and is used to generate a table of EUD versus normal tissue complication probability for the Emami-Burman parameter fits as well as for OAR parameter sets from more recent data.

Exponential fading to white of black holes in quantum gravity

NASA Astrophysics Data System (ADS)

Barceló, Carlos; Carballo-Rubio, Raúl; Garay, Luis J.

2017-05-01

Quantization of the gravitational field may allow the existence of a decay channel of black holes into white holes with an explicit time-reversal symmetry. The definition of a meaningful decay probability for this channel is studied in spherically symmetric situations. As a first nontrivial calculation, we present the functional integration over a set of geometries using a single-variable function to interpolate between black-hole and white-hole geometries in a bounded region of spacetime. This computation gives a finite result which depends only on the Schwarzschild mass and a parameter measuring the width of the interpolating region. The associated probability distribution displays an exponential decay law on the latter parameter, with a mean lifetime inversely proportional to the Schwarzschild mass. In physical terms this would imply that matter collapsing to a black hole from a finite radius bounces back elastically and instantaneously, with negligible time delay as measured by external observers. These results invite to reconsider the ultimate nature of astrophysical black holes, providing a possible mechanism for the formation of black stars instead of proper general relativistic black holes. The existence of both this decay channel and black stars can be tested in future observations of gravitational waves.

Charge relaxation and dynamics in organic semiconductors

NASA Astrophysics Data System (ADS)

Kwok, H. L.

2006-08-01

Charge relaxation in dispersive materials is often described in terms of the stretched exponential function (Kohlrausch law). The process can be explained using a "hopping" model which in principle, also applies to charge transport such as current conduction. This work analyzed reported transient photoconductivity data on functionalized pentacene single crystals using a geometric hopping model developed by B. Sturman et al and extracted values (or range of values) on the materials parameters relevant to charge relaxation as well as charge transport. Using the correlated disorder model (CDM), we estimated values of the carrier mobility for the pentacene samples. From these results, we observed the following: i) the transport site density appeared to be of the same order of magnitude as the carrier density; ii) it was possible to extract lower bound values on the materials parameters linked to the transport process; and iii) by matching the simulated charge decay to the transient photoconductivity data, we were able to refine estimates on the materials parameters. The data also allowed us to simulate the stretched exponential decay. Our observations suggested that the stretching index and the carrier mobility were related. Physically, such interdependence would allow one to demarcate between localized molecular interactions and distant coulomb interactions.

Exponential decline of aftershocks of the M7.9 1868 great Kau earthquake, Hawaii, through the 20th century

USGS Publications Warehouse

Klein, F.W.; Wright, Tim

2008-01-01

The remarkable catalog of Hawaiian earthquakes going back to the 1820s is based on missionary diaries, newspaper accounts, and instrumental records and spans the great M7.9 Kau earthquake of April 1868 and its aftershock sequence. The earthquake record since 1868 defines a smooth curve complete to M5.2 of the declining rate into the 21st century, after five short volcanic swarms are removed. A single aftershock curve fits the earthquake record, even with numerous M6 and 7 main shocks and eruptions. The timing of some moderate earthquakes may be controlled by magmatic stresses, but their overall long-term rate reflects one of aftershocks of the Kau earthquake. The 1868 earthquake is, therefore, the largest and most controlling stress event in the 19th and 20th centuries. We fit both the modified Omori (power law) and stretched exponential (SE) functions to the earthquakes. We found that the modified Omori law is a good fit to the M ??? 5.2 earthquake rate for the first 10 years or so and the more rapidly declining SE function fits better thereafter, as supported by three statistical tests. The switch to exponential decay suggests that a possible change in aftershock physics may occur from rate and state fault friction, with no change in the stress rate, to viscoelastic stress relaxation. The 61-year exponential decay constant is at the upper end of the range of geodetic relaxation times seen after other global earthquakes. Modeling deformation in Hawaii is beyond the scope of this paper, but a simple interpretation of the decay suggests an effective viscosity of 1019 to 1020 Pa s pertains in the volcanic spreading of Hawaii's flanks. The rapid decline in earthquake rate poses questions for seismic hazard estimates in an area that is cited as one of the most hazardous in the United States.

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…

Spacecraft Solar Particle Event (SPE) Shielding: Shielding Effectiveness as a Function of SPE model as Determined with the FLUKA Radiation Transport Code

NASA Technical Reports Server (NTRS)

Koontz, Steve; Atwell, William; Reddell, Brandon; Rojdev, Kristina

2010-01-01

Analysis of both satellite and surface neutron monitor data demonstrate that the widely utilized Exponential model of solar particle event (SPE) proton kinetic energy spectra can seriously underestimate SPE proton flux, especially at the highest kinetic energies. The more recently developed Band model produces better agreement with neutron monitor data ground level events (GLEs) and is believed to be considerably more accurate at high kinetic energies. Here, we report the results of modeling and simulation studies in which the radiation transport code FLUKA (FLUktuierende KAskade) is used to determine the changes in total ionizing dose (TID) and single-event environments (SEE) behind aluminum, polyethylene, carbon, and titanium shielding masses when the assumed form (i. e., Band or Exponential) of the solar particle event (SPE) kinetic energy spectra is changed. FLUKA simulations have fully three dimensions with an isotropic particle flux incident on a concentric spherical shell shielding mass and detector structure. The effects are reported for both energetic primary protons penetrating the shield mass and secondary particle showers caused by energetic primary protons colliding with shielding mass nuclei. Our results, in agreement with previous studies, show that use of the Exponential form of the event

Intermittent fluctuations in the Alcator C-Mod scrape-off layer for ohmic and high confinement mode plasmas

NASA Astrophysics Data System (ADS)

Garcia, O. E.; Kube, R.; Theodorsen, A.; LaBombard, B.; Terry, J. L.

2018-05-01

Plasma fluctuations in the scrape-off layer of the Alcator C-Mod tokamak in ohmic and high confinement modes have been analyzed using gas puff imaging data. In all cases investigated, the time series of emission from a single spatially resolved view into the gas puff are dominated by large-amplitude bursts, attributed to blob-like filament structures moving radially outwards and poloidally. There is a remarkable similarity of the fluctuation statistics in ohmic plasmas and in edge localized mode-free and enhanced D-alpha high confinement mode plasmas. Conditionally averaged waveforms have a two-sided exponential shape with comparable temporal scales and asymmetry, while the burst amplitudes and the waiting times between them are exponentially distributed. The probability density functions and the frequency power spectral densities are similar for all these confinement modes. These results provide strong evidence in support of a stochastic model describing the plasma fluctuations in the scrape-off layer as a super-position of uncorrelated exponential pulses. Predictions of this model are in excellent agreement with experimental measurements in both ohmic and high confinement mode plasmas. The stochastic model thus provides a valuable tool for predicting fluctuation-induced plasma-wall interactions in magnetically confined fusion plasmas.

Coagulation-Fragmentation Model for Animal Group-Size Statistics

NASA Astrophysics Data System (ADS)

Degond, Pierre; Liu, Jian-Guo; Pego, Robert L.

2017-04-01

We study coagulation-fragmentation equations inspired by a simple model proposed in fisheries science to explain data for the size distribution of schools of pelagic fish. Although the equations lack detailed balance and admit no H-theorem, we are able to develop a rather complete description of equilibrium profiles and large-time behavior, based on recent developments in complex function theory for Bernstein and Pick functions. In the large-population continuum limit, a scaling-invariant regime is reached in which all equilibria are determined by a single scaling profile. This universal profile exhibits power-law behavior crossing over from exponent -2/3 for small size to -3/2 for large size, with an exponential cutoff.

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.

Cross-catalytic hairpin assembly-based exponential signal amplification for CRET assay with low background noise.

PubMed

Yue, Shuzhen; Zhao, Tingting; Qi, Hongjie; Yan, Yongcun; Bi, Sai

2017-08-15

A toehold-mediated strand displacement (TMSD)-based cross-catalytic hairpin assembly (C-CHA) is demonstrated in this study, achieving exponential amplification of nucleic acids. Functionally, this system consists of four hairpins (H1, H2, H3 and H4) and one single-stranded initiator (I). Upon the introduction of I, the first CHA reaction (CHA1) is triggered, leading to the self-assembly of hybrid H1·H2 that then initiates the second CHA reaction (CHA2) to obtain the hybrid H3·H4. Since the single-stranded region in H3·H4 is identical to I, a new CHA1 is initiated, which thus achieves cross operation of CHA1 and CHA2 and exponential growth kinetics. Interestingly, because the C-CHA performs in a cascade manner, this system can be considered as multi-level molecular logic circuits with feedback mechanism. Moreover, through incorporating G-quadruplex subunits and fluorescein isothiocyanate (FITC) in the product of H1·H2, this C-CHA is readily utilized to fabricate a chemiluminescence resonance energy transfer (CRET) biosensing platform, achieving sensitive and selective detection of DNA and microRNA in real samples. Since the high background signal induced by FITC in the absence of initiator is greatly reduced through labeling quencher in H1, the signal-to-noise ratio and detection sensitivity are improved significantly. Therefore, our proposed C-CHA protocol holds a great potential for further applications in not only building complex autonomous systems but also the development of biosensing platforms and DNA nanotechnology. Copyright © 2017 Elsevier B.V. All rights reserved.

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

Ring-Shaped Microlanes and Chemical Barriers as a Platform for Probing Single-Cell Migration.

PubMed

Schreiber, Christoph; Segerer, Felix J; Wagner, Ernst; Roidl, Andreas; Rädler, Joachim O

2016-05-31

Quantification and discrimination of pharmaceutical and disease-related effects on cell migration requires detailed characterization of single-cell motility. In this context, micropatterned substrates that constrain cells within defined geometries facilitate quantitative readout of locomotion. Here, we study quasi-one-dimensional cell migration in ring-shaped microlanes. We observe bimodal behavior in form of alternating states of directional migration (run state) and reorientation (rest state). Both states show exponential lifetime distributions with characteristic persistence times, which, together with the cell velocity in the run state, provide a set of parameters that succinctly describe cell motion. By introducing PEGylated barriers of different widths into the lane, we extend this description by quantifying the effects of abrupt changes in substrate chemistry on migrating cells. The transit probability decreases exponentially as a function of barrier width, thus specifying a characteristic penetration depth of the leading lamellipodia. Applying this fingerprint-like characterization of cell motion, we compare different cell lines, and demonstrate that the cancer drug candidate salinomycin affects transit probability and resting time, but not run time or run velocity. Hence, the presented assay allows to assess multiple migration-related parameters, permits detailed characterization of cell motility, and has potential applications in cell biology and advanced drug screening.

Stochastic Individual-Based Modeling of Bacterial Growth and Division Using Flow Cytometry.

PubMed

García, Míriam R; Vázquez, José A; Teixeira, Isabel G; Alonso, Antonio A

2017-01-01

A realistic description of the variability in bacterial growth and division is critical to produce reliable predictions of safety risks along the food chain. Individual-based modeling of bacteria provides the theoretical framework to deal with this variability, but it requires information about the individual behavior of bacteria inside populations. In this work, we overcome this problem by estimating the individual behavior of bacteria from population statistics obtained with flow cytometry. For this objective, a stochastic individual-based modeling framework is defined based on standard assumptions during division and exponential growth. The unknown single-cell parameters required for running the individual-based modeling simulations, such as cell size growth rate, are estimated from the flow cytometry data. Instead of using directly the individual-based model, we make use of a modified Fokker-Plank equation. This only equation simulates the population statistics in function of the unknown single-cell parameters. We test the validity of the approach by modeling the growth and division of Pediococcus acidilactici within the exponential phase. Estimations reveal the statistics of cell growth and division using only data from flow cytometry at a given time. From the relationship between the mother and daughter volumes, we also predict that P. acidilactici divide into two successive parallel planes.

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.

Tachyon inflation in the large-N formalism

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

Barbosa-Cendejas, Nandinii; De-Santiago, Josue; German, Gabriel

2015-11-01

We study tachyon inflation within the large-N formalism, which takes a prescription for the small Hubble flow slow-roll parameter ε{sub 1} as a function of the large number of e-folds N. This leads to a classification of models through their behaviour at large N. In addition to the perturbative N class, we introduce the polynomial and exponential classes for the ε{sub 1} parameter. With this formalism we reconstruct a large number of potentials used previously in the literature for tachyon inflation. We also obtain new families of potentials from the polynomial class. We characterize the realizations of tachyon inflation bymore » computing the usual cosmological observables up to second order in the Hubble flow slow-roll parameters. This allows us to look at observable differences between tachyon and canonical single field inflation. The analysis of observables in light of the Planck 2015 data shows the viability of some of these models, mostly for certain realization of the polynomial and exponential classes.« less

Simultaneous estimation of multiple phases in digital holographic interferometry using state space analysis

NASA Astrophysics Data System (ADS)

Kulkarni, Rishikesh; Rastogi, Pramod

2018-05-01

A new approach is proposed for the multiple phase estimation from a multicomponent exponential phase signal recorded in multi-beam digital holographic interferometry. It is capable of providing multidimensional measurements in a simultaneous manner from a single recording of the exponential phase signal encoding multiple phases. Each phase within a small window around each pixel is appproximated with a first order polynomial function of spatial coordinates. The problem of accurate estimation of polynomial coefficients, and in turn the unwrapped phases, is formulated as a state space analysis wherein the coefficients and signal amplitudes are set as the elements of a state vector. The state estimation is performed using the extended Kalman filter. An amplitude discrimination criterion is utilized in order to unambiguously estimate the coefficients associated with the individual signal components. The performance of proposed method is stable over a wide range of the ratio of signal amplitudes. The pixelwise phase estimation approach of the proposed method allows it to handle the fringe patterns that may contain invalid regions.

Optical spectroscopy of BaY2F8:Dy3+

NASA Astrophysics Data System (ADS)

Parisi, Daniela; Toncelli, Alessandra; Tonelli, Mauro; Cavalli, Enrico; Bovero, Enrico; Belletti, Alessandro

2005-05-01

The optical spectra of the BaY2F8:Dy3+ laser crystal have been investigated in the 5000-30 000 cm-1 range. The Judd-Ofelt parametrization scheme has been applied to the analysis of the room temperature absorption spectra. The calculated radiative lifetime of the 4F9/2 state is 1.48 ms. Decay curves of the visible emission have been measured as a function of the temperature for two different Dy3+ concentrations (0.5 and 4.4%). In the case of the diluted crystal the emission profiles are single exponential with decay times consistent with the radiative lifetime. The decay curves of the concentrated crystal are not exponential and they obey the Inokuti-Hirayama model for energy transfer for an electric dipole-dipole interaction in the absence of diffusion among the donors. The emission cross section at 575 nm has been estimated using the integral β-τ method in order to assess the potentialities of this compound as a solid state laser material in the yellow region.

Modeling the Role of Dislocation Substructure During Class M and Exponential Creep. Revised

NASA Technical Reports Server (NTRS)

Raj, S. V.; Iskovitz, Ilana Seiden; Freed, A. D.

1995-01-01

The different substructures that form in the power-law and exponential creep regimes for single phase crystalline materials under various conditions of stress, temperature and strain are reviewed. The microstructure is correlated both qualitatively and quantitatively with power-law and exponential creep as well as with steady state and non-steady state deformation behavior. These observations suggest that creep is influenced by a complex interaction between several elements of the microstructure, such as dislocations, cells and subgrains. The stability of the creep substructure is examined in both of these creep regimes during stress and temperature change experiments. These observations are rationalized on the basis of a phenomenological model, where normal primary creep is interpreted as a series of constant structure exponential creep rate-stress relationships. The implications of this viewpoint on the magnitude of the stress exponent and steady state behavior are discussed. A theory is developed to predict the macroscopic creep behavior of a single phase material using quantitative microstructural data. In this technique the thermally activated deformation mechanisms proposed by dislocation physics are interlinked with a previously developed multiphase, three-dimensional. dislocation substructure creep model. This procedure leads to several coupled differential equations interrelating macroscopic creep plasticity with microstructural evolution.

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.

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…

The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time

NASA Astrophysics Data System (ADS)

Hu, Xiaohu; Hong, Liang; Dean Smith, Micholas; Neusius, Thomas; Cheng, Xiaolin; Smith, Jeremy C.

2016-02-01

Internal motions of proteins are essential to their function. The time dependence of protein structural fluctuations is highly complex, manifesting subdiffusive, non-exponential behaviour with effective relaxation times existing over many decades in time, from ps up to ~102 s (refs ,,,). Here, using molecular dynamics simulations, we show that, on timescales from 10-12 to 10-5 s, motions in single proteins are self-similar, non-equilibrium and exhibit ageing. The characteristic relaxation time for a distance fluctuation, such as inter-domain motion, is observation-time-dependent, increasing in a simple, power-law fashion, arising from the fractal nature of the topology and geometry of the energy landscape explored. Diffusion over the energy landscape follows a non-ergodic continuous time random walk. Comparison with single-molecule experiments suggests that the non-equilibrium self-similar dynamical behaviour persists up to timescales approaching the in vivo lifespan of individual protein molecules.

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.

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

Friedman, B.; DuCharme, G.

We present a semi-empirical scaling law for non-resonant ion–atom single charge exchange cross sections for collisions with velocities frommore » $${10}^{7}\\,{\\rm{t}}{\\rm{o}}\\,{10}^{9}\\,\\mathrm{cm}\\,{{\\rm{s}}}^{-1}$$ and ions with positive charge $$q\\lt 8$$. Non-resonant cross sections tend to have a velocity peak at collision velocities $$v\\lesssim 1\\ {\\rm{a}}{\\rm{u}}$$ with exponential decay around this peak. We construct a scaling formula for the location of this peak then choose a functional form for the cross section curve and scale it. The velocity at which the cross section peaks, v m, is proportional to the energy defect of the collision, $${\\rm{\\Delta }}E$$, which we predict with the decay approximation. The value of the cross section maximum is proportional to the charge state q, inversely proportional to the target ionization energy I T, and inversely proportional to v m. For the shape of the cross section curve, we use a function that decays exponentially asymptotically at high and low velocities. We scale this function with parameters $${v}_{{\\rm{m}}},{I}_{{\\rm{T}}},{Z}_{{\\rm{T}}},\\mathrm{and}\\ {Z}_{{\\rm{P}}}$$, where the $${Z}_{{\\rm{T}},{\\rm{P}}}$$ are the target and projectile atomic numbers. In conclusion, for the more than 100 cross section curves that we use to find the scaling rules, the scaling law predicts cross sections within a little over a factor of 2 on average.« less

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.

On the heterogeneity of fluorescence lifetime of room temperature ionic liquids: onset of a journey for exploring red emitting dyes.

PubMed

Ghosh, Anup; Chatterjee, Tanmay; Mandal, Prasun K

2012-06-25

An excitation and emission wavelength dependent non-exponential fluorescence decay behaviour of room temperature ionic liquids (RTILs) has been noted. Average fluorescence lifetimes have been found to vary by a factor of three or more. Red emitting dyes dissolved in RTILs are found to follow hitherto unobserved single exponential fluorescence decay behaviour.

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

Motion of Molecular Probes and Viscosity Scaling in Polyelectrolyte Solutions at Physiological Ionic Strength

PubMed Central

Sozanski, Krzysztof; Wisniewska, Agnieszka; Kalwarczyk, Tomasz; Sznajder, Anna; Holyst, Robert

2016-01-01

We investigate transport properties of model polyelectrolyte systems at physiological ionic strength (0.154 M). Covering a broad range of flow length scales—from diffusion of molecular probes to macroscopic viscous flow—we establish a single, continuous function describing the scale dependent viscosity of high-salt polyelectrolyte solutions. The data are consistent with the model developed previously for electrically neutral polymers in a good solvent. The presented approach merges the power-law scaling concepts of de Gennes with the idea of exponential length scale dependence of effective viscosity in complex liquids. The result is a simple and applicable description of transport properties of high-salt polyelectrolyte solutions at all length scales, valid for motion of single molecules as well as macroscopic flow of the complex liquid. PMID:27536866

Triply differential measurements of single ionization of argon by 1-keV positron and electron impact

NASA Astrophysics Data System (ADS)

Gavin, J.; de Lucio, O. G.; DuBois, R. D.

2017-06-01

By establishing coincidences between target ions and scattered projectiles, and coincidences between target ions, scattered projectiles, and ejected electrons, triply differential cross-section (TDCS) information was generated in terms of projectile energy loss and scattering angles for interactions between 1-keV positrons and electrons and Ar atoms. The conversion of the raw experimental information to the TDCS is discussed. The single-ionization TDCS exhibits two distinguishable regions (lobes) where binary and recoil interactions can be described by two peaks. A comparison of the positron and electron impact data shows that the relative intensity of both binary and recoil interactions decreases exponentially as a function of the momentum transfer and is larger when ionization is induced by positron impact, when compared with electron impact.

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

Turbulent particle transport in streams: can exponential settling be reconciled with fluid mechanics?

PubMed

McNair, James N; Newbold, J Denis

2012-05-07

Most ecological studies of particle transport in streams that focus on fine particulate organic matter or benthic invertebrates use the Exponential Settling Model (ESM) to characterize the longitudinal pattern of particle settling on the bed. The ESM predicts that if particles are released into a stream, the proportion that have not yet settled will decline exponentially with transport time or distance and will be independent of the release elevation above the bed. To date, no credible basis in fluid mechanics has been established for this model, nor has it been rigorously tested against more-mechanistic alternative models. One alternative is the Local Exchange Model (LEM), which is a stochastic advection-diffusion model that includes both longitudinal and vertical spatial dimensions and is based on classical fluid mechanics. The LEM predicts that particle settling will be non-exponential in the near field but will become exponential in the far field, providing a new theoretical justification for far-field exponential settling that is based on plausible fluid mechanics. We review properties of the ESM and LEM and compare these with available empirical evidence. Most evidence supports the prediction of both models that settling will be exponential in the far field but contradicts the ESM's prediction that a single exponential distribution will hold for all transport times and distances. Copyright © 2012 Elsevier Ltd. All rights reserved.

Stochastic scheduling on a repairable manufacturing system

NASA Astrophysics Data System (ADS)

Li, Wei; Cao, Jinhua

1995-08-01

In this paper, we consider some stochastic scheduling problems with a set of stochastic jobs on a manufacturing system with a single machine that is subject to multiple breakdowns and repairs. When the machine processing a job fails, the job processing must restart some time later when the machine is repaired. For this typical manufacturing system, we find the optimal policies that minimize the following objective functions: (1) the weighed sum of the completion times; (2) the weighed number of late jobs having constant due dates; (3) the weighted number of late jobs having random due dates exponentially distributed, which generalize some previous results.

Collapse of a self-similar cylindrical scalar field with non-minimal coupling II: strong cosmic censorship

NASA Astrophysics Data System (ADS)

Condron, Eoin; Nolan, Brien C.

2014-08-01

We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is shown that the scalar field is dependent on a single unknown function of the same variable and that the scalar field potential has exponential form. The Einstein equations then take the form of a set of ODEs. Self-similarity also gives rise to a singularity at the scaling origin. We extend the work of Condron and Nolan (2014 Class. Quantum Grav. 31 015015), which determined the global structure of all solutions with a regular axis in the causal past of the singularity. We identified a class of solutions that evolves through the past null cone of the singularity. We give the global structure of these solutions and show that the singularity is censored in all cases.

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.

A fuzzy adaptive network approach to parameter estimation in cases where independent variables come from an exponential distribution

NASA Astrophysics Data System (ADS)

Dalkilic, Turkan Erbay; Apaydin, Aysen

2009-11-01

In a regression analysis, it is assumed that the observations come from a single class in a data cluster and the simple functional relationship between the dependent and independent variables can be expressed using the general model; Y=f(X)+[epsilon]. However; a data cluster may consist of a combination of observations that have different distributions that are derived from different clusters. When faced with issues of estimating a regression model for fuzzy inputs that have been derived from different distributions, this regression model has been termed the [`]switching regression model' and it is expressed with . Here li indicates the class number of each independent variable and p is indicative of the number of independent variables [J.R. Jang, ANFIS: Adaptive-network-based fuzzy inference system, IEEE Transaction on Systems, Man and Cybernetics 23 (3) (1993) 665-685; M. Michel, Fuzzy clustering and switching regression models using ambiguity and distance rejects, Fuzzy Sets and Systems 122 (2001) 363-399; E.Q. Richard, A new approach to estimating switching regressions, Journal of the American Statistical Association 67 (338) (1972) 306-310]. In this study, adaptive networks have been used to construct a model that has been formed by gathering obtained models. There are methods that suggest the class numbers of independent variables heuristically. Alternatively, in defining the optimal class number of independent variables, the use of suggested validity criterion for fuzzy clustering has been aimed. In the case that independent variables have an exponential distribution, an algorithm has been suggested for defining the unknown parameter of the switching regression model and for obtaining the estimated values after obtaining an optimal membership function, which is suitable for exponential distribution.

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.

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

Zhou, Quanlin; Oldenburg, Curtis M.; Spangler, Lee H.

Analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low-permeability blocks and high-permeability zones in the subsurface. Truncation of these series is often employed by neglecting the early-time regime. Here in this paper, we present unified-form approximate solutions in which the early-time and the late-time solutions are continuous at a switchover time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent only on the dimensionless area-to-volume ratio. The last two coefficients are either determined analytically for isotropic blocks (e.g., spheresmore » and slabs) or obtained by fitting the exact solutions, and they solely depend on the aspect ratios for rectangular columns and parallelepipeds. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The optimal switchover time is between 0.157 and 0.229, with highest relative approximation error less than 0.2%. The solutions are used to demonstrate the storage of dissolved CO 2 in fractured reservoirs with low-permeability matrix blocks of single and multiple shapes and sizes. These approximate solutions are building blocks for development of analytical and numerical tools for hydraulic, solute, and thermal diffusion processes in low-permeability matrix blocks.« less

Polypeptide multilayer films on colloidal particles: an in situ electro-optical study.

PubMed

Radeva, Tsetska; Kamburova, Kamelia

2007-04-15

The buildup of poly(L-glutamic acid) (PGA) and poly(L-lysine) (PLL) multilayers on beta-FeOOH colloidal particles was investigated by means of electro-optics and electrophoresis. The films were built at different (acidic) pH in the absence of salt. We found that the thickness of the film grows linearly when the fully charged PLL (at pH 5.5) is combined with almost fully charged PGA (at pH 6.5), with a thickness of about 2 nm per single layer. When the fully charged PLL is combined with weakly charged PGA (at pH 4.5), the film thickness increases exponentially with the number of deposited layers. The thickness of the exponentially growing film increases to 300 nm after deposition of 16 layers. The exponential film growth is attributed to the ability of the PLL to diffuse "in" and "out" of the film bulk at each deposition step. The variation in the electrical polarizability of the film-coated particles was also monitored as a function of the number of adsorbed layers. The result reveals that the PLL chains, which can diffuse into the film bulk, have no measurable contribution to the electro-optical effect of the films terminated with PLL. It is only due to the polarization of counterions of the PLL adsorbed on the film surface.

Lithium ion dynamics in Li2S+GeS2+GeO2 glasses studied using (7)Li NMR field-cycling relaxometry and line-shape analysis.

PubMed

Gabriel, Jan; Petrov, Oleg V; Kim, Youngsik; Martin, Steve W; Vogel, Michael

2015-09-01

We use (7)Li NMR to study the ionic jump motion in ternary 0.5Li2S+0.5[(1-x)GeS2+xGeO2] glassy lithium ion conductors. Exploring the "mixed glass former effect" in this system led to the assumption of a homogeneous and random variation of diffusion barriers in this system. We exploit that combining traditional line-shape analysis with novel field-cycling relaxometry, it is possible to measure the spectral density of the ionic jump motion in broad frequency and temperature ranges and, thus, to determine the distribution of activation energies. Two models are employed to parameterize the (7)Li NMR data, namely, the multi-exponential autocorrelation function model and the power-law waiting times model. Careful evaluation of both of these models indicates a broadly inhomogeneous energy landscape for both the single (x=0.0) and the mixed (x=0.1) network former glasses. The multi-exponential autocorrelation function model can be well described by a Gaussian distribution of activation barriers. Applicability of the methods used and their sensitivity to microscopic details of ionic motion are discussed. Copyright © 2015 Elsevier Inc. All rights reserved.

Spherical space Bessel-Legendre-Fourier localized modes solver for electromagnetic waves.

PubMed

Alzahrani, Mohammed A; Gauthier, Robert C

2015-10-05

Maxwell's vector wave equations are solved for dielectric configurations that match the symmetry of a spherical computational domain. The electric or magnetic field components and the inverse of the dielectric profile are series expansion defined using basis functions composed of the lowest order spherical Bessel function, polar angle single index dependant Legendre polynomials and azimuthal complex exponential (BLF). The series expressions and non-traditional form of the basis functions result in an eigenvalue matrix formulation of Maxwell's equations that are relatively compact and accurately solvable on a desktop PC. The BLF matrix returns the frequencies and field profiles for steady states modes. The key steps leading to the matrix populating expressions are provided. The validity of the numerical technique is confirmed by comparing the results of computations to those published using complementary techniques.

Polynomial solution of quantum Grassmann matrices

NASA Astrophysics Data System (ADS)

Tierz, Miguel

2017-05-01

We study a model of quantum mechanical fermions with matrix-like index structure (with indices N and L) and quartic interactions, recently introduced by Anninos and Silva. We compute the partition function exactly with q-deformed orthogonal polynomials (Stieltjes-Wigert polynomials), for different values of L and arbitrary N. From the explicit evaluation of the thermal partition function, the energy levels and degeneracies are determined. For a given L, the number of states of different energy is quadratic in N, which implies an exponential degeneracy of the energy levels. We also show that at high-temperature we have a Gaussian matrix model, which implies a symmetry that swaps N and L, together with a Wick rotation of the spectral parameter. In this limit, we also write the partition function, for generic L and N, in terms of a single generalized Hermite polynomial.

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.

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.

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.

VO2 Off Transient Kinetics in Extreme Intensity Swimming.

PubMed

Sousa, Ana; Figueiredo, Pedro; Keskinen, Kari L; Rodríguez, Ferran A; Machado, Leandro; Vilas-Boas, João P; Fernandes, Ricardo J

2011-01-01

Inconsistencies about dynamic asymmetry between the on- and off- transient responses in oxygen uptake are found in the literature. Therefore, the purpose of this study was to characterize the oxygen uptake off-transient kinetics during a maximal 200-m front crawl effort, as examining the degree to which the on/off regularity of the oxygen uptake kinetics response was preserved. Eight high level male swimmers performed a 200-m front crawl at maximal speed during which oxygen uptake was directly measured through breath-by-breath oxymetry (averaged every 5 s). This apparatus was connected to the swimmer by a low hydrodynamic resistance respiratory snorkel and valve system. The on- and off-transient phases were symmetrical in shape (mirror image) once they were adequately fitted by a single-exponential regression models, and no slow component for the oxygen uptake response was developed. Mean (± SD) peak oxygen uptake was 69.0 (± 6.3) mL·kg(-1)·min(-1), significantly correlated with time constant of the off- transient period (r = 0.76, p < 0.05) but not with any of the other oxygen off-transient kinetic parameters studied. A direct relationship between time constant of the off-transient period and mean swimming speed of the 200-m (r = 0.77, p < 0.05), and with the amplitude of the fast component of the effort period (r = 0.72, p < 0.05) were observed. The mean amplitude and time constant of the off-transient period values were significantly greater than the respective on- transient. In conclusion, although an asymmetry between the on- and off kinetic parameters was verified, both the 200-m effort and the respectively recovery period were better characterized by a single exponential regression model. Key pointsThe VO2 slow component was not observed in the recovery period of swimming extreme efforts;The on and off transient periods were better fitted by a single exponential function, and so, these effort and recovery periods of swimming extreme efforts are symmetrical;The rate of VO2 decline during the recovery period may be due to not only the magnitude of oxygen debt but also the VO2peak obtained during the effort period.

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.

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.

Responses of single cells in cat visual cortex to prolonged stimulus movement: neural correlates of visual aftereffects.

PubMed

Vautin, R G; Berkley, M A

1977-09-01

1. The activity of single cortical cells in area 17 of anesthetized and unanesthetized cats was recorded in response to prolonged stimulation with moving stimuli. 2. Under the appropriate conditions, all cells observed showed a progressive response decrement during the stimulation period, regardless of cell classification, i.e., simple, complex, or hypercomplex. 3. The observed response decrement was shown to be largely cortical in origin and could be adequately described with an exponential function of the form R = Rf +(R1-Rf)e-t/T. Time constants derived from such calculations yielded values ranging from 1.92 to 12.45 s under conditions of optimal-stimulation. 4. Most cells showed poststimulation effects, usually a brief period of reduced responsiveness that recovered exponentially. Recovery was essentially complete in about 5-35 s. 5. The degree to which stimuli were effective at inducing response was shown to have significant effects on the magnitude of the response decrement. 6. Several cells showed neural patterns of response and recovery that suggested the operation of intracortical inhibitory mechanisms. 7. A simple two-process model that adequately describes the behavior of all the studied cells is presented. 8. Because the properties of the cells studied correlate well with human psychophysical measures of contour and movement adaptation and recovery, a causal relationship to similar neural mechanisms in humans is suggested.

Stochastic modelling of a single ion channel: an alternating renewal approach with application to limited time resolution.

PubMed

Milne, R K; Yeo, G F; Edeson, R O; Madsen, B W

1988-04-22

Stochastic models of ion channels have been based largely on Markov theory where individual states and transition rates must be specified, and sojourn-time densities for each state are constrained to be exponential. This study presents an approach based on random-sum methods and alternating-renewal theory, allowing individual states to be grouped into classes provided the successive sojourn times in a given class are independent and identically distributed. Under these conditions Markov models form a special case. The utility of the approach is illustrated by considering the effects of limited time resolution (modelled by using a discrete detection limit, xi) on the properties of observable events, with emphasis on the observed open-time (xi-open-time). The cumulants and Laplace transform for a xi-open-time are derived for a range of Markov and non-Markov models; several useful approximations to the xi-open-time density function are presented. Numerical studies show that the effects of limited time resolution can be extreme, and also highlight the relative importance of the various model parameters. The theory could form a basis for future inferential studies in which parameter estimation takes account of limited time resolution in single channel records. Appendixes include relevant results concerning random sums and a discussion of the role of exponential distributions in Markov models.

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.

The study of autism as a distributed disorder

PubMed Central

Müller, Ralph-Axel

2010-01-01

Past autism research has often been dedicated to tracing the causes of the disorder to a localized neurological abnormality, a single functional network, or a single cognitive-behavioral domain. In this review, I argue that autism is a ‘distributed disorder’ on various levels of study (genetic, neuroanatomical, neurofunctional, behavioral). ‘Localizing’ models are therefore not promising. The large array of potential genetic risk factors suggests that multiple (or all) emerging functional brain networks are affected during early development. This is supported by widespread growth abnormalities throughout the brain. Interactions during development between affected functional networks and atypical experiential effects (associated with atypical behavior) in children with autism further complicate the neurological bases of the disorder, resulting in an ‘exponentially distributed’ profile. Promising approaches to a better characterization of neural endophenotypes in autism are provided by techniques investigating white matter and connectivity, such as MR spectroscopy, diffusion tensor imaging (DTI), and functional connectivity MRI. According to a recent hypothesis, the autistic brain is generally characterized by ‘underconnectivity’. However, not all findings are consistent with this view. The concepts and methodology of functional connectivity need to be refined and results need to be corroborated by anatomical studies (such as DTI tractography) before definitive conclusions can be drawn. PMID:17326118

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.

Motion of the two-control airplane in rectilinear flight after initial disturbances with introduction of controls following an exponential law

NASA Technical Reports Server (NTRS)

Klemin, Alexander

1937-01-01

An airplane in steady rectilinear flight was assumed to experience an initial disturbance in rolling or yawing velocity. The equations of motion were solved to see if it was possible to hasten recovery of a stable airplane or to secure recovery of an unstable airplane by the application of a single lateral control following an exponential law. The sample computations indicate that, for initial disturbances complex in character, it would be difficult to secure correlation with any type of exponential control. The possibility is visualized that the two-control operation may seriously impair the ability to hasten recovery or counteract instability.

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.

Disordered Kitaev chains with long-range pairing.

PubMed

Cai, Xiaoming

2017-03-22

We study the competition of disorder and superconductivity for a generalized Kitaev model in incommensurate potentials. The generalized Kitaev model describes one dimensional spinless fermions with long-range p-wave superconducting pairing, which decays with distance l as a power law  ∼[Formula: see text]. We focus on the transition from the topological superconducting phase to the topologically trivial Anderson localized phase, and effects of the exponent α on this phase transition. In the topological superconducting phase, for a system under open boundary condition the amplitude of zero-mode Majorana fermion has a hybrid exponential-algebraic decay as the distance increases from the edge. In the Anderson localized phase, some single-particle states remain critical for very strong disorders and the number of critical states increases as α decreases. In addition, except for critical disorders, the correlation function always has an exponential decay at the short range and an algebraic decay at the long range. Phase transition points are also numerically determined and the topological phase transition happens earlier at a smaller disorder strength for a system with smaller α.

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.

Multi-step rhodopsin inactivation schemes can account for the size variability of single photon responses in Limulus ventral photoreceptors

PubMed Central

1994-01-01

Limulus ventral photoreceptors generate highly variable responses to the absorption of single photons. We have obtained data on the size distribution of these responses, derived the distribution predicted from simple transduction cascade models and compared the theory and data. In the simplest of models, the active state of the visual pigment (defined by its ability to activate G protein) is turned off in a single reaction. The output of such a cascade is predicted to be highly variable, largely because of stochastic variation in the number of G proteins activated. The exact distribution predicted is exponential, but we find that an exponential does not adequately account for the data. The data agree much better with the predictions of a cascade model in which the active state of the visual pigment is turned off by a multi-step process. PMID:8057085

Simultaneous water activation and glucose metabolic rate imaging with PET

NASA Astrophysics Data System (ADS)

Verhaeghe, Jeroen; Reader, Andrew J.

2013-02-01

A novel imaging and signal separation strategy is proposed to be able to separate [18F]FDG and multiple [15O]H2O signals from a simultaneously acquired dynamic PET acquisition of the two tracers. The technique is based on the fact that the dynamics of the two tracers are very distinct. By adopting an appropriate bolus injection strategy and by defining tailored sets of basis functions that model either the FDG or water component, it is possible to separate the FDG and water signal. The basis functions are inspired from the spectral analysis description of dynamic PET studies and are defined as the convolution of estimated generating functions (GFs) with a set of decaying exponential functions. The GFs are estimated from the overall measured head curve, while the decaying exponential functions are pre-determined. In this work, the time activity curves (TACs) are modelled post-reconstruction but the model can be incorporated in a global 4D reconstruction strategy. Extensive PET simulation studies are performed considering single [18F]FDG and 6 [15O]H2O bolus injections for a total acquisition time of 75 min. The proposed method is evaluated at multiple noise levels and different parameters were estimated such as [18F]FDG uptake and blood flow estimated from the [15O]H2O component, requiring a full dynamic analysis of the two components, static images of [18F]FDG and the water components as well as [15O]H2O activation. It is shown that the resulting images and parametric values in ROIs are comparable to images obtained from separate imaging, illustrating the feasibility of simultaneous imaging of [18F]FDG and [15O]H2O components. For more information on this article, see medicalphysicsweb.org

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.

The dynamics of single protein molecules is non-equilibrium and self-similar over thirteen decades in time

DOE PAGES

Hu, Xiaohu; Hong, Liang; Smith, Micholas Dean; ...

2015-11-23

Here, internal motions of proteins are essential to their function. The time dependence of protein structural fluctuations is highly complex, manifesting subdiffusive, non-exponential behavior with effective relaxation times existing over many decades in time, from ps up to ~10 2s (refs 1-4). Here, using molecular dynamics simulations, we show that, on timescales from 10 –12 to 10 –5s, motions in single proteins are self-similar, non-equilibrium and exhibit ageing. The characteristic relaxation time for a distance fluctuation, such as inter-domain motion, is observation-time-dependent, increasing in a simple, power-law fashion, arising from the fractal nature of the topology and geometry of themore » energy landscape explored. Diffusion over the energy landscape follows a non-ergodic continuous time random walk. Comparison with single-molecule experiments suggests that the non-equilibrium self-similar dynamical behavior persists up to timescales approaching the in vivo lifespan of individual protein molecules.« less

The dynamics of charge transfer with and without a barrier: A very simplified model of cyclic voltammetry.

PubMed

Ouyang, Wenjun; Subotnik, Joseph E

2017-05-07

Using the Anderson-Holstein model, we investigate charge transfer dynamics between a molecule and a metal surface for two extreme cases. (i) With a large barrier, we show that the dynamics follow a single exponential decay as expected; (ii) without any barrier, we show that the dynamics are more complicated. On the one hand, if the metal-molecule coupling is small, single exponential dynamics persist. On the other hand, when the coupling between the metal and the molecule is large, the dynamics follow a biexponential decay. We analyze the dynamics using the Smoluchowski equation, develop a simple model, and explore the consequences of biexponential dynamics for a hypothetical cyclic voltammetry experiment.

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.

Approximate solutions for diffusive fracture-matrix transfer: Application to storage of dissolved CO 2 in fractured rocks

DOE PAGES

Zhou, Quanlin; Oldenburg, Curtis M.; Spangler, Lee H.; ...

2017-01-05

Analytical solutions with infinite exponential series are available to calculate the rate of diffusive transfer between low-permeability blocks and high-permeability zones in the subsurface. Truncation of these series is often employed by neglecting the early-time regime. Here in this paper, we present unified-form approximate solutions in which the early-time and the late-time solutions are continuous at a switchover time. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent only on the dimensionless area-to-volume ratio. The last two coefficients are either determined analytically for isotropic blocks (e.g., spheresmore » and slabs) or obtained by fitting the exact solutions, and they solely depend on the aspect ratios for rectangular columns and parallelepipeds. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The optimal switchover time is between 0.157 and 0.229, with highest relative approximation error less than 0.2%. The solutions are used to demonstrate the storage of dissolved CO 2 in fractured reservoirs with low-permeability matrix blocks of single and multiple shapes and sizes. These approximate solutions are building blocks for development of analytical and numerical tools for hydraulic, solute, and thermal diffusion processes in low-permeability matrix blocks.« less

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.

Modeling Rabbit Responses to Single and Multiple Aerosol ...

EPA Pesticide Factsheets

Journal Article Survival models are developed here to predict response and time-to-response for mortality in rabbits following exposures to single or multiple aerosol doses of Bacillus anthracis spores. Hazard function models were developed for a multiple dose dataset to predict the probability of death through specifying dose-response functions and the time between exposure and the time-to-death (TTD). Among the models developed, the best-fitting survival model (baseline model) has an exponential dose-response model with a Weibull TTD distribution. Alternative models assessed employ different underlying dose-response functions and use the assumption that, in a multiple dose scenario, earlier doses affect the hazard functions of each subsequent dose. In addition, published mechanistic models are analyzed and compared with models developed in this paper. None of the alternative models that were assessed provided a statistically significant improvement in fit over the baseline model. The general approach utilizes simple empirical data analysis to develop parsimonious models with limited reliance on mechanistic assumptions. The baseline model predicts TTDs consistent with reported results from three independent high-dose rabbit datasets. More accurate survival models depend upon future development of dose-response datasets specifically designed to assess potential multiple dose effects on response and time-to-response. The process used in this paper to dev

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)

Precipitation phase separation schemes in the Naqu River basin, eastern Tibetan plateau

NASA Astrophysics Data System (ADS)

Liu, Shaohua; Yan, Denghua; Qin, Tianling; Weng, Baisha; Lu, Yajing; Dong, Guoqiang; Gong, Boya

2018-01-01

Precipitation phase has a profound influence on the hydrological processes in the Naqu River basin, eastern Tibetan plateau. However, there are only six meteorological stations with precipitation phase (rainfall/snowfall/sleet) before 1979 within and around the basin. In order to separate snowfall from precipitation, a new separation scheme with S-shaped curve of snowfall proportion as an exponential function of daily mean temperature was developed. The determinations of critical temperatures in the single/two temperature threshold (STT/TTT2) methods were explored accordingly, and the temperature corresponding to the 50 % snowfall proportion (SP50 temperature) is an efficiently critical temperature for the STT, and two critical temperatures in TTT2 can be determined based on the exponential function and SP50 temperature. Then, different separation schemes were evaluated in separating snowfall from precipitation in the Naqu River basin. The results show that the S-shaped curve methods outperform other separation schemes. Although the STT and TTT2 slightly underestimate and overestimate the snowfall when the temperature is higher and colder than SP50 temperature respectively, the monthly and annual separation snowfalls are generally consistent with the observed snowfalls. On the whole, S-shaped curve methods, STT, and TTT2 perform well in separating snowfall from precipitation with the Pearson correlation coefficient of annual separation snowfall above 0.8 and provide possible approaches to separate the snowfall from precipitation for hydrological modelling.

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.

Anomalous length dependence of conductance of aromatic nanoribbons with amine anchoring groups

NASA Astrophysics Data System (ADS)

Bilić, Ante; Sanvito, Stefano

2012-09-01

Two sets of aromatic nanoribbons, based around a common hexagonal scaffolding, with single and dual terminal amine groups have been considered as potential molecular wires in a junction formed by gold leads. Charge transport through the two-terminal device has been modeled using density functional theory (with and without self-interaction correction) and the nonequilibrium Green's function method. The effects of wire length, multiple terminal contacts, and pathways across the junction have been investigated. For nanoribbons with the oligopyrene motif and conventional single amine terminal groups, an increase in the wire length causes an exponential drop in the conductance. In contrast, for the nanoribbons with the oligoperylene motif and dual amine anchoring groups the predicted conductance rises with the wire length over the whole range of investigated lengths. Only when the effects of self-interaction correction are taken into account, the conductance of the oligoperylene ribbons exhibits saturation for longer members of the series. The oligoperylene nanoribbons, with dual amine groups at both terminals, show the potential to fully harness the highly conjugated system of π molecular orbitals across the junction.

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

Life prediction for high temperature low cycle fatigue of two kinds of titanium alloys based on exponential function

NASA Astrophysics Data System (ADS)

Mu, G. Y.; Mi, X. Z.; Wang, F.

2018-01-01

The high temperature low cycle fatigue tests of TC4 titanium alloy and TC11 titanium alloy are carried out under strain controlled. The relationships between cyclic stress-life and strain-life are analyzed. The high temperature low cycle fatigue life prediction model of two kinds of titanium alloys is established by using Manson-Coffin method. The relationship between failure inverse number and plastic strain range presents nonlinear in the double logarithmic coordinates. Manson-Coffin method assumes that they have linear relation. Therefore, there is bound to be a certain prediction error by using the Manson-Coffin method. In order to solve this problem, a new method based on exponential function is proposed. The results show that the fatigue life of the two kinds of titanium alloys can be predicted accurately and effectively by using these two methods. Prediction accuracy is within ±1.83 times scatter zone. The life prediction capability of new methods based on exponential function proves more effective and accurate than Manson-Coffin method for two kinds of titanium alloys. The new method based on exponential function can give better fatigue life prediction results with the smaller standard deviation and scatter zone than Manson-Coffin method. The life prediction results of two methods for TC4 titanium alloy prove better than TC11 titanium alloy.

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.

Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification

PubMed Central

Lemonde, Marc-Antoine; Didier, Nicolas; Clerk, Aashish A.

2016-01-01

The quantum nonlinear regime of optomechanics is reached when nonlinear effects of the radiation pressure interaction are observed at the single-photon level. This requires couplings larger than the mechanical frequency and cavity-damping rate, and is difficult to achieve experimentally. Here we show how to exponentially enhance the single-photon optomechanical coupling strength using only additional linear resources. Our method is based on using a large-amplitude, strongly detuned mechanical parametric drive to amplify mechanical zero-point fluctuations and hence enhance the radiation pressure interaction. It has the further benefit of allowing time-dependent control, enabling pulsed schemes. For a two-cavity optomechanical set-up, we show that our scheme generates photon blockade for experimentally accessible parameters, and even makes the production of photonic states with negative Wigner functions possible. We discuss how our method is an example of a more general strategy for enhancing boson-mediated two-particle interactions and nonlinearities. PMID:27108814

Thermal conductance of interfaces with molecular layers - low temperature transient absorption study on gold nanorods supported on self assembled monolayers

NASA Astrophysics Data System (ADS)

Wang, Wei; Huang, Jingyu; Murphy, Catherine; Cahill, David; University of Illinois At Urbana Champaign, Department of Materials Science; Engineering Team; Department Collaboration

2011-03-01

While heat transfer via phonons across solid-solid boundary has been a core field in condense matter physics for many years, vibrational energy transport across molecular layers has been less well elucidated. We heat rectangular-shaped gold nanocrystals (nanorods) with Ti-sapphire femtosecond pulsed laser at their longitudinal surface plasmon absorption wavelength to watch how their temperature evolves in picoseconds transient. We observed single exponential decay behavior, which suggests that the heat dissipation is only governed by a single interfacial conductance value. The ``RC'' time constant was 300ps, corresponding to a conductance value of 95MW/ m 2 K. This interfacial conductance value is also a function of ambient temperature since at temperatures as low as 80K, which are below the Debye temperature of organic layers, several phonon modes were quenched, which shut down the dominating channels that conduct heat at room temperature.

Low temperature time resolved photoluminescence in ordered and disordered Cu2ZnSnS4 single crystals

NASA Astrophysics Data System (ADS)

Raadik, Taavi; Krustok, Jüri; Kauk-Kuusik, M.; Timmo, K.; Grossberg, M.; Ernits, K.; Bleuse, J.

2017-03-01

In this work we performed time-resolved micro-photoluminescence (TRPL) studies of Cu2ZnSnS4 (CZTS) single crystals grown in molten KI salt. The order/disorder degree of CZTS was varied by the thermal post treatment temperature. Photoluminescence spectra measured at T=8 K showed an asymmetric band with a peak position of 1.33 eV and 1.27 eV for partially ordered and disordered structures, respectively. Thermal activation energies were found to be ET (PO) =65±9 meV for partially ordered and ET (PD) =27±4 meV for partially disordered. These low activation energy values indicating to the defect cluster recombination model for both partially ordered and disordered structures. TRPL was measured for both crystals and their decay curves were fitted with a stretched exponential function, in order to describe the charge carriers' recombination dynamics at low temperature.

A generalized non-Gaussian consistency relation for single field inflation

NASA Astrophysics Data System (ADS)

Bravo, Rafael; Mooij, Sander; Palma, Gonzalo A.; Pradenas, Bastián

2018-05-01

We show that a perturbed inflationary spacetime, driven by a canonical single scalar field, is invariant under a special class of coordinate transformations together with a field reparametrization of the curvature perturbation in co-moving gauge. This transformation may be used to derive the squeezed limit of the 3-point correlation function of the co-moving curvature perturbations valid in the case that these do not freeze after horizon crossing. This leads to a generalized version of Maldacena's non-Gaussian consistency relation in the sense that the bispectrum squeezed limit is completely determined by spacetime diffeomorphisms. Just as in the case of the standard consistency relation, this result may be understood as the consequence of how long-wavelength modes modulate those of shorter wavelengths. This relation allows one to derive the well known violation to the consistency relation encountered in ultra slow-roll, where curvature perturbations grow exponentially after horizon crossing.

An optical conveyor for molecules.

PubMed

Weinert, Franz M; Braun, Dieter

2009-12-01

Trapping single ions under vacuum allows for precise spectroscopy in atomic physics. The confinement of biological molecules in bulk water is hindered by the lack of comparably strong forces. Molecules have been immobilized to surfaces, however often with detrimental effects on their function. Here, we optically trap molecules by creating the microscale analogue of a conveyor belt: a bidirectional flow is combined with a perpendicular thermophoretic molecule drift. Arranged in a toroidal geometry, the conveyor accumulates a hundredfold excess of 5-base DNA within seconds. The concentrations of the trapped DNA scale exponentially with length, reaching trapping potential depths of 14 kT for 50 bases. The mechanism does not require microfluidics, electrodes, or surface modifications. As a result, the trap can be dynamically relocated. The optical conveyor can be used to enhance diffusion-limited surface reactions, redirect cellular signaling, observe individual biomolecules over a prolonged time, or approach single-molecule chemistry in bulk water.

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.)

Single Nanoparticle Translocation Through Chemically Modified Solid Nanopore

NASA Astrophysics Data System (ADS)

Tan, Shengwei; Wang, Lei; Liu, Hang; Wu, Hongwen; Liu, Quanjun

2016-02-01

The nanopore sensor as a high-throughput and low-cost technology can detect single nanoparticle in solution. In the present study, the silicon nitride nanopores were fabricated by focused Ga ion beam (FIB), and the surface was functionalized with 3-aminopropyltriethoxysilane to change its surface charge density. The positively charged nanopore surface attracted negatively charged nanoparticles when they were in the vicinity of the nanopore. And, nanoparticle translocation speed was slowed down to obtain a clear and deterministic signal. Compared with previous studied small nanoparticles, the electrophoretic translocation of negatively charged polystyrene (PS) nanoparticles (diameter ~100 nm) was investigated in solution using the Coulter counter principle in which the time-dependent nanopore current was recorded as the nanoparticles were driven across the nanopore. A linear dependence was found between current drop and biased voltage. An exponentially decaying function ( t d ~ e -v/v0 ) was found between the duration time and biased voltage. The interaction between the amine-functionalized nanopore wall and PS microspheres was discussed while translating PS microspheres. We explored also translocations of PS microspheres through amine-functionalized solid-state nanopores by varying the solution pH (5.4, 7.0, and 10.0) with 0.02 M potassium chloride (KCl). Surface functionalization showed to provide a useful step to fine-tune the surface property, which can selectively transport molecules or particles. This approach is likely to be applied to gene sequencing.

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.

Calm Multi-Baryon Operators

NASA Astrophysics Data System (ADS)

Berkowitz, Evan; Nicholson, Amy; Chang, Chia Cheng; Rinaldi, Enrico; Clark, M. A.; Joó, Bálint; Kurth, Thorsten; Vranas, Pavlos; Walker-Loud, André

2018-03-01

There are many outstanding problems in nuclear physics which require input and guidance from lattice QCD calculations of few baryons systems. However, these calculations suffer from an exponentially bad signal-to-noise problem which has prevented a controlled extrapolation to the physical point. The variational method has been applied very successfully to two-meson systems, allowing for the extraction of the two-meson states very early in Euclidean time through the use of improved single hadron operators. The sheer numerical cost of using the same techniques in two-baryon systems has so far been prohibitive. We present an alternate strategy which offers some of the same advantages as the variational method while being significantly less numerically expensive. We first use the Matrix Prony method to form an optimal linear combination of single baryon interpolating fields generated from the same source and different sink interpolating fields. Very early in Euclidean time this optimal linear combination is numerically free of excited state contamination, so we coin it a calm baryon. This calm baryon operator is then used in the construction of the two-baryon correlation functions. To test this method, we perform calculations on the WM/JLab iso-clover gauge configurations at the SU(3) flavor symmetric point with mπ 800 MeV — the same configurations we have previously used for the calculation of two-nucleon correlation functions. We observe the calm baryon significantly removes the excited state contamination from the two-nucleon correlation function to as early a time as the single-nucleon is improved, provided non-local (displaced nucleon) sources are used. For the local two-nucleon correlation function (where both nucleons are created from the same space-time location) there is still improvement, but there is significant excited state contamination in the region the single calm baryon displays no excited state contamination.

Postseismic deformation following the 2010 Mw 8.8 Maule and 2014 Mw 8.1 Pisagua megathrust earthquakes in Chile

NASA Astrophysics Data System (ADS)

Weiss, J. R.; Saunders, A.; Qiu, Q.; Foster, J. H.; Gomez, D.; Bevis, M. G.; Smalley, R., Jr.; Cimbaro, S.; Lenzano, L. E.; Barón, J.; Baez, J. C.; Echalar, A.; Avery, J.; Wright, T. J.

2017-12-01

We use a large regional network of continuous GPS sites to investigate postseismic deformation following the Mw 8.8 Maule and Mw 8.1 Pisagua earthquakes in Chile. Geodetic observations of surface displacements associated with megathrust earthquakes aid our understanding of the subduction zone earthquake cycle including postseismic processes such as afterslip and viscoelastic relaxation. The observations also help place constraints on the rheology and structure of the crust and upper mantle. We first empirically model the data and find that, while single-term logarithmic functions adequately fit the postseismic timeseries, they do a poor job of characterizing the rapid displacements in the days to weeks following the earthquakes. Combined exponential-logarithmic functions better capture the inferred near-field transition between afterslip and viscous relaxation, however displacements are best fit by three-term exponential functions with characteristic decay times of 15, 250, and 1500 days. Viscoelastic modeling of the velocity field and timeseries following the Maule earthquake suggests that the rheology is complex but is consistent with a 100-km-thick asthenosphere channel of viscosity 1018 Pa s sandwiched between a 40-km-thick elastic lid and a strong viscoelastic upper mantle. Variations in lid thickness of up to 40 km may be present and in some locations rapid deformation within the first months to years following the Maule event requires an even lower effective viscosity or a significant contribution from afterslip. We investigate this further by jointly inverting the GPS data for the time evolution of afterslip and viscous flow in the mantle wedge surrounding the Maule event.

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.

On new non-modal hydrodynamic stability modes and resulting non-exponential growth rates - a Lie symmetry approach

NASA Astrophysics Data System (ADS)

Oberlack, Martin; Nold, Andreas; Sanjon, Cedric Wilfried; Wang, Yongqi; Hau, Jan

2016-11-01

Classical hydrodynamic stability theory for laminar shear flows, no matter if considering long-term stability or transient growth, is based on the normal-mode ansatz, or, in other words, on an exponential function in space (stream-wise direction) and time. Recently, it became clear that the normal mode ansatz and the resulting Orr-Sommerfeld equation is based on essentially three fundamental symmetries of the linearized Euler and Navier-Stokes equations: translation in space and time and scaling of the dependent variable. Further, Kelvin-mode of linear shear flows seemed to be an exception in this context as it admits a fourth symmetry resulting in the classical Kelvin mode which is rather different from normal-mode. However, very recently it was discovered that most of the classical canonical shear flows such as linear shear, Couette, plane and round Poiseuille, Taylor-Couette, Lamb-Ossen vortex or asymptotic suction boundary layer admit more symmetries. This, in turn, led to new problem specific non-modal ansatz functions. In contrast to the exponential growth rate in time of the modal-ansatz, the new non-modal ansatz functions usually lead to an algebraic growth or decay rate, while for the asymptotic suction boundary layer a double-exponential growth or decay is observed.

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

Numerically stable formulas are presented for the closed-form analytical solution of the X-IVAS scheme in 3D. This scheme is a state-of-the-art particle-based explicit exponential integrator developed for the particle finite element method. Algebraically, this scheme involves two steps: (1) the solution of tangent curves for piecewise linear vector fields defined on simplicial meshes and (2) the solution of line integrals of piecewise linear vector-valued functions along these tangent curves. Hence, the stable formulas presented here have general applicability, e.g. exact integration of trajectories in particle-based (Lagrangian-type) methods, flow visualization and computer graphics. The Newton form of the polynomial interpolation definition is used to express exponential functions of matrices which appear in the analytical solution of the X-IVAS scheme. The divided difference coefficients in these expressions are defined in a piecewise manner, i.e. in a prescribed neighbourhood of removable singularities their series approximations are computed. An optimal series approximation of divided differences is presented which plays a critical role in this methodology. At least ten significant decimal digits in the formula computations are guaranteed to be exact using double-precision floating-point arithmetic. The worst case scenarios occur in the neighbourhood of removable singularities found in fourth-order divided differences of the exponential function.

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.

Channel response to sediment release: insights from a paired analysis of dam removal

USGS Publications Warehouse

Collins, Mathias J.; Snyder, Noah P.; Boardman, Graham; Banks, William S.; Andrews, Mary; Baker, Matthew E.; Conlon, Maricate; Gellis, Allen; McClain, Serena; Miller, Andrew; Wilcock, Peter

2017-01-01

Dam removals with unmanaged sediment releases are good opportunities to learn about channel response to abruptly increased bed material supply. Understanding these events is important because they affect aquatic habitats and human uses of floodplains. A longstanding paradigm in geomorphology holds that response rates to landscape disturbance exponentially decay through time. However, a previous study of the Merrimack Village Dam (MVD) removal on the Souhegan River in New Hampshire, USA, showed that an exponential function poorly described the early geomorphic response. Erosion of impounded sediments there was two-phased. We had an opportunity to quantitatively test the two-phase response model proposed for MVD by extending the record there and comparing it with data from the Simkins Dam removal on the Patapsco River in Maryland, USA. The watershed sizes are the same order of magnitude (102 km2), and at both sites low-head dams were removed (~3–4 m) and ~65 000 m3 of sand-sized sediments were discharged to low-gradient reaches. Analyzing four years of repeat morphometry and sediment surveys at the Simkins site, as well as continuous discharge and turbidity data, we observed the two-phase erosion response described for MVD. In the early phase, approximately 50% of the impounded sediment at Simkins was eroded rapidly during modest flows. After incision to base level and widening, a second phase began when further erosion depended on floods large enough to go over bank and access impounded sediments more distant from the newly-formed channel. Fitting functional forms to the data for both sites, we found that two-phase exponential models with changing decay constants fit the erosion data better than single-phase models. Valley width influences the two-phase erosion responses upstream, but downstream responses appear more closely related to local gradient, sediment re-supply from the upstream impoundments, and base flows.

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)

A quasi-likelihood approach to non-negative matrix factorization

PubMed Central

Devarajan, Karthik; Cheung, Vincent C.K.

2017-01-01

A unified approach to non-negative matrix factorization based on the theory of generalized linear models is proposed. This approach embeds a variety of statistical models, including the exponential family, within a single theoretical framework and provides a unified view of such factorizations from the perspective of quasi-likelihood. Using this framework, a family of algorithms for handling signal-dependent noise is developed and its convergence proven using the Expectation-Maximization algorithm. In addition, a measure to evaluate the goodness-of-fit of the resulting factorization is described. The proposed methods allow modeling of non-linear effects via appropriate link functions and are illustrated using an application in biomedical signal processing. PMID:27348511

Dynamics of optical matter creation and annihilation in colloidal liquids controlled by laser trapping power.

PubMed

Liu, Jin; Dai, Qiao-Feng; Huang, Xu-Guang; Wu, Li-Jun; Guo, Qi; Hu, Wei; Yang, Xiang-Bo; Lan, Sheng; Gopal, Achanta Venu; Trofimov, Vyacheslav A

2008-11-15

We investigate the dynamics of optical matter creation and annihilation in a colloidal liquid that was employed to construct an all-optical switch. It is revealed that the switching-on process can be characterized by the Fermi-Dirac distribution function, while the switching-off process can be described by a steady state followed by a single exponential decay. The phase transition times exhibit a strong dependence on trapping power. With an increasing trapping power, while the switching-on time decreases rapidly, the switch-off time increases significantly, indicating the effects of optical binding and van der Waals force on the lifetime of the optical matter.

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

From webs to polylogarithms

NASA Astrophysics Data System (ADS)

Gardi, Einan

2014-04-01

We compute a class of diagrams contributing to the multi-leg soft anomalous dimension through three loops, by renormalizing a product of semi-infinite non-lightlike Wilson lines in dimensional regularization. Using non-Abelian exponentiation we directly compute contributions to the exponent in terms of webs. We develop a general strategy to compute webs with multiple gluon exchanges between Wilson lines in configuration space, and explore their analytic structure in terms of α ij , the exponential of the Minkowski cusp angle formed between the lines i and j. We show that beyond the obvious inversion symmetry α ij → 1 /α ij , at the level of the symbol the result also admits a crossing symmetry α ij → - α ij , relating spacelike and timelike kinematics, and hence argue that in this class of webs the symbol alphabet is restricted to α ij and . We carry out the calculation up to three gluons connecting four Wilson lines, finding that the contributions to the soft anomalous dimension are remarkably simple: they involve pure functions of uniform weight, which are written as a sum of products of polylogarithms, each depending on a single cusp angle. We conjecture that this type of factorization extends to all multiple-gluon-exchange contributions to the anomalous dimension.

Role of community tolerance level (CTL) in predicting the prevalence of the annoyance of road and rail noise.

PubMed

Schomer, Paul; Mestre, Vincent; Fidell, Sanford; Berry, Bernard; Gjestland, Truls; Vallet, Michel; Reid, Timothy

2012-04-01

Fidell et al. [(2011), J. Acoust. Soc. Am. 130(2), 791-806] have shown (1) that the rate of growth of annoyance with noise exposure reported in attitudinal surveys of the annoyance of aircraft noise closely resembles the exponential rate of change of loudness with sound level, and (2) that the proportion of a community highly annoyed and the variability in annoyance prevalence rates in communities are well accounted for by a simple model with a single free parameter: a community tolerance level (abbreviated CTL, and represented symbolically in mathematical expressions as L(ct)), expressed in units of DNL. The current study applies the same modeling approach to predicting the prevalence of annoyance of road traffic and rail noise. The prevalence of noise-induced annoyance of all forms of transportation noise is well accounted for by a simple, loudness-like exponential function with community-specific offsets. The model fits all of the road traffic findings well, but the prevalence of annoyance due to rail noise is more accurately predicted separately for interviewing sites with and without high levels of vibration and/or rattle.

Scintillation properties of Ce-doped (Gd0.32Y0.68)3Al5O12 transparent ceramics

NASA Astrophysics Data System (ADS)

Hirano, Shotaro; Okada, Go; Kawaguchi, Noriaki; Yagi, Hideki; Yanagitani, Takagimi; Yanagida, Takayuki

2017-04-01

In this work, we have investigated optical and scintillation properties of 0.35-0.65% Ce:(Gd0.32Y0.68)3Al5O12 (Ce:GYAG) transparent ceramics prepared by the vacuum sintering method. Obtained samples showed high transmittance in the spectral region longer than 500 nm, and two strong absorption bands were clearly observed below 380 nm and between 400 and 500 nm due to the 4f-5d transitions of Ce3+. Under UV and X-rays, we have also observed emission due to the 5d-4f transitions of Ce3+ which appeared around 500-700 nm. The emission decay profile of PL consisted of a single exponential decay component with the decay time of 62.7-64.1 ns while the scintillation decay profile was approximated by a second-order exponential decay function with the decay times of 87.3-100 ns and 1.14-1.32 μs. In addition, it has been revealed that 0.65% Ce:GYAG transparent ceramic showed a notable light yield of 18,000 ph/MeV and low afterglow (13 ppm).

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.

Rapid Global Fitting of Large Fluorescence Lifetime Imaging Microscopy Datasets

PubMed Central

Warren, Sean C.; Margineanu, Anca; Alibhai, Dominic; Kelly, Douglas J.; Talbot, Clifford; Alexandrov, Yuriy; Munro, Ian; Katan, Matilda

2013-01-01

Fluorescence lifetime imaging (FLIM) is widely applied to obtain quantitative information from fluorescence signals, particularly using Förster Resonant Energy Transfer (FRET) measurements to map, for example, protein-protein interactions. Extracting FRET efficiencies or population fractions typically entails fitting data to complex fluorescence decay models but such experiments are frequently photon constrained, particularly for live cell or in vivo imaging, and this leads to unacceptable errors when analysing data on a pixel-wise basis. Lifetimes and population fractions may, however, be more robustly extracted using global analysis to simultaneously fit the fluorescence decay data of all pixels in an image or dataset to a multi-exponential model under the assumption that the lifetime components are invariant across the image (dataset). This approach is often considered to be prohibitively slow and/or computationally expensive but we present here a computationally efficient global analysis algorithm for the analysis of time-correlated single photon counting (TCSPC) or time-gated FLIM data based on variable projection. It makes efficient use of both computer processor and memory resources, requiring less than a minute to analyse time series and multiwell plate datasets with hundreds of FLIM images on standard personal computers. This lifetime analysis takes account of repetitive excitation, including fluorescence photons excited by earlier pulses contributing to the fit, and is able to accommodate time-varying backgrounds and instrument response functions. We demonstrate that this global approach allows us to readily fit time-resolved fluorescence data to complex models including a four-exponential model of a FRET system, for which the FRET efficiencies of the two species of a bi-exponential donor are linked, and polarisation-resolved lifetime data, where a fluorescence intensity and bi-exponential anisotropy decay model is applied to the analysis of live cell homo-FRET data. A software package implementing this algorithm, FLIMfit, is available under an open source licence through the Open Microscopy Environment. PMID:23940626

Verification of the exponential model of body temperature decrease after death in pigs.

PubMed

Kaliszan, Michal; Hauser, Roman; Kaliszan, Roman; Wiczling, Paweł; Buczyñski, Janusz; Penkowski, Michal

2005-09-01

The authors have conducted a systematic study in pigs to verify the models of post-mortem body temperature decrease currently employed in forensic medicine. Twenty-four hour automatic temperature recordings were performed in four body sites starting 1.25 h after pig killing in an industrial slaughterhouse under typical environmental conditions (19.5-22.5 degrees C). The animals had been randomly selected under a regular manufacturing process. The temperature decrease time plots drawn starting 75 min after death for the eyeball, the orbit soft tissues, the rectum and muscle tissue were found to fit the single-exponential thermodynamic model originally proposed by H. Rainy in 1868. In view of the actual intersubject variability, the addition of a second exponential term to the model was demonstrated to be statistically insignificant. Therefore, the two-exponential model for death time estimation frequently recommended in the forensic medicine literature, even if theoretically substantiated for individual test cases, provides no advantage as regards the reliability of estimation in an actual case. The improvement of the precision of time of death estimation by the reconstruction of an individual curve on the basis of two dead body temperature measurements taken 1 h apart or taken continuously for a longer time (about 4 h), has also been proved incorrect. It was demonstrated that the reported increase of precision of time of death estimation due to use of a multiexponential model, with individual exponential terms to account for the cooling rate of the specific body sites separately, is artifactual. The results of this study support the use of the eyeball and/or the orbit soft tissues as temperature measuring sites at times shortly after death. A single-exponential model applied to the eyeball cooling has been shown to provide a very precise estimation of the time of death up to approximately 13 h after death. For the period thereafter, a better estimation of the time of death is obtained from temperature data collected from the muscles or the rectum.

Single Session Web-Based Counselling: A Thematic Analysis of Content from the Perspective of the Client

ERIC Educational Resources Information Center

Rodda, S. N.; Lubman, D. I.; Cheetham, A.; Dowling, N. A.; Jackson, A. C.

2015-01-01

Despite the exponential growth of non-appointment-based web counselling, there is limited information on what happens in a single session intervention. This exploratory study, involving a thematic analysis of 85 counselling transcripts of people seeking help for problem gambling, aimed to describe the presentation and content of online…

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.

Integration and manufacture of multifunctional planar lightwave circuits

NASA Astrophysics Data System (ADS)

Lipscomb, George F.; Ticknor, Anthony J.; Stiller, Marc A.; Chen, Wenjie; Schroeter, Paul

2001-11-01

The demands of exponentially growing Internet traffic, coupled with the advent of Dense Wavelength Division Multiplexing (DWDM) fiber optic systems to meet those demands, have triggered a revolution in the telecommunications industry. This dramatic change has been built upon, and has driven, improvements in fiber optic component technology. The next generation of systems for the all optical network will require higher performance components coupled with dramatically lower costs. One approach to achieve significantly lower costs per function is to employ Planar Lightwave Circuits (PLC) to integrate multiple optical functions in a single package. PLCs are optical circuits laid out on a silicon wafer, and are made using tools and techniques developed to extremely high levels by the semi-conductor industry. In this way multiple components can be fabricated and interconnected at once, significantly reducing both the manufacturing and the packaging/assembly costs. Currently, the predominant commercial application of PLC technology is arrayed-waveguide gratings (AWG's) for multiplexing and demultiplexing multiple wavelength channels in a DWDM system. Although this is generally perceived as a single-function device, it can be performing the function of more than 100 discrete fiber-optic components and already represents a considerable degree of integration. Furthermore, programmable functions such as variable-optical attenuators (VOAs) and switches made with compatible PLC technology are now moving into commercial production. In this paper, we present results on the integration of active and passive functions together using PLC technology, e.g. a 40 channel AWG multiplexer with 40 individually controllable VOAs.

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.

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.

Exact simulation of integrate-and-fire models with exponential currents.

PubMed

Brette, Romain

2007-10-01

Neural networks can be simulated exactly using event-driven strategies, in which the algorithm advances directly from one spike to the next spike. It applies to neuron models for which we have (1) an explicit expression for the evolution of the state variables between spikes and (2) an explicit test on the state variables that predicts whether and when a spike will be emitted. In a previous work, we proposed a method that allows exact simulation of an integrate-and-fire model with exponential conductances, with the constraint of a single synaptic time constant. In this note, we propose a method, based on polynomial root finding, that applies to integrate-and-fire models with exponential currents, with possibly many different synaptic time constants. Models can include biexponential synaptic currents and spike-triggered adaptation currents.

Crystal growth and scintillation properties of Nd-doped Lu 3Al 5O 12 single crystals with different Nd concentrations

NASA Astrophysics Data System (ADS)

Sugiyama, Makoto; Fujimoto, Yutaka; Yanagida, Takayuki; Yokota, Yuui; Pejchal, Jan; Furuya, Yuki; Tanaka, Hidehiko; Yoshikawa, Akira

2011-04-01

Nd 0.1%, 0.5%, 1% and 3% doped Lu 3Al 5O 12 (Nd:LuAG) single crystals were grown in the nitrogen atmosphere by the micro-pulling down (μ-PD) method. The grown crystals had a single-phase confirmed by powder XRD analysis. In absorption spectra, some weak absorption lines due to Nd 3+ 4f-4f transitions were observed and their intensity increased with the increase of Nd concentration. When excited by 241Am α-ray, a broad emission peak due to defects in the host lattice at 320 nm and some sharp lines due to Nd 3+ 4f-4f transitions at wavelength longer than 400 nm were observed. The decay time profiles of Nd:LuAG under γ-ray excitation were well approximated by two exponential function of 340-760 ns and 3-5 μs for each sample. By pulse height measurement using 137Cs, Nd 0.5%:LuAG showed the highest light yield of 7600 ± 760 photons/MeV.

Functional network inference of the suprachiasmatic nucleus

PubMed Central

Abel, John H.; Meeker, Kirsten; Granados-Fuentes, Daniel; St. John, Peter C.; Wang, Thomas J.; Bales, Benjamin B.; Doyle, Francis J.; Herzog, Erik D.; Petzold, Linda R.

2016-01-01

In the mammalian suprachiasmatic nucleus (SCN), noisy cellular oscillators communicate within a neuronal network to generate precise system-wide circadian rhythms. Although the intracellular genetic oscillator and intercellular biochemical coupling mechanisms have been examined previously, the network topology driving synchronization of the SCN has not been elucidated. This network has been particularly challenging to probe, due to its oscillatory components and slow coupling timescale. In this work, we investigated the SCN network at a single-cell resolution through a chemically induced desynchronization. We then inferred functional connections in the SCN by applying the maximal information coefficient statistic to bioluminescence reporter data from individual neurons while they resynchronized their circadian cycling. Our results demonstrate that the functional network of circadian cells associated with resynchronization has small-world characteristics, with a node degree distribution that is exponential. We show that hubs of this small-world network are preferentially located in the central SCN, with sparsely connected shells surrounding these cores. Finally, we used two computational models of circadian neurons to validate our predictions of network structure. PMID:27044085

Intermittent electron density and temperature fluctuations and associated fluxes in the Alcator C-Mod scrape-off layer

NASA Astrophysics Data System (ADS)

Kube, R.; Garcia, O. E.; Theodorsen, A.; Brunner, D.; Kuang, A. Q.; LaBombard, B.; Terry, J. L.

2018-06-01

The Alcator C-Mod mirror Langmuir probe system has been used to sample data time series of fluctuating plasma parameters in the outboard mid-plane far scrape-off layer. We present a statistical analysis of one second long time series of electron density, temperature, radial electric drift velocity and the corresponding particle and electron heat fluxes. These are sampled during stationary plasma conditions in an ohmically heated, lower single null diverted discharge. The electron density and temperature are strongly correlated and feature fluctuation statistics similar to the ion saturation current. Both electron density and temperature time series are dominated by intermittent, large-amplitude burst with an exponential distribution of both burst amplitudes and waiting times between them. The characteristic time scale of the large-amplitude bursts is approximately 15 μ {{s}}. Large-amplitude velocity fluctuations feature a slightly faster characteristic time scale and appear at a faster rate than electron density and temperature fluctuations. Describing these time series as a superposition of uncorrelated exponential pulses, we find that probability distribution functions, power spectral densities as well as auto-correlation functions of the data time series agree well with predictions from the stochastic model. The electron particle and heat fluxes present large-amplitude fluctuations. For this low-density plasma, the radial electron heat flux is dominated by convection, that is, correlations of fluctuations in the electron density and radial velocity. Hot and dense blobs contribute only a minute fraction of the total fluctuation driven heat flux.

Thermal decay of Coulomb blockade oscillations

NASA Astrophysics Data System (ADS)

Idrisov, Edvin G.; Levkivskyi, Ivan P.; Sukhorukov, Eugene V.

2017-10-01

We study transport properties and the charge quantization phenomenon in a small metallic island connected to the leads through two quantum point contacts (QPCs). The linear conductance is calculated perturbatively with respect to weak tunneling and weak backscattering at QPCs as a function of the temperature T and gate voltage. The conductance shows Coulomb blockade (CB) oscillations as a function of the gate voltage that decay with the temperature as a result of thermally activated fluctuations of the charge in the island. The regimes of quantum T ≪EC and thermal T ≫EC fluctuations are considered, where EC is the charging energy of an isolated island. Our predictions for CB oscillations in the quantum regime coincide with previous findings by Furusaki and Matveev [Phys. Rev. B 52, 16676 (1995), 10.1103/PhysRevB.52.16676]. In the thermal regime the visibility of Coulomb blockade oscillations decays with the temperature as √{T /EC }exp(-π2T /EC) , where the exponential dependence originates from the thermal averaging over the instant charge fluctuations, while the prefactor has a quantum origin. This dependence does not depend on the strength of couplings to the leads. The differential capacitance, calculated in the case of a single tunnel junction, shows the same exponential decay, however the prefactor is linear in the temperature. This difference can be attributed to the nonlocality of the quantum effects. Our results agree with the recent experiment [Nature (London) 536, 58 (2016), 10.1038/nature19072] in the whole range of the parameter T /EC .

Event-based cluster synchronization of coupled genetic regulatory networks

NASA Astrophysics Data System (ADS)

Yue, Dandan; Guan, Zhi-Hong; Li, Tao; Liao, Rui-Quan; Liu, Feng; Lai, Qiang

2017-09-01

In this paper, the cluster synchronization of coupled genetic regulatory networks with a directed topology is studied by using the event-based strategy and pinning control. An event-triggered condition with a threshold consisting of the neighbors' discrete states at their own event time instants and a state-independent exponential decay function is proposed. The intra-cluster states information and extra-cluster states information are involved in the threshold in different ways. By using the Lyapunov function approach and the theories of matrices and inequalities, we establish the cluster synchronization criterion. It is shown that both the avoidance of continuous transmission of information and the exclusion of the Zeno behavior are ensured under the presented triggering condition. Explicit conditions on the parameters in the threshold are obtained for synchronization. The stability criterion of a single GRN is also given under the reduced triggering condition. Numerical examples are provided to validate the theoretical results.

Directed evolution of a synthetic phylogeny of programmable Trp repressors.

PubMed

Ellefson, Jared W; Ledbetter, Michael P; Ellington, Andrew D

2018-04-01

As synthetic regulatory programs expand in sophistication, an ever increasing number of biological components with predictable phenotypes is required. Regulators are often 'part mined' from a diverse, but uncharacterized, array of genomic sequences, often leading to idiosyncratic behavior. Here, we generate an entire synthetic phylogeny from the canonical allosteric transcription factor TrpR. Iterative rounds of positive and negative compartmentalized partnered replication (CPR) led to the exponential amplification of variants that responded with high affinity and specificity to halogenated tryptophan analogs and novel operator sites. Fourteen repressor variants were evolved with unique regulatory profiles across five operators and three ligands. The logic of individual repressors can be modularly programmed by creating heterodimeric fusions, resulting in single proteins that display logic functions, such as 'NAND'. Despite the evolutionarily limited regulatory role of TrpR, vast functional spaces exist around this highly conserved protein scaffold and can be harnessed to create synthetic regulatory programs.

Partially coherent isodiffracting pulsed beams

NASA Astrophysics Data System (ADS)

Koivurova, Matias; Ding, Chaoliang; Turunen, Jari; Pan, Liuzhan

2018-02-01

We investigate a class of isodiffracting pulsed beams, which are superpositions of transverse modes supported by spherical-mirror laser resonators. By employing modal weights that, for stationary light, produce a Gaussian Schell-model beam, we extend this standard model to pulsed beams. We first construct the two-frequency cross-spectral density function that characterizes the spatial coherence in the space-frequency domain. By assuming a power-exponential spectral profile, we then employ the generalized Wiener-Khintchine theorem for nonstationary light to derive the two-time mutual coherence function that describes the space-time coherence of the ensuing beams. The isodiffracting nature of the laser resonator modes permits all (paraxial-domain) calculations at any propagation distance to be performed analytically. Significant spatiotemporal coupling is revealed in subcycle, single-cycle, and few-cycle domains, where the partial spatial coherence also leads to reduced temporal coherence even though full spectral coherence is assumed.

A separation of antiferromagnetic spin motion modes in the training effect of exchange biased Co/CoO film with in-plane anisotropy

NASA Astrophysics Data System (ADS)

Wu, R.; Yun, C.; Ding, S. L.; Wen, X.; Liu, S. Q.; Wang, C. S.; Han, J. Z.; Du, H. L.; Yang, J. B.

2016-08-01

The motion of antiferromagnetic interfacial spins is investigated through the temperature evolution of training effect in a Co/CoO film with in-plane biaxial anisotropy. Significant differences in the training effect and its temperature dependence are observed in the magnetic easy axis and hard axis (HA) and ascribed to the different motion modes of antiferromagnetic interfacial spins, the collective spin cluster rotation (CSR) and the single spin reversal (SSR), caused by different magnetization reversal modes of ferromagnetic layer. These motion modes of antiferromagnetic spins are successfully separated using a combination of an exponential function and a classic n-1/2 function. A larger CSR to SSR ratio and a shorter lifetime of CSR found in the HA indicates that the domain rotation in the ferromagnetic layer tends to activate and accelerate a CSR mode in the antiferromagnetic spins.

Resistance distribution in the hopping percolation model.

PubMed

Strelniker, Yakov M; Havlin, Shlomo; Berkovits, Richard; Frydman, Aviad

2005-07-01

We study the distribution function P (rho) of the effective resistance rho in two- and three-dimensional random resistor networks of linear size L in the hopping percolation model. In this model each bond has a conductivity taken from an exponential form sigma proportional to exp (-kappar) , where kappa is a measure of disorder and r is a random number, 0< or = r < or =1 . We find that in both the usual strong-disorder regime L/ kappa(nu) >1 (not sensitive to removal of any single bond) and the extreme-disorder regime L/ kappa(nu) <1 (very sensitive to such a removal) the distribution depends only on L/kappa(nu) and can be well approximated by a log-normal function with dispersion b kappa(nu) /L , where b is a coefficient which depends on the type of lattice, and nu is the correlation critical exponent.

Output of skeletal muscle contractions. a study of isokinetic plantar flexion in athletes.

PubMed

Fugl-Meyer, A R; Mild, K H; Hörnsten, J

1982-06-01

Maximum torques, total work and mean power of isokinetic plantar flexions were measured with simultaneous registrations. The integrated electromyograms (iEMG) were obtained by surface electrodes from all three heads of the m. triceps surae. The method applied offers possibilities for adequate description of dynamic muscular work which in the case of plantar flexion in trained man declines as a negative exponential function of angular motion velocity. The decline is parallel to that of maximum torques. The summed triceps surae iEMG was inversely proportional to the velocity and direct proportional to time suggesting that structural rather than neural factors determine the relationships between velocity of angular motion and maximum torque/total work of single Mmaneuvers. Moreover, the fact that maximum mean power as well as maximum electrical efficiency were reached at the functional velocity of toe-off during gait suggests an influence of pragmatic demands on plantar flexion mechanical output.

Secondary ion emission from Ti, V, Cu, Ag and Au surfaces under KeV Cs + irradiation

NASA Astrophysics Data System (ADS)

van der Heide, P. A. W.

2005-02-01

Low energy mono-atomic singly charged secondary ion emissions from Ti, V, Cu, Ag and Au substrates during the initial stages of sputtering with Cs + primary ions have been studied. With the exception of the Ag - secondary ions, all exhibited exponential like correlations with the Cs induced work function changes. This, along with the lack of variations in the valence band structure around the Fermi edge, is consistent with resonance charge transfer to/from states located at the Fermi edge. The insensitivity of Ag - to work function appears to stem from the dominance of a separate ion formation process, namely charge transfer into vacant 4d states in the sputtered population, which themselves appear to be produced through collective oscillations. A similar excitation-mediated process involving different levels also appears to be active in the formation of other negatively charged transition metal ions, albeit to a much lesser degree.

Generation of highly pure Schrödinger's cat states and real-time quadrature measurements via optical filtering

NASA Astrophysics Data System (ADS)

Asavanant, Warit; Nakashima, Kota; Shiozawa, Yu; Yoshikawa, Jun-Ichi; Furusawa, Akira

2017-12-01

Until now, Schr\\"odinger's cat states are generated by subtracting single photons from the whole bandwidth of squeezed vacua. However, it was pointed out recently that the achievable purities are limited in such method (J. Yoshikawa, W. Asavanant, and A. Furusawa, arXiv:1707.08146 [quant-ph] (2017)). In this paper, we used our new photon subtraction method with a narrowband filtering cavity and generated a highly pure Schr\\"odinger's cat state with the value of $-0.184$ at the origin of the Wigner function. To our knowledge, this is the highest value ever reported without any loss corrections. The temporal mode also becomes exponentially rising in our method, which allows us to make a real-time quadrature measurement on Schr\\"odinger's cat states, and we obtained the value of $-0.162$ at the origin of the Wigner function.

Anomalous yet Brownian.

PubMed

Wang, Bo; Anthony, Stephen M; Bae, Sung Chul; Granick, Steve

2009-09-08

We describe experiments using single-particle tracking in which mean-square displacement is simply proportional to time (Fickian), yet the distribution of displacement probability is not Gaussian as should be expected of a classical random walk but, instead, is decidedly exponential for large displacements, the decay length of the exponential being proportional to the square root of time. The first example is when colloidal beads diffuse along linear phospholipid bilayer tubes whose radius is the same as that of the beads. The second is when beads diffuse through entangled F-actin networks, bead radius being less than one-fifth of the actin network mesh size. We explore the relevance to dynamic heterogeneity in trajectory space, which has been extensively discussed regarding glassy systems. Data for the second system might suggest activated diffusion between pores in the entangled F-actin networks, in the same spirit as activated diffusion and exponential tails observed in glassy systems. But the first system shows exceptionally rapid diffusion, nearly as rapid as for identical colloids in free suspension, yet still displaying an exponential probability distribution as in the second system. Thus, although the exponential tail is reminiscent of glassy systems, in fact, these dynamics are exceptionally rapid. We also compare with particle trajectories that are at first subdiffusive but Fickian at the longest measurement times, finding that displacement probability distributions fall onto the same master curve in both regimes. The need is emphasized for experiments, theory, and computer simulation to allow definitive interpretation of this simple and clean exponential probability distribution.

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)

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…

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.

Ascending-ramp biphasic waveform has a lower defibrillation threshold and releases less troponin I than a truncated exponential biphasic waveform.

PubMed

Huang, Jian; Walcott, Gregory P; Ruse, Richard B; Bohanan, Scott J; Killingsworth, Cheryl R; Ideker, Raymond E

2012-09-11

We tested the hypothesis that the shape of the shock waveform affects not only the defibrillation threshold but also the amount of cardiac damage. Defibrillation thresholds were determined for 11 waveforms-3 ascending-ramp waveforms, 3 descending-ramp waveforms, 3 rectilinear first-phase biphasic waveforms, a Gurvich waveform, and a truncated exponential biphasic waveform-in 6 pigs with electrodes in the right ventricular apex and superior vena cava. The ascending, descending, and rectilinear waveforms had 4-, 8-, and 16-millisecond first phases and a 3.5-millisecond rectilinear second phase that was half the voltage of the first phase. The exponential biphasic waveform had a 60% first-phase and a 50% second-phase tilt. In a second study, we attempted to defibrillate after 10 seconds of ventricular fibrillation with a single ≈30-J shock (6 pigs successfully defibrillated with 8-millisecond ascending, 8-millisecond rectilinear, and truncated exponential biphasic waveforms). Troponin I blood levels were determined before and 2 to 10 hours after the shock. The lowest-energy defibrillation threshold was for the 8-milliseconds ascending ramp (14.6±7.3 J [mean±SD]), which was significantly less than for the truncated exponential (19.6±6.3 J). Six hours after shock, troponin I was significantly less for the ascending-ramp waveform (0.80±0.54 ng/mL) than for the truncated exponential (1.92±0.47 ng/mL) or the rectilinear waveform (1.17±0.45 ng/mL). The ascending ramp has a significantly lower defibrillation threshold and at ≈30 J causes 58% less troponin I release than the truncated exponential biphasic shock. Therefore, the shock waveform affects both the defibrillation threshold and the amount of cardiac damage.

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.

Single-channel activations and concentration jumps: comparison of recombinant NR1a/NR2A and NR1a/NR2D NMDA receptors

PubMed Central

Wyllie, David J A; Béhé, Philippe; Colquhoun, David

1998-01-01

We have expressed recombinant NR1a/NR2A and NR1a/NR2D N-methyl-D-aspartate (NMDA) receptor channels in Xenopus oocytes and made recordings of single-channel and macroscopic currents in outside-out membrane patches. For each receptor type we measured (a) the individual single-channel activations evoked by low glutamate concentrations in steady-state recordings, and (b) the macroscopic responses elicited by brief concentration jumps with high agonist concentrations, and we explore the relationship between these two sorts of observation. Low concentration (5–100 nM) steady-state recordings of NR1a/NR2A and NR1a/NR2D single-channel activity generated shut-time distributions that were best fitted with a mixture of five and six exponential components, respectively. Individual activations of either receptor type were resolved as bursts of openings, which we refer to as ‘super-clusters’. During a single activation, NR1a/NR2A receptors were open for 36 % of the time, but NR1a/NR2D receptors were open for only 4 % of the time. For both, distributions of super-cluster durations were best fitted with a mixture of six exponential components. Their overall mean durations were 35.8 and 1602 ms, respectively. Steady-state super-clusters were aligned on their first openings and averaged. The average was well fitted by a sum of exponentials with time constants taken from fits to super-cluster length distributions. It is shown that this is what would be expected for a channel that shows simple Markovian behaviour. The current through NR1a/NR2A channels following a concentration jump from zero to 1 mM glutamate for 1 ms was well fitted by three exponential components with time constants of 13 ms (rising phase), 70 ms and 350 ms (decaying phase). Similar concentration jumps on NR1a/NR2D channels were well fitted by two exponentials with means of 45 ms (rising phase) and 4408 ms (decaying phase) components. During prolonged exposure to glutamate, NR1a/NR2A channels desensitized with a time constant of 649 ms, while NR1a/NR2D channels exhibited no apparent desensitization. We show that under certain conditions, the time constants for the macroscopic jump response should be the same as those for the distribution of super-cluster lengths, though the resolution of the latter is so much greater that it cannot be expected that all the components will be resolvable in a macroscopic current. Good agreement was found for jumps on NR1a/NR2D receptors, and for some jump experiments on NR1a/NR2A. However, the latter were rather variable and some were slower than predicted. Slow decays were associated with patches that had large currents. PMID:9625862

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.

Voigt equivalent widths and spectral-bin single-line transmittances: Exact expansions and the MODTRAN®5 implementation

NASA Astrophysics Data System (ADS)

Berk, Alexander

2013-03-01

Exact expansions for Voigt line-shape total, line-tail and spectral bin equivalent widths and for Voigt finite spectral bin single-line transmittances have been derived in terms of optical depth dependent exponentially-scaled modified Bessel functions of integer order and optical depth independent Fourier integral coefficients. The series are convergent for the full range of Voigt line-shapes, from pure Doppler to pure Lorentzian. In the Lorentz limit, the expansion reduces to the Ladenburg and Reiche function for the total equivalent width. Analytic expressions are derived for the first 8 Fourier coefficients for pure Lorentzian lines, for pure Doppler lines and for Voigt lines with at most moderate Doppler dependence. A strong-line limit sum rule on the Fourier coefficients is enforced to define an additional Fourier coefficient and to optimize convergence of the truncated expansion. The moderate Doppler dependence scenario is applicable to and has been implemented in the MODTRAN5 atmospheric band model radiative transfer software. Finite-bin transmittances computed with the truncated expansions reduce transmittance residuals compared to the former Rodgers-Williams equivalent width based approach by ∼2 orders of magnitude.

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.

Constraint and Contingency in Multifunctional Gene Regulatory Circuits

PubMed Central

Payne, Joshua L.; Wagner, Andreas

2013-01-01

Gene regulatory circuits drive the development, physiology, and behavior of organisms from bacteria to humans. The phenotypes or functions of such circuits are embodied in the gene expression patterns they form. Regulatory circuits are typically multifunctional, forming distinct gene expression patterns in different embryonic stages, tissues, or physiological states. Any one circuit with a single function can be realized by many different regulatory genotypes. Multifunctionality presumably constrains this number, but we do not know to what extent. We here exhaustively characterize a genotype space harboring millions of model regulatory circuits and all their possible functions. As a circuit's number of functions increases, the number of genotypes with a given number of functions decreases exponentially but can remain very large for a modest number of functions. However, the sets of circuits that can form any one set of functions becomes increasingly fragmented. As a result, historical contingency becomes widespread in circuits with many functions. Whether a circuit can acquire an additional function in the course of its evolution becomes increasingly dependent on the function it already has. Circuits with many functions also become increasingly brittle and sensitive to mutation. These observations are generic properties of a broad class of circuits and independent of any one circuit genotype or phenotype. PMID:23762020

Detector response function of an energy-resolved CdTe single photon counting detector.

PubMed

Liu, Xin; Lee, Hyoung Koo

2014-01-01

While spectral CT using single photon counting detector has shown a number of advantages in diagnostic imaging, knowledge of the detector response function of an energy-resolved detector is needed to correct the signal bias and reconstruct the image more accurately. The objective of this paper is to study the photo counting detector response function using laboratory sources, and investigate the signal bias correction method. Our approach is to model the detector response function over the entire diagnostic energy range (20 keV

Markov Analysis of Sleep Dynamics

NASA Astrophysics Data System (ADS)

Kim, J. W.; Lee, J.-S.; Robinson, P. A.; Jeong, D.-U.

2009-05-01

A new approach, based on a Markov transition matrix, is proposed to explain frequent sleep and wake transitions during sleep. The matrix is determined by analyzing hypnograms of 113 obstructive sleep apnea patients. Our approach shows that the statistics of sleep can be constructed via a single Markov process and that durations of all states have modified exponential distributions, in contrast to recent reports of a scale-free form for the wake stage and an exponential form for the sleep stage. Hypnograms of the same subjects, but treated with Continuous Positive Airway Pressure, are analyzed and compared quantitatively with the pretreatment ones, suggesting potential clinical applications.

Weighted Scaling in Non-growth Random Networks

NASA Astrophysics Data System (ADS)

Chen, Guang; Yang, Xu-Hua; Xu, Xin-Li

2012-09-01

We propose a weighted model to explain the self-organizing formation of scale-free phenomenon in non-growth random networks. In this model, we use multiple-edges to represent the connections between vertices and define the weight of a multiple-edge as the total weights of all single-edges within it and the strength of a vertex as the sum of weights for those multiple-edges attached to it. The network evolves according to a vertex strength preferential selection mechanism. During the evolution process, the network always holds its total number of vertices and its total number of single-edges constantly. We show analytically and numerically that a network will form steady scale-free distributions with our model. The results show that a weighted non-growth random network can evolve into scale-free state. It is interesting that the network also obtains the character of an exponential edge weight distribution. Namely, coexistence of scale-free distribution and exponential distribution emerges.

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.

SELEX-Based Screening of Exosome-Tropic RNA.

PubMed

Yamashita, Takuma; Shinotsuka, Haruka; Takahashi, Yuki; Kato, Kana; Nishikawa, Makiya; Takakura, Yoshinobu

2017-01-01

Cell-derived nanosized vesicles or exosomes are expected to become delivery carriers for functional RNAs, such as small interfering RNA (siRNA). A method to efficiently load functional RNAs into exosomes is required for the development of exosome-based delivery carriers of functional RNAs. However, there is no method to find exosome-tropic exogenous RNA sequences. In this study, we used a systematic evolution of ligands by exponential enrichment (SELEX) method to screen exosome-tropic RNAs that can be used to load functional RNAs into exosomes by conjugation. Pooled single stranded 80-base RNAs, each of which contains a randomized 40-base sequence, were transfected into B16-BL6 murine melanoma cells and exosomes were collected from the cells. RNAs extracted from the exosomes were subjected to next round of SELEX. Cloning and sequencing of RNAs in SELEX-screened RNA pools showed that 29 of 56 clones had a typical RNA sequence. The sequence found by SELEX was enriched in exosomes after transfection to B16-BL6 cells. The results show that the SELEX-based method can be used for screening of exosome-tropic RNAs.

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.

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.

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.

Firing patterns in the adaptive exponential integrate-and-fire model.

PubMed

Naud, Richard; Marcille, Nicolas; Clopath, Claudia; Gerstner, Wulfram

2008-11-01

For simulations of large spiking neuron networks, an accurate, simple and versatile single-neuron modeling framework is required. Here we explore the versatility of a simple two-equation model: the adaptive exponential integrate-and-fire neuron. We show that this model generates multiple firing patterns depending on the choice of parameter values, and present a phase diagram describing the transition from one firing type to another. We give an analytical criterion to distinguish between continuous adaption, initial bursting, regular bursting and two types of tonic spiking. Also, we report that the deterministic model is capable of producing irregular spiking when stimulated with constant current, indicating low-dimensional chaos. Lastly, the simple model is fitted to real experiments of cortical neurons under step current stimulation. The results provide support for the suitability of simple models such as the adaptive exponential integrate-and-fire neuron for large network simulations.

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.

Cell responses to single pheromone molecules may reflect the activation kinetics of olfactory receptor molecules.

PubMed

Minor, A V; Kaissling, K-E

2003-03-01

Olfactory receptor cells of the silkmoth Bombyx mori respond to single pheromone molecules with "elementary" electrical events that appear as discrete "bumps" a few milliseconds in duration, or bursts of bumps. As revealed by simulation, one bump may result from a series of random openings of one or several ion channels, producing an average inward membrane current of 1.5 pA. The distributions of durations of bumps and of gaps between bumps in a burst can be fitted by single exponentials with time constants of 10.2 ms and 40.5 ms, respectively. The distribution of burst durations is a sum of two exponentials; the number of bumps per burst obeyed a geometric distribution (mean 3.2 bumps per burst). Accordingly the elementary events could reflect transitions among three states of the pheromone receptor molecule: the vacant receptor (state 1), the pheromone-receptor complex (state 2), and the activated complex (state 3). The calculated rate constants of the transitions between states are k(21)=7.7 s(-1), k(23)=16.8 s(-1), and k(32)=98 s(-1).

Decomposition of Atmospheric Aerosol Phase Function by Particle Size and Morphology via Single Particle Scattering Measurements

NASA Astrophysics Data System (ADS)

Aptowicz, K. B.; Pan, Y.; Martin, S.; Fernandez, E.; Chang, R.; Pinnick, R. G.

2013-12-01

We report upon an experimental approach that provides insight into how particle size and shape affect the scattering phase function of atmospheric aerosol particles. Central to our approach is the design of an apparatus that measures the forward and backward scattering hemispheres (scattering patterns) of individual atmospheric aerosol particles in the coarse mode range. The size and shape of each particle is discerned from the corresponding scattering pattern. In particular, autocorrelation analysis is used to differentiate between spherical and non-spherical particles, the calculated asphericity factor is used to characterize the morphology of non-spherical particles, and the integrated irradiance is used for particle sizing. We found the fraction of spherical particles decays exponentially with particle size, decreasing from 11% for particles on the order of 1 micrometer to less than 1% for particles over 5 micrometer. The average phase functions of subpopulations of particles, grouped by size and morphology, are determined by averaging their corresponding scattering patterns. The phase functions of spherical and non-spherical atmospheric particles are shown to diverge with increasing size. In addition, the phase function of non-spherical particles is found to vary little as a function of the asphericity factor.

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

Kinetics of Cell Fusion Induced by a Syncytia-Producing Mutant of Herpes Simplex Virus Type I

PubMed Central

Person, Stanley; Knowles, Robert W.; Read, G. Sullivan; Warner, Susan C.; Bond, Vincent C.

1976-01-01

We have isolated a number of plaque-morphology mutants from a strain of herpes simplex virus type I which, unlike the wild type, cause extensive cell fusion during a productive viral infection. After the onset of fusion, there is an exponential decrease in the number of single cells as a function of time after infection. At a multiplicity of infection (MOI) of 3.8 plaque-forming units per cell, fusion begins 5.3 h after infection with the number of single cells decreasing to 10% of the original number 10.2 h after infection. As the MOI is gradually increased from 0.4 to 8, the onset of fusion occurs earlier during infection. However, when the MOI is increased from 8 to 86, the onset of fusion does not occur any earlier. The rate of fusion is independent of the MOI for an MOI greater than 1. The rate of fusion varies linearly with initial cell density up to 3.5 × 104 cells/cm2 and is independent of initial cell density at higher cell concentrations. To assay cell fusion we have developed a simple quantitative assay using a Coulter counter to measure the number of single cells as a function of time after infection. Data obtained using a Coulter counter are similar to those obtained with a microscope assay. PMID:173881

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.

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.

The mechanism of double-exponential growth in hyper-inflation

NASA Astrophysics Data System (ADS)

Mizuno, T.; Takayasu, M.; Takayasu, H.

2002-05-01

Analyzing historical data of price indices, we find an extraordinary growth phenomenon in several examples of hyper-inflation in which, price changes are approximated nicely by double-exponential functions of time. In order to explain such behavior we introduce the general coarse-graining technique in physics, the Monte Carlo renormalization group method, to the price dynamics. Starting from a microscopic stochastic equation describing dealers’ actions in open markets, we obtain a macroscopic noiseless equation of price consistent with the observation. The effect of auto-catalytic shortening of characteristic time caused by mob psychology is shown to be responsible for the double-exponential behavior.

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.

Dynamical Casimir effect in stochastic systems: Photon harvesting through noise

NASA Astrophysics Data System (ADS)

Román-Ancheyta, Ricardo; Ramos-Prieto, Irán; Perez-Leija, Armando; Busch, Kurt; León-Montiel, Roberto de J.

2017-09-01

We theoretically investigate the dynamical Casimir effect in a single-mode cavity endowed with a driven off-resonant mirror. We explore the dynamics of photon generation as a function of the ratio between the cavity mode and the mirror's driving frequency. Interestingly, we find that this ratio defines a threshold—which we referred to as a metal-insulator phase transition—between exponential growth and low photon production. The low photon production is due to Bloch-like oscillations that produce a strong localization of the initial vacuum state, thus preventing higher generation of photons. To break localization of the vacuum state and enhance the photon generation, we impose a dephasing mechanism, based on dynamic disorder, into the driving frequency of the mirror. Additionally, we explore the effects of finite temperature on the photon production. Concurrently, we propose a classical analog of the dynamical Casimir effect in engineered photonic lattices, where the propagation of classical light emulates the photon generation from the quantum vacuum of a single-mode tunable cavity.

Scintillation and optical properties of Sn-doped Ga2O3 single crystals

NASA Astrophysics Data System (ADS)

Usui, Yuki; Nakauchi, Daisuke; Kawano, Naoki; Okada, Go; Kawaguchi, Noriaki; Yanagida, Takayuki

2018-06-01

Sn-doped Ga2O3 single crystals were synthesized by the Floating Zone (FZ) method. In photoluminescence (PL) under the excitation wavelength of 280 nm, we observed two types of luminescence: (1) defect luminescence due to recombination of the donor/acceptor pairs which appears at 430 nm and (2) the nsnp-ns2 transitions of Sn2+ which appear at 530 nm. The PL and scintillation decay time curves of the Sn-doped samples were approximated by a sum of exponential decay functions. The faster two components were ascribed to the defect luminescence, and the slowest component was owing to the nsnp-ns2 transitions. In the pulse height spectrum measurements under 241Am α-rays irradiation, all the Sn-doped Ga2O3 samples were confirmed to show a full energy absorption peak but the undoped one. Among the present samples, the 1% Sn-doped sample exhibited the highest scintillation light yield (1,500 ± 150 ph/5.5 MeV-α).

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.

The ATP hydrolysis and phosphate release steps control the time course of force development in rabbit skeletal muscle.

PubMed

Sleep, John; Irving, Malcolm; Burton, Kevin

2005-03-15

The time course of isometric force development following photolytic release of ATP in the presence of Ca(2+) was characterized in single skinned fibres from rabbit psoas muscle. Pre-photolysis force was minimized using apyrase to remove contaminating ATP and ADP. After the initial force rise induced by ATP release, a rapid shortening ramp terminated by a step stretch to the original length was imposed, and the time course of the subsequent force redevelopment was again characterized. Force development after ATP release was accurately described by a lag phase followed by one or two exponential components. At 20 degrees C, the lag was 5.6 +/- 0.4 ms (s.e.m., n = 11), and the force rise was well fitted by a single exponential with rate constant 71 +/- 4 s(-1). Force redevelopment after shortening-restretch began from about half the plateau force level, and its single-exponential rate constant was 68 +/- 3 s(-1), very similar to that following ATP release. When fibres were activated by the addition of Ca(2+) in ATP-containing solution, force developed more slowly, and the rate constant for force redevelopment following shortening-restretch reached a maximum value of 38 +/- 4 s(-1) (n = 6) after about 6 s of activation. This lower value may be associated with progressive sarcomere disorder at elevated temperature. Force development following ATP release was much slower at 5 degrees C than at 20 degrees C. The rate constant of a single-exponential fit to the force rise was 4.3 +/- 0.4 s(-1) (n = 22), and this was again similar to that after shortening-restretch in the same activation at this temperature, 3.8 +/- 0.2 s(-1). We conclude that force development after ATP release and shortening-restretch are controlled by the same steps in the actin-myosin ATPase cycle. The present results and much previous work on mechanical-chemical coupling in muscle can be explained by a kinetic scheme in which force is generated by a rapid conformational change bracketed by two biochemical steps with similar rate constants -- ATP hydrolysis and the release of inorganic phosphate -- both of which combine to control the rate of force development.

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

Kinetics of oxygen consumption after a single flash of light in photoreceptors of the drone (Apis mellifera)

PubMed Central

1982-01-01

The time course of the rate of oxygen consumption (QO2) after a single flash of light has been measured in 300-micrometers slices of drone retina at 22 degrees C. To measure delta QO2(t), the change in QO2 from its level in darkness, the transients of the partial pressure of O2 (PO2) were recorded with O2 microelectrodes simultaneously in two sites in the slice and delta QO2 was calculated by a computer using Fourier transforms. After a 40-ms flash of intense light, delta QO2, reached a peak of 40 microliters O2/g.min and then declined exponentially to the baseline with a time constant tau 1 = 4.96 +/- 0.49 s (SD, n = 10). The rising phase was characterized by a time constant tau 2 = 1.90 +/- 0.35 s (SD, n = 10). The peak amplitude of delta QO2 increased linearly with the log of the light intensity. Replacement of Na+ by choline, known to decrease greatly the light-induced transmembrane current, caused a 63% decrease of delta QO2. With these changes, however, the kinetics of delta QO2 (t) were unchanged. This suggest that the recovery phase is rate-limited by a single reaction with apparent first-order kinetics. Evidence is provided that suggests that this reaction may be the working of the sodium pump. Exposure of the retina to high concentrations of ouabain or strophanthidin (inhibitors of the sodium pump) reduced the peak amplitude of delta QO2 by approximately 80% and increased tau 1. The increase of tau 1 was an exponential function of the time of exposure to the cardioactive steroids. Hence, it seems likely that the greatest part of delta QO2 is used for the working of the pump, whose activity is the mechanism underlying the rate constant of the descending limb of delta QO2 (t). PMID:6288837

A note on free and forced Rossby wave solutions: The case of a straight coast and a channel

NASA Astrophysics Data System (ADS)

Graef, Federico

2017-03-01

The free Rossby wave (RW) solutions in an ocean with a straight coast when the offshore wavenumber of incident (l1) and reflected (l2) wave are equal or complex are discussed. If l1 = l2 the energy streams along the coast and a uniformly valid solution cannot be found; if l1,2 are complex it yields the sum of an exponentially decaying and growing (away from the coast) Rossby wave. The channel does not admit these solutions as free modes. If the wavenumber vectors of the RWs are perpendicular to the coast, the boundary condition of no normal flow is trivially satisfied and the value of the streamfunction does not need to vanish at the coast. A solution that satisfies Kelvin's theorem of time-independent circulation at the coast is proposed. The forced RW solutions when the ocean's forcing is a single Fourier component are studied. If the forcing is resonant, i.e. a free Rossby wave (RW), the linear response will depend critically on whether the wave carries energy perpendicular to the channel or not. In the first case, the amplitude of the response is linear in the direction normal to the channel, y, and in the second it has a parabolic profile in y. Examples of these solutions are shown for channels with parameters resembling the Mozambique Channel, the Tasman Sea, the Denmark Strait and the English Channel. The solutions for the single coast are unbounded, except when the forcing is a RW trapped against the coast. If the forcing is non-resonant, exponentially decaying or trapped RWs could be excited in the coast and both the exponentially ;decaying; and exponentially ;growing; RW could be excited in the channel.

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).

Recurrence plot statistics and the effect of embedding

NASA Astrophysics Data System (ADS)

March, T. K.; Chapman, S. C.; Dendy, R. O.

2005-01-01

Recurrence plots provide a graphical representation of the recurrent patterns in a timeseries, the quantification of which is a relatively new field. Here we derive analytical expressions which relate the values of key statistics, notably determinism and entropy of line length distribution, to the correlation sum as a function of embedding dimension. These expressions are obtained by deriving the transformation which generates an embedded recurrence plot from an unembedded plot. A single unembedded recurrence plot thus provides the statistics of all possible embedded recurrence plots. If the correlation sum scales exponentially with embedding dimension, we show that these statistics are determined entirely by the exponent of the exponential. This explains the results of Iwanski and Bradley [J.S. Iwanski, E. Bradley, Recurrence plots of experimental data: to embed or not to embed? Chaos 8 (1998) 861-871] who found that certain recurrence plot statistics are apparently invariant to embedding dimension for certain low-dimensional systems. We also examine the relationship between the mutual information content of two timeseries and the common recurrent structure seen in their recurrence plots. This allows time-localized contributions to mutual information to be visualized. This technique is demonstrated using geomagnetic index data; we show that the AU and AL geomagnetic indices share half their information, and find the timescale on which mutual features appear.

Applicaton of the Calculating Formula for Mean Neutron Exposure on Barium stars

NASA Astrophysics Data System (ADS)

Zhang, F. H.; Zhang, L.; Cui, W. Y.; Zhang, B.

2017-11-01

Latest studies have shown that, in the s-process nucleosynthesis model for the low-mass asymptotic giant branch (AGB) star with (13C) pocket radiative burning during the interpulse period, the distribution of neutron exposures in the nucleosynthesis region can be regarded as an exponential function, and the relation between the mean neutron exposure (τ0) and the model parameters is (τ0} = - Δ τ/ln [q/(1 - r + q)]), in which (Δ τ) is the exposure value of each neutron irradiation, (r) is the overlap factor, and (q) is the mass ratio of the (13C) shell to the He intershell. In this paper the formula is applied to 26 samples of barium stars to test its reliability, and furthermore the neutron exposure nature in the AGB companion stars of 26 barium stars are analyzed. The results show that, the formula is reliable; in the AGB companion stars of 26 barium stars, at least 8 stars definitely have and 12 stars are highly likely to have exponential distribution of neutron exposures, while 4 stars tend to experience single neutron exposure; most of the AGB companion stars may have experienced fewer times of neutron irradiations before the element abundance distribution of the s-process comes to asymptotic condition.

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.

Mapping Horizontal Spread of Activity in Monkey Motor Cortex Using Single Pulse Microstimulation

PubMed Central

Riehle, Alexa; Brochier, Thomas G.

2016-01-01

Anatomical studies have demonstrated that distant cortical points are interconnected through long range axon collaterals of pyramidal cells. However, the functional properties of these intrinsic synaptic connections, especially their relationship with the cortical representations of body movements, have not been systematically investigated. To address this issue, we used multielectrode arrays chronically implanted in the motor cortex of two rhesus monkeys to analyze the effects of single-pulse intracortical microstimulation (sICMS) applied at one electrode on the neuronal activities recorded at all other electrodes. The temporal and spatial distribution of the evoked responses of single and multiunit activities was quantified to determine the properties of horizontal propagation. The typical responses were characterized by a brief excitatory peak followed by inhibition of longer duration. Significant excitatory responses to sICMS could be evoked up to 4 mm away from the stimulation site, but the strength of the response decreased exponentially and its latency increased linearly with the distance. We then quantified the direction and strength of the propagation in relation to the somatotopic organization of the motor cortex. We observed that following sICMS the propagation of neural activity is mainly directed rostro-caudally near the central sulcus but follows medio-lateral direction at the most anterior electrodes. The fact that these interactions are not entirely symmetrical may characterize a critical functional property of the motor cortex for the control of upper limb movements. Overall, these results support the assumption that the motor cortex is not functionally homogeneous but forms a complex network of interacting subregions. PMID:28018182

Pre-steady-state DNA unwinding by bacteriophage T4 Dda helicase reveals a monomeric molecular motor.

PubMed

Nanduri, Bindu; Byrd, Alicia K; Eoff, Robert L; Tackett, Alan J; Raney, Kevin D

2002-11-12

Helicases are molecular motor enzymes that unwind and translocate nucleic acids. One of the central questions regarding helicase activity is whether the process of coupling ATP hydrolysis to DNA unwinding requires an oligomeric form of the enzyme. We have applied a pre-steady-state kinetics approach to address this question with the bacteriophage T4 Dda helicase. If a helicase can function as a monomer, then the burst amplitude in the pre-steady state might be similar to the concentration of enzyme, whereas if the helicase required oligomerization, then the amplitude would be significantly less than the enzyme concentration. DNA unwinding of an oligonucleotide substrate was conducted by using a Kintek rapid quench-flow instrument. The substrate consisted of 12 bp adjacent to 12 nucleotides of single-stranded DNA. Dda (4 nM) was incubated with substrate (16 nM) in buffer, and the unwinding reaction was initiated by the addition of ATP (5 mM) and Mg(2+) (10 mM). The reaction was stopped by the addition of 400 mM EDTA. Product formation exhibited biphasic kinetics, and the data were fit to the equation for a single exponential followed by a steady state. The amplitude of the first phase was 3.5 +/- 0.2 nM, consistent with a monomeric helicase. The burst amplitude of product formation was measured over a range of enzyme and substrate concentrations and remained consistent with a functional monomer. Thus, Dda can rapidly unwind oligonucleotide substrates as a monomer, indicating that the functional molecular motor component of a helicase can reside within a single polypeptide.

Human germline and pan-cancer variomes and their distinct functional profiles

PubMed Central

Pan, Yang; Karagiannis, Konstantinos; Zhang, Haichen; Dingerdissen, Hayley; Shamsaddini, Amirhossein; Wan, Quan; Simonyan, Vahan; Mazumder, Raja

2014-01-01

Identification of non-synonymous single nucleotide variations (nsSNVs) has exponentially increased due to advances in Next-Generation Sequencing technologies. The functional impacts of these variations have been difficult to ascertain because the corresponding knowledge about sequence functional sites is quite fragmented. It is clear that mapping of variations to sequence functional features can help us better understand the pathophysiological role of variations. In this study, we investigated the effect of nsSNVs on more than 17 common types of post-translational modification (PTM) sites, active sites and binding sites. Out of 1 705 285 distinct nsSNVs on 259 216 functional sites we identified 38 549 variations that significantly affect 10 major functional sites. Furthermore, we found distinct patterns of site disruptions due to germline and somatic nsSNVs. Pan-cancer analysis across 12 different cancer types led to the identification of 51 genes with 106 nsSNV affected functional sites found in 3 or more cancer types. 13 of the 51 genes overlap with previously identified Significantly Mutated Genes (Nature. 2013 Oct 17;502(7471)). 62 mutations in these 13 genes affecting functional sites such as DNA, ATP binding and various PTM sites occur across several cancers and can be prioritized for additional validation and investigations. PMID:25232094

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,

QMRA for Drinking Water: 1. Revisiting the Mathematical Structure of Single-Hit Dose-Response Models.

PubMed

Nilsen, Vegard; Wyller, John

2016-01-01

Dose-response models are essential to quantitative microbial risk assessment (QMRA), providing a link between levels of human exposure to pathogens and the probability of negative health outcomes. In drinking water studies, the class of semi-mechanistic models known as single-hit models, such as the exponential and the exact beta-Poisson, has seen widespread use. In this work, an attempt is made to carefully develop the general mathematical single-hit framework while explicitly accounting for variation in (1) host susceptibility and (2) pathogen infectivity. This allows a precise interpretation of the so-called single-hit probability and precise identification of a set of statistical independence assumptions that are sufficient to arrive at single-hit models. Further analysis of the model framework is facilitated by formulating the single-hit models compactly using probability generating and moment generating functions. Among the more practically relevant conclusions drawn are: (1) for any dose distribution, variation in host susceptibility always reduces the single-hit risk compared to a constant host susceptibility (assuming equal mean susceptibilities), (2) the model-consistent representation of complete host immunity is formally demonstrated to be a simple scaling of the response, (3) the model-consistent expression for the total risk from repeated exposures deviates (gives lower risk) from the conventional expression used in applications, and (4) a model-consistent expression for the mean per-exposure dose that produces the correct total risk from repeated exposures is developed. © 2016 Society for Risk Analysis.

Statistical mechanics and scaling of fault populations with increasing strain in the Corinth Rift

NASA Astrophysics Data System (ADS)

Michas, Georgios; Vallianatos, Filippos; Sammonds, Peter

2015-12-01

Scaling properties of fracture/fault systems are studied in order to characterize the mechanical properties of rocks and to provide insight into the mechanisms that govern fault growth. A comprehensive image of the fault network in the Corinth Rift, Greece, obtained through numerous field studies and marine geophysical surveys, allows for the first time such a study over the entire area of the Rift. We compile a detailed fault map of the area and analyze the scaling properties of fault trace-lengths by using a statistical mechanics model, derived in the framework of generalized statistical mechanics and associated maximum entropy principle. By using this framework, a range of asymptotic power-law to exponential-like distributions are derived that can well describe the observed scaling patterns of fault trace-lengths in the Rift. Systematic variations and in particular a transition from asymptotic power-law to exponential-like scaling are observed to be a function of increasing strain in distinct strain regimes in the Rift, providing quantitative evidence for such crustal processes in a single tectonic setting. These results indicate the organization of the fault system as a function of brittle strain in the Earth's crust and suggest there are different mechanisms for fault growth in the distinct parts of the Rift. In addition, other factors such as fault interactions and the thickness of the brittle layer affect how the fault system evolves in time. The results suggest that regional strain, fault interactions and the boundary condition of the brittle layer may control fault growth and the fault network evolution in the Corinth Rift.

Extending unified-theory-of-reinforcement neural networks to steady-state operant behavior.

PubMed

Calvin, Olivia L; McDowell, J J

2016-06-01

The unified theory of reinforcement has been used to develop models of behavior over the last 20 years (Donahoe et al., 1993). Previous research has focused on the theory's concordance with the respondent behavior of humans and animals. In this experiment, neural networks were developed from the theory to extend the unified theory of reinforcement to operant behavior on single-alternative variable-interval schedules. This area of operant research was selected because previously developed neural networks could be applied to it without significant alteration. Previous research with humans and animals indicates that the pattern of their steady-state behavior is hyperbolic when plotted against the obtained rate of reinforcement (Herrnstein, 1970). A genetic algorithm was used in the first part of the experiment to determine parameter values for the neural networks, because values that were used in previous research did not result in a hyperbolic pattern of behavior. After finding these parameters, hyperbolic and other similar functions were fitted to the behavior produced by the neural networks. The form of the neural network's behavior was best described by an exponentiated hyperbola (McDowell, 1986; McLean and White, 1983; Wearden, 1981), which was derived from the generalized matching law (Baum, 1974). In post-hoc analyses the addition of a baseline rate of behavior significantly improved the fit of the exponentiated hyperbola and removed systematic residuals. The form of this function was consistent with human and animal behavior, but the estimated parameter values were not. Copyright © 2016 Elsevier B.V. All rights reserved.

The coherent interlayer resistance of a single, rotated interface between two stacks of AB graphite

NASA Astrophysics Data System (ADS)

Habib, K. M. Masum; Sylvia, Somaia S.; Ge, Supeng; Neupane, Mahesh; Lake, Roger K.

2013-12-01

The coherent, interlayer resistance of a misoriented, rotated interface between two stacks of AB graphite is determined for a variety of misorientation angles. The quantum-resistance of the ideal AB stack is on the order of 1 to 10 mΩ μm2. For small rotation angles, the coherent interlayer resistance exponentially approaches the ideal quantum resistance at energies away from the charge neutrality point. Over a range of intermediate angles, the resistance increases exponentially with cell size for minimum size unit cells. Larger cell sizes, of similar angles, may not follow this trend. The energy dependence of the interlayer transmission is described.

Revealing the Raft Domain Organization in the Plasma Membrane by Single-Molecule Imaging of Fluorescent Ganglioside Analogs.

PubMed

Suzuki, Kenichi G N; Ando, Hiromune; Komura, Naoko; Konishi, Miku; Imamura, Akihiro; Ishida, Hideharu; Kiso, Makoto; Fujiwara, Takahiro K; Kusumi, Akihiro

2018-01-01

Gangliosides have been implicated in a variety of physiological processes, particularly in the formation and function of raft domains in the plasma membrane. However, the scarcity of suitable fluorescent ganglioside analogs had long prevented us from determining exactly how gangliosides perform their functions in the live-cell plasma membrane. With the development of new fluorescent ganglioside analogs, as described by Komura et al. (2017), this barrier has been broken. We can now address the dynamic behaviors of gangliosides in the live-cell plasma membrane, using fluorescence microscopy, particularly by single-fluorescent molecule imaging and tracking. Single-molecule tracking of fluorescent GM1 and GM3 revealed that these molecules are transiently and dynamically recruited to monomers (monomer-associated rafts) and homodimer rafts of the raftophilic GPI-anchored protein CD59 in quiescent cells, with exponential residency times of 12 and 40ms, respectively, in a manner dependent on raft-lipid interactions. Upon CD59 stimulation, which induces CD59-cluster signaling rafts, the fluorescent GM1 and GM3 analogs were recruited to the signaling rafts, with a lifetime of 48ms. These results represent the first direct evidence that GPI-anchored receptors and gangliosides interact in a cholesterol-dependent manner. Furthermore, they show that gangliosides continually move in and out of rafts that contain CD59 in an extremely dynamic manner, with much higher frequency than expected previously. Such studies would not have been possible without fluorescent ganglioside probes, which exhibit native-like behavior and single-molecule tracking. In this chapter, we review the methods for single-molecule tracking of fluorescent ganglioside analogs and the results obtained by applying these methods. © 2018 Elsevier Inc. All rights reserved.

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.

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.

Engineering of an ultra-thin molecular superconductor by charge transfer

DOEpatents

Hla, Saw Wai; Hassanien, Abdelrahim; Kendal, Clark

2016-06-07

A method of forming a superconductive device of a single layer of (BETS).sub.2GaCl.sub.4 molecules on a substrate surface which displays a superconducting gap that increases exponentially with the length of the molecular chain is provided.

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.

Strain sensing using optical fibers

NASA Technical Reports Server (NTRS)

Houghton, Richard; Hiles, Steven

1994-01-01

The main source of attenuation which will be studied is the optical fiber's sensitivity to bending at radii that are much larger than the radius of the fiber. This type of environmental attenuation causes losses that are a function of the severity of the bend. The average attenuation caused by bending varies exponentially with the bend radius. There are many different fibers, sources, and testing equipment available. This thesis describes tests that were performed to evaluate the variables that effect bending related attenuation and will discuss the consistency of the results. Descriptions and comparisons will be made between single mode and multimode fibers as well as instrumentation comparisons between detection equipment. Detailed analysis of the effects of the whispering gallery mode will be performed along with theorized methods for characterization of these modes.

[Renal excretion of methylene-diphosphate-technium-99m. Preliminary observations].

PubMed

Vattimo, A; Martini, G

1983-11-30

The purpose of this study is to elucidate the mechanism of the renal excretion of 99mTc-MDP in man. We compared the renal clearance of 99mTc-MDP and 51Cr-EDTA (glomerular filtration rate agent). Since the 99mTc-MDP is bound to the plasma protein, the free fraction was calculated by dialysis. The clearances were obtained by single-injection technique. The plasma disappearance of the tracers was resolved into three exponential functions and area was calculated. The clearance was calculated by dividing the amount of the tracers excreted during the first four hours and the plasma area. In this study no difference was found in the clearance of the two agents. These findings suggest that the renal excretion of diphosphonate is related to the glomerular filtration rate.

Dual emission fluorescent silver nanoclusters for sensitive detection of the biological coenzyme NAD+/NADH.

PubMed

Yuan, Yufeng; Huang, Kehan; Chang, Mengfang; Qin, Cuifang; Zhang, Sanjun; Pan, Haifeng; Chen, Yan; Xu, Jianhua

2016-02-01

Fluorescent silver nanoclusters (Ag NCs) displaying dual-excitation and dual-emission properties have been developed for the specific detection of NAD(+) (nicotinamide adenine dinucleotide, oxidized form). With the increase of NAD(+) concentrations, the longer wavelength emission (with the peak at 550 nm) was gradually quenched due to the strong interactions between the NAD(+) and Ag NCs, whereas the shorter wavelength emission (peaking at 395 nm) was linearly enhanced. More important, the dual-emission intensity ratio (I395/I550), fitting by a single-exponential decay function, can efficiently detect various NAD(+) levels from 100 to 4000 μM, as well as label NAD(+)/NADH (reduced form of NAD) ratios in the range of 1-50. Copyright © 2015 Elsevier Inc. All rights reserved.

Charge retention behavior of preferentially oriented and textured Bi3.25La0.75Ti3O12 thin films by electrostatic force microscopy

NASA Astrophysics Data System (ADS)

Kim, T. Y.; Lee, J. H.; Oh, Y. J.; Choi, M. R.; Jo, W.

2007-02-01

The authors report charge retention in preferentially (117) oriented and textured c-axis oriented ferroelectric Bi3.25La0.75Ti3O12 thin films by electrostatic force microscopy. Surface charges of the films were observed as a function of time in a selected area which consists of a single-poled region and a reverse-poled region. The highly (117) oriented film shows the extended exponential decay with characteristic scaling exponents, n =1.5-1.6. The preferentially c-axis oriented film shows a remarkable retained behavior regardless of the poling. Decay and retention mechanisms of the regions are explained by space-charge redistribution and trapping of defects in the films.

Coherent forward broadening in cold atom clouds

NASA Astrophysics Data System (ADS)

Sutherland, R. T.; Robicheaux, F.

2016-02-01

It is shown that homogeneous line-broadening in a diffuse cold atom cloud is proportional to the resonant optical depth of the cloud. Furthermore, it is demonstrated how the strong directionality of the coherent interactions causes the cloud's spectra to depend strongly on its shape, even when the cloud is held at constant densities. These two numerical observations can be predicted analytically by extending the single-photon wave-function model. Lastly, elongating a cloud along the line of laser propagation causes the excitation probability distribution to deviate from the exponential decay predicted by the Beer-Lambert law to the extent where the atoms at the back of the cloud are more excited than the atoms at the front. These calculations are conducted at the low densities relevant to recent experiments.

Functional network inference of the suprachiasmatic nucleus

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

Abel, John H.; Meeker, Kirsten; Granados-Fuentes, Daniel

2016-04-04

In the mammalian suprachiasmatic nucleus (SCN), noisy cellular oscillators communicate within a neuronal network to generate precise system-wide circadian rhythms. Although the intracellular genetic oscillator and intercellular biochemical coupling mechanisms have been examined previously, the network topology driving synchronization of the SCN has not been elucidated. This network has been particularly challenging to probe, due to its oscillatory components and slow coupling timescale. In this work, we investigated the SCN network at a single-cell resolution through a chemically induced desynchronization. We then inferred functional connections in the SCN by applying the maximal information coefficient statistic to bioluminescence reporter data frommore » individual neurons while they resynchronized their circadian cycling. Our results demonstrate that the functional network of circadian cells associated with resynchronization has small-world characteristics, with a node degree distribution that is exponential. We show that hubs of this small-world network are preferentially located in the central SCN, with sparsely connected shells surrounding these cores. Finally, we used two computational models of circadian neurons to validate our predictions of network structure.« less

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.

Obstructive sleep apnea alters sleep stage transition dynamics.

PubMed

Bianchi, Matt T; Cash, Sydney S; Mietus, Joseph; Peng, Chung-Kang; Thomas, Robert

2010-06-28

Enhanced characterization of sleep architecture, compared with routine polysomnographic metrics such as stage percentages and sleep efficiency, may improve the predictive phenotyping of fragmented sleep. One approach involves using stage transition analysis to characterize sleep continuity. We analyzed hypnograms from Sleep Heart Health Study (SHHS) participants using the following stage designations: wake after sleep onset (WASO), non-rapid eye movement (NREM) sleep, and REM sleep. We show that individual patient hypnograms contain insufficient number of bouts to adequately describe the transition kinetics, necessitating pooling of data. We compared a control group of individuals free of medications, obstructive sleep apnea (OSA), medical co-morbidities, or sleepiness (n = 374) with mild (n = 496) or severe OSA (n = 338). WASO, REM sleep, and NREM sleep bout durations exhibited multi-exponential temporal dynamics. The presence of OSA accelerated the "decay" rate of NREM and REM sleep bouts, resulting in instability manifesting as shorter bouts and increased number of stage transitions. For WASO bouts, previously attributed to a power law process, a multi-exponential decay described the data well. Simulations demonstrated that a multi-exponential process can mimic a power law distribution. OSA alters sleep architecture dynamics by decreasing the temporal stability of NREM and REM sleep bouts. Multi-exponential fitting is superior to routine mono-exponential fitting, and may thus provide improved predictive metrics of sleep continuity. However, because a single night of sleep contains insufficient transitions to characterize these dynamics, extended monitoring of sleep, probably at home, would be necessary for individualized clinical application.

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

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.

{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

Robust Bayesian Fluorescence Lifetime Estimation, Decay Model Selection and Instrument Response Determination for Low-Intensity FLIM Imaging

PubMed Central

Rowley, Mark I.; Coolen, Anthonius C. C.; Vojnovic, Borivoj; Barber, Paul R.

2016-01-01

We present novel Bayesian methods for the analysis of exponential decay data that exploit the evidence carried by every detected decay event and enables robust extension to advanced processing. Our algorithms are presented in the context of fluorescence lifetime imaging microscopy (FLIM) and particular attention has been paid to model the time-domain system (based on time-correlated single photon counting) with unprecedented accuracy. We present estimates of decay parameters for mono- and bi-exponential systems, offering up to a factor of two improvement in accuracy compared to previous popular techniques. Results of the analysis of synthetic and experimental data are presented, and areas where the superior precision of our techniques can be exploited in Förster Resonance Energy Transfer (FRET) experiments are described. Furthermore, we demonstrate two advanced processing methods: decay model selection to choose between differing models such as mono- and bi-exponential, and the simultaneous estimation of instrument and decay parameters. PMID:27355322

A separation of antiferromagnetic spin motion modes in the training effect of exchange biased Co/CoO film with in-plane anisotropy

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

Wu, R.; Department of Materials Science and Metallurgy, University of Cambridge, Cambridge CB3 0FS; Yun, C.

2016-08-07

The motion of antiferromagnetic interfacial spins is investigated through the temperature evolution of training effect in a Co/CoO film with in-plane biaxial anisotropy. Significant differences in the training effect and its temperature dependence are observed in the magnetic easy axis and hard axis (HA) and ascribed to the different motion modes of antiferromagnetic interfacial spins, the collective spin cluster rotation (CSR) and the single spin reversal (SSR), caused by different magnetization reversal modes of ferromagnetic layer. These motion modes of antiferromagnetic spins are successfully separated using a combination of an exponential function and a classic n{sup −1/2} function. A largermore » CSR to SSR ratio and a shorter lifetime of CSR found in the HA indicates that the domain rotation in the ferromagnetic layer tends to activate and accelerate a CSR mode in the antiferromagnetic spins.« less

Reanimating the arm and hand with intraspinal microstimulation

NASA Astrophysics Data System (ADS)

Zimmermann, Jonas B.; Seki, Kazuhiko; Jackson, Andrew

2011-10-01

To date, there is no effective therapy for spinal cord injury, and many patients could benefit dramatically from at least partial restoration of arm and hand function. Despite a substantial body of research investigating intraspinal microstimulation (ISMS) in frogs, rodents and cats, little is known about upper-limb responses to cervical stimulation in the primate. Here, we show for the first time that long trains of ISMS delivered to the macaque spinal cord can evoke functional arm and hand movements. Complex movements involving coordinated activation of multiple muscles could be elicited from a single electrode, while just two electrodes were required for independent control of reaching and grasping. We found that the motor responses to ISMS were described by a dual exponential model that depended only on stimulation history. We demonstrate that this model can be inverted to generate stimulus trains capable of eliciting arbitrary, graded motor responses, and could be used to restore volitional movements in a closed-loop brain-machine interface.

Generalized conformal structure, dilaton gravity and SYK

NASA Astrophysics Data System (ADS)

Taylor, Marika

2018-01-01

A theory admits generalized conformal structure if the only scale in the quantum theory is set by a dimensionful coupling. SYK is an example of a theory with generalized conformal structure and in this paper we investigate the consequences of this structure for correlation functions and for the holographic realization of SYK. The Ward identities associated with the generalized conformal structure of SYK are implemented holographically in gravity/multiple scalar theories, which always have a parent AdS3 origin. For questions involving only the graviton/running scalar sector, one can always describe the bulk running in terms of a single scalar but multiple running scalars are in general needed once one includes the bulk fields corresponding to all SYK operators. We then explore chaos in holographic theories with generalized conformal structure. The four point function explored by Maldacena, Shenker and Stanford exhibits exactly the same chaotic behaviour in any such theory as in holographic realizations of conformal theories i.e. the dimensionful coupling scale does not affect the chaotic exponential growth.

Nanoparticles of adaptive supramolecular networks self-assembled from nucleotides and lanthanide ions.

PubMed

Nishiyabu, Ryuhei; Hashimoto, Nozomi; Cho, Ten; Watanabe, Kazuto; Yasunaga, Takefumi; Endo, Ayataka; Kaneko, Kenji; Niidome, Takuro; Murata, Masaharu; Adachi, Chihaya; Katayama, Yoshiki; Hashizume, Makoto; Kimizuka, Nobuo

2009-02-18

Amorphous nanoparticles of supramolecular coordination polymer networks are spontaneously self-assembled from nucleotides and lanthanide ions in water. They show intrinsic functions such as energy transfer from nucleobase to lanthanide ions and excellent performance as contrast enhancing agents for magnetic resonance imaging (MRI). Furthermore, adaptive inclusion properties are observed in the self-assembly process: functional materials such as fluorescent dyes, metal nanoparticles, and proteins are facilely encapsulated. Dyes in these nanoparticles fluoresce in high quantum yields with a single exponential decay, indicating that guest molecules are monomerically wrapped in the network. Gold nanoparticles and ferritin were also wrapped by the supramolecular shells. In addition, these nucleotide/lanthanide nanoparticles also serve as scaffolds for immobilizing enzymes. The adaptive nature of present supramolecular nanoparticles provides a versatile platform that can be utilized in a variety of applications ranging from material to biomedical sciences. As examples, biocompatibility and liver-directing characteristics in in vivo tissue localization experiments are demonstrated.

Using absolute gravimeter data to determine vertical gravity gradients

USGS Publications Warehouse

Robertson, D.S.

2001-01-01

The position versus time data from a free-fall absolute gravimeter can be used to estimate the vertical gravity gradient in addition to the gravity value itself. Hipkin has reported success in estimating the vertical gradient value using a data set of unusually good quality. This paper explores techniques that may be applicable to a broader class of data that may be contaminated with "system response" errors of larger magnitude than were evident in the data used by Hipkin. This system response function is usually modelled as a sum of exponentially decaying sinusoidal components. The technique employed here involves combining the x0, v0 and g parameters from all the drops made during a site occupation into a single least-squares solution, and including the value of the vertical gradient and the coefficients of system response function in the same solution. The resulting non-linear equations must be solved iteratively and convergence presents some difficulties. Sparse matrix techniques are used to make the least-squares problem computationally tractable.

Superstatistical generalised Langevin equation: non-Gaussian viscoelastic anomalous diffusion

NASA Astrophysics Data System (ADS)

Ślęzak, Jakub; Metzler, Ralf; Magdziarz, Marcin

2018-02-01

Recent advances in single particle tracking and supercomputing techniques demonstrate the emergence of normal or anomalous, viscoelastic diffusion in conjunction with non-Gaussian distributions in soft, biological, and active matter systems. We here formulate a stochastic model based on a generalised Langevin equation in which non-Gaussian shapes of the probability density function and normal or anomalous diffusion have a common origin, namely a random parametrisation of the stochastic force. We perform a detailed analysis demonstrating how various types of parameter distributions for the memory kernel result in exponential, power law, or power-log law tails of the memory functions. The studied system is also shown to exhibit a further unusual property: the velocity has a Gaussian one point probability density but non-Gaussian joint distributions. This behaviour is reflected in the relaxation from a Gaussian to a non-Gaussian distribution observed for the position variable. We show that our theoretical results are in excellent agreement with stochastic simulations.

Towards metabolic mapping of the human retina.

PubMed

Schweitzer, D; Schenke, S; Hammer, M; Schweitzer, F; Jentsch, S; Birckner, E; Becker, W; Bergmann, A

2007-05-01

Functional alterations are first signs of a starting pathological process. A device that measures parameter for the characterization of the metabolism at the human eye-ground would be a helpful tool for early diagnostics in stages when alterations are yet reversible. Measurements of blood flow and of oxygen saturation are necessary but not sufficient. The new technique of auto-fluorescence lifetime measurement (FLIM) opens in combination with selected excitation and emission ranges the possibility for metabolic mapping. FLIM not only adds an additional discrimination parameter to distinguish different fluorophores but also resolves different quenching states of the same fluorophore. Because of its high sensitivity and high temporal resolution, its capability to resolve multi-exponential decay functions, and its easy combination with laser scanner ophthalmoscopy, multi-dimensional time-correlated single photon counting was used for fundus imaging. An optimized set up for in vivo lifetime measurements at the human eye-ground will be explained. In this, the fundus fluorescence is excited at 446 or 468 nm and the time-resolved autofluorescence is detected in two spectral ranges between 510 and 560 nm as well as between 560 and 700 nm simultaneously. Exciting the fundus at 446 nm, several fluorescence maxima of lifetime t1 were detected between 100 and 220 ps in lifetime histograms of 40 degrees fundus images. In contrast, excitation at 468 nm results in a single maximum of lifetime t1 = 190 +/- 16 ps. Several fundus layers contribute to the fluorescence intensity in the short-wave emission range 510-560 nm. In contrast, the fluorescence intensity in the long-wave emission range between 560 and 700 nm is dominated by the fluorescence of lipofuscin in the retinal pigment epithelium. Comparing the lateral distribution of parameters of a tri-exponential model function in lifetime images of the fundus with the layered anatomical fundus structure, the shortest component (t1 = 190 ps) originates from the retinal pigment epithelium and the second lifetime (t2 = 1,000 ps) from the neural retina. The lifetime t3 approximately 5.5 ns might be influenced by the long decay of the fluorescence in the crystalline lens. In vitro analysis of the spectral properties of expected fluorophores under the condition of the living eye lightens the interpretation of in vivo measurements. Taking into account the transmission of the ocular media, the excitation of NADH is unlikely at the fundus. Copyright 2007 Wiley-Liss, Inc.

Evolution and mass extinctions as lognormal stochastic processes

NASA Astrophysics Data System (ADS)

Maccone, Claudio

2014-10-01

In a series of recent papers and in a book, this author put forward a mathematical model capable of embracing the search for extra-terrestrial intelligence (SETI), Darwinian Evolution and Human History into a single, unified statistical picture, concisely called Evo-SETI. The relevant mathematical tools are: (1) Geometric Brownian motion (GBM), the stochastic process representing evolution as the stochastic increase of the number of species living on Earth over the last 3.5 billion years. This GBM is well known in the mathematics of finances (Black-Sholes models). Its main features are that its probability density function (pdf) is a lognormal pdf, and its mean value is either an increasing or, more rarely, decreasing exponential function of the time. (2) The probability distributions known as b-lognormals, i.e. lognormals starting at a certain positive instant b>0 rather than at the origin. These b-lognormals were then forced by us to have their peak value located on the exponential mean-value curve of the GBM (Peak-Locus theorem). In the framework of Darwinian Evolution, the resulting mathematical construction was shown to be what evolutionary biologists call Cladistics. (3) The (Shannon) entropy of such b-lognormals is then seen to represent the `degree of progress' reached by each living organism or by each big set of living organisms, like historic human civilizations. Having understood this fact, human history may then be cast into the language of b-lognormals that are more and more organized in time (i.e. having smaller and smaller entropy, or smaller and smaller `chaos'), and have their peaks on the increasing GBM exponential. This exponential is thus the `trend of progress' in human history. (4) All these results also match with SETI in that the statistical Drake equation (generalization of the ordinary Drake equation to encompass statistics) leads just to the lognormal distribution as the probability distribution for the number of extra-terrestrial civilizations existing in the Galaxy (as a consequence of the central limit theorem of statistics). (5) But the most striking new result is that the well-known `Molecular Clock of Evolution', namely the `constant rate of Evolution at the molecular level' as shown by Kimura's Neutral Theory of Molecular Evolution, identifies with growth rate of the entropy of our Evo-SETI model, because they both grew linearly in time since the origin of life. (6) Furthermore, we apply our Evo-SETI model to lognormal stochastic processes other than GBMs. For instance, we provide two models for the mass extinctions that occurred in the past: (a) one based on GBMs and (b) the other based on a parabolic mean value capable of covering both the extinction and the subsequent recovery of life forms. (7) Finally, we show that the Markov & Korotayev (2007, 2008) model for Darwinian Evolution identifies with an Evo-SETI model for which the mean value of the underlying lognormal stochastic process is a cubic function of the time. In conclusion: we have provided a new mathematical model capable of embracing molecular evolution, SETI and entropy into a simple set of statistical equations based upon b-lognormals and lognormal stochastic processes with arbitrary mean, of which the GBMs are the particular case of exponential growth.

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.

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.

Production of a Biosurfactant from Torulopsis bombicola

PubMed Central

Cooper, D. G.; Paddock, D. A.

1984-01-01

Two types of carbon sources—carbohydrate and vegetable oil—are necessary to obtain large yields of biosurfactant from Torulopsis bombicola ATCC 22214. Most of the surfactant is produced in the late exponential phase of growth. It is possible to grow the yeast on a single carbon source and then add the other type of substrate, after the exponential growth phase, and cause a burst of surfactant production. This product is a mixture of glycolipids. The maximum yield is 70 g liter−1, or 35% of the weight of the substrate used. An economic comparison demonstrated that this biosurfactant could be produced significantly more cheaply than any of the previously reported microbial surfactants. PMID:16346455

Water movement through plant roots - exact solutions of the water flow equation in roots with linear or exponential piecewise hydraulic properties

NASA Astrophysics Data System (ADS)

Meunier, Félicien; Couvreur, Valentin; Draye, Xavier; Zarebanadkouki, Mohsen; Vanderborght, Jan; Javaux, Mathieu

2017-12-01

In 1978, Landsberg and Fowkes presented a solution of the water flow equation inside a root with uniform hydraulic properties. These properties are root radial conductivity and axial conductance, which control, respectively, the radial water flow between the root surface and xylem and the axial flow within the xylem. From the solution for the xylem water potential, functions that describe the radial and axial flow along the root axis were derived. These solutions can also be used to derive root macroscopic parameters that are potential input parameters of hydrological and crop models. In this paper, novel analytical solutions of the water flow equation are developed for roots whose hydraulic properties vary along their axis, which is the case for most plants. We derived solutions for single roots with linear or exponential variations of hydraulic properties with distance to root tip. These solutions were subsequently combined to construct single roots with complex hydraulic property profiles. The analytical solutions allow one to verify numerical solutions and to get a generalization of the hydric behaviour with the main influencing parameters of the solutions. The resulting flow distributions in heterogeneous roots differed from those in uniform roots and simulations led to more regular, less abrupt variations of xylem suction or radial flux along root axes. The model could successfully be applied to maize effective root conductance measurements to derive radial and axial hydraulic properties. We also show that very contrasted root water uptake patterns arise when using either uniform or heterogeneous root hydraulic properties in a soil-root model. The optimal root radius that maximizes water uptake under a carbon cost constraint was also studied. The optimal radius was shown to be highly dependent on the root hydraulic properties and close to observed properties in maize roots. We finally used the obtained functions for evaluating the impact of root maturation versus root growth on water uptake. Very diverse uptake strategies arise from the analysis. These solutions open new avenues to investigate for optimal genotype-environment-management interactions by optimization, for example, of plant-scale macroscopic hydraulic parameters used in ecohydrogolocial models.

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.

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…

Markov chain formalism for generalized radiative transfer in a plane-parallel medium, accounting for polarization

NASA Astrophysics Data System (ADS)

Xu, Feng; Davis, Anthony B.; Diner, David J.

2016-11-01

A Markov chain formalism is developed for computing the transport of polarized radiation according to Generalized Radiative Transfer (GRT) theory, which was developed recently to account for unresolved random fluctuations of scattering particle density and can also be applied to unresolved spectral variability of gaseous absorption as an improvement over the standard correlated-k method. Using Gamma distribution to describe the probability density function of the extinction or absorption coefficient, a shape parameter a that quantifies the variability is introduced, defined as the mean extinction or absorption coefficient squared divided by its variance. It controls the decay rate of a power-law transmission that replaces the usual exponential Beer-Lambert-Bouguer law. Exponential transmission, hence classic RT, is recovered when a→∞. The new approach is verified to high accuracy against numerical benchmark results obtained with a custom Monte Carlo method. For a<∞, angular reciprocity is violated to a degree that increases with the spatial variability, as observed for finite portions of real-world cloudy scenes. While the degree of linear polarization in liquid water cloudbows, supernumerary bows, and glories is affected by spatial heterogeneity, the positions in scattering angle of these features are relatively unchanged. As a result, a single-scattering model based on the assumption of subpixel homogeneity can still be used to derive droplet size distributions from polarimetric measurements of extended stratocumulus clouds.

Sodium and calcium currents in neuroblastoma x glioma hybrid cells before and after morphological differentiation by dibutyryl cyclic AMP.

PubMed

Bodewei, R; Hering, S; Schubert, B; Wollenberger, A

1985-04-01

Sodium and calcium inward currents (INa and ICa) were measured in neuroblastoma X glioma hybrid cells of clones 108CC5 and 108CC15 by a single suction pipette method for internal perfusion and voltage clamp. Morphologically undifferentiated, exponentially growing cells were compared with cells differentiated by cultivation with 1 mmol/l dibutyryl cyclic AMP. Outward currents were eliminated by perfusing the cells with a K+-free solution. Voltage dependence and ion selectivity as well as steady state inactivation characteristics of INa and ICa resembled those of differentiated mouse neuroblastoma cells, clone N1E-115 (Moolenaar and Spector 1978, 1979). These parameters were identical in undifferentiated and differentiated cells of both clones. After differentiation the average density of the peak sodium and calcium currents was increased two and four-fold, respectively, in both cell lines. Our data indicate that exponentially growing, morphologically undifferentiated 108CC5 and 108CC15 neuroblastoma X glioma hybrid cells possess functional Na+ and Ca2+ channels undistinguishable from those of non-proliferating cells of these clones differentiated morphologically by treatment with dibutyryl cyclic AMP. That Na+ and Ca2+ spikes were not detected by other authors in these cells prior to morphological differentiation by dibutyryl cyclic AMP may be attributed to the fact that at the low resting membrane potential measured the Na+ and Ca2+ channels are inactivated.

Distribution of fixed beneficial mutations and the rate of adaptation in asexual populations

PubMed Central

Good, Benjamin H.; Rouzine, Igor M.; Balick, Daniel J.; Hallatschek, Oskar; Desai, Michael M.

2012-01-01

When large asexual populations adapt, competition between simultaneously segregating mutations slows the rate of adaptation and restricts the set of mutations that eventually fix. This phenomenon of interference arises from competition between mutations of different strengths as well as competition between mutations that arise on different fitness backgrounds. Previous work has explored each of these effects in isolation, but the way they combine to influence the dynamics of adaptation remains largely unknown. Here, we describe a theoretical model to treat both aspects of interference in large populations. We calculate the rate of adaptation and the distribution of fixed mutational effects accumulated by the population. We focus particular attention on the case when the effects of beneficial mutations are exponentially distributed, as well as on a more general class of exponential-like distributions. In both cases, we show that the rate of adaptation and the influence of genetic background on the fixation of new mutants is equivalent to an effective model with a single selection coefficient and rescaled mutation rate, and we explicitly calculate these effective parameters. We find that the effective selection coefficient exactly coincides with the most common fixed mutational effect. This equivalence leads to an intuitive picture of the relative importance of different types of interference effects, which can shift dramatically as a function of the population size, mutation rate, and the underlying distribution of fitness effects. PMID:22371564

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

Calculating the trap density of states in organic field-effect transistors from experiment: A comparison of different methods

NASA Astrophysics Data System (ADS)

Kalb, Wolfgang L.; Batlogg, Bertram

2010-01-01

The spectral density of localized states in the band gap of pentacene (trap DOS) was determined with a pentacene-based thin-film transistor from measurements of the temperature dependence and gate-voltage dependence of the contact-corrected field-effect conductivity. Several analytical methods to calculate the trap DOS from the measured data were used to clarify, if the different methods lead to comparable results. We also used computer simulations to further test the results from the analytical methods. Most methods predict a trap DOS close to the valence-band edge that can be very well approximated by a single exponential function with a slope in the range of 50-60 meV and a trap density at the valence-band edge of ≈2×1021eV-1cm-3 . Interestingly, the trap DOS is always slightly steeper than exponential. An important finding is that the choice of the method to calculate the trap DOS from the measured data can have a considerable effect on the final result. We identify two specific simplifying assumptions that lead to significant errors in the trap DOS. The temperature dependence of the band mobility should generally not be neglected. Moreover, the assumption of a constant effective accumulation-layer thickness leads to a significant underestimation of the slope of the trap DOS.

Deformation, Stress Relaxation, and Crystallization of Lithium Silicate Glass Fibers Below the Glass Transition Temperature

NASA Technical Reports Server (NTRS)

Ray, Chandra S.; Brow, Richard K.; Kim, Cheol W.; Reis, Signo T.

2004-01-01

The deformation and crystallization of Li(sub 2)O (center dot) 2SiO2 and Li(sub 2)O (center dot) 1.6SiO2 glass fibers subjected to a bending stress were measured as a function of time over the temperature range -50 to -150 C below the glass transition temperature (Tg). The glass fibers can be permanently deformed at temperatures about 100 C below T (sub)g, and they crystallize significantly at temperatures close to, but below T,, about 150 C lower than the onset temperature for crystallization for these glasses in the no-stress condition. The crystallization was found to occur only on the surface of the glass fibers with no detectable difference in the extent of crystallization in tensile and compressive stress regions. The relaxation mechanism for fiber deformation can be best described by a stretched exponential (Kohlrausch-Williams-Watt (KWW) approximation), rather than a single exponential model.The activation energy for stress relaxation, Es, for the glass fibers ranges between 175 and 195 kJ/mol, which is considerably smaller than the activation energy for viscous flow, E, (about 400 kJ/mol) near T, for these glasses at normal, stress-free condition. It is suspected that a viscosity relaxation mechanism could be responsible for permanent deformation and crystallization of the glass fibers below T,

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.

Universal model for collective access patterns in the Internet traffic dynamics: A superstatistical approach

NASA Astrophysics Data System (ADS)

Tamazian, A.; Nguyen, V. D.; Markelov, O. A.; Bogachev, M. I.

2016-07-01

We suggest a universal phenomenological description for the collective access patterns in the Internet traffic dynamics both at local and wide area network levels that takes into account erratic fluctuations imposed by cooperative user behaviour. Our description is based on the superstatistical approach and leads to the q-exponential inter-session time and session size distributions that are also in perfect agreement with empirical observations. The validity of the proposed description is confirmed explicitly by the analysis of complete 10-day traffic traces from the WIDE backbone link and from the local campus area network downlink from the Internet Service Provider. Remarkably, the same functional forms have been observed in the historic access patterns from single WWW servers. The suggested approach effectively accounts for the complex interplay of both “calm” and “bursty” user access patterns within a single-model setting. It also provides average sojourn time estimates with reasonable accuracy, as indicated by the queuing system performance simulation, this way largely overcoming the failure of Poisson modelling of the Internet traffic dynamics.

Large deviation probabilities for correlated Gaussian stochastic processes and daily temperature anomalies

NASA Astrophysics Data System (ADS)

Massah, Mozhdeh; Kantz, Holger

2016-04-01

As we have one and only one earth and no replicas, climate characteristics are usually computed as time averages from a single time series. For understanding climate variability, it is essential to understand how close a single time average will typically be to an ensemble average. To answer this question, we study large deviation probabilities (LDP) of stochastic processes and characterize them by their dependence on the time window. In contrast to iid variables for which there exists an analytical expression for the rate function, the correlated variables such as auto-regressive (short memory) and auto-regressive fractionally integrated moving average (long memory) processes, have not an analytical LDP. We study LDP for these processes, in order to see how correlation affects this probability in comparison to iid data. Although short range correlations lead to a simple correction of sample size, long range correlations lead to a sub-exponential decay of LDP and hence to a very slow convergence of time averages. This effect is demonstrated for a 120 year long time series of daily temperature anomalies measured in Potsdam (Germany).

Temperature dependence of ion transport: the compensated Arrhenius equation.

PubMed

Petrowsky, Matt; Frech, Roger

2009-04-30

The temperature-dependent conductivity originating in a thermally activated process is often described by a simple Arrhenius expression. However, this expression provides a poor description of the data for organic liquid electrolytes and amorphous polymer electrolytes. Here, we write the temperature dependence of the conductivity as an Arrhenius expression and show that the experimentally observed non-Arrhenius behavior is due to the temperature dependence of the dielectric constant contained in the exponential prefactor. Scaling the experimentally measured conductivities to conductivities at a chosen reference temperature leads to a "compensated" Arrhenius equation that provides an excellent description of temperature-dependent conductivities. A plot of the prefactors as a function of the solvent dielectric constant results in a single master curve for each family of solvents. These data suggest that ion transport in these and related systems is governed by a single activated process differing only in the activation energy for each family of solvents. Connection is made to the shift factor used to describe electrical and mechanical relaxation in a wide range of phenomena, suggesting that this scaling procedure might have broad applications.

Wakefield potentials of corrugated structures

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

Novokhatski, A.

A corrugated structure, which is used in “dechirper” devices, is usually a pipe or two plates with small corrugations (bumps) on the walls. There is a good single-mode description of the wake potentials excited by a relativistic bunch if the wave length of the mode is much longer than the distance between the bumps in the pipe. However, ultrashort bunches, which are now used in free electron lasers, excite much higher frequency fields and the corresponding wake potentials will be very different from the single-mode description. We have made analyses of these wake potentials based on a numerical solution ofmore » Maxwell’s equations. It was confirmed that the behavior of the wakefields of ultrashort bunches in corrugated structures is not much different from the fields excited usually in accelerating structures where the wake potentials are described by the exponential function. For a practical application we present results for the SLAC “dechirper.” We also carried out calculations for a similar device, that was installed and measured at the Pohang Accelerator Laboratory, Korea. As a result, we find very good agreement with the experimental results.« less

Wakefield potentials of corrugated structures

DOE PAGES

Novokhatski, A.

2015-10-22

A corrugated structure, which is used in “dechirper” devices, is usually a pipe or two plates with small corrugations (bumps) on the walls. There is a good single-mode description of the wake potentials excited by a relativistic bunch if the wave length of the mode is much longer than the distance between the bumps in the pipe. However, ultrashort bunches, which are now used in free electron lasers, excite much higher frequency fields and the corresponding wake potentials will be very different from the single-mode description. We have made analyses of these wake potentials based on a numerical solution ofmore » Maxwell’s equations. It was confirmed that the behavior of the wakefields of ultrashort bunches in corrugated structures is not much different from the fields excited usually in accelerating structures where the wake potentials are described by the exponential function. For a practical application we present results for the SLAC “dechirper.” We also carried out calculations for a similar device, that was installed and measured at the Pohang Accelerator Laboratory, Korea. As a result, we find very good agreement with the experimental results.« less

Single-molecule conductance through multiple π-π-stacked benzene rings determined with direct electrode-to-benzene ring connections.

PubMed

Schneebeli, Severin T; Kamenetska, Maria; Cheng, Zhanling; Skouta, Rachid; Friesner, Richard A; Venkataraman, Latha; Breslow, Ronald

2011-02-23

Understanding electron transport across π-π-stacked systems will help to answer fundamental questions about biochemical redox processes and benefit the design of new materials and molecular devices. Herein we employed the STM break-junction technique to measure the single-molecule conductance of multiple π-π-stacked aromatic rings. We studied electron transport through up to four stacked benzene rings held together in an eclipsed fashion via a paracyclophane scaffold. We found that the strained hydrocarbons studied herein couple directly to gold electrodes during the measurements; hence, we did not require any heteroatom binding groups as electrical contacts. Density functional theory-based calculations suggest that the gold atoms of the electrodes bind to two neighboring carbon atoms of the outermost cyclophane benzene rings in η(2) fashion. Our measurements show an exponential decay of the conductance with an increasing number of stacked benzene rings, indicating a nonresonant tunneling mechanism. Furthermore, STM tip-substrate displacement data provide additional evidence that the electrodes bind to the outermost benzene rings of the π-π-stacked molecular wires.

Superconducting compounds and alloys research

NASA Technical Reports Server (NTRS)

Otto, G.

1975-01-01

Resistivity measurements as a function of temperature were performed on alloys of the binary material system In sub(1-x) Bi sub x for x varying between 0 and 1. It was found that for all single-phase alloys (the pure elements, alpha-In, and the three intermetallic compounds) at temperatures sufficiently above the Debye-temperature, the resistivity p can be expressed as p = a sub o T(n), where a sub o and n are composition-dependent constants. The same exponential relationship can also be applied for the sub-system In-In2Bi, when the two phases are in compositional equilibrium. Superconductivity measurements on single and two-phase alloys can be explained with respect to the phase diagram. There occur three superconducting phases (alpha-In, In2Bi, and In5Bi3) with different transition temperatures in the alloying system. The magnitude of the transition temperatures for the various intermetallic phases of In-Bi is such that the disappearance or occurrence of a phase in two component alloys can be demonstrated easily by means of superconductivity measurements.

Heterogeneous Nature of Relaxation Dynamics of Room-Temperature Ionic Liquids (EMIm) 2[Co(NCS) 4] and (BMIm) 2[Co(NCS) 4

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

Hensel-Bielowka, Stella; Wojnarowska, Zaneta; Dzida, Marzena

2015-08-11

Dynamic crossover above T g has been recognized as a characteristic feature of molecular dynamics of liquids approaching glass transition. Experimentally, it is manifested as a change in Vogel–Fulcher–Tammann dependence or a breakdown of the Stokes–Einstein and related relations. In this study, we report the exception from this rather general pattern of behavior. By means of dielectric, ultrasonic, rheological, and calorimetric methods, dynamics of two good ionic conductors (BMIm) 2[Co(NCS) 4] and (EMIm) 2[Co(NCS) 4] of less common stoichiometry (2:1) was studied in a very broad temperature range. However, none of the mentioned dynamic changes was observed in the entiremore » studied temperature range. On the contrary, the single VFT and the same fractional Walden coefficient were found for conductivity and viscosity changes over 12 decades. Finally and moreover, ultrasonic studies revealed that the data at temperatures which cover the normal liquid region cannot be fitted by a single exponential decay, and the Cole–Cole function should be used instead.« less

Heterogeneous nature of relaxation dynamics of room-temperature ionic liquids (EMIm) 2[Co(NCS) 4] and (BMIm) 2[Co(NCS) 4

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

Hensel-Bielowka, Stella; Wojnarowska, Zaneta E.; Dzida, Marzena

2015-08-11

Dynamic crossover above T g has been recognized as a characteristic feature of molecular dynamics of liquids approaching glass transition. Experimentally, it is manifested as a change in Vogel Fulcher Tammann dependence or a breakdown of the Stokes Einstein and related relations. In this paper, we report the exception from this rather general pattern of behavior. By means of dielectric, ultrasonic, rheological, and calorimetric methods, dynamics of two good ionic conductors (BMIm) 2[Co(NCS) 4] and (EMIm) 2[Co(NCS) 4] of less common stoichiometry (2:1) was studied in a very broad temperature range. However, none of the mentioned dynamic changes was observedmore » in the entire studied temperature range. On the contrary, the single VFT and the same fractional Walden coefficient were found for conductivity and viscosity changes over 12 decades. Furthermore, ultrasonic studies revealed that the data at temperatures which cover the normal liquid region cannot be fitted by a single exponential decay, and the Cole Cole function should be used instead.« less

Measurement of the volume growth rate of single budding yeast with the MOSFET-based microfluidic Coulter counter

PubMed Central

Sun, Jiashu; Stowers, Chris C.; Boczko, Erik M.

2012-01-01

We report on measurements of the volume growth rate of ten individual budding yeast cells using a recently developed MOSFET-based microfluidic Coulter counter. The MOSFET-based microfluidic Coulter counter is very sensitive, provides signals that are immune from the baseline drift, and can work with cell culture media of complex composition. These desirable features allow us to directly measure the volume growth rate of single cells of Saccharomyces cerevisiae LYH3865 strain budding yeast in YNB culture media over a whole cell cycle. Results indicate that all budding yeast follow a sigmoid volume growth profile with reduced growth rates at the initial stage before the bud emerges and the final stage after the daughter gets mature. Analysis of the data indicates that even though all piecewise linear, Gomperitz, and Hill’s function models can fit the global growth profile equally well, the data strongly support local exponential growth phenomenon. Accurate volume growth measurements are important for applications in systems biology where quantitative parameters are required for modeling and simulation. PMID:20717618

Measurement of the volume growth rate of single budding yeast with the MOSFET-based microfluidic Coulter counter.

PubMed

Sun, Jiashu; Stowers, Chris C; Boczko, Erik M; Li, Deyu

2010-11-07

We report on measurements of the volume growth rate of ten individual budding yeast cells using a recently developed MOSFET-based microfluidic Coulter counter. The MOSFET-based microfluidic Coulter counter is very sensitive, provides signals that are immune from the baseline drift, and can work with cell culture media of complex composition. These desirable features allow us to directly measure the volume growth rate of single cells of Saccharomyces cerevisiae LYH3865 strain budding yeast in YNB culture media over a whole cell cycle. Results indicate that all budding yeast follow a sigmoid volume growth profile with reduced growth rates at the initial stage before the bud emerges and the final stage after the daughter gets mature. Analysis of the data indicates that even though all piecewise linear, Gomperitz, and Hill's function models can fit the global growth profile equally well, the data strongly support local exponential growth phenomenon. Accurate volume growth measurements are important for applications in systems biology where quantitative parameters are required for modeling and simulation.

Widefield TSCSPC-systems with large-area-detectors: application in simultaneous multi-channel-FLIM

NASA Astrophysics Data System (ADS)

Stepanov, Sergei; Bakhlanov, Sergei; Drobchenko, Evgeny; Eckert, Hann-Jörg; Kemnitz, Klaus

2010-11-01

Novel proximity-type Time- and Space-Correlated Single Photon Counting (TSCSPC) crossed-delay-line (DL)- and multi-anode (MA)-systems of outstanding performance and homogeneity were developed, using large-area detector heads of 25 and 40 mm diameter. Instrument response functions IRF(space) = (60 +/- 5) μm FWHM and IRF(time) = (28 +/- 3) ps FWHM were achieved over the full 12 cm2 area of the detector. Deadtime at throughput of 105 cps is 10% for "high-resolution" system and 5% in the "video"-system at 106 cps, at slightly reduced time- and space resolution. A fluorescence lifetime of (3.5 +/- 1) ps can be recovered from multi-exponential dynamics of a single living cyanobacterium (Acaryochloris marina). The present large-area detectors are particularly useful in simultaneous multichannel applications, such as 2-colour anisotropy or 4-colour lifetime imaging, utilizing dual- or quad-view image splitters. The long-term stability, low- excitation-intensity (< 100 mW/cm2) widefield systems enable minimal-invasive observation, without significant bleaching or photodynamic reactions, thus allowing long-period observation of up to several hours in living cells.

Function approximation using combined unsupervised and supervised learning.

PubMed

Andras, Peter

2014-03-01

Function approximation is one of the core tasks that are solved using neural networks in the context of many engineering problems. However, good approximation results need good sampling of the data space, which usually requires exponentially increasing volume of data as the dimensionality of the data increases. At the same time, often the high-dimensional data is arranged around a much lower dimensional manifold. Here we propose the breaking of the function approximation task for high-dimensional data into two steps: (1) the mapping of the high-dimensional data onto a lower dimensional space corresponding to the manifold on which the data resides and (2) the approximation of the function using the mapped lower dimensional data. We use over-complete self-organizing maps (SOMs) for the mapping through unsupervised learning, and single hidden layer neural networks for the function approximation through supervised learning. We also extend the two-step procedure by considering support vector machines and Bayesian SOMs for the determination of the best parameters for the nonlinear neurons in the hidden layer of the neural networks used for the function approximation. We compare the approximation performance of the proposed neural networks using a set of functions and show that indeed the neural networks using combined unsupervised and supervised learning outperform in most cases the neural networks that learn the function approximation using the original high-dimensional data.

Functional anatomy of complement factor H.

PubMed

Makou, Elisavet; Herbert, Andrew P; Barlow, Paul N

2013-06-11

Factor H (FH) is a soluble regulator of the proteolytic cascade at the core of the evolutionarily ancient vertebrate complement system. Although FH consists of a single chain of similar protein modules, it has a demanding job description. Its chief role is to prevent complement-mediated injury to healthy host cells and tissues. This entails recognition of molecular patterns on host surfaces combined with control of one of nature's most dangerous examples of a positive-feedback loop. In this way, FH modulates, where and when needed, an amplification process that otherwise exponentially escalates the production of the pro-inflammatory, pro-phagocytic, and pro-cytolytic cleavage products of complement proteins C3 and C5. Mutations and single-nucleotide polymorphisms in the FH gene and autoantibodies against FH predispose individuals to diseases, including age-related macular degeneration, dense-deposit disease, and atypical hemolytic uremic syndrome. Moreover, deletions or variations of genes for FH-related proteins also influence the risk of disease. Numerous pathogens hijack FH and use it for self-defense. As reviewed herein, a molecular understanding of FH function is emerging. While its functional oligomeric status remains uncertain, progress has been achieved in characterizing its three-dimensional architecture and, to a lesser extent, its intermodular flexibility. Models are proposed, based on the reconciliation of older data with a wealth of recent evidence, in which a latent circulating form of FH is activated by its principal target, C3b tethered to a self-surface. Such models suggest hypotheses linking sequence variations to pathophysiology, but improved, more quantitative, functional assays and rigorous data analysis are required to test these ideas.

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...

Elementary Theoretical Forms for the Spatial Power Spectrum of Earth's Crustal Magnetic Field

NASA Technical Reports Server (NTRS)

Voorhies, C.

1998-01-01

The magnetic field produced by magnetization in Earth's crust and lithosphere can be distinguished from the field produced by electric currents in Earth's core because the spatial magnetic power spectrum of the crustal field differs from that of the core field. Theoretical forms for the spectrum of the crustal field are derived by treating each magnetic domain in the crust as the point source of a dipole field. The geologic null-hypothesis that such moments are uncorrelated is used to obtain the magnetic spectrum expected from a randomly magnetized, or unstructured, spherical crust of negligible thickness. This simplest spectral form is modified to allow for uniform crustal thickness, ellipsoidality, and the polarization of domains by an periodically reversing, geocentric axial dipole field from Earth's core. Such spectra are intended to describe the background crustal field. Magnetic anomalies due to correlated magnetization within coherent geologic structures may well be superimposed upon this background; yet representing each such anomaly with a single point dipole may lead to similar spectral forms. Results from attempts to fit these forms to observational spectra, determined via spherical harmonic analysis of MAGSAT data, are summarized in terms of amplitude, source depth, and misfit. Each theoretical spectrum reduces to a source factor multiplied by the usual exponential function of spherical harmonic degree n due to geometric attenuation with attitude above the source layer. The source factors always vary with n and are approximately proportional to n(exp 3) for degrees 12 through 120. The theoretical spectra are therefore not directly proportional to an exponential function of spherical harmonic degree n. There is no radius at which these spectra are flat, level, or otherwise independent of n.

Pharmacokinetics of lidocaine and bupivacaine following subarachnoid administration in surgical patients: simultaneous investigation of absorption and disposition kinetics using stable isotopes

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

Burm, A.G.; Van Kleef, J.W.; Vermeulen, N.P.

1988-10-01

The pharmacokinetics of lidocaine and bupivacaine following subarachnoid administration were studied in 12 surgical patients using a stable isotope method. After subarachnoid administration of the agent to be evaluated, a deuterium-labelled analogue was administered intravenously. Blood samples were collected for 24 h. Plasma concentrations of the unlabelled and the deuterium-labelled local anesthetics were determined using a combination of capillary gas chromatography and mass fragmentography. Bi-exponential functions were fitted to the plasma concentration-time data of the deuterium-labelled local anesthetics. The progression of the absorption was evaluated using deconvolution. Mono- and bi-exponential functions were then fitted to the fraction absorbed versus timemore » data. The distribution and elimination half-lives of the deuterium-labelled analogues were 25 +/- 13 min (mean +/- SD) and 121 +/- 31 min for lidocaine and 19 +/- 10 min and 131 +/- 33 min for bupivacaine. The volumes of the central compartment and steady-state volumes of distribution were: lidocaine 57 +/- 10 l and 105 +/- 25 l, bupivacaine 25 +/- 6 l and 63 +/- 22 l. Total plasma clearance values averaged 0.97 +/- 0.21 l/min for lidocaine and 0.56 +/- 0.14 l/min for bupivacaine. The absorption of lidocaine could be described by a single first order absorption process, characterized by a half-life of 71 +/- 17 min in five out of six patients. The absorption of bupivacaine could be described adequately assuming two parallel first order absorption processes in all six patients. The half-lives, characterizing the fast and slow absorption processes of bupivacaine, were 50 +/- 27 min and 408 +/- 275 min, respectively. The fractions of the dose, absorbed in the fast and slow processes, were 0.35 +/- 0.17 and 0.61 +/- 0.16, respectively.« less

Alteration of the fast excitatory postsynaptic current by barium in voltage-clamped amphibian sympathetic ganglion cells.

PubMed Central

Connor, E. A.; Parsons, R. L.

1984-01-01

Barium-induced alterations in fast excitatory postsynaptic currents (e.p.s.cs) have been studied in voltage-clamped bullfrog sympathetic ganglion B cells. In the presence of 2-8 mM barium, e.p.s.c. decay was prolonged and in many cells the e.p.s.c. decay phase deviated from a single exponential function. The decay phase in these cases was more accurately described as the sum of two exponential functions. The frequency of occurrence of a complex decay increased both with increasing barium concentration and with hyperpolarization. Miniature e.p.s.c. decay also was prolonged in barium-treated cells. E.p.s.c. amplitude was not markedly affected by barium (2-8 mM) in cells voltage-clamped to -50 mV whereas at -90 mV there was a progressive increase in peak size with increasing barium concentration. In control cells the e.p.s.c.-voltage relationship was linear between -20 and -100 mV; however, this relationship became progressively non-linear with membrane hyperpolarization in barium-treated cells. The e.p.s.c. reversal potential was shifted to a more negative value in the presence of barium. There was a voltage-dependent increase in charge movement during the e.p.s.c. in barium-treated cells which was not present in control cells. We conclude that the voltage-dependent alteration in e.p.s.c. decay time course, peak amplitude and charge movement in barium-treated cells is due to a direct postsynaptic action of barium on the kinetics of receptor-channel gating in postganglionic sympathetic neurones. PMID:6333261

The size distribution of Pacific Seamounts

NASA Astrophysics Data System (ADS)

Smith, Deborah K.; Jordan, Thomas H.

1987-11-01

An analysis of wide-beam, Sea Beam and map-count data in the eastern and southern Pacific confirms the hypothesis that the average number of "ordinary" seamounts with summit heights h ≥ H can be approximated by the exponential frequency-size distribution: v(H) = vo e-βH. The exponential model, characterized by the single scale parameter β-1, is found to be superior to a power-law (self-similar) model. The exponential model provides a good first-order description of the summit-height distribution over a very broad spectrum of seamount sizes, from small cones (h < 300 m) to tall composite volcanoes (h > 3500 m). The distribution parameters obtained from 157,000 km of wide-beam profiles in the eastern and southern Pacific Ocean are vo = (5.4 ± 0.65) × 10-9m-2 and β = (3.5 ± 0.21) × 10-3 m-1, yielding an average of 5400 ± 650 seamounts per million square kilometers, of which 170 ± 17 are greater than one kilometer in height. The exponential distribution provides a reference for investigating the populations of not-so-ordinary seamounts, such as those on hotspot swells and near fracture zones, and seamounts in other ocean basins. If we assume that volcano height is determined by a hydraulic head proportional to the source depth of the magma column, then our observations imply an approximately exponential distribution of source depths. For reasonable values of magma and crustal densities, a volcano with the characteristic height β-1 = 285 m has an apparent source depth on the order of the crustal thickness.

Self-organized Segregation on the Grid

NASA Astrophysics Data System (ADS)

Omidvar, Hamed; Franceschetti, Massimo

2018-02-01

We consider an agent-based model with exponentially distributed waiting times in which two types of agents interact locally over a graph, and based on this interaction and on the value of a common intolerance threshold τ , decide whether to change their types. This is equivalent to a zero-temperature ising model with Glauber dynamics, an asynchronous cellular automaton with extended Moore neighborhoods, or a Schelling model of self-organized segregation in an open system, and has applications in the analysis of social and biological networks, and spin glasses systems. Some rigorous results were recently obtained in the theoretical computer science literature, and this work provides several extensions. We enlarge the intolerance interval leading to the expected formation of large segregated regions of agents of a single type from the known size ɛ >0 to size ≈ 0.134. Namely, we show that for 0.433< τ < 1/2 (and by symmetry 1/2<τ <0.567), the expected size of the largest segregated region containing an arbitrary agent is exponential in the size of the neighborhood. We further extend the interval leading to expected large segregated regions to size ≈ 0.312 considering "almost segregated" regions, namely regions where the ratio of the number of agents of one type and the number of agents of the other type vanishes quickly as the size of the neighborhood grows. In this case, we show that for 0.344 < τ ≤ 0.433 (and by symmetry for 0.567 ≤ τ <0.656) the expected size of the largest almost segregated region containing an arbitrary agent is exponential in the size of the neighborhood. This behavior is reminiscent of supercritical percolation, where small clusters of empty sites can be observed within any sufficiently large region of the occupied percolation cluster. The exponential bounds that we provide also imply that complete segregation, where agents of a single type cover the whole grid, does not occur with high probability for p=1/2 and the range of intolerance considered.

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.

Absorbed dose estimates from a single measurement one to three days after the administration of 177Lu-DOTATATE/-TOC.

PubMed

Hänscheid, Heribert; Lapa, Constantin; Buck, Andreas K; Lassmann, Michael; Werner, Rudolf A

2017-01-01

To retrospectively analyze the accuracy of absorbed dose estimates from a single measurement of the activity concentrations in tumors and relevant organs one to three days after the administration of 177 Lu-DOTA-TATE/TOC assuming tissue specific effective half-lives. Activity kinetics in 54 kidneys, 30 neuroendocrine tumor lesions, 25 livers, and 27 spleens were deduced from series of planar images in 29 patients. After adaptation of mono- or bi-exponential fit functions to the measured data, it was analyzed for each fit function how precise the time integral can be estimated from fixed tissue-specific half-lives and a single measurement at 24, 48, or 72 h after the administration. For the kidneys, assuming a fixed tissue-specific half-life of 50 h, the deviations of the estimate from the actual integral were median (5 % percentile, 95 % percentile): -3 °% (-15 %>; +16 °%) for measurements after 24 h, +2 %> (-9 %>; +12 %>) for measurements after 48 h, and 0 % (-2 %; +12 %) for measurements after 72 h. The corresponding values for the other tissues, assuming fixed tissue-specific half-lives of 67 h for liver and spleen and 77 h for tumors, were +2 % (-25 %; +20 %) for measurements after 24 h, +2 °% (-16 %>; +17 %>) for measurements after 48 h, and +2 %> (-11 %>; +10 %>) for measurements after 72 h. Especially for the kidneys, which often represent the dose limiting organ, but also for liver, spleen, and neuroendocrine tumors, a meaningful absorbed dose estimate is possible from a single measurement after 2, more preferably 3 days after the administration of 177 Lu-DOTA-TATE/-TOC assuming fixed tissue specific effective half-lives. Schattauer GmbH.

Heat flow in chains driven by thermal noise

NASA Astrophysics Data System (ADS)

Fogedby, Hans C.; Imparato, Alberto

2012-04-01

We consider the large deviation function for a classical harmonic chain composed of N particles driven at the end points by heat reservoirs, first derived in the quantum regime by Saito and Dhar (2007 Phys. Rev. Lett. 99 180601) and in the classical regime by Saito and Dhar (2011 Phys. Rev. E 83 041121) and Kundu et al (2011 J. Stat. Mech. P03007). Within a Langevin description we perform this calculation on the basis of a standard path integral calculation in Fourier space. The cumulant generating function yielding the large deviation function is given in terms of a transmission Green's function and is consistent with the fluctuation theorem. We find a simple expression for the tails of the heat distribution, which turns out to decay exponentially. We, moreover, consider an extension of a single-particle model suggested by Derrida and Brunet (2005 Einstein Aujourd'hui (Les Ulis: EDP Sciences)) and discuss the two-particle case. We also discuss the limit for large N and present a closed expression for the cumulant generating function. Finally, we present a derivation of the fluctuation theorem on the basis of a Fokker-Planck description. This result is not restricted to the harmonic case but is valid for a general interaction potential between the particles.

Fluorescence kinetics of emission from a small finite volume of a biological system

NASA Astrophysics Data System (ADS)

Dagen, A. J.; Alfano, R. R.; Zilinskas, B. A.; Swenberg, C. E.

1985-07-01

The fluorescence decay, apparent quantum yield and transmission from chromophores constrained to a microscopic volume using a single picosecond laser excitation were measured as a function of incident intensity. The β subunit of phycoeryhthrin aggregate isolated from the photosynthetic antenna system of Nostoc sp. was selected since it contains only four chromophores in a volume of less than 5.6×10 4 Å 3. The non-exponential fluorescence decay profiles were intensity independent for the intensity range studied (5 × 10 13 - 2 × 10 15 photon cm -2 per pulse). The apparent decrease in the relative fluorescence quantum yield and increase of the relative transmission with increasing excitation intensity is attributed to the combined effects of ground state depletion and upper excited state absorption. Evidence suggests that exciton annihilation is absent within isolated β subunits.

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.

Coherence and linewidth studies of a 4-nm high power FEL

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

Fawley, W.M.; Sessler, A.M.; Scharlemann, E.T.

Recently the SSRL/SLAC and its collaborators elsewhere have considered the merits of a 2 to 4-nm high power FEL utilizing the SLAC linac electron beam. The FEL would be a single pass amplifier excited by spontaneous emission rather than an oscillator, in order to eliminate the need for a soft X-ray resonant cavity. We have used GINGER, a multifrequency 2D FEL simulation code, to study the expected linewidth and coherence properties of the FEL, in both the exponential and saturated gain regimes. We present results concerning the effective shot noise input power and mode shape, the expected subpercent output linemore » widths, photon flux, and the field temporal and spatial correlation functions. We also discuss the effects of tapering the wiggler upon the output power and line width.« less

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.

Compactness and robustness: Applications in the solution of integral equations for chemical kinetics and electromagnetic scattering

NASA Astrophysics Data System (ADS)

Zhou, Yajun

This thesis employs the topological concept of compactness to deduce robust solutions to two integral equations arising from chemistry and physics: the inverse Laplace problem in chemical kinetics and the vector wave scattering problem in dielectric optics. The inverse Laplace problem occurs in the quantitative understanding of biological processes that exhibit complex kinetic behavior: different subpopulations of transition events from the "reactant" state to the "product" state follow distinct reaction rate constants, which results in a weighted superposition of exponential decay modes. Reconstruction of the rate constant distribution from kinetic data is often critical for mechanistic understandings of chemical reactions related to biological macromolecules. We devise a "phase function approach" to recover the probability distribution of rate constants from decay data in the time domain. The robustness (numerical stability) of this reconstruction algorithm builds upon the continuity of the transformations connecting the relevant function spaces that are compact metric spaces. The robust "phase function approach" not only is useful for the analysis of heterogeneous subpopulations of exponential decays within a single transition step, but also is generalizable to the kinetic analysis of complex chemical reactions that involve multiple intermediate steps. A quantitative characterization of the light scattering is central to many meteoro-logical, optical, and medical applications. We give a rigorous treatment to electromagnetic scattering on arbitrarily shaped dielectric media via the Born equation: an integral equation with a strongly singular convolution kernel that corresponds to a non-compact Green operator. By constructing a quadratic polynomial of the Green operator that cancels out the kernel singularity and satisfies the compactness criterion, we reveal the universality of a real resonance mode in dielectric optics. Meanwhile, exploiting the properties of compact operators, we outline the geometric and physical conditions that guarantee a robust solution to the light scattering problem, and devise an asymptotic solution to the Born equation of electromagnetic scattering for arbitrarily shaped dielectric in a non-perturbative manner.

Adaptive kanban control mechanism for a single-stage hybrid system

NASA Astrophysics Data System (ADS)

Korugan, Aybek; Gupta, Surendra M.

2002-02-01

In this paper, we consider a hybrid manufacturing system with two discrete production lines. Here the output of either production line can satisfy the demand for the same type of product without any penalties. The interarrival times for demand occurrences and service completions are exponentially distributed i.i.d. variables. In order to control this type of manufacturing system we suggest a single stage pull type control mechanism with adaptive kanbans and state independent routing of the production information.

Computerized Method for the Generation of Molecular Transmittance Functions in the Infrared Region.

DTIC Science & Technology

1979-12-31

exponent of the double exponential function were ’bumpy’ for some cases. Since the nature of the transmittance does not predict this behavior, we...T ,IS RECOMPUTED FOR THE ORIGIONAL DATA *USING THE PIECEWISE- ANALITICAL TRANSMISSION FUNCTION.’//20X, *’STANDARD DEVIATIONS BETWEEN THE ACTUAL TAU

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.

A 20-year period of orthotopic liver transplantation activity in a single center: a time series analysis performed using the R Statistical Software.

PubMed

Santori, G; Andorno, E; Morelli, N; Casaccia, M; Bottino, G; Di Domenico, S; Valente, U

2009-05-01

In many Western countries a "minimum volume rule" policy has been adopted as a quality measure for complex surgical procedures. In Italy, the National Transplant Centre set the minimum number of orthotopic liver transplantation (OLT) procedures/y at 25/center. OLT procedures performed in a single center for a reasonably large period may be treated as a time series to evaluate trend, seasonal cycles, and nonsystematic fluctuations. Between January 1, 1987 and December 31, 2006, we performed 563 cadaveric donor OLTs to adult recipients. During 2007, there were another 28 procedures. The greatest numbers of OLTs/y were performed in 2001 (n = 51), 2005 (n = 50), and 2004 (n = 49). A time series analysis performed using R Statistical Software (Foundation for Statistical Computing, Vienna, Austria), a free software environment for statistical computing and graphics, showed an incremental trend after exponential smoothing as well as after seasonal decomposition. The predicted OLT/mo for 2007 calculated with the Holt-Winters exponential smoothing applied to the previous period 1987-2006 helped to identify the months where there was a major difference between predicted and performed procedures. The time series approach may be helpful to establish a minimum volume/y at a single-center level.

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.

Efficient full decay inversion of MRS data with a stretched-exponential approximation of the ? distribution

NASA Astrophysics Data System (ADS)

Behroozmand, Ahmad A.; Auken, Esben; Fiandaca, Gianluca; Christiansen, Anders Vest; Christensen, Niels B.

2012-08-01

We present a new, efficient and accurate forward modelling and inversion scheme for magnetic resonance sounding (MRS) data. MRS, also called surface-nuclear magnetic resonance (surface-NMR), is the only non-invasive geophysical technique that directly detects free water in the subsurface. Based on the physical principle of NMR, protons of the water molecules in the subsurface are excited at a specific frequency, and the superposition of signals from all protons within the excited earth volume is measured to estimate the subsurface water content and other hydrological parameters. In this paper, a new inversion scheme is presented in which the entire data set is used, and multi-exponential behaviour of the NMR signal is approximated by the simple stretched-exponential approach. Compared to the mono-exponential interpretation of the decaying NMR signal, we introduce a single extra parameter, the stretching exponent, which helps describe the porosity in terms of a single relaxation time parameter, and helps to determine correct initial amplitude and relaxation time of the signal. Moreover, compared to a multi-exponential interpretation of the MRS data, the decay behaviour is approximated with considerably fewer parameters. The forward response is calculated in an efficient numerical manner in terms of magnetic field calculation, discretization and integration schemes, which allows fast computation while maintaining accuracy. A piecewise linear transmitter loop is considered for electromagnetic modelling of conductivities in the layered half-space providing electromagnetic modelling of arbitrary loop shapes. The decaying signal is integrated over time windows, called gates, which increases the signal-to-noise ratio, particularly at late times, and the data vector is described with a minimum number of samples, that is, gates. The accuracy of the forward response is investigated by comparing a MRS forward response with responses from three other approaches outlining significant differences between the three approaches. All together, a full MRS forward response is calculated in about 20 s and scales so that on 10 processors the calculation time is reduced to about 3-4 s. The proposed approach is examined through synthetic data and through a field example, which demonstrate the capability of the scheme. The results of the field example agree well the information from an in-site borehole.

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.

Nonlinear analogue of the May−Wigner instability transition

PubMed Central

Fyodorov, Yan V.; Khoruzhenko, Boris A.

2016-01-01

We study a system of N≫1 degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing to an equilibrium with rate μ. We show that, while increasing the ratio of the coupling strength to the relaxation rate, the system experiences an abrupt transition from a topologically trivial phase portrait with a single equilibrium into a topologically nontrivial regime characterized by an exponential number of equilibria, the vast majority of which are expected to be unstable. It is suggested that this picture provides a global view on the nature of the May−Wigner instability transition originally discovered by local linear stability analysis. PMID:27274077

Anderson localization of partially incoherent light

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

Capeta, D.; Radic, J.; Buljan, H.

We study Anderson localization and propagation of partially spatially incoherent wavepackets in linear disordered potentials, motivated by the insight that interference phenomena resulting from multiple scattering are affected by the coherence of the waves. We find that localization is delayed by incoherence: the more incoherent the waves are, the longer they diffusively spread while propagating in the medium. However, if all the eigenmodes of the system are exponentially localized (as in one- and two-dimensional disordered systems), any partially incoherent wavepacket eventually exhibits localization with exponentially decaying tails, after sufficiently long propagation distances. Interestingly, we find that the asymptotic behavior ofmore » the incoherent beam is similar to that of a single instantaneous coherent realization of the beam.« less

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

High Electrical Conductivity of Single Metal-Organic Chains.

PubMed

Ares, Pablo; Amo-Ochoa, Pilar; Soler, José M; Palacios, Juan José; Gómez-Herrero, Julio; Zamora, Félix

2018-05-01

Molecular wires are essential components for future nanoscale electronics. However, the preparation of individual long conductive molecules is still a challenge. MMX metal-organic polymers are quasi-1D sequences of single halide atoms (X) bridging subunits with two metal ions (MM) connected by organic ligands. They are excellent electrical conductors as bulk macroscopic crystals and as nanoribbons. However, according to theoretical calculations, the electrical conductance found in the experiments should be even higher. Here, a novel and simple drop-casting procedure to isolate bundles of few to single MMX chains is demonstrated. Furthermore, an exponential dependence of the electrical resistance of one or two MMX chains as a function of their length that does not agree with predictions based on their theoretical band structure is reported. This dependence is attributed to strong Anderson localization originated by structural defects. Theoretical modeling confirms that the current is limited by structural defects, mainly vacancies of iodine atoms, through which the current is constrained to flow. Nevertheless, measurable electrical transport along distances beyond 250 nm surpasses that of all other molecular wires reported so far. This work places in perspective the role of defects in 1D wires and their importance for molecular electronics. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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

Proton sensitivity of rat cerebellar granule cell GABAA receptors: dependence on neuronal development

PubMed Central

Krishek, Belinda J; Smart, Trevor G

2001-01-01

The effect of GABAA receptor development in culture on the modulation of GABA-induced currents by external H+ was examined in cerebellar granule cells using whole-cell and single-channel recording. Equilibrium concentration-response curves revealed a lower potency for GABA between 11 and 12 days in vitro (DIV) resulting in a shift of the EC50 from 10.7 to 2.4 μM. For granule cells before 11 DIV, the peak GABA-activated current was inhibited at low external pH and enhanced at high pH with a pKa of 6.65. For the steady-state response, low pH was inhibitory with a pKa of 5.56. After 11 DIV, the peak GABA-activated current was largely pH insensitive; however, the steady-state current was potentiated at low pH with a pKa of 6.84. Single GABA-activated ion channels were recorded from outside-out patches of granule cell bodies. At pH 5.4-9.4, single GABA channels exhibited multiple conductance states occurring at 22-26, 16-17 and 12-14 pS. The conductance levels were not significantly altered over the time period of study, nor by changing the external H+ concentration. Two exponential functions were required to fit the open-time frequency histograms at both early (< 11 DIV) and late (> 11 DIV) development times at each H+ concentration. The short and long open time constants were unaffected either by the extracellular H+ concentration or by neuronal development. The distribution of all shut times was fitted by the sum of three exponentials designated as short, intermediate and long. At acidic pH, the long shut time constant decreased with development as did the relative contribution of these components to the overall distribution. This was concurrent with an increase in the mean probability of channel opening. In conclusion, this study demonstrates in cerebellar granule cells that external pH can either reduce, have no effect on, or enhance GABA-activated responses depending on the stage of development, possibly related to the subunit composition of the GABAA receptors. The mode of interaction of H+ at the single-channel level and implications of such interactions at cerebellar granule cell GABAA receptors are discussed. PMID:11208970

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"…

Color Profile Trends of Dwarf Galaxies

NASA Astrophysics Data System (ADS)

Herrmann, Kimberly A.; LITTLE THINGS Team

2012-01-01

Radial stellar surface brightness profiles of spiral galaxies can be classified into three types: (I) single exponential, (II) truncated: the light falls off with one exponential out to a break radius and then falls off more steeply, and (III) anti-truncated: the light falls off with one exponential out to a break radius and then falls off less steeply. Stellar surface brightness profile breaks are also found in dwarf disk galaxies, but with an additional category: (FI) flat-inside: the light is roughly constant or increasing and then falls off beyond a break. Additionally, Bakos, Trujillo, & Pohlen (2008) showed that for spirals, each profile type has a characteristic color trend with respect to the break location. Furthermore, color trends reveal information about possible stellar population changes at the breaks. Here we show color trends for the four profile types from a large multi-wavelength photometric study of dwarf disk galaxies (the 141 dwarf parent sample of the LITTLE THINGS galaxies). We explore the similarities and differences between spirals and dwarfs and also between different colors. We gratefully acknowledge funding for this research from the National Science Foundation (AST-0707563).

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.

Development of a microprocessing-assisted cell-systematic evolution of ligands by exponential enrichment method for human umbilical vein endothelial cells

NASA Astrophysics Data System (ADS)

Terazono, Hideyuki; Kim, Hyonchol; Nomura, Fumimasa; Yasuda, Kenji

2016-06-01

We developed a microprocessing-assisted technique to select single-strand DNA aptamers that bind to unknown targets on the cell surface by modifying the conventional systematic evolution of ligands by exponential enrichment (cell-SELEX). Our technique involves 1) the specific selection of target-cell-surface-bound aptamers without leakage of intracellular components by trypsinization and 2) cloning of aptamers by microprocessing-assisted picking of single cells using magnetic beads. After cell-SELEX, the enriched aptamers were conjugated with magnetic beads. The aptamer-magnetic beads conjugates attached to target cells were collected individually by microassisted procedures using microneedles under a microscope. After that, the sequences of the collected magnetic-bead-bound aptamers were identified. As a result, a specific aptamer for the surface of target cells, e.g., human umbilical vein endothelial cells (HUVECs), was chosen and its specificity was examined using other cell types, e.g., HeLa cells. The results indicate that this microprocessing-assisted cell-SELEX method for identifying aptamers is applicable in biological research and clinical diagnostics.

Physical mechanism responsible for the stretched exponential decay behavior of aging organic light-emitting diodes

NASA Astrophysics Data System (ADS)

Féry, C.; Racine, B.; Vaufrey, D.; Doyeux, H.; Cinà, S.

2005-11-01

The main process responsible for the luminance degradation in organic light-emitting diodes (OLEDs) driven under constant current has not yet been identified. In this paper, we propose an approach to describe the intrinsic mechanisms involved in the OLED aging. We first show that a stretched exponential decay can be used to fit almost all the luminance versus time curves obtained under different driving conditions. In this way, we are able to prove that they can all be described by employing a single free parameter model. By using an approach based on local relaxation events, we will demonstrate that a single mechanism is responsible for the dominant aging process. Furthermore, we will demonstrate that the main relaxation event is the annihilation of one emissive center. We then use our model to fit all the experimental data measured under different driving condition, and show that by carefully fitting the accelerated luminance lifetime-curves, we can extrapolate the low-luminance lifetime needed for real display applications, with a high degree of accuracy.

Coherent energy scale revealed by ultrafast dynamics of UX3 (X = Al, Sn, Ga) single crystals

NASA Astrophysics Data System (ADS)

Nair, Saritha K.; Zhu, J.-X.; Sarrao, J. L.; Taylor, A. J.; Chia, Elbert E. M.

2012-09-01

The temperature dependence of relaxation dynamics of UX3 (X = Al, Ga, Sn) compounds is studied using the time-resolved pump-probe technique in reflectance geometry. For UGa3, our data are consistent with the formation of a spin density wave gap as evidenced from the quasidivergence of the relaxation time τ near the Néel temperature TN. For UAl3 and USn3, the relaxation dynamics shows a change from single-exponential to two-exponential behavior below a particular temperature, suggestive of coherence formation of the 5f electrons with the conduction band electrons. This particular temperature can be attributed to the spin fluctuation temperature Tsf, a measure of the strength of Kondo coherence. Our Tsf is consistent with other data such as resistivity and susceptibility measurements. The temperature dependence of the relaxation amplitude and time of UAl3 and USn3 were also fitted by the Rothwarf-Taylor model. Our results show that ultrafast optical spectroscopy is sensitive to c-f Kondo hybridization in the f-electron systems.

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.

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.

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.

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.

Relaxation processes of the liquid crystal ME6N in the isotropic phase studied by Raman scattering experiments

NASA Astrophysics Data System (ADS)

Giorgini, Maria Grazia; Arcioni, Alberto; Polizzi, Ciro; Musso, Maurizio; Ottaviani, Paolo

2004-03-01

We have investigated the Raman profiles of the ν(C≡N) and ν(C=O) vibrational modes of the nematic liquid crystal ME6N (4-cyanophenyl-4'-hexylbenzoate) in the isotropic phase at different temperatures and used them as probes of the dynamics and structural organization of this liquid. The vibrational time correlation functions of the ν(C≡N) mode, rather adequately interpreted within the assumption of exponential modulation function (the Kubo-Rothschild theory), indicate that the system experiences an intermediate dynamical regime that gets only slightly faster with increasing temperature. However, this theory fails in predicting the non-exponential behavior that the time correlation functions manifest in the long time range (t>3 ps). For this reason we have additionally approached the interpretation of vibrational correlation functions in terms of the theory formulated by Rothschild and co-workers for locally structured liquids. The application of this theory reveals that the molecular dynamics in this liquid crystal in the isotropic phase is that deriving from a distribution of differently sized clusters, which narrows as the temperature increases. Even at the highest temperature reached in this study (87 °C above the nematic-isotropic transition), the liquid has not yet achieved the structure of the simple liquid and the dynamics has not reached the limit of the single channel process. The vibrational and orientational relaxations occur in very different time scales. The temperature independence of the orientational dynamics in the whole range from 55 °C to 135 °C has been referred to the nonhydrodynamic behavior of the system, arising when local pseudonematic structures persist for times longer than the orientational relaxation. The occurrence of the process of resonant vibrational energy transfer between the C=O groups of adjacent molecules has been revealed in the isotropic phase by a slightly positive Raman noncoincidence effect in the band associated with the ν(C=O) mode. A qualitative interpretation is tentatively given in terms of partial cancellation of contributions deriving from structures having opposite orientations of their C=O groups.

Time-resolved scattering of a single photon by a single atom

PubMed Central

Leong, Victor; Seidler, Mathias Alexander; Steiner, Matthias; Cerè, Alessandro; Kurtsiefer, Christian

2016-01-01

Scattering of light by matter has been studied extensively in the past. Yet, the most fundamental process, the scattering of a single photon by a single atom, is largely unexplored. One prominent prediction of quantum optics is the deterministic absorption of a travelling photon by a single atom, provided the photon waveform matches spatially and temporally the time-reversed version of a spontaneously emitted photon. Here we experimentally address this prediction and investigate the influence of the photon's temporal profile on the scattering dynamics using a single trapped atom and heralded single photons. In a time-resolved measurement of atomic excitation we find a 56(11)% increase of the peak excitation by photons with an exponentially rising profile compared with a decaying one. However, the overall scattering probability remains unchanged within the experimental uncertainties. Our results demonstrate that envelope tailoring of single photons enables precise control of the photon–atom interaction. PMID:27897173

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...

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.

Fluorescence quenching by TEMPO: a sub-30 A single-molecule ruler.

PubMed

Zhu, Peizhi; Clamme, Jean-Pierre; Deniz, Ashok A

2005-11-01

A series of DNA molecules labeled with 5-carboxytetramethylrhodamine (5-TAMRA) and the small nitroxide radical TEMPO were synthesized and tested to investigate whether the intramolecular quenching efficiency can be used to measure short intramolecular distances in small ensemble and single-molecule experiments. In combination with distance calculations using molecular mechanics modeling, the experimental results from steady-state ensemble fluorescence and fluorescence correlation spectroscopy measurements both show an exponential decrease in the quenching rate constant with the dye-quencher distance in the 10-30 A range. The results demonstrate that TEMPO-5-TAMRA fluorescence quenching is a promising method to measure short distance changes within single biomolecules.

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.

Bayesian view of single-qubit clocks, and an energy versus accuracy tradeoff

NASA Astrophysics Data System (ADS)

Gopalkrishnan, Manoj; Kandula, Varshith; Sriram, Praveen; Deshpande, Abhishek; Muralidharan, Bhaskaran

2017-09-01

We bring a Bayesian approach to the analysis of clocks. Using exponential distributions as priors for clocks, we analyze how well one can keep time with a single qubit freely precessing under a magnetic field. We find that, at least with a single qubit, quantum mechanics does not allow exact timekeeping, in contrast to classical mechanics, which does. We find the design of the single-qubit clock that leads to maximum accuracy. Further, we find an energy versus accuracy tradeoff—the energy cost is at least kBT times the improvement in accuracy as measured by the entropy reduction in going from the prior distribution to the posterior distribution. We propose a physical realization of the single-qubit clock using charge transport across a capacitively coupled quantum dot.

A new algorithm and system for the characterization of handwriting strokes with delta-lognormal parameters.

PubMed

Djioua, Moussa; Plamondon, Réjean

2009-11-01

In this paper, we present a new analytical method for estimating the parameters of Delta-Lognormal functions and characterizing handwriting strokes. According to the Kinematic Theory of rapid human movements, these parameters contain information on both the motor commands and the timing properties of a neuromuscular system. The new algorithm, called XZERO, exploits relationships between the zero crossings of the first and second time derivatives of a lognormal function and its four basic parameters. The methodology is described and then evaluated under various testing conditions. The new tool allows a greater variety of stroke patterns to be processed automatically. Furthermore, for the first time, the extraction accuracy is quantified empirically, taking advantage of the exponential relationships that link the dispersion of the extraction errors with its signal-to-noise ratio. A new extraction system which combines this algorithm with two other previously published methods is also described and evaluated. This system provides researchers involved in various domains of pattern analysis and artificial intelligence with new tools for the basic study of single strokes as primitives for understanding rapid human movements.

Model of a fluxtube with a twisted magnetic field in the stratified solar atmosphere

NASA Astrophysics Data System (ADS)

Sen, S.; Mangalam, A.

2018-01-01

We build a single vertical straight magnetic fluxtube spanning the solar photosphere and the transition region which does not expand with height. We assume that the fluxtube containing twisted magnetic fields is in magnetohydrostatic equilibrium within a realistic stratified atmosphere subject to solar gravity. Incorporating specific forms of current density and gas pressure in the Grad-Shafranov equation, we solve the magnetic flux function, and find it to be separable with a Coulomb wave function in radial direction while the vertical part of the solution decreases exponentially. We employ improved fluxtube boundary conditions and take a realistic ambient external pressure for the photosphere to transition region, to derive a family of solutions for reasonable values of the fluxtube radius and magnetic field strength at the base of the axis that are the free parameters in our model. We find that our model estimates are consistent with the magnetic field strength and the radii of Magnetic bright points (MBPs) as estimated from observations. We also derive thermodynamic quantities inside the fluxtube.

Rotation of a spheroid in a Couette flow at moderate Reynolds numbers.

PubMed

Yu, Zhaosheng; Phan-Thien, Nhan; Tanner, Roger I

2007-08-01

The rotation of a single spheroid in a planar Couette flow as a model for simple shear flow is numerically simulated with the distributed Lagrangian multiplier based fictitious domain method. The study is focused on the effects of inertia on the orbital behavior of prolate and oblate spheroids. The numerical orbits are found to be well described by a simple empirical model, which states that the rate of the spheroid rotation about the vorticity axis is a sinusoidal function of the corresponding projection angle in the flow-gradient plane, and that the exponential growth rate of the orbit function is a constant. The following transitions in the steady state with increasing Reynolds number are identified: Jeffery orbit, tumbling, quasi-Jeffery orbit, log rolling, and inclined rolling for a prolate spheroid; and Jeffery orbit, log rolling, inclined rolling, and motionless state for an oblate spheroid. In addition, it is shown that the orbit behavior is sensitive to the initial orientation in the case of strong inertia and there exist different steady states for certain shear Reynolds number regimes.

Two Mechanisms Determine Quantum Dot Blinking.

PubMed

Yuan, Gangcheng; Gómez, Daniel E; Kirkwood, Nicholas; Boldt, Klaus; Mulvaney, Paul

2018-04-24

Many potential applications of quantum dots (QDs) can only be realized once the luminescence from single nanocrystals (NCs) is understood. These applications include the development of quantum logic devices, single-photon sources, long-life LEDs, and single-molecule biolabels. At the single-nanocrystal level, random fluctuations in the QD photoluminescence occur, a phenomenon termed blinking. There are two competing models to explain this blinking: Auger recombination and surface trap induced recombination. Here we use lifetime scaling on core-shell chalcogenide NCs to demonstrate that both types of blinking occur in the same QDs. We prove that Auger-blinking can yield single-exponential on/off times in contrast to earlier work. The surface passivation strategy determines which blinking mechanism dominates. This study summarizes earlier studies on blinking mechanisms and provides some clues that stable single QDs can be engineered for optoelectronic applications.

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.

Quantitative Universality for a Class of Weakly Chaotic Systems

NASA Astrophysics Data System (ADS)

Venegeroles, Roberto

2014-02-01

We consider a general class of intermittent maps designed to be weakly chaotic, i.e., for which the separation of trajectories of nearby initial conditions is weaker than exponential. We show that all its spatio and temporal properties, hitherto regarded independently in the literature, can be represented by a single characteristic function ϕ. A universal criterion for the choice of ϕ is obtained within the Feigenbaum's renormalization-group approach. We find a general expression for the dispersion rate ζ( t) of initially nearby trajectories and we show that the instability scenario for weakly chaotic systems is more general than that originally proposed by Gaspard and Wang (Proc. Natl. Acad. Sci. USA 85:4591, 1988). We also consider a spatially extended version of such class of maps, which leads to anomalous diffusion, and we show that the mean squared displacement satisfies σ 2( t)˜ ζ( t). To illustrate our results, some examples are discussed in detail.

Production cross sections of hyperons and charmed baryons from e+e- annihilation near √{s }=10.52 GeV

NASA Astrophysics Data System (ADS)

Niiyama, M.; Sumihama, M.; Nakano, T.; Adachi, I.; Aihara, H.; Al Said, S.; Asner, D. M.; Aulchenko, V.; Aushev, T.; Ayad, R.; Babu, V.; Badhrees, I.; Bakich, A. M.; Bansal, V.; Barberio, E.; Berger, M.; Bhardwaj, V.; Bhuyan, B.; Biswal, J.; Bobrov, A.; Bonvicini, G.; Bozek, A.; Bračko, M.; Browder, T. E.; Červenkov, D.; Chang, M.-C.; Chekelian, V.; Chen, A.; Cheon, B. G.; Chilikin, K.; Chistov, R.; Cho, K.; Choi, Y.; Cinabro, D.; Dash, N.; Di Carlo, S.; Doležal, Z.; Drásal, Z.; Dutta, D.; Eidelman, S.; Farhat, H.; Fast, J. E.; Ferber, T.; Fulsom, B. G.; Gaur, V.; Gabyshev, N.; Garmash, A.; Gillard, R.; Goldenzweig, P.; Haba, J.; Hara, T.; Hayasaka, K.; Hayashii, H.; Iijima, T.; Inami, K.; Ishikawa, A.; Itoh, R.; Iwasaki, Y.; Jacobs, W. W.; Jaegle, I.; Jin, Y.; Joffe, D.; Joo, K. K.; Julius, T.; Karyan, G.; Kato, Y.; Katrenko, P.; Kim, D. Y.; Kim, H. J.; Kim, J. B.; Kim, K. T.; Kim, M. J.; Kim, S. H.; Kim, Y. J.; Kinoshita, K.; Kodyš, P.; Kotchetkov, D.; Križan, P.; Krokovny, P.; Kulasiri, R.; Kuzmin, A.; Kwon, Y.-J.; Lange, J. S.; Lee, I. S.; Li, C. H.; Li, L.; Li, Y.; Li Gioi, L.; Libby, J.; Liventsev, D.; Luo, T.; Masuda, M.; Matsuda, T.; Matvienko, D.; Merola, M.; Miyabayashi, K.; Miyata, H.; Mizuk, R.; Moon, H. K.; Mori, T.; Mussa, R.; Nakano, E.; Nakao, M.; Nanut, T.; Nath, K. J.; Natkaniec, Z.; Nayak, M.; Nisar, N. K.; Nishida, S.; Ogawa, S.; Ono, H.; Pakhlov, P.; Pakhlova, G.; Pal, B.; Pardi, S.; Park, H.; Pedlar, T. K.; Piilonen, L. E.; Pulvermacher, C.; Ritter, M.; Sahoo, H.; Sakai, Y.; Sandilya, S.; Santelj, L.; Sato, Y.; Savinov, V.; Schneider, O.; Schnell, G.; Schwanda, C.; Seidl, R.; Seino, Y.; Senyo, K.; Sevior, M. E.; Shebalin, V.; Shen, C. P.; Shibata, T.-A.; Shiu, J.-G.; Shwartz, B.; Simon, F.; Sokolov, A.; Solovieva, E.; Starič, M.; Sumiyoshi, T.; Takizawa, M.; Tanida, K.; Tenchini, F.; Uchida, M.; Uehara, S.; Uglov, T.; Unno, Y.; Uno, S.; Van Hulse, C.; Varner, G.; Vossen, A.; Wang, C. H.; Wang, M.-Z.; Wang, P.; Watanabe, Y.; Widmann, E.; Williams, K. M.; Won, E.; Yamashita, Y.; Ye, H.; Yuan, C. Z.; Yusa, Y.; Zhang, Z. P.; Zhilich, V.; Zhulanov, V.; Zupanc, A.; Belle Collaboration

2018-04-01

We measure the inclusive production cross sections of hyperons and charmed baryons from e+e- annihilation using a 800 fb-1 data sample taken near the ϒ (4 S ) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. The feed-down contributions from heavy particles are subtracted using our data, and the direct production cross sections are presented for the first time. The production cross sections divided by the number of spin states for S =-1 hyperons follow an exponential function with a single slope parameter except for the Σ (1385 )+resonance. Suppression for Σ (1385 )+ and Ξ (1530 )0 hyperons is observed. Among the production cross sections of charmed baryons, a factor of 3 difference for Λc+ states over Σc states is observed. This observation suggests a diquark structure for these baryons.

Phenotypic plasticity as an adaptation to a functional trade-off

PubMed Central

Yi, Xiao; Dean, Antony M

2016-01-01

We report the evolution of a phenotypically plastic behavior that circumvents the hardwired trade-off that exists when resources are partitioned between growth and motility in Escherichia coli. We propagated cultures in a cyclical environment, alternating between growth up to carrying capacity and selection for chemotaxis. Initial adaptations boosted overall swimming speed at the expense of growth. The effect of the trade-off was subsequently eased through a change in behavior; while individual cells reduced motility during exponential growth, the faction of the population that was motile increased as the carrying capacity was approached. This plastic behavior was produced by a single amino acid replacement in FliA, a regulatory protein central to the chemotaxis network. Our results illustrate how phenotypic plasticity potentiates evolvability by opening up new regions of the adaptive landscape. DOI: http://dx.doi.org/10.7554/eLife.19307.001 PMID:27692064

Slow domain reconfiguration causes power-law kinetics in a two-state enzyme.

PubMed

Grossman-Haham, Iris; Rosenblum, Gabriel; Namani, Trishool; Hofmann, Hagen

2018-01-16

Protein dynamics are typically captured well by rate equations that predict exponential decays for two-state reactions. Here, we describe a remarkable exception. The electron-transfer enzyme quiescin sulfhydryl oxidase (QSOX), a natural fusion of two functionally distinct domains, switches between open- and closed-domain arrangements with apparent power-law kinetics. Using single-molecule FRET experiments on time scales from nanoseconds to milliseconds, we show that the unusual open-close kinetics results from slow sampling of an ensemble of disordered domain orientations. While substrate accelerates the kinetics, thus suggesting a substrate-induced switch to an alternative free energy landscape of the enzyme, the power-law behavior is also preserved upon electron load. Our results show that the slow sampling of open conformers is caused by a variety of interdomain interactions that imply a rugged free energy landscape, thus providing a generic mechanism for dynamic disorder in multidomain enzymes.

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.

Light-Curing Volumetric Shrinkage in Dimethacrylate-Based Dental Composites by Nanoindentation and PAL Study.

PubMed

Shpotyuk, Olha; Adamiak, Stanislaw; Bezvushko, Elvira; Cebulski, Jozef; Iskiv, Maryana; Shpotyuk, Oleh; Balitska, Valentina

2017-12-01

Light-curing volumetric shrinkage in dimethacrylate-based dental resin composites Dipol® is examined through comprehensive kinetics research employing nanoindentation measurements and nanoscale atomic-deficient study with lifetime spectroscopy of annihilating positrons. Photopolymerization kinetics determined through nanoindentation testing is shown to be described via single-exponential relaxation function with character time constants reaching respectively 15.0 and 18.7 s for nanohardness and elastic modulus. Atomic-deficient characteristics of composites are extracted from positron lifetime spectra parameterized employing unconstrained x3-term fitting. The tested photopolymerization kinetics can be adequately reflected in time-dependent changes observed in average positron lifetime (with 17.9 s time constant) and fractional free volume of positronium traps (with 18.6 s time constant). This correlation proves that fragmentation of free-volume positronium-trapping sites accompanied by partial positronium-to-positron traps conversion determines the light-curing volumetric shrinkage in the studied composites.

Stochastic Model of Vesicular Sorting in Cellular Organelles

NASA Astrophysics Data System (ADS)

Vagne, Quentin; Sens, Pierre

2018-02-01

The proper sorting of membrane components by regulated exchange between cellular organelles is crucial to intracellular organization. This process relies on the budding and fusion of transport vesicles, and should be strongly influenced by stochastic fluctuations, considering the relatively small size of many organelles. We identify the perfect sorting of two membrane components initially mixed in a single compartment as a first passage process, and we show that the mean sorting time exhibits two distinct regimes as a function of the ratio of vesicle fusion to budding rates. Low ratio values lead to fast sorting but result in a broad size distribution of sorted compartments dominated by small entities. High ratio values result in two well-defined sorted compartments but sorting is exponentially slow. Our results suggest an optimal balance between vesicle budding and fusion for the rapid and efficient sorting of membrane components and highlight the importance of stochastic effects for the steady-state organization of intracellular compartments.

Production cross sections of hyperons and charmed baryons from e + e - annihilation near s = 10.52 GeV

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

Niiyama, M.; Sumihama, M.; Nakano, T.

Here, we measure the inclusive production cross sections of hyperons and charmed baryons from e +e - annihilation using a 800 fb -1 data sample taken near the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e +e - collider. The feed-down contributions from heavy particles are subtracted using our data, and the direct production cross sections are presented for the first time. The production cross sections divided by the number of spin states for S = -1 hyperons follow an exponential function with a single slope parameter except for the Σ(1385) + resonance. Suppression for Σ(1385) + and Ξ(1530) 0 hyperons is observed. Among the production cross sections of charmed baryons, a factor of 3 difference for Λmore » $$+\\atop{c}$$ states over Σ c states is observed. This observation suggests a diquark structure for these baryons.« less

Solar cells for terrestrial applications

NASA Technical Reports Server (NTRS)

Chernow, F.

1975-01-01

The power efficiency curves of photovoltaic solar cells were investigated as a function of the forbidden energy gap (E sub g) and the current-voltage characteristic of the diode. Minority carrier injection, depletion layer recombination, and interface recombination terms were considered in models for the I-V characteristic. The collection efficiency for photons with energy between (E sub g) and an upper energy cutoff (E sub w) was assumed to be 100% and zero otherwise. Results are presented in terms of a single parameter related to the ratio of depletion layer width and minority carrier diffusion length. It was found that increasing depletion layer recombination shifts the efficiency curves to larger values of the energy without changing the shape of the efficiency curve appreciably. It is believed that similar results would be obtained whenever the quality factors in the exponential energy gap and forward bias terms are equal.

Production cross sections of hyperons and charmed baryons from e + e - annihilation near s = 10.52 GeV

DOE PAGES

Niiyama, M.; Sumihama, M.; Nakano, T.; ...

2018-04-09

Here, we measure the inclusive production cross sections of hyperons and charmed baryons from e +e - annihilation using a 800 fb -1 data sample taken near the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e +e - collider. The feed-down contributions from heavy particles are subtracted using our data, and the direct production cross sections are presented for the first time. The production cross sections divided by the number of spin states for S = -1 hyperons follow an exponential function with a single slope parameter except for the Σ(1385) + resonance. Suppression for Σ(1385) + and Ξ(1530) 0 hyperons is observed. Among the production cross sections of charmed baryons, a factor of 3 difference for Λmore » $$+\\atop{c}$$ states over Σ c states is observed. This observation suggests a diquark structure for these baryons.« less

Aptamer-based technology for food analysis.

PubMed

Liu, Xiaofei; Zhang, Xuewu

2015-01-01

Aptamers are short and functional single-stranded oligonucleotide sequences selected from systematic evolution of ligands by exponential enrichment (SELEX) process, which have the capacity to recognize various classes of target molecules with high affinity and specificity. Various analytical aptamers acquired by SELEX are widely used in many research fields, such as medicine, biology, and chemistry. However, the application of this innovative and emerging technology to food safety is just in infant stage. Food safety plays a very important role in our daily lives because varieties of poisonous and harmful substances in food affect human health. Aptamer technique is promising, which can overcome many disadvantages of existing detection methods in food safety, such as long detection time, low sensitivity, difficult, and expensive antibody preparation. This review provides an overview of various aptamer screening technologies and summarizes the recent applications of aptamers in food safety, and future prospects are also discussed.

Performance improvements of wavelength-shifting-fiber neutron detectors using high-resolution positioning algorithms

DOE PAGES

Wang, C. L.

2016-05-17

On the basis of FluoroBancroft linear-algebraic method [S.B. Andersson, Opt. Exp. 16, 18714 (2008)] three highly-resolved positioning methods were proposed for wavelength-shifting fiber (WLSF) neutron detectors. Using a Gaussian or exponential-decay light-response function (LRF), the non-linear relation of photon-number profiles vs. x-pixels was linearized and neutron positions were determined. The proposed algorithms give an average 0.03-0.08 pixel position error, much smaller than that (0.29 pixel) from a traditional maximum photon algorithm (MPA). The new algorithms result in better detector uniformity, less position misassignment (ghosting), better spatial resolution, and an equivalent or better instrument resolution in powder diffraction than the MPA.more » Moreover, these characters will facilitate broader applications of WLSF detectors at time-of-flight neutron powder diffraction beamlines, including single-crystal diffraction and texture analysis.« less

Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes.

PubMed

Uhl, Jonathan T; Pathak, Shivesh; Schorlemmer, Danijel; Liu, Xin; Swindeman, Ryan; Brinkman, Braden A W; LeBlanc, Michael; Tsekenis, Georgios; Friedman, Nir; Behringer, Robert; Denisov, Dmitry; Schall, Peter; Gu, Xiaojun; Wright, Wendelin J; Hufnagel, Todd; Jennings, Andrew; Greer, Julia R; Liaw, P K; Becker, Thorsten; Dresen, Georg; Dahmen, Karin A

2015-11-17

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or "quakes". We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects "tuned critical" behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes.

Universal Quake Statistics: From Compressed Nanocrystals to Earthquakes

PubMed Central

Uhl, Jonathan T.; Pathak, Shivesh; Schorlemmer, Danijel; Liu, Xin; Swindeman, Ryan; Brinkman, Braden A. W.; LeBlanc, Michael; Tsekenis, Georgios; Friedman, Nir; Behringer, Robert; Denisov, Dmitry; Schall, Peter; Gu, Xiaojun; Wright, Wendelin J.; Hufnagel, Todd; Jennings, Andrew; Greer, Julia R.; Liaw, P. K.; Becker, Thorsten; Dresen, Georg; Dahmen, Karin A.

2015-01-01

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or “quakes”. We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects “tuned critical” behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simple mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stress-dependent cutoff function. The results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes. PMID:26572103

Nucleation study for an undercooled melt of intermetallic NiZr

NASA Astrophysics Data System (ADS)

Kobold, R.; Kolbe, M.; Hornfeck, W.; Herlach, D. M.

2018-03-01

Electrostatic levitation is applied in order to undercool liquid glass forming NiZr significantly below its melting temperature. For NiZr large undercoolings are found to be highly reproducible with this experimental method. One single NiZr sample of high purity is undercooled 200 consecutive times which leads to a distribution function of undercooling temperatures. Within a statistical approach of classical nucleation theory, the undercooling distribution is analyzed yielding parameters, e.g., a pre-exponential factor of KV ≈ 1035 m-3 s-1, which indicates homogeneous nucleation. This result is consistent with the crystallization behavior of NiZr at high undercooling and with the corresponding microstructural analysis. Since NiZr is a representative of the very common CrB structure type, with 132 isostructural phases existing, understanding its nucleation behavior adds important knowledge to the nucleation of binary alloys in general.

Experimental realization of a one-way quantum computer algorithm solving Simon's problem.

PubMed

Tame, M S; Bell, B A; Di Franco, C; Wadsworth, W J; Rarity, J G

2014-11-14

We report an experimental demonstration of a one-way implementation of a quantum algorithm solving Simon's problem-a black-box period-finding problem that has an exponential gap between the classical and quantum runtime. Using an all-optical setup and modifying the bases of single-qubit measurements on a five-qubit cluster state, key representative functions of the logical two-qubit version's black box can be queried and solved. To the best of our knowledge, this work represents the first experimental realization of the quantum algorithm solving Simon's problem. The experimental results are in excellent agreement with the theoretical model, demonstrating the successful performance of the algorithm. With a view to scaling up to larger numbers of qubits, we analyze the resource requirements for an n-qubit version. This work helps highlight how one-way quantum computing provides a practical route to experimentally investigating the quantum-classical gap in the query complexity model.

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

Uhl, Jonathan T.; Pathak, Shivesh; Schorlemmer, Danijel

Slowly-compressed single crystals, bulk metallic glasses (BMGs), rocks, granular materials, and the earth all deform via intermittent slips or “quakes”. We find that although these systems span 12 decades in length scale, they all show the same scaling behavior for their slip size distributions and other statistical properties. Remarkably, the size distributions follow the same power law multiplied with the same exponential cutoff. The cutoff grows with applied force for materials spanning length scales from nanometers to kilometers. The tuneability of the cutoff with stress reflects “tuned critical” behavior, rather than self-organized criticality (SOC), which would imply stress-independence. A simplemore » mean field model for avalanches of slipping weak spots explains the agreement across scales. It predicts the observed slip-size distributions and the observed stressdependent cutoff function. In conclusion, the results enable extrapolations from one scale to another, and from one force to another, across different materials and structures, from nanocrystals to earthquakes.« less

Cardiac sodium channel Markov model with temperature dependence and recovery from inactivation.

PubMed Central

Irvine, L A; Jafri, M S; Winslow, R L

1999-01-01

A Markov model of the cardiac sodium channel is presented. The model is similar to the CA1 hippocampal neuron sodium channel model developed by Kuo and Bean (1994. Neuron. 12:819-829) with the following modifications: 1) an additional open state is added; 2) open-inactivated transitions are made voltage-dependent; and 3) channel rate constants are exponential functions of enthalpy, entropy, and voltage and have explicit temperature dependence. Model parameters are determined using a simulated annealing algorithm to minimize the error between model responses and various experimental data sets. The model reproduces a wide range of experimental data including ionic currents, gating currents, tail currents, steady-state inactivation, recovery from inactivation, and open time distributions over a temperature range of 10 degrees C to 25 degrees C. The model also predicts measures of single channel activity such as first latency, probability of a null sweep, and probability of reopening. PMID:10096885

Adaptive guidance for an aero-assisted boost vehicle

NASA Astrophysics Data System (ADS)

Pamadi, Bandu N.; Taylor, Lawrence W., Jr.; Price, Douglas B.

An adaptive guidance system incorporating dynamic pressure constraint is studied for a single stage to low earth orbit (LEO) aero-assist booster with thrust gimbal angle as the control variable. To derive an adaptive guidance law, cubic spline functions are used to represent the ascent profile. The booster flight to LEO is divided into initial and terminal phases. In the initial phase, the ascent profile is continuously updated to maximize the performance of the boost vehicle enroute. A linear feedback control is used in the terminal phase to guide the aero-assisted booster onto the desired LEO. The computer simulation of the vehicle dynamics considers a rotating spherical earth, inverse square (Newtonian) gravity field and an exponential model for the earth's atmospheric density. This adaptive guidance algorithm is capable of handling large deviations in both atmospheric conditions and modeling uncertainties, while ensuring maximum booster performance.

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...

Stopped-flow kinetic studies of sphere-to-rod transitions of sodium alkyl sulfate micelles induced by hydrotropic salt.

PubMed

Zhang, Jingyan; Ge, Zhishen; Jiang, Xiaoze; Hassan, P A; Liu, Shiyong

2007-12-15

The kinetics and mechanism of sphere-to-rod transitions of sodium alkyl sulfate micelles induced by hydrotropic salt, p-toluidine hydrochloride (PTHC), were investigated by stopped-flow with light scattering detection. Spherical sodium dodecyl sulfate (SDS) micelles transform into short ellipsoidal shapes at low salt concentrations ([PTHC]/[SDS], chi(PTHC)=0.3 and 0.4). Upon stopped-flow mixing aqueous solutions of spherical SDS micelles with PTHC, the scattered light intensity gradually increases with time. Single exponential fitting of the dynamic traces leads to characteristic relaxation time, tau(g), for the growth process from spherical to ellipsoidal micelles, and it increases with increasing SDS concentrations. This suggests that ellipsoidal micelles might be produced by successive insertion of unimers into spherical micelles, similar to the case of formation of spherical micelles as suggested by Aniansson-Wall (A-W) theory. At chi(PTHC) > or = 0.5, rod-like micelles with much higher axial ratio form. The scattered light intensity exhibits an initially abrupt increase and then levels off. The dynamic curves can be well fitted with single exponential functions, and the obtained tau(g) decreases with increasing SDS concentration. Thus, the growth from spherical to rod-like micelles might proceed via fusion of spherical micelles, in agreement with mechanism proposed by Ikeda et al. At chi(PTHC)=0.3 and 0.6, the apparent activation energies obtained from temperature dependent kinetic studies for the micellar growth are 40.4 and 3.6 kJ/mol, respectively. The large differences between activation energies for the growth from spherical to ellipsoidal micelles at low chi(PTHC) and the sphere-to-rod transition at high chi(PTHC) further indicate that they should follow different mechanisms. Moreover, the sphere-to-rod transition kinetics of sodium alkyl sulfate with varying hydrophobic chain lengths (n=10, 12, 14, and 16) are also studied. The longer the carbon chain lengths, the slower the sphere-to-rod transition.

Levitation effect in zeolites: Quasielastic neutron scattering and molecular dynamics study of pentane isomers in zeolite NaY.

PubMed

Borah, Bhaskar J; Jobic, H; Yashonath, S

2010-04-14

We report the quasielastic neutron scattering (QENS) and molecular dynamics (MD) investigations into diffusion of pentane isomers in zeolite NaY. The molecular cross section perpendicular to the long molecular axis varies for the three isomers while the mass and the isomer-zeolite interaction remains essentially unchanged. Both QENS and MD results show that the branched isomers neopentane and isopentane have higher self-diffusivities as compared with n-pentane at 300 K in NaY zeolite. This result provides direct experimental evidence for the existence of nonmonotonic, anomalous dependence of self-diffusivity on molecular diameter known as the levitation effect. The energetic barrier at the bottleneck derived from MD simulations exists for n-pentane which lies in the linear regime while no such barrier is seen for neopentane which is located clearly in the anomalous regime. Activation energy is in the order E(a)(n-pentane)>E(a)(isopentane)>E(a)(neopentane) consistent with the predictions of the levitation effect. In the liquid phase, it is seen that D(n-pentane)>D(isopentane)>D(neopentane) and E(a)(n-pentane)

Levitation effect in zeolites: Quasielastic neutron scattering and molecular dynamics study of pentane isomers in zeolite NaY

NASA Astrophysics Data System (ADS)

Borah, Bhaskar J.; Jobic, H.; Yashonath, S.

2010-04-01

We report the quasielastic neutron scattering (QENS) and molecular dynamics (MD) investigations into diffusion of pentane isomers in zeolite NaY. The molecular cross section perpendicular to the long molecular axis varies for the three isomers while the mass and the isomer-zeolite interaction remains essentially unchanged. Both QENS and MD results show that the branched isomers neopentane and isopentane have higher self-diffusivities as compared with n-pentane at 300 K in NaY zeolite. This result provides direct experimental evidence for the existence of nonmonotonic, anomalous dependence of self-diffusivity on molecular diameter known as the levitation effect. The energetic barrier at the bottleneck derived from MD simulations exists for n-pentane which lies in the linear regime while no such barrier is seen for neopentane which is located clearly in the anomalous regime. Activation energy is in the order Ea(n-pentane)>Ea(isopentane)>Ea(neopentane) consistent with the predictions of the levitation effect. In the liquid phase, it is seen that D(n-pentane)>D(isopentane)>D(neopentane) and Ea(n-pentane)

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)

Single-qubit unitary gates by graph scattering

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

Blumer, Benjamin A.; Underwood, Michael S.; Feder, David L.

2011-12-15

We consider the effects of plane-wave states scattering off finite graphs as an approach to implementing single-qubit unitary operations within the continuous-time quantum walk framework of universal quantum computation. Four semi-infinite tails are attached at arbitrary points of a given graph, representing the input and output registers of a single qubit. For a range of momentum eigenstates, we enumerate all of the graphs with up to n=9 vertices for which the scattering implements a single-qubit gate. As n increases, the number of new unitary operations increases exponentially, and for n>6 the majority correspond to rotations about axes distributed roughly uniformlymore » across the Bloch sphere. Rotations by both rational and irrational multiples of {pi} are found.« less

CaV 3.1 and CaV 3.3 account for T-type Ca2+ current in GH3 cells.

PubMed

Mudado, M A; Rodrigues, A L; Prado, V F; Beirão, P S L; Cruz, J S

2004-06-01

T-type Ca2+ channels are important for cell signaling by a variety of cells. We report here the electrophysiological and molecular characteristics of the whole-cell Ca2+ current in GH3 clonal pituitary cells. The current inactivation at 0 mV was described by a single exponential function with a time constant of 18.32 +/- 1.87 ms (N = 16). The I-V relationship measured with Ca2+ as a charge carrier was shifted to the left when we applied a conditioning pre-pulse of up to -120 mV, indicating that a low voltage-activated current may be present in GH3 cells. Transient currents were first activated at -50 mV and peaked around -20 mV. The half-maximal voltage activation and the slope factors for the two conditions are -35.02 +/- 2.4 and 6.7 +/- 0.3 mV (pre-pulse of -120 mV, N = 15), and -27.0 +/- 0.97 and 7.5 +/- 0.7 mV (pre-pulse of -40 mV, N = 9). The 8-mV shift in the activation mid-point was statistically significant (P < 0.05). The tail currents decayed bi-exponentially suggesting two different T-type Ca2+ channel populations. RT-PCR revealed the presence of alpha1G (CaV3.1) and alpha1I (CaV3.3) T-type Ca2+ channel mRNA transcripts.

A universal procedure for primer labelling of amplicons.

PubMed Central

Neilan, B A; Wilton, A N; Jacobs, D

1997-01-01

Detection and visualisation of nucleic acids is integral to genome analyses. Exponential amplification procedures have provided the means for the manipulation of nucleic acid sequences, which were otherwise inaccessible. We describe the development and application of a universal method for the labelling of any PCR product using a single end-labelled primer. Amplification was performed in a single reaction with the resulting amplicon labelled to a high specific activity. The method was adapted to a wide range of PCRs and significantly reduced the expense of such analyses. PMID:9207046

Photometric normalization of LROC WAC images

NASA Astrophysics Data System (ADS)

Sato, H.; Denevi, B.; Robinson, M. S.; Hapke, B. W.; McEwen, A. S.; LROC Science Team

2010-12-01

The Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC) acquires near global coverage on a monthly basis. The WAC is a push frame sensor with a 90° field of view (FOV) in BW mode and 60° FOV in 7-color mode (320 nm to 689 nm). WAC images are acquired during each orbit in 10° latitude segments with cross track coverage of ~50 km. Before mosaicking, WAC images are radiometrically calibrated to remove instrumental artifacts and to convert at sensor radiance to I/F. Images are also photometrically normalized to common viewing and illumination angles (30° phase), a challenge due to the wide angle nature of the WAC where large differences in phase angle are observed in a single image line (±30°). During a single month the equatorial incidence angle drifts about 28° and over the course of ~1 year the lighting completes a 360° cycle. The light scattering properties of the lunar surface depend on incidence(i), emission(e), and phase(p) angles as well as soil properties such as single-scattering albedo and roughness that vary with terrain type and state of maturity [1]. We first tested a Lommel-Seeliger Correction (LSC) [cos(i)/(cos(i) + cos(e))] [2] with a phase function defined by an exponential decay plus 4th order polynomial term [3] which did not provide an adequate solution. Next we employed a LSC with an exponential 2nd order decay phase correction that was an improvement, but still exhibited unacceptable frame-to-frame residuals. In both cases we fitted the LSC I/F vs. phase angle to derive the phase corrections. To date, the best results are with a lunar-lambert function [4] with exponential 2nd order decay phase correction (LLEXP2) [(A1exp(B1p)+A2exp(B2p)+A3) * cos(i)/(cos(e) + cos(i)) + B3cos(i)]. We derived the parameters for the LLEXP2 from repeat imaging of a small region and then corrected that region with excellent results. When this correction was applied to the whole Moon the results were less than optimal - no surprise given the variability of the regolith from region to region. As the fitting area increases, the accuracy of curve fitting decreases due to the larger variety of albedo, topography, and composition. Thus we have adopted an albedo-dependent photometric normalization routine. Phase curves are derived for discreet bins of preliminary normalized reflectance calculated from Clementine global mosaic in a fitting area that is composed of predominantly mare in Oceanus Procellarum. The global WAC mosaic was then corrected pixel-by-pixel according to its preliminary reflectance map with satisfactory results. We observed that the phase curves per normalized-reflectance bins become steeper as the reflectance value increases. Further filtering by using FeO, TiO2, or optical maturity [5] for parameter calculations may help elucidate the effects of surface composition and maturity on photometric properties of the surface. [1] Hapke, B.W. (1993) Theory of Reflectance and Emittance Spectroscopy, Cambridge Univ. Press. [2] Schoenberg (1925) Ada. Soc. Febb., vol. 50. [3] Hillier et al. (1999) Icarus 141, 205-225. [4] McEwen (1991) Icarus 92, 298-311. [5] Lucey et al. (2000) JGR, v105, no E8, p20377-20386.

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.

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.

Single pulse two-photon fluorescence lifetime imaging (SP-FLIM) with MHz pixel rate and an all fiber based setup

NASA Astrophysics Data System (ADS)

Eibl, Matthias; Karpf, Sebastian; Hakert, Hubertus; Weng, Daniel; Pfeiffer, Tom; Kolb, Jan Philip; Huber, Robert

2017-07-01

Newly developed microscopy methods have the goal to give researches in bio-molecular science a better understanding of processes ongoing on a cellular level. Especially two-photon excited fluorescence (TPEF) microscopy is a readily applied and widespread modality. Compared to one photon fluorescence imaging, it is possible to image not only the surface but also deeper lying structures. Together with fluorescence lifetime imaging (FLIM), which provides information on the chemical composition of a specimen, deeper insights on a molecular level can be gained. However, the need for elaborate light sources for TPEF and speed limitations for FLIM hinder an even wider application. In this contribution, we present a way to overcome this limitations by combining a robust and inexpensive fiber laser for nonlinear excitation with a fast analog digitization method for rapid FLIM imaging. The applied sub nanosecond pulsed laser source is perfectly suited for fiber delivery as typically limiting non-linear effects like self-phase or cross-phase modulation (SPM, XPM) are negligible. Furthermore, compared to the typically applied femtosecond pulses, our longer pulses produce much more fluorescence photons per single shot. In this paper, we show that this higher number of fluorescence photons per pulse combined with a high analog bandwidth detection makes it possible to not only use a single pulse per pixel for TPEF imaging but also to resolve the exponential time decay for FLIM. To evaluate our system, we acquired FLIM images of a dye solution with single exponential behavior to assess the accuracy of our lifetime determination and also FLIM images of a plant stem at a pixel rate of 1 MHz to show the speed performance of our single pulse two-photon FLIM (SP-FLIM) system.

A time series analysis performed on a 25-year period of kidney transplantation activity in a single center.

PubMed

Santori, G; Fontana, I; Bertocchi, M; Gasloli, G; Valente, U

2010-05-01

Following the example of many Western countries, where a "minimum volume rule" policy has been adopted as a quality parameter for complex surgical procedures, the Italian National Transplant Centre set the minimum number of kidney transplantation procedures/y at 30/center. The number of procedures performed in a single center over a large period may be treated as a time series to evaluate trends, seasonal cycles, and nonsystematic fluctuations. Between January 1, 1983, and December 31, 2007, we performed 1376 procedures in adult or pediatric recipients from living or cadaveric donors. The greatest numbers of cases/y were performed in 1998 (n = 86) followed by 2004 (n = 82), 1996 (n = 75), and 2003 (n = 73). A time series analysis performed using R Statistical Software (Foundation for Statistical Computing, Vienna, Austria), a free software environment for statistical computing and graphics, showed a whole incremental trend after exponential smoothing as well as after seasonal decomposition. However, starting from 2005, we observed a decreased trend in the series. The number of kidney transplants expected to be performed for 2008 by using the Holt-Winters exponential smoothing applied to the period 1983 to 2007 suggested 58 procedures, while in that year there were 52. The time series approach may be helpful to establish a minimum volume/y at a single-center level. Copyright (c) 2010 Elsevier Inc. All rights reserved.