Illustrating the Central Limit Theorem
ERIC Educational Resources Information Center
Corcoran, Mimi
2016-01-01
Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…
Illustrating the Central Limit Theorem
ERIC Educational Resources Information Center
Corcoran, Mimi
2016-01-01
Statistics is enjoying some well-deserved limelight across mathematics curricula of late. Some statistical concepts, however, are not especially intuitive, and students struggle to comprehend and apply them. As an AP Statistics teacher, the author appreciates the central limit theorem as a foundational concept that plays a crucial role in…
Visualizing the Central Limit Theorem through Simulation
ERIC Educational Resources Information Center
Ruggieri, Eric
2016-01-01
The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…
Visualizing the Central Limit Theorem through Simulation
ERIC Educational Resources Information Center
Ruggieri, Eric
2016-01-01
The Central Limit Theorem is one of the most important concepts taught in an introductory statistics course, however, it may be the least understood by students. Sure, students can plug numbers into a formula and solve problems, but conceptually, do they really understand what the Central Limit Theorem is saying? This paper describes a simulation…
"Dealing" with the Central Limit Theorem
ERIC Educational Resources Information Center
Matz, David C.; Hause, Emily L.
2008-01-01
We describe an easy-to-employ, hands-on demonstration using playing cards to illustrate the central limit theorem. This activity allows students to see how a collection of sample means drawn from a nonnormally distributed population will be normally distributed. Students who took part in the demonstration reported it to be helpful in understanding…
Illustrating the Central Limit Theorem through Microsoft Excel Simulations
ERIC Educational Resources Information Center
Moen, David H.; Powell, John E.
2005-01-01
Using Microsoft Excel, several interactive, computerized learning modules are developed to demonstrate the Central Limit Theorem. These modules are used in the classroom to enhance the comprehension of this theorem. The Central Limit Theorem is a very important theorem in statistics, and yet because it is not intuitively obvious, statistics…
Central limit theorems under special relativity.
McKeague, Ian W
2015-04-01
Several relativistic extensions of the Maxwell-Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior.
Central limit theorems under special relativity
McKeague, Ian W.
2015-01-01
Several relativistic extensions of the Maxwell–Boltzmann distribution have been proposed, but they do not explain observed lognormal tail-behavior in the flux distribution of various astrophysical sources. Motivated by this question, extensions of classical central limit theorems are developed under the conditions of special relativity. The results are related to CLTs on locally compact Lie groups developed by Wehn, Stroock and Varadhan, but in this special case the asymptotic distribution has an explicit form that is readily seen to exhibit lognormal tail behavior. PMID:25798020
Central limit theorem: the cornerstone of modern statistics
2017-01-01
According to the central limit theorem, the means of a random sample of size, n, from a population with mean, µ, and variance, σ2, distribute normally with mean, µ, and variance, σ2n. Using the central limit theorem, a variety of parametric tests have been developed under assumptions about the parameters that determine the population probability distribution. Compared to non-parametric tests, which do not require any assumptions about the population probability distribution, parametric tests produce more accurate and precise estimates with higher statistical powers. However, many medical researchers use parametric tests to present their data without knowledge of the contribution of the central limit theorem to the development of such tests. Thus, this review presents the basic concepts of the central limit theorem and its role in binomial distributions and the Student's t-test, and provides an example of the sampling distributions of small populations. A proof of the central limit theorem is also described with the mathematical concepts required for its near-complete understanding. PMID:28367284
Improving Conceptions in Analytical Chemistry: The Central Limit Theorem
ERIC Educational Resources Information Center
Rodriguez-Lopez, Margarita; Carrasquillo, Arnaldo, Jr.
2006-01-01
This article describes the central limit theorem (CLT) and its relation to analytical chemistry. The pedagogic rational, which argues for teaching the CLT in the analytical chemistry classroom, is discussed. Some analytical chemistry concepts that could be improved through an understanding of the CLT are also described. (Contains 2 figures.)
Understanding the Sampling Distribution and the Central Limit Theorem.
ERIC Educational Resources Information Center
Lewis, Charla P.
The sampling distribution is a common source of misuse and misunderstanding in the study of statistics. The sampling distribution, underlying distribution, and the Central Limit Theorem are all interconnected in defining and explaining the proper use of the sampling distribution of various statistics. The sampling distribution of a statistic is…
Central limit theorems for percolation models
NASA Astrophysics Data System (ADS)
Cox, J. Theodore; Grimmett, Geoffrey
1981-06-01
Let p ≠ 1/2 be the open-bond probability in Broadbent and Hammersley's percolation model on the square lattice. Let W x be the cluster of sites connected to x by open paths, and let γ(n) be any sequence of circuits with interiors|γ limits^ circ (n)| to infty . It is shown that for certain sequences of functions { f n },S_n = sum _{x in γ limits^ circ (n)} f_n (W_x ) converges in distribution to the standard normal law when properly normalized. This result answers a problem posed by Kunz and Souillard, proving that the number S n of sites inside γ(n) which are connected by open paths to γ(n) is approximately normal for large circuits γ(n).
Entropy Inequalities for Stable Densities and Strengthened Central Limit Theorems
NASA Astrophysics Data System (ADS)
Toscani, Giuseppe
2016-10-01
We consider the central limit theorem for stable laws in the case of the standardized sum of independent and identically distributed random variables with regular probability density function. By showing decay of different entropy functionals along the sequence we prove convergence with explicit rate in various norms to a Lévy centered density of parameter λ >1 . This introduces a new information-theoretic approach to the central limit theorem for stable laws, in which the main argument is shown to be the relative fractional Fisher information, recently introduced in Toscani (Ricerche Mat 65(1):71-91, 2016). In particular, it is proven that, with respect to the relative fractional Fisher information, the Lévy density satisfies an analogous of the logarithmic Sobolev inequality, which allows to pass from the monotonicity and decay to zero of the relative fractional Fisher information in the standardized sum to the decay to zero in relative entropy with an explicit decay rate.
Central Limit Theorem: New SOCR Applet and Demonstration Activity.
Dinov, Ivo D; Christou, Nicolas; Sanchez, Juana
2008-07-01
Modern approaches for information technology based blended education utilize a variety of novel instructional, computational and network resources. Such attempts employ technology to deliver integrated, dynamically linked, interactive content and multifaceted learning environments, which may facilitate student comprehension and information retention. In this manuscript, we describe one such innovative effort of using technological tools for improving student motivation and learning of the theory, practice and usability of the Central Limit Theorem (CLT) in probability and statistics courses. Our approach is based on harnessing the computational libraries developed by the Statistics Online Computational Resource (SOCR) to design a new interactive Java applet and a corresponding demonstration activity that illustrate the meaning and the power of the CLT. The CLT applet and activity have clear common goals; to provide graphical representation of the CLT, to improve student intuition, and to empirically validate and establish the limits of the CLT. The SOCR CLT activity consists of four experiments that demonstrate the assumptions, meaning and implications of the CLT and ties these to specific hands-on simulations. We include a number of examples illustrating the theory and applications of the CLT. Both the SOCR CLT applet and activity are freely available online to the community to test, validate and extend (Applet: http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and Activity: http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials_Activities_GeneralCentralLimitTheorem).
Using Computers To Teach the Concepts of the Central Limit Theorem.
ERIC Educational Resources Information Center
Mittag, Kathleen Cage
A pivotal theorem which is of critical importance to statistical inference in probability and statistics is the Central Limit Theorem (CLT). The theorem concerns the sampling distribution of random samples taken from a population, including population distributions that do not have to be normal distributions. This paper contains a brief history of…
Planetary Accretion, Oxygen Isotopes and the Central Limit Theorem
NASA Technical Reports Server (NTRS)
Nuth, Joseph A., III; Hill, Hugh G. M.; Vondrak, Richard R. (Technical Monitor)
2001-01-01
The accumulation of presolar dust into increasingly larger aggregates (CAIs and Chondrules, Asteroids, Planets) should result in a very drastic reduction in the numerical spread in oxygen isotopic composition between bodies of similar size, in accord with the Central Limit Theorem. Observed variations in oxygen isotopic composition are many orders of magnitude larger than would be predicted by a simple, random accumulation model that begins in a well-mixed nebula - no matter which size-scale objects are used as the beginning or end points of the calculation. This discrepancy implies either that some as yet unspecified process acted on the solids in the Solar Nebula to increase the spread in oxygen isotopic composition during each and every stage of accumulation or that the nebula was heterogeneous and maintained this heterogeneity throughout most of nebular history. Large-scale nebular heterogeneity would have significant consequences for many areas of cosmochemistry, including the application of some well-known isotopic systems to the dating of nebular events or the prediction of bulk compositions of planetary bodies on the basis of a uniform cosmic abundance.
models are called conditionally linear processes, and the description of the correlator output requires a central limit theorem for sums of dependent...random variables. The conditions for the central limit theorem are related to physically reasonable conditions on the model. The results of the study
Central limit theorems and suppression of anomalous diffusion for systems with symmetry
NASA Astrophysics Data System (ADS)
Gottwald, Georg A.; Melbourne, Ian
2016-10-01
We give general conditions for the central limit theorem and weak convergence to Brownian motion (the weak invariance principle/functional central limit theorem) to hold for observables of compact group extensions of nonuniformly expanding maps. In particular, our results include situations where the central limit theorem would fail, and anomalous behaviour would prevail, if the compact group were not present. This has important consequences for systems with noncompact Euclidean symmetry and provides the rigorous proof for a conjecture made in our paper: a Huygens principle for diffusion and anomalous diffusion in spatially extended systems. Gottwald and Melbourne (2013 Proc. Natl Acad. Sci. USA 110 8411-6).
Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices
NASA Astrophysics Data System (ADS)
Benaych-Georges, Florent; Guionnet, Alice; Male, Camille
2014-07-01
We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.
Central limit theorem and related results for the elephant random walk
NASA Astrophysics Data System (ADS)
Coletti, Cristian F.; Gava, Renato; Schütz, Gunter M.
2017-05-01
We study the so-called elephant random walk (ERW) which is a non-Markovian discrete-time random walk on ℤ with unbounded memory which exhibits a phase transition from a diffusive to superdiffusive behavior. We prove a law of large numbers and a central limit theorem. Remarkably the central limit theorem applies not only to the diffusive regime but also to the phase transition point which is superdiffusive. Inside the superdiffusive regime, the ERW converges to a non-degenerate random variable which is not normal. We also obtain explicit expressions for the correlations of increments of the ERW.
The Power of Doing: A Learning Exercise That Brings the Central Limit Theorem to Life
ERIC Educational Resources Information Center
Price, Barbara A.; Zhang, Xiaolong
2007-01-01
This article demonstrates an active learning technique for teaching the Central Limit Theorem (CLT) in an introductory undergraduate business statistics class. Groups of students carry out one of two experiments in the lab, tossing a die in sets of 5 rolls or tossing a die in sets of 10 rolls. They are asked to calculate the sample average of each…
NASA Astrophysics Data System (ADS)
Biskup, M.; Salvi, M.; Wolff, T.
2014-06-01
Given a resistor network on with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the minimum of the Dirichlet energy over functions with the prescribed boundary values. For shift-ergodic conductances, linear (Dirichlet) boundary conditions and square boxes, the effective conductance scaled by the volume of the box converges to a deterministic limit as the box-size tends to infinity. Here we prove that, for i.i.d. conductances with a small ellipticity contrast, also a (non-degenerate) central limit theorem holds. The proof is based on the corrector method and the Martingale Central Limit Theorem; a key integrability condition is furnished by the Meyers estimate. More general domains, boundary conditions and ellipticity contrasts will be addressed in a subsequent paper.
A Central Limit Theorem for Random Walks on the Dual of a Compact Grassmannian
NASA Astrophysics Data System (ADS)
Rösler, Margit; Voit, Michael
2015-02-01
We consider compact Grassmann manifolds G/K over the real, complex or quaternionic numbers whose spherical functions are Heckman-Opdam polynomials of type BC. From an explicit integral representation of these polynomials we deduce a sharp Mehler-Heine formula, that is an approximation of the Heckman-Opdam polynomials in terms of Bessel functions, with a precise estimate on the error term. This result is used to derive a central limit theorem for random walks on the semi-lattice parametrizing the dual of G/K, which are constructed by successive decompositions of tensor powers of spherical representations of G. The limit is the distribution of a Laguerre ensemble in random matrix theory. Most results of this paper are established for a larger continuous set of multiplicity parameters beyond the group cases.
Sanov and central limit theorems for output statistics of quantum Markov chains
Horssen, Merlijn van; Guţă, Mădălin
2015-02-15
In this paper, we consider the statistics of repeated measurements on the output of a quantum Markov chain. We establish a large deviations result analogous to Sanov’s theorem for the multi-site empirical measure associated to finite sequences of consecutive outcomes of a classical stochastic process. Our result relies on the construction of an extended quantum transition operator (which keeps track of previous outcomes) in terms of which we compute moment generating functions, and whose spectral radius is related to the large deviations rate function. As a corollary to this, we obtain a central limit theorem for the empirical measure. Such higher level statistics may be used to uncover critical behaviour such as dynamical phase transitions, which are not captured by lower level statistics such as the sample mean. As a step in this direction, we give an example of a finite system whose level-1 (empirical mean) rate function is independent of a model parameter while the level-2 (empirical measure) rate is not.
Practical issues in decoy-state quantum key distribution based on the central limit theorem
NASA Astrophysics Data System (ADS)
Trushechkin, A. S.; Kiktenko, E. O.; Fedorov, A. K.
2017-08-01
Decoy-state quantum key distribution (QKD) is a standard tool for long-distance quantum communications. An important issue in this field is processing the decoy-state statistics taking into account statistical fluctuations (or "finite-key effects"). In this work, we propose and analyze an option for decoy statistics processing, which is based on the central limit theorem. We discuss such practical issues as inclusion of the failure probability of the decoy-state statistical estimates in the total failure probability of a QKD protocol and also taking into account the deviations of the binomially distributed random variables used in the estimations from the Gaussian distribution. The results of numerical simulations show that the obtained estimations are quite tight. The proposed technique can be used as a part of post-processing procedures for industrial quantum key distribution systems.
The Star Forming Main Sequence and its Scatter as Conequences of the Central Limit Theorem
NASA Astrophysics Data System (ADS)
Kelson, Daniel
2015-01-01
Star formation rates of disk galaxies strongly correlate with stellar mass, with a small dispersion in specific star formation rate at fixed mass. With such small scattter this main sequence of star formation has been interpreted as deterministic and fundamental. Here it is demonstrated that it is a simple consequence off he central limit theorem. Treating the star formation histories of galaxies as integrable, non-differentiable functions, where stochastic changes in star formation rate in a galaxy's history are not fully independent of each other, we derive the median specific star formation rate for the flat part of the main sequence from 0
Does the central limit theorem always apply to phase noise? Some implications for radar problems
NASA Astrophysics Data System (ADS)
Gray, John E.; Addison, Stephen R.
2017-05-01
The phase noise problem or Rayleigh problem occurs in all aspects of radar. It is an effect that a radar engineer or physicist always has to take into account as part of a design or in attempt to characterize the physics of a problem such as reverberation. Normally, the mathematical difficulties of phase noise characterization are avoided by assuming the phase noise probability distribution function (PDF) is uniformly distributed, and the Central Limit Theorem (CLT) is invoked to argue that the superposition of relatively few random components obey the CLT and hence the superposition can be treated as a normal distribution. By formalizing the characterization of phase noise (see Gray and Alouani) for an individual random variable, the summation of identically distributed random variables is the product of multiple characteristic functions (CF). The product of the CFs for phase noise has a CF that can be analyzed to understand the limitations CLT when applied to phase noise. We mirror Kolmogorov's original proof as discussed in Papoulis to show the CLT can break down for receivers that gather limited amounts of data as well as the circumstances under which it can fail for certain phase noise distributions. We then discuss the consequences of this for matched filter design as well the implications for some physics problems.
ERIC Educational Resources Information Center
Yu, Chong Ho; And Others
Central limit theorem (CLT) is considered an important topic in statistics, because it serves as the basis for subsequent learning in other crucial concepts such as hypothesis testing and power analysis. There is an increasing popularity in using dynamic computer software for illustrating CLT. Graphical displays do not necessarily clear up…
Salgado-García, R; Maldonado, Cesar
2013-12-01
We study the diffusion of an ensemble of overdamped particles sliding over a tilted random potential (produced by the interaction of a particle with a random polymer) with long-range correlations. We found that the diffusion properties of such a system are closely related to the correlation function of the corresponding potential. We model the substrate as a symbolic trajectory of a shift space which enables us to obtain a general formula for the diffusion coefficient when normal diffusion occurs. The total time that the particle takes to travel through n monomers can be seen as an ergodic sum to which we can apply the central limit theorem. The latter can be implemented if the correlations decay fast enough in order for the central limit theorem to be valid. On the other hand, we presume that when the central limit theorem breaks down the system give rise to anomalous diffusion. We give two examples exhibiting a transition from normal to anomalous diffusion due to this mechanism. We also give analytical expressions for the diffusion exponents in both cases by assuming convergence to a stable law. Finally we test our predictions by means of numerical simulations.
ERIC Educational Resources Information Center
Moen, David H.; Powell, John E.
2008-01-01
Using Microsoft® Excel, several interactive, computerized learning modules are developed to illustrate the Central Limit Theorem's appropriateness for comparing the difference between the means of any two populations. These modules are used in the classroom to enhance the comprehension of this theorem as well as the concepts that provide the…
Höpfner, Reinhard; Brodda, Klaus
2006-04-01
The paper deals with information transmission in large systems of neurons. We model the membrane potential in a single neuron belonging to a cell tissue by a non time-homogeneous Cox-Ingersoll-Ross type diffusion; in terms of its time-varying expectation, this stochastic process can convey deterministic signals. We model the spike train emitted by this neuron as a Poisson point process compensated by the occupation time of the membrane potential process beyond the excitation threshold. In a large system of neurons 1 < or = i < or = N processing independently the same deterministic signal, we prove a functional central limit theorem for the pooled spike train collected from the N neurons. This pooled spike train allows to recover the deterministic signal, up to some shape transformation which is explicit.
STOCHASTIC POINT PROCESSES: LIMIT THEOREMS.
A stochastic point process in R(n) is a triple (M,B,P) where M is the class of all countable sets in R(n) having no limit points, B is the smallest...converge to a mixture of Poisson processes. These results are established via a generalization of a classical limit theorem for Bernoulli trials. (Author)
ERIC Educational Resources Information Center
See, Lai-Chu; Huang, Yu-Hsun; Chang, Yi-Hu; Chiu, Yeo-Ju; Chen, Yi-Fen; Napper, Vicki S.
2010-01-01
This study examines the timing using computer-enriched instruction (CEI), before or after a traditional lecture to determine cross-over effect, period effect, and learning effect arising from sequencing of instruction. A 2 x 2 cross-over design was used with CEI to teach central limit theorem (CLT). Two sequences of graduate students in nursing…
ERIC Educational Resources Information Center
Lunsford, M. Leigh; Rowell, Ginger Holmes; Goodson-Espy, Tracy
2006-01-01
We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we…
Kim, Seonjin; Zhao, Zhibiao; Shao, Xiaofeng
2015-01-01
This paper is concerned with the inference of nonparametric mean function in a time series context. The commonly used kernel smoothing estimate is asymptotically normal and the traditional inference procedure then consistently estimates the asymptotic variance function and relies upon normal approximation. Consistent estimation of the asymptotic variance function involves another level of nonparametric smoothing. In practice, the choice of the extra bandwidth parameter can be difficult, the inference results can be sensitive to bandwidth selection and the normal approximation can be quite unsatisfactory in small samples leading to poor coverage. To alleviate the problem, we propose to extend the recently developed self-normalized approach, which is a bandwidth free inference procedure developed for parametric inference, to construct point-wise confidence interval for nonparametric mean function. To justify asymptotic validity of the self-normalized approach, we establish a functional central limit theorem for recursive nonparametric mean regression function estimates under primitive conditions and show that the limiting process is a Gaussian process with non-stationary and dependent increments. The superior finite sample performance of the new approach is demonstrated through simulation studies.
Central limit theorem for the solution to the heat equation with moving time
NASA Astrophysics Data System (ADS)
Liu, Junfeng; Tudor, Ciprian A.
2016-03-01
We consider the solution to the stochastic heat equation driven by the time-space white noise and study the asymptotic behavior of its spatial quadratic variations with “moving time”, meaning that the time variable is not fixed and its values are allowed to be very big or very small. We investigate the limit distribution of these variations via Malliavin calculus.
Generalised Central Limit Theorems for Growth Rate Distribution of Complex Systems
NASA Astrophysics Data System (ADS)
Takayasu, Misako; Watanabe, Hayafumi; Takayasu, Hideki
2014-04-01
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling properties and distributions reported for growth rates of complex systems in a variety of fields can be derived from this basic physical model. Statistical data of growth rates for about 1 million business firms are analysed as a real-world example of randomly growing systems. Not only are the scaling relations consistent with the theoretical solution, but the entire functional form of the growth rate distribution is fitted with a theoretical distribution that has a power-law tail.
Strong Large Deviation and Local Limit Theorems
1989-08-01
Strong Large Deviation and Local Limit Theorenisi by (D -N araitia Rao Chaganty and Jayaraii Setrhurainari ____Old DoiinUnitnerity and Florida State...deviations, Local Limit Theorems. El L ,CT OCQT23 1989 u2 ’JB 169 Abstract M os t laCd~viaio re11 t ; asym~1O 5 Iptotic expressions to log P( In > ! y...ji(S) < xandl let b",-*x Define q,,(y,; b, S) = V(b,,/p(S)) P(?),(!I, - Y) E S)]. as the pseudo-density futnction of I- . By a local limit theorem
NASA Astrophysics Data System (ADS)
Sadel, Christian; Virág, Bálint
2016-05-01
We consider products of random matrices that are small, independent identically distributed perturbations of a fixed matrix T_0. Focusing on the eigenvalues of T_0 of a particular size we obtain a limit to a SDE in a critical scaling. Previous results required T_0 to be a (conjugated) unitary matrix so it could not have eigenvalues of different modulus. From the result we can also obtain a limit SDE for the Markov process given by the action of the random products on the flag manifold. Applying the result to random Schrödinger operators we can improve some results by Valko and Virag showing GOE statistics for the rescaled eigenvalue process of a sequence of Anderson models on long boxes. In particular, we solve a problem posed in their work.
Pérez-Rodríguez, Fernando; Zwietering, Marcel H
2012-02-15
The Central Limit Theorem (CLT) is proposed as a means of understanding microbial risk in foods from a Public Health perspective. One variant of the CLT states that as the number of random variables, each with a finite mean and variance, increases (→∞), the distribution of the sum (or mean) of those variables approximates a normal distribution. On the basis of the CLT, the hypothesis introduced by this paper states that the Coefficient of Variation (CV) of the annual number of food-borne illness cases decreases as a result of a larger number of exposures (or servings) (n). Second-order Monte-Carlo analysis and classical statistics were used to support the hypothesis, based on existing risk models on Listeria monocytogenes in deli meat products focused on elderly people in the United States. Likewise, the hypothesis was tested on epidemiological data of annual incidence of salmonellosis and listeriosis in different countries (i.e. different n). Although different sources of error affected the accuracy of the results, both the Monte-Carlo analysis (in silico) and epidemiological data (in vivo), especially for salmonellosis, demonstrated that the CV of the annual number of cases decreased as n increased as stated by the CLT. Furthermore, results from this work showed that classical statistical methods can be helpful to provide reliable risk estimates based on simple and well-established statistical principles.
Temporal Distributional Limit Theorems for Dynamical Systems
NASA Astrophysics Data System (ADS)
Dolgopyat, Dmitry; Sarig, Omri
2017-02-01
Suppose {T^t} is a Borel flow on a complete separable metric space X, f:X→ R is Borel, and xin X. A temporal distributional limit theorem is a scaling limit for the distributions of the random variables X_T:=int _0^t f(T^s x)ds, where t is chosen randomly uniformly from [0, T], x is fixed, and T→ ∞. We discuss such laws for irrational rotations, Anosov flows, and horocycle flows.
On a Limit Theorem and Invariance Principle for Symmetric Statistics.
1986-07-01
A177 292 ON A LIMIT THEOREM AND INVARIANCE PRINCIPLE FOR / SYMMETRIC STATISTICS .(U) NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROC...TI TLE (Include SeCUPntY Claaftceaon, .12F20 "On a limit theorem and invariance princinle ior symmetricls- j 12. PERSONAL AUTHI4O( M.andrekar, V. 13...University of North Carolina Chapel Hill, North Carolina ON A LIMIT THEOREM AND INVARIANCE PRINCIPLE FOR SYMMIETRIC STATISTICS Approved for public release
Some functional limit theorems for compound Cox processes
Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.
2016-06-08
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
Some functional limit theorems for compound Cox processes
NASA Astrophysics Data System (ADS)
Korolev, Victor Yu.; Chertok, A. V.; Korchagin, A. Yu.; Kossova, E. V.; Zeifman, Alexander I.
2016-06-01
An improved version of the functional limit theorem is proved establishing weak convergence of random walks generated by compound doubly stochastic Poisson processes (compound Cox processes) to Lévy processes in the Skorokhod space under more realistic moment conditions. As corollaries, theorems are proved on convergence of random walks with jumps having finite variances to Lévy processes with variance-mean mixed normal distributions, in particular, to stable Lévy processes.
Nonlinear Extensions of a Limit Theorem,
n) such that the distribution of (V(xn)-alpha n)/beta n converges weakly to a limit G and to evaluate this limit . Sufficient conditions are presented...that ensure the existence of the limit G, and it is shown that G is simply related to F. To illustrate the variety of limit laws that can arise, several examples are considered. (Author)
TOW PROBABILITY LIMIT THEOREMS AND AN APPLICATION,
A necessary and sufficient condition that the limit distribution of a log-normal random variable be normal as the mean becomes large is presented. A...Trotter’s, is given for the limit normality, without assuming moments, for a class of distributions depending on a continuous parameter that tends to
ERIC Educational Resources Information Center
Gkioulekas, Eleftherios
2013-01-01
Many limits, typically taught as examples of applying the "squeeze" theorem, can be evaluated more easily using the proposed zero-bounded limit theorem. The theorem applies to functions defined as a product of a factor going to zero and a factor that remains bounded in some neighborhood of the limit. This technique is immensely useful…
Mixing rates and limit theorems for random intermittent maps
NASA Astrophysics Data System (ADS)
Bahsoun, Wael; Bose, Christopher
2016-04-01
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps {{T}α} using the full parameter range 0<α <∞ , in general. We derive a number of results around a common theme that illustrates in detail how the constituent map that is fastest mixing (i.e. smallest α) combined with details of the randomizing process, determines the asymptotic properties of the random transformation. Our key result (theorem 1.1) establishes sharp estimates on the position of return time intervals for the quenched dynamics. The main applications of this estimate are to limit laws (in particular, CLT and stable laws, depending on the parameters chosen in the range 0<α <1 ) for the associated skew product; these are detailed in theorem 3.2. Since our estimates in theorem 1.1 also hold for 1≤slant α <∞ we study a second class of random transformations derived from piecewise affine Gaspard-Wang maps, prove existence of an infinite (σ-finite) invariant measure and study the corresponding correlation asymptotics. To the best of our knowledge, this latter kind of result is completely new in the setting of random transformations.
A pointwise limit theorem for filtered backprojection in computed tomography.
Ye, Yangbo; Zhu, Jiehua; Wang, Ge
2003-05-01
Computed tomography (CT) is one of the most important areas in the modern science and technology. The most popular approach for image reconstruction is filtered backprojection. It is essential to understand the limit behavior of the filtered backprojection algorithms. The classic results on the limit of image reconstruction are typically done in the norm sense. In this paper, we use the method of limited bandwidth to handle filtered backprojection-based image reconstruction when the spectrum of an underlying image is not absolutely integrable. Our main contribution is, assuming the method of limited bandwidth, to prove a pointwise limit theorem for a class of functions practically relevant and quite general. Further work is underway to extend the theory and explore its practical applications.
On a new proof of the Lindeberg-Feller classical limit theorem
NASA Astrophysics Data System (ADS)
Formanov, Shakir Kasimovich; Akanbay, Nursadyk; Akhmedov, Askar Bekenovich
2015-09-01
In recent papers researchers describe some of the new types of properties characterization of the normal distribution. This paper gives a new one based on the characterization of these properties, the proof of the classical limit theorem Lindeberg-Feller.
Uniform Limit Theorems for Synchronous Processes with Applications to Queues
1989-10-01
first moment. In the present paper we investi gate conditions under which the Cesaro averaged functionals ;(f) 1- jfoE((6,X))dj converge uniformly...Proposition 3.1 both apply to positive HRMP’s. So, for example, given any initial state Z 0 = :, it follows that the Cesaro averaged measures (A) 1! 7foEIA o...collection of measures (see Theorem 2.1 of [41)). Continuing in the spirit of Cesaro convergence we have Proposition 4.1. If Z is a positive HRMP with
The Implicit Function Theorem and Non-Existence of Limit of Functions of Several Variables
ERIC Educational Resources Information Center
dos Santos, A. L. C.; da Silva, P. N.
2008-01-01
We use the Implicit Function Theorem to establish a result of non-existence of limit to a certain class of functions of several variables. We consider functions given by quotients such that both the numerator and denominator functions are null at the limit point. We show that the non-existence of the limit of such function is related with the…
The Implicit Function Theorem and Non-Existence of Limit of Functions of Several Variables
ERIC Educational Resources Information Center
dos Santos, A. L. C.; da Silva, P. N.
2008-01-01
We use the Implicit Function Theorem to establish a result of non-existence of limit to a certain class of functions of several variables. We consider functions given by quotients such that both the numerator and denominator functions are null at the limit point. We show that the non-existence of the limit of such function is related with the…
Limit theorems for Lévy walks in d dimensions: rare and bulk fluctuations
NASA Astrophysics Data System (ADS)
Fouxon, Itzhak; Denisov, Sergey; Zaburdaev, Vasily; Barkai, Eli
2017-04-01
We consider super-diffusive Lévy walks in d≥slant 2 dimensions when the duration of a single step, i.e. a ballistic motion performed by a walker, is governed by a power-law tailed distribution of infinite variance and finite mean. We demonstrate that the probability density function (PDF) of the coordinate of the random walker has two different scaling limits at large times. One limit describes the bulk of the PDF. It is the d-dimensional generalization of the one-dimensional Lévy distribution and is the counterpart of the central limit theorem (CLT) for random walks with finite dispersion. In contrast with the one-dimensional Lévy distribution and the CLT this distribution does not have a universal shape. The PDF reflects anisotropy of the single-step statistics however large the time is. The other scaling limit, the so-called ‘infinite density’, describes the tail of the PDF which determines second (dispersion) and higher moments of the PDF. This limit repeats the angular structure of the PDF of velocity in one step. A typical realization of the walk consists of anomalous diffusive motion (described by anisotropic d-dimensional Lévy distribution) interspersed with long ballistic flights (described by infinite density). The long flights are rare but due to them the coordinate increases so much that their contribution determines the dispersion. We illustrate the concept by considering two types of Lévy walks, with isotropic and anisotropic distributions of velocities. Furthermore, we show that for isotropic but otherwise arbitrary velocity distributions the d-dimensional process can be reduced to a one-dimensional Lévy walk. We briefly discuss the consequences of non-universality for the d > 1 dimensional fractional diffusion equation, in particular the non-uniqueness of the fractional Laplacian.
Abdellah, Marwan; Abdallah, Mohamed; Alzanati, Mohamed; Eldeib, Ayman
2016-08-01
Digitally reconstructed radiographs (DRRs) play a significant role in modern clinical radiation therapy. They are used to verify patient alignments during image guided therapies with 2D-3D image registration. The generation of DRRs can be implemented intuitively in O(N3) relying on direct volume rendering (DVR) methods, such as ray marching. This complexity imposes certain limitations on the rendering performance if high quality DRR images are needed. Those DRRs can be alternatively generated in the k-space using the central slice theorem in O(N2logN). Several rendering pipelines have been designed to create the DRRs in the k-space, but they were either limited to specific vendor or entail particular software requirements. We present a high performance implementation of a k-space-based DRR generation pipeline that is executable on various heterogeneous computing architectures using OpenCL. Our implementation generates a DRR for a 5123 CT volume in 6, 2.7 and 0.68 milli-seconds on a commodity CPU, mid-range and high-end GPUs respectively.
A rigorous proof of the Bohr-van Leeuwen theorem in the semiclassical limit
NASA Astrophysics Data System (ADS)
Savoie, Baptiste
2015-10-01
The original formulation of the Bohr-van Leeuwen (BvL) theorem states that, in a uniform magnetic field and in thermal equilibrium, the magnetization of an electron gas in the classical Drude-Lorentz model vanishes identically. This stems from classical statistics which assign the canonical momenta all values ranging from -∞ to ∞ that makes the free energy density magnetic-field-independent. When considering a classical (Maxwell-Boltzmann) interacting electron gas, it is usually admitted that the BvL theorem holds upon condition that the potentials modeling the interactions are particle-velocities-independent and do not cause the system to rotate after turning on the magnetic field. From a rigorous viewpoint, when treating large macroscopic systems, one expects the BvL theorem to hold provided the thermodynamic limit of the free energy density exists (and the equivalence of ensemble holds). This requires suitable assumptions on the many-body interactions potential and on the possible external potentials to prevent the system from collapsing or flying apart. Starting from quantum statistical mechanics, the purpose of this paper is to give, within the linear-response theory, a proof of the BvL theorem in the semiclassical limit when considering a dilute electron gas in the canonical conditions subjected to a class of translational invariant external potentials.
Central Limit Theorem: New SOCR Applet and Demonstration Activity
ERIC Educational Resources Information Center
Dinov, Ivo D.; Christou, Nicholas; Sanchez, Juana
2008-01-01
Modern approaches for information technology based blended education utilize a variety of novel instructional, computational and network resources. Such attempts employ technology to deliver integrated, dynamically linked, interactive content and multi-faceted learning environments, which may facilitate student comprehension and information…
Central Limit Theorem: New SOCR Applet and Demonstration Activity
ERIC Educational Resources Information Center
Dinov, Ivo D.; Christou, Nicholas; Sanchez, Juana
2008-01-01
Modern approaches for information technology based blended education utilize a variety of novel instructional, computational and network resources. Such attempts employ technology to deliver integrated, dynamically linked, interactive content and multi-faceted learning environments, which may facilitate student comprehension and information…
Pedagogical Simulation of Sampling Distributions and the Central Limit Theorem
ERIC Educational Resources Information Center
Hagtvedt, Reidar; Jones, Gregory Todd; Jones, Kari
2007-01-01
Students often find the fact that a sample statistic is a random variable very hard to grasp. Even more mysterious is why a sample mean should become ever more Normal as the sample size increases. This simulation tool is meant to illustrate the process, thereby giving students some intuitive grasp of the relationship between a parent population…
Day, Troy
2012-04-07
The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century, there have been remarkable advances in the development of theory for this diversification, and the theory's success rests, in part, on the scope of its applicability. A great deal of this theory focuses on a relatively small subset of the space of potential genotypes, chosen largely based on historical or contemporary patterns, and then predicts the evolutionary dynamics within this pre-defined set. To what extent can such an approach be pushed to a broader perspective that accounts for the potential open-endedness of evolutionary diversification? There have been a number of significant theoretical developments along these lines but the question of how far such theory can be pushed has not been addressed. Here a theorem is proven demonstrating that, because of the digital nature of inheritance, there are inherent limits on the kinds of questions that can be answered using such an approach. In particular, even in extremely simple evolutionary systems, a complete theory accounting for the potential open-endedness of evolution is unattainable unless evolution is progressive. The theorem is closely related to Gödel's incompleteness theorem, and to the halting problem from computability theory.
Day, Troy
2012-01-01
The process of evolutionary diversification unfolds in a vast genotypic space of potential outcomes. During the past century, there have been remarkable advances in the development of theory for this diversification, and the theory's success rests, in part, on the scope of its applicability. A great deal of this theory focuses on a relatively small subset of the space of potential genotypes, chosen largely based on historical or contemporary patterns, and then predicts the evolutionary dynamics within this pre-defined set. To what extent can such an approach be pushed to a broader perspective that accounts for the potential open-endedness of evolutionary diversification? There have been a number of significant theoretical developments along these lines but the question of how far such theory can be pushed has not been addressed. Here a theorem is proven demonstrating that, because of the digital nature of inheritance, there are inherent limits on the kinds of questions that can be answered using such an approach. In particular, even in extremely simple evolutionary systems, a complete theory accounting for the potential open-endedness of evolution is unattainable unless evolution is progressive. The theorem is closely related to Gödel's incompleteness theorem, and to the halting problem from computability theory. PMID:21849390
Limit Theorems for Functionals of Markov Processes and Renormalizable Stable Fields
1993-01-01
g(xl,Yl) ... g(xk,yk), 92(a,x) = g2 (a1, x).. .g 2 (ak,-k) (13) (see Feldman and Rachev , 1993), we restrict our parameter set to functions from the...authors would like to thank Svetlozar Rachev for helpful discussions of stable distributions and processes. We would like to thank Makoto Maejima for...limit theorems for functionals of the Brownian sheet, Annals of Probability, 17, 538-558. Feldman, R.E. and Rachev , S.T. (1993), U-statistics of random
The Central Role of Bayes' Theorem for Joint Estimation of Causal Effects and Propensity Scores.
Zigler, Corwin Matthew
2016-03-31
Although propensity scores have been central to the estimation of causal effects for over 30 years, only recently has the statistical literature begun to consider in detail methods for Bayesian estimation of propensity scores and causal effects. Underlying this recent body of literature on Bayesian propensity score estimation is an implicit discordance between the goal of the propensity score and the use of Bayes theorem. The propensity score condenses multivariate covariate information into a scalar to allow estimation of causal effects without specifying a model for how each covariate relates to the outcome. Avoiding specification of a detailed model for the outcome response surface is valuable for robust estimation of causal effects, but this strategy is at odds with the use of Bayes theorem, which presupposes a full probability model for the observed data that adheres to the likelihood principle. The goal of this paper is to explicate this fundamental feature of Bayesian estimation of causal effects with propensity scores in order to provide context for the existing literature and for future work on this important topic.
Guseinov, Israfil
2003-06-01
By the use of complete orthonormal sets of psi(alpha)-ETOs (alpha=1, 0, m1, m2,...) introduced by the author, new addition theorems are derived for STOs and arbitrary central and noncentral interaction potentials (CIPs and NCIPs). The expansion coefficients in these addition theorems are expressed through the Gaunt and Gegenbauer coefficients. Using the addition theorems obtained for STOs and potentials, general formulae in terms of three-center overlap integrals are established for the multicenter t-electron integrals of CIPs and NCIPs that arise in the solution of the N-electron atomic and molecular problem (2hthN) when a Hylleraas approximation in Hartree-Fock-Roothaan theory is employed. With the help of expansion formulae for translation of STOs, the three-center overlap integrals are expressed through the two-center overlap integrals. The formulae obtained are valid for arbitrary quantum numbers, screening constants and location of orbitals.
Moons, K G; van Es, G A; Deckers, J W; Habbema, J D; Grobbee, D E
1997-01-01
We evaluated the extent to which the sensitivity, specificity, and likelihood ratio of the exercise test to diagnose coronary artery disease vary across subgroups of a certain patient population. Among 295 patients suspected of coronary artery disease, as independently determined by coronary angiography, we assessed variation in sensitivity and specificity according to patient history, physical examination, exercise test results, and disease severity in 207 patients with and 88 patients without coronary artery disease, respectively. The sensitivity varied substantially according to sex (women 30% and men 64%), systolic blood pressure at baseline (53% to 65%), expected workload (50% to 64%), systolic blood pressure at peak exercise (50% to 67%), relative workload (33% to 68%), and number of diseased vessels (39% to 77%). The specificity varied across subgroups of sex (men 89% and women 97%) and relative workload (85% to 98%). The likelihood ratio varied (3.8 to 17.0) across the same patient subgroups, as did the sensitivity. As each population tends to be heterogeneous with respect to patient characteristics, no single level of these parameters can be given that is adequate for all subgroups. Use of these parameters as a basis for calculating diagnostic probabilities in individual patients using Bayes' theorem has serious limitations.
Levine, James A
2016-08-01
The Wearable Technology market may increase fivefold by the end of the decade. There is almost no academic investigation as to what drives the investment hypothesis in wearable technologies. This paper seeks to examine this issue from an evidence-based perspective. There is a fundamental disconnect in how consumers view wearable sensors and how companies market them; this is called The Baetylus Theorem where people believe (falsely) that by buying a wearable sensor they will receive health benefit; data suggest that this is not the case. This idea is grounded social constructs, psychological theories and marketing approaches. A marketing proposal that fails to recognize The Baetylus Theorem and how it can be integrated into a business offering has not optimized its competitive advantage. More importantly, consumers should not falsely believe that purchasing a wearable technology, improves health.
NASA Astrophysics Data System (ADS)
Gheorghe, Munteanu Bogdan; Alexei, Leahu; Sergiu, Cataranciuc
2013-09-01
We prove the limit theorem for life time distribution connected with reliability systems when their life time is a Pascal Convolution of independent and identically distributed random variables. We show that, in some conditions, such distributions may be approximated by means of Erlang distributions. As a consequnce, survival functions for such systems may be, respectively, approximated by Erlang survival functions. By using Monte Carlo method we experimantally confirm the theoretical results of our theorem.
Boëlle, Pierre-Yves; Thomas, Guy
2016-12-01
The rise of bacterial resistance to antibiotics is a major Public Health concern. It is the result of two interacting processes: the selection of resistant bacterial strains under exposure to antibiotics and the dissemination of bacterial strains throughout the population by contact between colonized and uncolonized individuals. To investigate the resulting time evolution of bacterial resistance, Temime et al. (Emerg Infect Dis 9:411-417, 2003) developed a stochastic SIS model, which was structured by the level of resistance of bacterial strains. Here we study the asymptotic properties of this model when the population size is large. To this end, we cast the model within the framework of measure valued processes, using point measures to represent the pattern of bacterial resistance in the compartments of colonized individuals. We first show that the suitably normalized model tends in probability to the solution of a deterministic differential system. Then we prove that the process of fluctuations around this limit tends in law to a Gaussian process in a space of distributions. These results, which generalize those of Kurtz (CBMS-NSF regional conference series in applied mathematics, vol 36. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1981, chap. 8) on SIR models, support the validity of the deterministic approximation and quantify the rate of convergence.
Entropy and the Shannon-McMillan-Breiman Theorem for Beta Random Matrix Ensembles
NASA Astrophysics Data System (ADS)
Bufetov, Alexander; Mkrtchyan, Sevak; Shcherbina, Maria; Soshnikov, Alexander
2013-07-01
We show that beta ensembles in Random Matrix Theory with generic real analytic potential have the asymptotic equipartition property. In addition, we prove a Central Limit Theorem for the density of the eigenvalues of these ensembles.
NASA Astrophysics Data System (ADS)
Wright, James R.
2006-12-01
I present the use of Sherman's Theorem, and a development approach, for optimal solutions to real-time estimation problems that are multidimensional, nonlinear, stochastic, and have random multidimensional forcing function modeling errors that drive the state. Satisfaction of Sherman's Theorem guarantees that the mean-squared state estimate error on each state estimate component is minimized. Sherman's Theorem is not new, but my application of Sherman's Theorem is new. To Malcolm Shuster, who taught me about torque replacement modeling with rate-gyro sensors, and argues fiercely in defense of Maximum Likelihood Estimation (MLE).
Convolution Metrics and Rates of Convergence in the CLT (Central Limit Theorem).
1987-10-01
Carolina IT~ Convolution Metrics and Rates of Convergence in the CLT by O t S.T. Rachev F~C E~ andJA 4it J.E. Yukich Technical Report No. 210 October...and Rates of Convergence in the CLT by *1 S. T. Rachev Center for Stochastic Processes Department of Statitistics University of North Carolina and J.E...heR Thus, each random variable 0 generates a metric pur’ r > 0. When 0 c (B) we will also consider convolution metrics of the form [cf. Rachev and
A Strong Central Limit Theorem for a Class of Random Surfaces
NASA Astrophysics Data System (ADS)
Conlon, Joseph G.; Spencer, Thomas
2014-01-01
This paper is concerned with d = 2 dimensional lattice field models with action , where is a uniformly convex function. The fluctuations of the variable are studied for large | x| via the generating function given by . In two dimensions is proportional to . The main result of this paper is a bound on which is uniform in for a class of convex V. The proof uses integration by parts following Helffer-Sjöstrand and Witten, and relies on estimates of singular integral operators on weighted Hilbert spaces.
Fractional Edgeworth expansion: Corrections to the Gaussian-Lévy central-limit theorem
NASA Astrophysics Data System (ADS)
Hazut, Netanel; Medalion, Shlomi; Kessler, David A.; Barkai, Eli
2015-05-01
In this article we generalize the classical Edgeworth expansion for the probability density function (PDF) of sums of a finite number of symmetric independent identically distributed random variables with a finite variance to PDFs with a diverging variance, which converge to a Lévy α -stable density function. Our correction may be written by means of a series of fractional derivatives of the Lévy and the conjugate Lévy PDFs. This series expansion is general and applies also to the Gaussian regime. To describe the terms in the series expansion, we introduce a new family of special functions and briefly discuss their properties. We implement our generalization to the distribution of the momentum for atoms undergoing Sisyphus cooling, and show the improvement of our leading order approximation compared to previous approximations. In vicinity of the transition between Lévy and Gauss behaviors, convergence to asymptotic results slows down.
Evaluation of an Interactive Tutorial for Teaching the Central Limit Theorem.
ERIC Educational Resources Information Center
Aberson, Christopher L.; Berger, Dale E.; Healy, Michael R.; Kyle, Diana J.; Romero, Victoria L.
2000-01-01
Evaluates an interactive, Web-based tutorial that helps students learn about sampling distribution. 111 students enrolled in statistics or research methods courses used either the tutorial or attended a lecture/demonstration. Indicates through pre- and post-test quizzes both groups learned comparable amounts and reveals students' ratings of both…
ERIC Educational Resources Information Center
Davis, Philip J.
1993-01-01
Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)
ERIC Educational Resources Information Center
Davis, Philip J.
1993-01-01
Argues for a mathematics education that interprets the word "theorem" in a sense that is wide enough to include the visual aspects of mathematical intuition and reasoning. Defines the term "visual theorems" and illustrates the concept using the Marigold of Theodorus. (Author/MDH)
Limit loads for centrally cracked square plates under biaxial tension
NASA Astrophysics Data System (ADS)
Graba, Marcin
2016-12-01
This paper is concerned with the determination of limit loads for centrally cracked square plates subjected to biaxial tension. It briefly discusses the concept of limit loads and some aspects of numerical modelling. It presents results of numerical calculations conducted for two-dimensional (plane strain state and plane stress state) and three-dimensional cases. It also considers the relationship between the limit load and the crack length, the specimen thickness, the yield strength and the biaxial load factor, defined for the purpose of this work. The paper includes approximation formulae to calculate the limit load.
Analytical relation between peripheral and central density limit on FTU
NASA Astrophysics Data System (ADS)
Pucella, G.; D'Arcangelo, O.; Tudisco, O.; Belli, F.; Bin, W.; Botrugno, A.; Buratti, P.; Calabrò, G.; Esposito, B.; Giovannozzi, E.; Marocco, D.; Ramogida, G.; Sattin, F.; Spizzo, G.; Zanca, P.; Zuin, M.
2017-08-01
The commonly adopted scaling for the maximum achievable plasma density in tokamak fusion devices, the so-called ‘Greenwald limit’, refers to the line-averaged density along a central chord and depends only on the average plasma current density. However, the Greenwald limit has been exceeded in tokamak experiments in the case of peaked density profiles, indicating that the edge density is the real parameter responsible for the density limit. Furthermore, the Greenwald limit has been obtained for fixed density profiles, so that the scaling can be very different when introducing density profile dependencies on plasma parameters. Dedicated density limit experiments were performed in recent years on the Frascati Tokamak Upgrade, exploring the high density domain in a wide range of values of plasma current, toroidal magnetic field and edge safety factor. New data were collected in the latest experimental campaigns, extending the study of the density limit towards lower values of toroidal magnetic field and plasma current. These experiments confirmed the edge nature of the density limit, as a Greenwald-like scaling was obtained for the maximum achievable line-averaged density along a peripheral chord, while a clear scaling of the maximum achievable line-averaged density along a central chord with the toroidal magnetic field only was found and successfully interpreted as due to interplay between the peripheral Greenwald limit and the specific density profile behavior when approaching the density limit. In particular, an analytical relation between the peripheral and the central density limit was derived for the first time, with the introduction of a generalized parabolic density profile with the peaking factor dependent on the plasma parameters.
Range-limited centrality measures in complex networks
NASA Astrophysics Data System (ADS)
Ercsey-Ravasz, Mária; Lichtenwalter, Ryan N.; Chawla, Nitesh V.; Toroczkai, Zoltán
2012-06-01
Here we present a range-limited approach to centrality measures in both nonweighted and weighted directed complex networks. We introduce an efficient method that generates for every node and every edge its betweenness centrality based on shortest paths of lengths not longer than ℓ=1,...,L in the case of nonweighted networks, and for weighted networks the corresponding quantities based on minimum weight paths with path weights not larger than wℓ=ℓΔ, ℓ=1,2...,L=R/Δ. These measures provide a systematic description on the positioning importance of a node (edge) with respect to its network neighborhoods one step out, two steps out, etc., up to and including the whole network. They are more informative than traditional centrality measures, as network transport typically happens on all length scales, from transport to nearest neighbors to the farthest reaches of the network. We show that range-limited centralities obey universal scaling laws for large nonweighted networks. As the computation of traditional centrality measures is costly, this scaling behavior can be exploited to efficiently estimate centralities of nodes and edges for all ranges, including the traditional ones. The scaling behavior can also be exploited to show that the ranking top list of nodes (edges) based on their range-limited centralities quickly freezes as a function of the range, and hence the diameter-range top list can be efficiently predicted. We also show how to estimate the typical largest node-to-node distance for a network of N nodes, exploiting the afore-mentioned scaling behavior. These observations were made on model networks and on a large social network inferred from cell-phone trace logs (˜5.5×106 nodes and ˜2.7×107 edges). Finally, we apply these concepts to efficiently detect the vulnerability backbone of a network (defined as the smallest percolating cluster of the highest betweenness nodes and edges) and illustrate the importance of weight-based centrality measures in
Fluctuation theorem: A critical review
NASA Astrophysics Data System (ADS)
Malek Mansour, M.; Baras, F.
2017-10-01
Fluctuation theorem for entropy production is revisited in the framework of stochastic processes. The applicability of the fluctuation theorem to physico-chemical systems and the resulting stochastic thermodynamics were analyzed. Some unexpected limitations are highlighted in the context of jump Markov processes. We have shown that these limitations handicap the ability of the resulting stochastic thermodynamics to correctly describe the state of non-equilibrium systems in terms of the thermodynamic properties of individual processes therein. Finally, we considered the case of diffusion processes and proved that the fluctuation theorem for entropy production becomes irrelevant at the stationary state in the case of one variable systems.
NASA Astrophysics Data System (ADS)
Evans, Denis J.; Searles, Debra J.
2002-11-01
The question of how reversible microscopic equations of motion can lead to irreversible macroscopic behaviour has been one of the central issues in statistical mechanics for more than a century. The basic issues were known to Gibbs. Boltzmann conducted a very public debate with Loschmidt and others without a satisfactory resolution. In recent decades there has been no real change in the situation. In 1993 we discovered a relation, subsequently known as the Fluctuation Theorem (FT), which gives an analytical expression for the probability of observing Second Law violating dynamical fluctuations in thermostatted dissipative non-equilibrium systems. The relation was derived heuristically and applied to the special case of dissipative non-equilibrium systems subject to constant energy 'thermostatting'. These restrictions meant that the full importance of the Theorem was not immediately apparent. Within a few years, derivations of the Theorem were improved but it has only been in the last few of years that the generality of the Theorem has been appreciated. We now know that the Second Law of Thermodynamics can be derived assuming ergodicity at equilibrium, and causality. We take the assumption of causality to be axiomatic. It is causality which ultimately is responsible for breaking time reversal symmetry and which leads to the possibility of irreversible macroscopic behaviour. The Fluctuation Theorem does much more than merely prove that in large systems observed for long periods of time, the Second Law is overwhelmingly likely to be valid. The Fluctuation Theorem quantifies the probability of observing Second Law violations in small systems observed for a short time. Unlike the Boltzmann equation, the FT is completely consistent with Loschmidt's observation that for time reversible dynamics, every dynamical phase space trajectory and its conjugate time reversed 'anti-trajectory', are both solutions of the underlying equations of motion. Indeed the standard proofs of
the various weak limits , for the basic processes (Wn, n = or > 0), (W(t), t = or > 0) and (Q(t), t = or > 0), where Wn is the waiting time of...notion of an exceptional system, the author considers the limiting behavior of two additional variants of the single server queque. (Author)
NASA Technical Reports Server (NTRS)
Ristorcelli, J. R.; Lumley, J. L.; Abid, R.
1994-01-01
A nonlinear representation for the rapid-pressure correlation appearing in the Reynolds stress equations, consistent with the Taylor-Proudman theorem, is presented. The representation insures that the modeled second-order equations are frame-invariant with respect to rotation when the flow is two-dimensional in planes perpendicular to the axis of rotation. The representation satisfies realizability in a new way: a special ansatz is used to obtain analytically, the values of coefficients valid away from the realizability limit: the model coefficients are functions of the state of the turbulence that are valid for all states of the mechanical turbulence attaining their constant limiting values only when the limit state is achieved. Utilization of all the mathematical constraints are not enough to specify all the coefficients in the model. The unspecified coefficients appear as free parameters which are used to insure that the representation is asymptotically consistent with the known equilibrium states of a homogeneous sheared turbulence. This is done by insuring that the modeled evolution equations have the same fixed points as those obtained from computer and laboratory experiments for the homogeneous shear. Results of computations of the homogeneous shear, with and without rotation, and with stabilizing and destabilizing curvature, are shown. Results are consistently better, in a wide class of flows which the model not been calibrated, than those obtained with other nonlinear models.
Taylor's power law and fluctuation scaling explained by a central-limit-like convergence
NASA Astrophysics Data System (ADS)
Kendal, Wayne S.; Jørgensen, Bent
2011-06-01
A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities like free energy and an external field; the correspondence of these quantities with biological systems, though, remains unproven. Questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with Taylor's law. We note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the Tweedie exponential dispersion models. These latter models are characterized by variance-to-mean power functions; their phenomenological basis rests with a central-limit-theorem-like property that causes many statistical systems to converge mathematically toward a Tweedie form. We review evaluations of the Tweedie Poisson-gamma model for Taylor's law and provide three further cases to test: the clustering of single nucleotide polymorphisms (SNPs) within the horse chromosome 1, the clustering of genes within human chromosome 8, and the Mertens function. This latter case is a number theoretic function for which a thermodynamic model cannot explain Taylor's law, but where Tweedie convergence remains applicable. The Tweedie models are applicable to diverse biological, physical, and mathematical phenomena that express power variance functions over a wide range of measurement scales; they provide a probabilistic description for Taylor's law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism.
Taylor's power law and fluctuation scaling explained by a central-limit-like convergence.
Kendal, Wayne S; Jørgensen, Bent
2011-06-01
A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities like free energy and an external field; the correspondence of these quantities with biological systems, though, remains unproven. Questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with Taylor's law. We note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the Tweedie exponential dispersion models. These latter models are characterized by variance-to-mean power functions; their phenomenological basis rests with a central-limit-theorem-like property that causes many statistical systems to converge mathematically toward a Tweedie form. We review evaluations of the Tweedie Poisson-gamma model for Taylor's law and provide three further cases to test: the clustering of single nucleotide polymorphisms (SNPs) within the horse chromosome 1, the clustering of genes within human chromosome 8, and the Mertens function. This latter case is a number theoretic function for which a thermodynamic model cannot explain Taylor's law, but where Tweedie convergence remains applicable. The Tweedie models are applicable to diverse biological, physical, and mathematical phenomena that express power variance functions over a wide range of measurement scales; they provide a probabilistic description for Taylor's law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism.
ERIC Educational Resources Information Center
May, Henry
2014-01-01
Interest in variation in program impacts--How big is it? What might explain it?--has inspired recent work on the analysis of data from multi-site experiments. One critical aspect of this problem involves the use of random or fixed effect estimates to visualize the distribution of impact estimates across a sample of sites. Unfortunately, unless the…
ERIC Educational Resources Information Center
Van Duzer, Eric
2011-01-01
This report introduces a short, hands-on activity that addresses a key challenge in teaching quantitative methods to students who lack confidence or experience with statistical analysis. Used near the beginning of the course, this activity helps students develop an intuitive insight regarding a number of abstract concepts which are key to…
The Sampling Distribution and the Central Limit Theorem: What They Are and Why They're Important.
ERIC Educational Resources Information Center
Kennedy, Charlotte A.
The use of and emphasis on statistical significance testing has pervaded educational and behavioral research for many decades in spite of criticism by prominent researchers in this field. Much of the controversy is caused by lack of understanding or misinterpretations. This paper reviews criticisms of statistical significance testing and discusses…
Bell's theorem and Bayes' theorem
NASA Astrophysics Data System (ADS)
Garrett, A. J. M.
1990-12-01
Bell's theorem is expounded as an analysis in Bayesian probabilistic inference. Assume that the result of a spin measurement on a spin- 1/2 particle is governed by a variable internal to the particle (local, “hidden”), and examine pairs of particles having zero combined angular momentum so that their internal variables are correlated: knowing something about the internal variable of one tells us something about that of the other. By measuring the spin of one particle, we infer something about its internal variable; through the correlation, about the internal variable of the second particle, which may be arbitrarily distant and is by hypothesis unchanged by this measurement (locality); and make (probabilistic) prediction of spin observations on the second particle. Each link in this chain has a counterpart in the Bayesian analysis of the situation. Irrespective of the details of the internal variable description, such prediction is violated by measurements on many particle pairs, so that locality—effectively the only physics invoked—fails. The time ordering of the two measurements is not Lorentz-invariant, implying acausality. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of the statistics of the results imply it has a nonlocal—acausal interpretation; one such, the “transactional” interpretation, is presented to demonstrable advantage, and some misconceptions about quantum theory are pursued. The “unobservability” loophole in photonic Bell experiments is proven to be closed. It is shown that this mechanism cannot be used for signalling; signalling would become possible only if the hidden variables, which we insist must underlie the statistical character of the observations (the alternative is to give up), are uncovered in deviations from quantum predictions. Their reticence is understood as a consequence of their nonlocality: it is not easy to isolate and measure something nonlocal. Once the hidden variables
On Leighton's comparison theorem
NASA Astrophysics Data System (ADS)
Ghatasheh, Ahmed; Weikard, Rudi
2017-06-01
We give a simple proof of a fairly flexible comparison theorem for equations of the type -(p (u‧ + su)) ‧ + rp (u‧ + su) + qu = 0 on a finite interval where 1 / p, r, s, and q are real and integrable. Flexibility is provided by two functions which may be chosen freely (within limits) according to the situation at hand. We illustrate this by presenting some examples and special cases which include Schrödinger equations with distributional potentials as well as Jacobi difference equations.
The Limits of Subsistence: Agriculture and Industry in Central Appalachia.
ERIC Educational Resources Information Center
Pudup, Mary Beth
Current interpretations of central Appalachia's chronic poverty focus on the region's economic dependence on the bituminous coal industry, controlled by absentee investors and serving an external market. Such theories overlook the ways in which the agricultural sector shaped subsequent industrial development. By analyzing the farm economy of 16…
The Limits of Subsistence: Agriculture and Industry in Central Appalachia.
ERIC Educational Resources Information Center
Pudup, Mary Beth
Current interpretations of central Appalachia's chronic poverty focus on the region's economic dependence on the bituminous coal industry, controlled by absentee investors and serving an external market. Such theories overlook the ways in which the agricultural sector shaped subsequent industrial development. By analyzing the farm economy of 16…
Vorticity, Stokes' Theorem and the Gauss's Theorem
NASA Astrophysics Data System (ADS)
Narayanan, M.
2004-12-01
Vorticity is a property of the flow of any fluid and moving fluids acquire properties that allow an engineer to describe that particular flow in greater detail. It is important to recognize that mere motion alone does not guarantee that the air or any fluid has vorticity. Vorticity is one of four important quantities that define the kinematic properties of any fluid flow. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. However, the divergence theorem is a mathematical statement of the physical fact that, in the absence of the creation or destruction of matter, the density within a region of space can change only by having it flow into, or away from the region through its boundary. This is also known as Gauss's Theorem. It should also be noted that there are many useful extensions of Gauss's Theorem, including the extension to include surfaces of discontinuity in V. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. Integral (Surface) [(DEL X V)] . dS = Integral (Contour) [V . dx] In this paper, the author outlines and stresses the importance of studying and teaching these mathematical techniques while developing a course in Hydrology and Fluid Mechanics. References Arfken, G. "Gauss's Theorem." 1.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 57-61, 1985. Morse, P. M. and Feshbach, H. "Gauss's Theorem." In Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 37-38, 1953. Eric W. Weisstein. "Divergence Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DivergenceTheorem.html
Pion Electroproduction and Siegert's Theorem
NASA Astrophysics Data System (ADS)
Tiator, Lothar
2016-11-01
Nucleon to Resonance transition form factors are discussed within the MAID model for pion electroproduction on the nucleon. For low Q^2 the consequences of Siegert's theorem are presented and medium to large violations of the Long Wavelength Limit at the pseudo-threshold are observed for the phenomenological parametrizations of the longitudinal transition form factors of different nucleon resonances.
The New START Treaty: Central Limits and Key Provisions
2014-04-08
through which all vehicles large enough to carry items limited by the treaty (such as the first stage of a mobile ICBM) had to pass. The portal contained...little difficulty. The Foreign Affairs Committee of the Russian Duma had initially supported the treaty. However, in early November 2010, Konstantin
The New START Treaty: Central Limits and Key Provisions
2014-08-27
through which all vehicles large enough to carry items limited by the treaty (such as the first stage of a mobile ICBM) had to pass. The portal contained...difficulty. The Foreign Affairs Committee of the Russian Duma had initially supported the treaty. However, in early November 2010, Konstantin
Cohen, S.A.; Hosea, J.C.; Timberlake, J.R.
1984-10-19
A limiter with a specially contoured front face is provided. The front face of the limiter (the plasma-side face) is flat with a central indentation. In addition, the limiter shape is cylindrically symmetric so that the limiter can be rotated for greater heat distribution. This limiter shape accommodates the various power scrape-off distances lambda p, which depend on the parallel velocity, V/sub parallel/, of the impacting particles.
Cohen, Samuel A.; Hosea, Joel C.; Timberlake, John R.
1986-01-01
A limiter with a specially contoured front face accommodates the various power scrape-off distances .lambda..sub.p, which depend on the parallel velocity, V.sub..parallel., of the impacting particles. The front face of the limiter (the plasma-side face) is flat with a central indentation. In addition, the limiter shape is cylindrically symmetric so that the limiter can be rotated for greater heat distribution.
ERIC Educational Resources Information Center
Smith, Michael D.
2016-01-01
The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…
ERIC Educational Resources Information Center
Smith, Michael D.
2016-01-01
The Parity Theorem states that any permutation can be written as a product of transpositions, but no permutation can be written as a product of both an even number and an odd number of transpositions. Most proofs of the Parity Theorem take several pages of mathematical formalism to complete. This article presents an alternative but equivalent…
ERIC Educational Resources Information Center
Parameswaran, Revathy
2009-01-01
This paper reports on an experiment studying twelfth grade students' understanding of Rolle's Theorem. In particular, we study the influence of different concept images that students employ when solving reasoning tasks related to Rolle's Theorem. We argue that students' "container schema" and "motion schema" allow for rich…
A Central Capacity Limit to the Simultaneous Storage of Visual and Auditory Arrays in Working Memory
ERIC Educational Resources Information Center
Saults, J. Scott; Cowan, Nelson
2007-01-01
If working memory is limited by central capacity (e.g., the focus of attention; N. Cowan, 2001), then storage limits for information in a single modality should apply also to the simultaneous storage of information from different modalities. The authors investigated this by combining a visual-array comparison task with a novel auditory-array…
NASA Astrophysics Data System (ADS)
Guney, Veli Ugur
In this work we look for novel classes of Bell's inequalities and methods to produce them. We also find their quantum violations including, if possible, the maximum one. The Jordan bases method that we explain in Chapter 2 is about using a pair of certain type of orthonormal bases whose spans are subspaces related to measurement outcomes of incompatible quantities on the same physical system. Jordan vectors are the briefest way of expressing the relative orientation of any two subspaces. This feature helps us to reduce the dimensionality of the parameter space on which we do searches for optimization. The work is published in [24]. In Chapter 3, we attempt to find a connection between group theory and Bell's theorem. We devise a way of generating terms of a Bell's inequality that are related to elements of an algebraic group. The same group generates both the terms of the Bell's inequality and the observables that are used to calculate the quantum value of the Bell expression. Our results are published in [25][26]. In brief, Bell's theorem is the main tool of a research program that was started by Einstein, Podolsky, Rosen [19] and Bohr [8] in the early days of quantum mechanics in their discussions about the core nature of physical systems. These debates were about a novel type of physical states called superposition states, which are introduced by quantum mechanics and manifested in the apparent inevitable randomness in measurement outcomes of identically prepared systems. Bell's huge contribution was to find a means of quantifying the problem and hence of opening the way to experimental verification by rephrasing the questions as limits on certain combinations of correlations between measurement results of spatially separate systems [7]. Thanks to Bell, the fundamental questions related to the nature of quantum mechanical systems became quantifiable [6]. According to Bell's theorem, some correlations between quantum entangled systems that involve incompatible
The Floquet Adiabatic Theorem revisited
NASA Astrophysics Data System (ADS)
Weinberg, Phillip; Bukov, Marin; D'Alessio, Luca; Kolodrubetz, Michael; Davidson, Shainen; Polkovnikov, Anatoli
2015-03-01
The existance of the adiabatic theorem for Floquet systems has been the subject of an active debate with different articles reaching opposite conclusions over the years. In this talk we clarify the situation by deriving a systematic expansion in the time-derivatives of a slow parameter for the occupation probabilities of the Floque states. Our analysis shows that the in a certain limit the transition between Floquet eigenstates are suppressed and it is possible to define an adiabatic theorem for Floquet systems. Crucially we observe however that the conditions for adiabaticity in ordinary and Floquet systems are different and that this difference can become important when the amplitude of the periodic driving is large. We illustrate our results with specific examples of a periodically driven harmonic oscillator and cold atoms in optical lattices which are relevant in current experiments.
Cooperation Among Theorem Provers
NASA Technical Reports Server (NTRS)
Waldinger, Richard J.
1998-01-01
In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages.
Trigonometry, Including Snell's Theorem.
ERIC Educational Resources Information Center
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
Trigonometry, Including Snell's Theorem.
ERIC Educational Resources Information Center
Kent, David
1980-01-01
Aspects of the instruction of trigonometry in secondary school mathematics are reviewed. Portions of this document cover basic introductions, a student-developed theorem, the cosine rule, inverse functions, and a sample outdoor activity. (MP)
ERIC Educational Resources Information Center
Benyi, Arpad; Casu, Ioan
2009-01-01
Pompeiu's theorem states that if ABC is an "equilateral" triangle and M a point in its plane, then MA, MB, and MC form a new triangle. In this article, we have a new look at this theorem in the realm of arbitrary triangles. We discover what we call Pompeiu's Area Formula, a neat equality relating areas of triangles determined by the points A, B,…
ERIC Educational Resources Information Center
Benyi, Arpad; Casu, Ioan
2009-01-01
Pompeiu's theorem states that if ABC is an "equilateral" triangle and M a point in its plane, then MA, MB, and MC form a new triangle. In this article, we have a new look at this theorem in the realm of arbitrary triangles. We discover what we call Pompeiu's Area Formula, a neat equality relating areas of triangles determined by the points A, B,…
Navier Stokes Theorem in Hydrology
NASA Astrophysics Data System (ADS)
Narayanan, M.
2005-12-01
In a paper presented at the 2004 AGU International Conference, the author outlined and stressed the importance of studying and teaching certain important mathematical techniques while developing a course in Hydrology and Fluid Mechanics. The Navier-Stokes equations are the foundation of fluid mechanics, and Stokes' theorem is used in nearly every branch of mechanics as well as electromagnetics. Stokes' Theorem also plays a vital role in many secondary theorems such as those pertaining to vorticity and circulation. Mathematically expressed, Stokes' theorem can be expressed by considering a surface S having a bounding curve C. Here, V is any sufficiently smooth vector field defined on the surface and its bounding curve C. In an article entitled "Corrections to Fluid Dynamics" R. F. Streater, (Open Systems and Information Dynamics, 10, 3-30, 2003.) proposes a kinetic model of a fluid in which five macroscopic fields, the mass, energy, and three components of momentum, are conserved. The dynamics is constructed using the methods of statistical dynamics, and results in a non-linear discrete-time Markov chain for random fields on a lattice. In the continuum limit he obtains a non-linear coupled parabolic system of field equations, showing a correction to the Navier-Stokes equations. In 2001, David Hoff published an article in Journees Equations aux derivees partielles. (Art. No. 7, 9 p.). His paper is entitled : Dynamics of Singularity Surfaces for Compressible Navier-Stokes Flows in Two Space Dimensions. In his paper, David Hoff proves the global existence of solutions of the Navier-Stokes equations of compressible, barotropic flow in two space dimensions with piecewise smooth initial data. These solutions remain piecewise smooth for all time, retaining simple jump discontinuities in the density and in the divergence of the velocity across a smooth curve, which is convected with the flow. The strengths of these discontinuities are shown to decay exponentially in time
Energy turnover in European hares is centrally limited during early, but not during peak lactation.
Valencak, Teresa G; Ruf, Thomas
2009-11-01
We investigated metabolizable energy intake (MEI) and milk energy output in European hares throughout gestation and lactation in females raising three young, i.e., close to maximum litter size in this precocial species. We hypothesized that herbivorous hares may face a central limitation of energy turnover during lactation, imposed by maximum capacity of the gastrointestinal tract. Females were provided with low-energy or high-energy diets, either continually, or during lactation only. Unexpectedly, females on either diet reached identical peak MEIs (>6 times BMR) during late lactation, with females on low-energy diet increasing food intake proportionally. Thus, we reject our hypothesis that in lactating hares, peak MEI is centrally limited. During early lactation, MEI and milk transfer was, however, significantly impaired in females on the low-energy diet, indicating a temporal central limitation due to a time-lag caused by the readjustment of energy intake capacity. Importantly, irrespective of the diet, females significantly increased peak MEI late in the breeding season. Consequently, earlier in the season, when energy reserves are still high, energy throughput was not limited by physiological constraints at all. We conclude that extreme MEI may have fitness costs, and that females maximize lifetime reproductive success by actively down-regulating MEI whenever possible.
A generalization of Nekhoroshev's theorem
NASA Astrophysics Data System (ADS)
Bates, Larry; Cushman, Richard
2016-11-01
Nekhoroshev discovered a beautiful theorem in Hamiltonian systems that includes as special cases not only the Poincaré theorem on periodic orbits but also the theorem of Liouville-Arnol'd on completely integrable systems [7]. Sadly, his early death precluded him publishing a full account of his proof. The aim of this paper is twofold: first, to provide a complete proof of his original theorem and second a generalization to the noncommuting case. Our generalization of Nekhoroshev's theorem to the nonabelian case subsumes aspects of the theory of noncommutative complete integrability as found in Mishchenko and Fomenko [5] and is similar to what Nekhoroshev's theorem does in the abelian case.
NASA Astrophysics Data System (ADS)
Pérez-Espigares, Carlos; Redig, Frank; Giardinà, Cristian
2015-08-01
For non-equilibrium systems of interacting particles and for interacting diffusions in d-dimensions, a novel fluctuation relation is derived. The theorem establishes a quantitative relation between the probabilities of observing two current values in different spatial directions. The result is a consequence of spatial symmetries of the microscopic dynamics, generalizing in this way the Gallavotti-Cohen fluctuation theorem related to the time-reversal symmetry. This new perspective opens up the possibility of direct experimental measurements of fluctuation relations of vectorial observables.
Limits to northward drift of the Paleocene Cantwell Formation, central Alaska.
Hillhouse, J.W.; Gromme, C.S.
1982-01-01
Volcanic rocks of the Paleocene Cantwell Formation in central Alaska apparently originated at a paleolatitude of 83oN (alpha 95 = 9.7o), as indicated by paleomagnetic results. When compared with the Paleocene pole for the North American craton, the 95% confidence limits of the results suggest that terranes N of the Denali fault have moved no more than 550km northward relative to the North American craton since Paleocene time.-Authors
Kumagai, Kazuyuki; Hangai, Masanori; Furukawa, Mariko; Suetsugu, Tetsuyuki; Ogino, Nobuchika
2017-01-11
To report a case that showed centripetal movements of the capillaries in the central macular region after vitrectomy with internal limiting membrane peeling. A 57-year-old pseudophakic woman underwent successful vitrectomy with internal limiting membrane peeling and air tamponade for a vitreomacular traction. Optical coherence tomography angiographic images of the 3 mm × 3 mm inner retinal vascular plexus were examined preoperatively and at 3 months postoperatively. The changes in 93 corresponding bifurcations of the capillaries were assessed. The majority of the bifurcations were displaced towards the fovea at 3 months after the vitrectomy with internal limiting membrane peeling. Optical coherence tomography angiography was used to help visualize the centripetal movement of the inner retina around the fovea after the vitrectomy with internal limiting membrane peeling.
STABILITY OF GAS CLOUDS IN GALACTIC NUCLEI: AN EXTENDED VIRIAL THEOREM
Chen, Xian; Cuadra, Jorge; Amaro-Seoane, Pau E-mail: jcuadra@astro.puc.cl
2016-03-10
Cold gas entering the central 1–10{sup 2} pc of a galaxy fragments and condenses into clouds. The stability of the clouds determines whether they will be turned into stars or can be delivered to the central supermassive black hole (SMBH) to turn on an active galactic nucleus (AGN). The conventional criteria to assess the stability of these clouds, such as the Jeans criterion and Roche (or tidal) limit, are insufficient here, because they assume the dominance of self-gravity in binding a cloud, and neglect external agents, such as pressure and tidal forces, which are common in galactic nuclei. We formulate a new scheme for judging this stability. We first revisit the conventional Virial theorem, taking into account an external pressure, to identify the correct range of masses that lead to stable clouds. We then extend the theorem to further include an external tidal field, which is equally crucial for the stability in the region of our interest—in dense star clusters, around SMBHs. We apply our extended Virial theorem to find new solutions to controversial problems, namely, the stability of the gas clumps in AGN tori, the circum-nuclear disk in the Galactic Center, and the central molecular zone of the Milky Way. The masses we derive for these structures are orders of magnitude smaller than the commonly used Virial masses (equivalent to the Jeans mass). Moreover, we prove that these clumps are stable, contrary to what one would naively deduce from the Roche (tidal) limit.
Virial Theorem and Scale Transformations.
ERIC Educational Resources Information Center
Kleban, Peter
1979-01-01
Discussed is the virial theorem, which is useful in classical, quantum, and statistical mechanics. Two types of derivations of this theorem are presented and the relationship between the two is explored. (BT)
Rediscovering Schreinemakers' Theorem.
ERIC Educational Resources Information Center
Bathurst, Bruce
1983-01-01
Schreinemakers' theorem (arrangement of curves around an invariant point), derived from La Chatelier's principle, can be rediscovered by students asked to use the principle when solving a natural problem such as "How does diluting a mineral/fluid alter shape of a pressure/temperature diagram?" Background information and instructional…
ERIC Educational Resources Information Center
Musto, Garrod
2010-01-01
Within his classroom, the author is often confronted by students who fail to see, or accept, the relevance of mathematics both to their lives and the world around them. One topic which is regularly perceived as being disconnected from people's daily lives is that of circle theorems, especially among less motivated students. In this article, the…
Physical Activity, Central Adiposity, and Functional Limitations in Community-Dwelling Older Adults.
Germain, Cassandra M; Vasquez, Elizabeth; Batsis, John A
2016-01-01
Obesity and physical inactivity are independently associated with physical and functional limitations in older adults. The current study examines the impact of physical activity on odds of physical and functional limitations in older adults with central and general obesity. Data from 6279 community-dwelling adults aged 60 years or more from the Health and Retirement Study 2006 and 2008 waves were used to calculate prevalence and odds of physical and functional limitation among obese older adults with high waist circumference (waist circumference ≥88 cm in females and ≥102 cm in males) who were physically active versus inactive (engaging in moderate/vigorous activity less than once per week). Logistic regression models were adjusted for age, sex, race/ethnicity, education, smoking status, body mass index, and number of comorbidities. Physical activity was associated with lower odds of physical and functional limitations among older adults with high waist circumference (odds ratio [OR], 0.59; confidence interval [CI], 0.52-0.68, for physical limitations; OR, 0.52; CI, 0.44-0.62, for activities of daily living; and OR, 0.44; CI, 0.39-0.50, for instrumental activities of daily living). Physical activity is associated with significantly lower odds of physical and functional limitations in obese older adults regardless of how obesity is classified. Additional research is needed to determine whether physical activity moderates long-term physical and functional limitations.
Physical Activity, Central Adiposity and Functional Limitations in Community Dwelling Older Adults
Germain, Cassandra M.; Vasquez, Elizabeth; Batsis, John A.
2015-01-01
Background and Purpose Obesity and physical inactivity are independently associated with declines in physical and functional limitations in older adults. The current study examines the impact of physical activity on odds of physical and functional limitations in older adults with central and general obesity. Methods Data from 6,279 community dwelling adults aged ≥ 60 years from the Health and Retirement Study 2006 and 2008 waves were used to calculate prevalence and odds of physical and functional limitation among obese older adults with high waist circumference (WC) (WC ≥ 88cm in females and ≥ 102cm in males) who were physically active vs. inactive (engaging in moderate/vigorous activity less than once per week). Logistic regression models were adjusted for age, gender, race/ethnicity, education, smoking status, body mass index (BMI) and number of comorbidities. Results Physical activity was associated with lower odds of physical and functional limitations among older adults with high WC odds ratios (OR) and confidence intervals (CI) were OR 0.59 (CI: 0.52–0.68) for physical limitations, OR 0.52 (CI: .44–.62) for activities of daily living and OR 0.44 (CI: 0.39–0.50) for instrumental activities of daily living. Conclusion Physical activity is associated with significantly lower odds of physical and functional limitations in obese older adults regardless of how obesity is classified. Additional research is needed to determine whether physical activity moderates long-term physical and functional limitations. PMID:25794309
Cooperation Among Theorem Provers
NASA Technical Reports Server (NTRS)
Waldinger, Richard J.
1998-01-01
This is a final report, which supports NASA's PECSEE (Persistent Cognizant Software Engineering Environment) effort and complements the Kestrel Institute project "Inference System Integration via Logic Morphism". The ultimate purpose of the project is to develop a superior logical inference mechanism by combining the diverse abilities of multiple cooperating theorem provers. In many years of research, a number of powerful theorem-proving systems have arisen with differing capabilities and strengths. Resolution theorem provers (such as Kestrel's KITP or SRI's, SNARK) deal with first-order logic with equality but not the principle of mathematical induction. The Boyer-Moore theorem prover excels at proof by induction but cannot deal with full first-order logic. Both are highly automated but cannot accept user guidance easily. The PVS system (from SRI) in only automatic within decidable theories, but it has well-designed interactive capabilities: furthermore, it includes higher-order logic, not just first-order logic. The NuPRL system from Cornell University and the STeP system from Stanford University have facilities for constructive logic and temporal logic, respectively - both are interactive. It is often suggested - for example, in the anonymous "QED Manifesto"-that we should pool the resources of all these theorem provers into a single system, so that the strengths of one can compensate for the weaknesses of others, and so that effort will not be duplicated. However, there is no straightforward way of doing this, because each system relies on its own language and logic for its success. Thus. SNARK uses ordinary first-order logic with equality, PVS uses higher-order logic. and NuPRL uses constructive logic. The purpose of this project, and the companion project at Kestrel, has been to use the category-theoretic notion of logic morphism to combine systems with different logics and languages. Kestrel's SPECWARE system has been the vehicle for the implementation.
Generalized No-Broadcasting Theorem
NASA Astrophysics Data System (ADS)
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
2007-12-01
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with “superquantum” correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
Generalized no-broadcasting theorem.
Barnum, Howard; Barrett, Jonathan; Leifer, Matthew; Wilce, Alexander
2007-12-14
We prove a generalized version of the no-broadcasting theorem, applicable to essentially any nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with "superquantum" correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
ERIC Educational Resources Information Center
Russell, Alan R.
2004-01-01
Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.
ERIC Educational Resources Information Center
Russell, Alan R.
2004-01-01
Pick's theorem can be used in various ways just like a lemon. This theorem generally finds its way in the syllabus approximately at the middle school level and in fact at times students have even calculated the area of a state considering its outline with the help of the above theorem.
Non-traditional theorems unfolding
NASA Astrophysics Data System (ADS)
Wares, Arsalan
2015-02-01
The purpose of this paper is to provide examples of 'non-traditional' proof-related activities or theorems that can be explored through paper folding by university and high-school students. These theorems were encountered through playful acts of paper folding by the author. The author used these activities successfully with preservice teachers. The paper contains proof outlines for each theorem.
Adiabatic Theorem for Quantum Spin Systems
NASA Astrophysics Data System (ADS)
Bachmann, S.; De Roeck, W.; Fraas, M.
2017-08-01
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.
Adiabatic Theorem for Quantum Spin Systems.
Bachmann, S; De Roeck, W; Fraas, M
2017-08-11
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ϵ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.
A Central Capacity Limit to the Simultaneous Storage of Visual and Auditory Arrays in Working Memory
Saults, J. Scott; Cowan, Nelson
2008-01-01
If working memory is limited by central capacity (e.g., the focus of attention; Cowan, 2001) then storage limits for information in a single modality should also apply to the simultaneous storage of information from different modalities. We investigated this by combining a visual-array comparison task with a novel auditory-array comparison task in five experiments. Participants were to remember only the visual or only the auditory arrays (unimodal memory conditions) or both arrays (bimodal memory conditions). Experiments 1-2 showed significant dual-task tradeoffs for visual but not auditory capacity. In Experiments 3-5, modality-specific memory was eliminated using post-perceptual masks. Dual-task costs occurred for both modalities and the number of auditory and visual items remembered together was no more than the higher of the unimodal capacities (visual, 3-4 items). The findings suggest a central capacity supplemented by modality- or code-specific storage and point to avenues for further research on the role of processing in central storage. PMID:17999578
The Steep Nekhoroshev's Theorem
NASA Astrophysics Data System (ADS)
Guzzo, M.; Chierchia, L.; Benettin, G.
2016-03-01
Revising Nekhoroshev's geometry of resonances, we provide a fully constructive and quantitative proof of Nekhoroshev's theorem for steep Hamiltonian systems proving, in particular, that the exponential stability exponent can be taken to be {1/(2nα_1\\cdotsα_{n-2}}) ({α_i}'s being Nekhoroshev's steepness indices and {n ≥ 3} the number of degrees of freedom). On the base of a heuristic argument, we conjecture that the new stability exponent is optimal.
1987-03-20
with standard expressions of spherical trigonometry is sinr)0 = cos0 sini//0 (4.37) which is consistent with the results obtained previously with...theorems for discrete transforms. However, sampling questions inlroduce difficult obstacles in the develop- ment of a discrete theory. First, sampling...additional obstacle to discrete represen- tations of the CT. An example of qualitative predication of the shape of silhouettes with the Silhouette-Slice
Wheeler, W.
1998-12-01
This report estimates the economic and financial effects and the benefits of compliance with the proposed effluent limitations guidelines and standards for the Centralized Waste Treatment (CWT) industry. The Environmental Protection Agency (EPA) has measured these impacts in terms of changes in the profitability of waste treatment operations at CWT facilities, changes in market prices to CWT services, and changes in the quantities of waste management at CWT facilities in six geographic regions. EPA has also examined the impacts on companies owning CWT facilities (including impacts on small entities), on communities in which CWT facilities are located, and on environmental justice. EPA examined the benefits to society of the CWT effluent limitations guidelines and standards by examining cancer and non-cancer health effects of the regulation, recreational benefits, and cost savings to publicly owned treatment works (POTWs) to which indirect-discharging CWT facilities send their wastewater.
Muscle Strength, Physical Activity, and Functional Limitations in Older Adults with Central Obesity
Germain, Cassandra M.; Batsis, John A.; Vasquez, Elizabeth; McQuoid, Douglas R.
2016-01-01
Background. Obesity and muscle weakness are independently associated with increased risk of physical and functional impairment in older adults. It is unknown whether physical activity (PA) and muscle strength combined provide added protection against functional impairment. This study examines the association between muscle strength, PA, and functional outcomes in older adults with central obesity. Methods. Prevalence and odds of physical (PL), ADL, and IADL limitation were calculated for 6,388 community dwelling adults aged ≥ 60 with central obesity. Individuals were stratified by sex-specific hand grip tertiles and PA. Logistic models were adjusted for age, education, comorbidities, and body-mass index and weighted. Results. Overall prevalence of PL and ADL and IADL limitations were progressively lower by grip category. Within grip categories, prevalence was lower for individuals who were active than those who were inactive. Adjusted models showed significantly lower odds of PL OR 0.42 [0.31, 0.56]; ADL OR 0.60 [0.43, 0.84], and IADL OR 0.46 [0.35, 0.61] for those in the highest grip strength category as compared to those in the lowest grip category. Conclusion. Improving grip strength in obese elders who are not able to engage in traditional exercise is important for reducing odds of physical and functional impairment. PMID:27034833
Central Urocortin 3 Administration Decreases Limited Access Ethanol Intake in Non-Dependent Mice
Sharpe, Amanda L.; Phillips, Tamara J.
2010-01-01
Stress and alcohol abuse are co-related. Acute alcohol is anxiolytic, and stress is cited as a factor in relapse to alcohol use. A primary mediator of the stress response is the neuropeptide corticotrophin-releasing factor (CRF). The CRF family of endogenous ligands includes urocortin 3 (Ucn 3), which binds selectively to the CRF2 receptor and has been implicated in ethanol consumption in dependent and withdrawing rats. The objective of this study was to examine the effect of Ucn 3, delivered centrally to non-dependent mice, on limited-access ethanol consumption. Adult C57BL/6J mice were trained to self-administer 10% ethanol during daily, 2-hr limited access sessions using lickometers to assess drinking patterns for both ethanol and water. Sterile saline or 0.3, 1, or 3 nmol of Ucn 3 was microinjected into the lateral ventricle immediately before the limited-access session in a within-subjects design. There was a significant decrease in ethanol (both ml and g/kg), but not water, intake following Ucn 3 treatment, explained by a change in size of the largest lick run. Food intake at both 2- and 24-hours after injection was statistically unaffected by Ucn 3 administration. These results establish a role for CRF2R in a non-dependent, mouse model of ethanol self-administration. PMID:19581799
Recurrence theorems: A unified account
Wallace, David
2015-02-15
I discuss classical and quantum recurrence theorems in a unified manner, treating both as generalisations of the fact that a system with a finite state space only has so many places to go. Along the way, I prove versions of the recurrence theorem applicable to dynamics on linear and metric spaces and make some comments about applications of the classical recurrence theorem in the foundations of statistical mechanics.
Bayes' theorem in paleopathological diagnosis.
Byers, Steven N; Roberts, Charlotte A
2003-05-01
The utility of Bayes' theorem in paleopathological diagnoses is explored. Since this theorem has been used heavily by modern clinical medicine, its usefulness in that field is described first. Next, the mechanics of the theorem are discussed, along with methods for deriving the prior probabilities needed for its application. Following this, the sources of these prior probabilities and their accompanying problems in paleopathology are considered. Finally, an application using prehistoric rib lesions is presented to demonstrate the utility of this method to paleopathology.
Generalized Kochen-Specker theorem
NASA Astrophysics Data System (ADS)
Aravind, P. K.
2003-11-01
A proof of the generalized Kochen-Specker theorem in two dimensions due to Cabello and Nakamura [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)] is extended to all higher dimensions. A set of 18 states in four dimensions is used to give closely related proofs of the generalized Kochen-Specker, Kochen-Specker, and Bell theorems that shed some light on the relationship between these three theorems.
NASA Technical Reports Server (NTRS)
Viera, W. J.
1974-01-01
A method of determining the fuel bias for a bipropellant liquid rocket that minimizes outage associated penalties on payload potential is presented. A fuel bias so derived is normally called the optimum fuel bias. The subjects discussed are: (1) probability density function of outage, (2) computer program listing, and (3) choosing the optimum fuel bias.
Upper limits to the magnetic field in central stars of planetary nebulae
Asensio Ramos, A.; Martínez González, M. J.; Manso Sainz, R.; Corradi, R. L. M.; Leone, F.
2014-06-01
More than about 20 central stars of planetary nebulae (CSPNs) have been observed spectropolarimetrically, yet no clear, unambiguous signal of the presence of a magnetic field in these objects has been found. We perform a statistical (Bayesian) analysis of all the available spectropolarimetric observations of CSPN to constrain the magnetic fields in these objects. Assuming that the stellar field is dipolar and that the dipole axis of the objects is oriented randomly (isotropically), we find that the dipole magnetic field strength is smaller than 400 G with 95% probability using all available observations. The analysis introduced allows integration of future observations to further constrain the parameters of the distribution, and it is general, so that it can be easily applied to other classes of magnetic objects. We propose several ways to improve the upper limits found here.
Marra, Vincenzo; Burden, Jemima J.; Thorpe, Julian R.; Smith, Ikuko T.; Smith, Spencer L.; Häusser, Michael; Branco, Tiago; Staras, Kevin
2012-01-01
Summary At small central synapses, efficient turnover of vesicles is crucial for stimulus-driven transmission, but how the structure of this recycling pool relates to its functional role remains unclear. Here we characterize the organizational principles of functional vesicles at native hippocampal synapses with nanoscale resolution using fluorescent dye labeling and electron microscopy. We show that the recycling pool broadly scales with the magnitude of the total vesicle pool, but its average size is small (∼45 vesicles), highly variable, and regulated by CDK5/calcineurin activity. Spatial analysis demonstrates that recycling vesicles are preferentially arranged near the active zone and this segregation is abolished by actin stabilization, slowing the rate of activity-driven exocytosis. Our approach reveals a similarly biased recycling pool distribution at synapses in visual cortex activated by sensory stimulation in vivo. We suggest that in small native central synapses, efficient release of a limited pool of vesicles relies on their favored spatial positioning within the terminal. PMID:23141069
Multidimensional Tauberian theorems for generalized functions
NASA Astrophysics Data System (ADS)
Drozhzhinov, Yu N.
2016-12-01
This is a brief survey of multidimensional Tauberian theorems for generalized functions. Included are theorems of Hardy-Littlewood type, Tauberian and Abelian comparison theorems of Keldysh type, theorems of Wiener type, and Tauberian theorems for generalized functions with values in Banach spaces. Bibliography: 58 titles.
Area theorem and energy quantization for dissipative optical solitons
Renninger, William H.; Chong, Andy; Wise, Frank W.
2011-01-01
Soliton area theorems express the pulse energy as a function of the pulse shape and the system parameters. From an analytical solution to the cubic-quintic Ginzbug-Landau equation, we derive an area theorem for dissipative optical solitons. In contrast to area theorems for conservative optical solitons, the energy does not scale inversely with the pulse duration, and in addition there is an upper limit to the energy. Energy quantization explains the existence of, and conditions for, multiple-pulse solutions. The theoretical predictions are confirmed with numerical simulations and experiments in the context of dissipative soliton fiber lasers. PMID:21765589
Theorems on positive data: on the uniqueness of NMF.
Laurberg, Hans; Christensen, Mads Graesbøll; Plumbley, Mark D; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors.
Theorems on Positive Data: On the Uniqueness of NMF
Laurberg, Hans; Christensen, Mads Græsbøll; Plumbley, Mark D.; Hansen, Lars Kai; Jensen, Søren Holdt
2008-01-01
We investigate the conditions for which nonnegative matrix factorization (NMF) is unique and introduce several theorems which can determine whether the decomposition is in fact unique or not. The theorems are illustrated by several examples showing the use of the theorems and their limitations. We have shown that corruption of a unique NMF matrix by additive noise leads to a noisy estimation of the noise-free unique solution. Finally, we use a stochastic view of NMF to analyze which characterization of the underlying model will result in an NMF with small estimation errors. PMID:18497868
Tau leaping of stiff stochastic chemical systems via local central limit approximation
NASA Astrophysics Data System (ADS)
Yang, Yushu; Rathinam, Muruhan
2013-06-01
Stiffness manifests in stochastic dynamic systems in a more complex manner than in deterministic systems; it is not only important for a time-stepping method to remain stable but it is also important for the method to capture the asymptotic variances accurately. In the context of stochastic chemical systems, time stepping methods are known as tau leaping. Well known existing tau leaping methods have shortcomings in this regard. The implicit tau method is far more stable than the trapezoidal tau method but underestimates the asymptotic variance. On the other hand, the trapezoidal tau method which estimates the asymptotic variance exactly for linear systems suffers from the fact that the transients of the method do not decay fast enough in the context of very stiff systems. We propose a tau leaping method that possesses the same stability properties as the implicit method while it also captures the asymptotic variance with reasonable accuracy at least for the test system S1↔S2. The proposed method uses a central limit approximation (CLA) locally over the tau leaping interval and is referred to as the LCLA-τ. The CLA predicts the mean and covariance as solutions of certain differential equations (ODEs) and for efficiency we solve these using a single time step of a suitable low order method. We perform a mean/covariance stability analysis of various possible low order schemes to determine the best scheme. Numerical experiments presented show that LCLA-τ performs favorably for stiff systems and that the LCLA-τ is also able to capture bimodal distributions unlike the CLA itself. The proposed LCLA-τ method uses a split implicit step to compute the mean update. We also prove that any tau leaping method employing a split implicit step converges in the fluid limit to the implicit Euler method as applied to the fluid limit differential equation.
Tautenhahn, Susanne; Lichstein, Jeremy W; Jung, Martin; Kattge, Jens; Bohlman, Stephanie A; Heilmeier, Hermann; Prokushkin, Anatoly; Kahl, Anja; Wirth, Christian
2016-06-01
Fire is a primary driver of boreal forest dynamics. Intensifying fire regimes due to climate change may cause a shift in boreal forest composition toward reduced dominance of conifers and greater abundance of deciduous hardwoods, with potential biogeochemical and biophysical feedbacks to regional and global climate. This shift has already been observed in some North American boreal forests and has been attributed to changes in site conditions. However, it is unknown if the mechanisms controlling fire-induced changes in deciduous hardwood cover are similar among different boreal forests, which differ in the ecological traits of the dominant tree species. To better understand the consequences of intensifying fire regimes in boreal forests, we studied postfire regeneration in five burns in the Central Siberian dark taiga, a vast but poorly studied boreal region. We combined field measurements, dendrochronological analysis, and seed-source maps derived from high-resolution satellite images to quantify the importance of site conditions (e.g., organic layer depth) vs. seed availability in shaping postfire regeneration. We show that dispersal limitation of evergreen conifers was the main factor determining postfire regeneration composition and density. Site conditions had significant but weaker effects. We used information on postfire regeneration to develop a classification scheme for successional pathways, representing the dominance of deciduous hardwoods vs. evergreen conifers at different successional stages. We estimated the spatial distribution of different successional pathways under alternative fire regime scenarios. Under intensified fire regimes, dispersal limitation of evergreen conifers is predicted to become more severe, primarily due to reduced abundance of surviving seed sources within burned areas. Increased dispersal limitation of evergreen conifers, in turn, is predicted to increase the prevalence of successional pathways dominated by deciduous hardwoods
First Integrals, Liouville Theorem, and Dirac Brackets
NASA Astrophysics Data System (ADS)
Gleria, Iram; Filho, Tarcísio M. Rocha; Figueiredo Neto, Annibal D.; Vianna, José David M.
2017-08-01
In this paper, we discuss the conditions for the existence of first integrals of movement and the Liouville theorem on integrable systems. We revise the core results of the Hamilton-Jacobi theory and discuss the extension of the formalism to encompass constrained systems using Dirac brackets, originally developed in the context of the canonical quantization of constrained systems. As an application, we analyze a Hamiltonian that represents the classical limit of a Fermionic system of oscillators.
Wigner-Araki-Yanase theorem beyond conservation laws
NASA Astrophysics Data System (ADS)
Tukiainen, Mikko
2017-01-01
The ability to measure every quantum observable is ensured by a fundamental result in quantum measurement theory. Nevertheless, additive conservation laws associated with physical symmetries, such as the angular momentum conservation, may lead to restrictions on the measurability of the observables. Such limitations are imposed by the theorem of Wigner, Araki, and Yanase (WAY). In this paper a formulation of the WAY theorem is presented rephrasing the measurability limitations in terms of quantum incompatibility. This broader mathematical basis enables us to both capture and generalize the WAY theorem by allowing us to drop the assumptions of additivity and even conservation of the involved quantities. Moreover, we extend the WAY theorem to the general level of positive operator-valued measures.
The Non-Signalling theorem in generalizations of Bell's theorem
NASA Astrophysics Data System (ADS)
Walleczek, J.; Grössing, G.
2014-04-01
Does "epistemic non-signalling" ensure the peaceful coexistence of special relativity and quantum nonlocality? The possibility of an affirmative answer is of great importance to deterministic approaches to quantum mechanics given recent developments towards generalizations of Bell's theorem. By generalizations of Bell's theorem we here mean efforts that seek to demonstrate the impossibility of any deterministic theories to obey the predictions of Bell's theorem, including not only local hidden-variables theories (LHVTs) but, critically, of nonlocal hidden-variables theories (NHVTs) also, such as de Broglie-Bohm theory. Naturally, in light of the well-established experimental findings from quantum physics, whether or not a deterministic approach to quantum mechanics, including an emergent quantum mechanics, is logically possible, depends on compatibility with the predictions of Bell's theorem. With respect to deterministic NHVTs, recent attempts to generalize Bell's theorem have claimed the impossibility of any such approaches to quantum mechanics. The present work offers arguments showing why such efforts towards generalization may fall short of their stated goal. In particular, we challenge the validity of the use of the non-signalling theorem as a conclusive argument in favor of the existence of free randomness, and therefore reject the use of the non-signalling theorem as an argument against the logical possibility of deterministic approaches. We here offer two distinct counter-arguments in support of the possibility of deterministic NHVTs: one argument exposes the circularity of the reasoning which is employed in recent claims, and a second argument is based on the inconclusive metaphysical status of the non-signalling theorem itself. We proceed by presenting an entirely informal treatment of key physical and metaphysical assumptions, and of their interrelationship, in attempts seeking to generalize Bell's theorem on the basis of an ontic, foundational
Examples of probabilistic semantics of the basic coding theorem for uncertainty spaces
Diduk, N.N.
1995-03-01
The basic coding theorem for discrete uncertainty spaces is so far the central result of the developing uncertainty theory. The theorem was first published in and its proof in. A refinement of the basic coding theorem with a new proof was subsequently published. The theoretical value of the basic coding theorem is in that it essentially made possible the development of a general theoretical apparatus covering various types of uncertainty. But this theorem should not be regarded as a purely theoretical result, because it also has a clear applied meaning. Indeed, the theorem deals with what can and cannot be accomplished by encoding elements of uncertainty spaces. Such questions are of considerable practical importance, because problems of finding good information encoding techniques are encountered in many spheres of human activity. Moreover, possible applications of the theorem are not restricted to coding problems: we know that prefix coding is analogous to construction of successful search strategies. Search problems therefore constitute another potential application of the proposed theorem. It is thus useful to consider the practical aspects of the basic coding theorem. The basis for the application of the theorem is its semantics, i.e., the system of possible meaningful interpretations. The present paper examines examples of particular cases of the basic coding theorem which admit a probabilistic interpretation. The choice of the topic is motivated by the fact that uncertainty situations that have a probabilistic meaning are undoubtedly of exceptional interest from both theoretical and applied considerations.
Roo: A parallel theorem prover
Lusk, E.L.; McCune, W.W.; Slaney, J.K.
1991-11-01
We describe a parallel theorem prover based on the Argonne theorem-proving system OTTER. The parallel system, called Roo, runs on shared-memory multiprocessors such as the Sequent Symmetry. We explain the parallel algorithm used and give performance results that demonstrate near-linear speedups on large problems.
The 1965 Penrose singularity theorem
NASA Astrophysics Data System (ADS)
Senovilla, José M. M.; Garfinkle, David
2015-06-01
We review the first modern singularity theorem, published by Penrose in 1965. This is the first genuine post-Einsteinian result in general relativity, where the fundamental and fruitful concept of the closed trapped surface was introduced. We include historical remarks, an appraisal of the theorem's impact, and relevant current and future work that belongs to its legacy.
Geometry of the Adiabatic Theorem
ERIC Educational Resources Information Center
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
Geometry of the Adiabatic Theorem
ERIC Educational Resources Information Center
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
ERIC Educational Resources Information Center
Lopez-Real, Francis
2008-01-01
While the author was searching the web, he came across an article by Michael Keyton of IMSA (Illinois Mathematics and Science Academy) called "Theorems of mystery". The phrase is Keyton's own, and he defines such a theorem as "a result that has considerable structure with minimal hypotheses." The simplest of his 10 examples is one that many…
Equivalence theorem in effective theories
NASA Astrophysics Data System (ADS)
Chicherin, D.; Gorbenko, V.; Vereshagin, V.
2011-11-01
The famous equivalence theorem is reexamined in order to make it applicable to the case of effective theories. We slightly modify the formulation of this theorem and prove it based on the notion of the generating functional for Green functions. This allows one to trace (directly in terms of graphs) the mutual cancellation of different groups of contributions.
Four Theorems on the Psychometric Function
May, Keith A.; Solomon, Joshua A.
2013-01-01
In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, . This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull “slope” parameter, , can be approximated by , where is the of the Weibull function that fits best to the cumulative noise distribution, and depends on the transducer. We derive general expressions for and , from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when , . We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4–0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of for contrast discrimination suggests that, if internal noise is stimulus-independent, it has lower kurtosis than a Gaussian. PMID:24124456
A Decomposition Theorem for Finite Automata.
ERIC Educational Resources Information Center
Santa Coloma, Teresa L.; Tucci, Ralph P.
1990-01-01
Described is automata theory which is a branch of theoretical computer science. A decomposition theorem is presented that is easier than the Krohn-Rhodes theorem. Included are the definitions, the theorem, and a proof. (KR)
Point and Circle Configurations; A New Theorem.
ERIC Educational Resources Information Center
Dorwart, Harold L.
1988-01-01
Point and circle configurations are not well known, so Clifford's chain of theorems and Miquel's theorem, whose diagrams exhibit such configurations, are discussed. A new theorem similar to Miquel's is then presented. (MNS)
Food limitation of sea lion pups and the decline of forage off central and southern California
McClatchie, Sam; Field, John; Thompson, Andrew R.; Gerrodette, Tim; Lowry, Mark; Fiedler, Paul C.; Watson, William; Nieto, Karen M.; Vetter, Russell D.
2016-01-01
California sea lions increased from approximately 50 000 to 340 000 animals in the last 40 years, and their pups are starving and stranding on beaches in southern California, raising questions about the adequacy of their food supply. We investigated whether the declining sea lion pup weight at San Miguel rookery was associated with changes in abundance and quality of sardine, anchovy, rockfish and market squid forage. In the last decade off central California, where breeding female sea lions from San Miguel rookery feed, sardine and anchovy greatly decreased in biomass, whereas market squid and rockfish abundance increased. Pup weights fell as forage food quality declined associated with changes in the relative abundances of forage species. A model explained 67% of the variance in pup weights using forage from central and southern California and 81% of the variance in pup weights using forage from the female sea lion foraging range. A shift from high to poor quality forage for breeding females results in food limitation of the pups, ultimately flooding animal rescue centres with starving sea lion pups. Our study is unusual in using a long-term, fishery-independent dataset to directly address an important consequence of forage decline on the productivity of a large marine predator. Whether forage declines are environmentally driven, are due to a combination of environmental drivers and fishing removals, or are due to density-dependent interactions between forage and sea lions is uncertain. However, declining forage abundance and quality was coherent over a large area (32.5–38° N) for a decade, suggesting that trends in forage are environmentally driven. PMID:27069651
Food limitation of sea lion pups and the decline of forage off central and southern California.
McClatchie, Sam; Field, John; Thompson, Andrew R; Gerrodette, Tim; Lowry, Mark; Fiedler, Paul C; Watson, William; Nieto, Karen M; Vetter, Russell D
2016-03-01
California sea lions increased from approximately 50 000 to 340 000 animals in the last 40 years, and their pups are starving and stranding on beaches in southern California, raising questions about the adequacy of their food supply. We investigated whether the declining sea lion pup weight at San Miguel rookery was associated with changes in abundance and quality of sardine, anchovy, rockfish and market squid forage. In the last decade off central California, where breeding female sea lions from San Miguel rookery feed, sardine and anchovy greatly decreased in biomass, whereas market squid and rockfish abundance increased. Pup weights fell as forage food quality declined associated with changes in the relative abundances of forage species. A model explained 67% of the variance in pup weights using forage from central and southern California and 81% of the variance in pup weights using forage from the female sea lion foraging range. A shift from high to poor quality forage for breeding females results in food limitation of the pups, ultimately flooding animal rescue centres with starving sea lion pups. Our study is unusual in using a long-term, fishery-independent dataset to directly address an important consequence of forage decline on the productivity of a large marine predator. Whether forage declines are environmentally driven, are due to a combination of environmental drivers and fishing removals, or are due to density-dependent interactions between forage and sea lions is uncertain. However, declining forage abundance and quality was coherent over a large area (32.5-38° N) for a decade, suggesting that trends in forage are environmentally driven.
NASA Astrophysics Data System (ADS)
Eliazar, Iddo
2011-01-01
In this communication we establish stochastic limit laws leading from Zipf's law to Pareto's and Heaps' laws. We consider finite ensembles governed by Zipf's law and study their asymptotic statistics as the ensemble size tends to infinity. A Lorenz-curve analysis establishes three types of limit laws for the ensembles' statistical structure: 'communist', 'monarchic', and Paretian. Further considering a dynamic setting in which the ensembles grow stochastically in time, a functional central limit theorem analysis establishes a Gaussian approximation for the ensembles' stochastic growth. The Gaussian approximation provides a generalized and corrected formulation of Heaps' law.
On the Crooks fluctuation theorem and the Jarzynski equality
Chen, L. Y.
2008-01-01
The Jarzynski equality (JE) and the undergirding Crooks fluctuation theorem (CFT) have generated intense interest recently among researchers in physical and biological sciences. It has been held that the CFT has wider applicability than the JE. This note shows that the two are equally applicable and that their applicability is possibly limited to near-equilibrium processes, where the linear fluctuation-dissipation theorem holds. PMID:19044857
A new VLA/e-MERLIN limit on central images in the gravitational lens system CLASS B1030+074
NASA Astrophysics Data System (ADS)
Quinn, Jonathan; Jackson, Neal; Tagore, Amitpal; Biggs, Andrew; Birkinshaw, Mark; Chapman, Scott; De Zotti, Gianfranco; McKean, John; Pérez-Fournon, Ismael; Scott, Douglas; Serjeant, Stephen
2016-07-01
We present the new Very Large Array 22 GHz and extended Multi-Element Remote-Linked Interferometer Network 5 GHz observations of CLASS B1030+074, a two-image strong gravitational lens system whose background source is a compact flat-spectrum radio quasar. In such systems we expect a third image of the background source to form close to the centre of the lensing galaxy. The existence and brightness of such images is important for investigation of the central mass distributions of lensing galaxies, but only one secure detection has been made so far in a galaxy-scale lens system. The noise levels achieved in our new B1030+074 images reach 3 μJy beam-1 and represent an improvement in central image constraints of nearly an order of magnitude over previous work, with correspondingly better resulting limits on the shape of the central mass profile of the lensing galaxy. Simple models with an isothermal outer power-law slope now require either the influence of a central supermassive black hole (SMBH), or an inner power-law slope very close to isothermal, in order to suppress the central image below our detection limit. Using the central mass profiles inferred from light distributions in Virgo galaxies, moved to z = 0.5, and matching to the observed Einstein radius, we now find that 45 per cent of such mass profiles should give observable central images, 10 per cent should give central images with a flux density still below our limit, and the remaining systems have extreme demagnification produced by the central SMBH. Further observations of similar objects will therefore allow proper statistical constraints to be placed on the central properties of elliptical galaxies at high redshift.
Limits to physiological plasticity of the coral Pocillopora verrucosa from the central Red Sea
NASA Astrophysics Data System (ADS)
Ziegler, Maren; Roder, Cornelia M.; Büchel, Claudia; Voolstra, Christian R.
2014-12-01
Many coral species display changing distribution patterns across coral reef depths. While changes in the underwater light field and the ability to associate with different photosynthetic symbionts of the genus Symbiodinium explain some of the variation, the limits to physiological plasticity are unknown for most corals. In the central Red Sea, colonies of the branching coral Pocillopora verrucosa are most abundant in shallow high light environments and become less abundant in water depths below 10 m. To further understand what determines this narrow distribution, we conducted a cross-depths transplant experiment looking at physiological plasticity and acclimation in regard to depth. Colonies from 5, 10, and 20 m were collected, transplanted to all depths, and re-investigated after 30 and 210 d. All coral colonies transplanted downward from shallow to deep water displayed an increase in photosynthetic light-harvesting pigments, which resulted in higher photosynthetic efficiency. Shallow-water specimens transplanted to deeper water showed a significant decrease in total protein content after 30 and 210 d under low light conditions compared to specimens transplanted to shallow and medium depths. Stable isotope data suggest that heterotrophic input of carbon was not increased under low light, and consequently, decreasing protein levels were symptomatic of decreasing photosynthetic rates that could not be compensated for through higher light-harvesting efficiency. Our results provide insights into the physiological plasticity of P. verrucosa in changing light regimes and explain the observed depth distribution pattern. Despite its high abundance in shallow reef waters, P. verrucosa possesses limited heterotrophic acclimation potential, i.e., the ability to support its mainly photoautotrophic diet through heterotrophic feeding. We conclude that P. verrucosa might be a species vulnerable to sudden changes in underwater light fields resulting from processes such as
Using Bayes' theorem for free energy calculations
NASA Astrophysics Data System (ADS)
Rogers, David M.
Statistical mechanics is fundamentally based on calculating the probabilities of molecular-scale events. Although Bayes' theorem has generally been recognized as providing key guiding principals for setup and analysis of statistical experiments [83], classical frequentist models still predominate in the world of computational experimentation. As a starting point for widespread application of Bayesian methods in statistical mechanics, we investigate the central quantity of free energies from this perspective. This dissertation thus reviews the basics of Bayes' view of probability theory, and the maximum entropy formulation of statistical mechanics before providing examples of its application to several advanced research areas. We first apply Bayes' theorem to a multinomial counting problem in order to determine inner shell and hard sphere solvation free energy components of Quasi-Chemical Theory [140]. We proceed to consider the general problem of free energy calculations from samples of interaction energy distributions. From there, we turn to spline-based estimation of the potential of mean force [142], and empirical modeling of observed dynamics using integrator matching. The results of this research are expected to advance the state of the art in coarse-graining methods, as they allow a systematic connection from high-resolution (atomic) to low-resolution (coarse) structure and dynamics. In total, our work on these problems constitutes a critical starting point for further application of Bayes' theorem in all areas of statistical mechanics. It is hoped that the understanding so gained will allow for improvements in comparisons between theory and experiment.
Generalized Sampling Theorem for Bandpass Signals
NASA Astrophysics Data System (ADS)
Prokes, Ales
2006-12-01
The reconstruction of an unknown continuously defined function[InlineEquation not available: see fulltext.] from the samples of the responses of[InlineEquation not available: see fulltext.] linear time-invariant (LTI) systems sampled by the[InlineEquation not available: see fulltext.]th Nyquist rate is the aim of the generalized sampling. Papoulis (1977) provided an elegant solution for the case where[InlineEquation not available: see fulltext.] is a band-limited function with finite energy and the sampling rate is equal to[InlineEquation not available: see fulltext.] times cutoff frequency. In this paper, the scope of the Papoulis theory is extended to the case of bandpass signals. In the first part, a generalized sampling theorem (GST) for bandpass signals is presented. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed.
Analogues of Chernoff's theorem and the Lie-Trotter theorem
Neklyudov, Alexander Yu
2009-10-31
This paper is concerned with the abstract Cauchy problem .x=Ax, x(0)=x{sub 0} element of D(A), where A is a densely defined linear operator on a Banach space X. It is proved that a solution x( {center_dot} ) of this problem can be represented as the weak limit lim {sub n{yields}}{sub {infinity}}{l_brace}F(t/n){sup n}x{sub 0}{r_brace}, where the function F:[0,{infinity}){yields}L(X) satisfies the equality F'(0)y=Ay, y element of D(A), for a natural class of operators. As distinct from Chernoff's theorem, the existence of a global solution to the Cauchy problem is not assumed. Based on this result, necessary and sufficient conditions are found for the linear operator C to be closable and for its closure to be the generator of a C{sub 0}-semigroup. Also, we obtain new criteria for the sum of two generators of C{sub 0}-semigroups to be the generator of a C{sub 0}-semigroup and for the Lie-Trotter formula to hold. Bibliography: 13 titles.
Floquet theorem with open systems and its applications
NASA Astrophysics Data System (ADS)
Dai, C. M.; Shi, Z. C.; Yi, X. X.
2016-03-01
For a closed quantum system described by a time-periodic Hamiltonian, Floquet theorem says that the time evolution operator can be written as U (t ,0 ) ≡P (t ) e-i/ℏ HFt with P (t +T )=P (t ) , and HF is Hermitian and time independent and called the Floquet Hamiltonian. In this work, we extend the Floquet theorem from closed to open systems described by a time-periodic Lindblad master equation with period T =2/π ω . We derive an expansion for the Lindbladian in powers of 1/ω . Two examples are presented to illustrate the theorem. We find that the results given by the Lindbladian expansion based on the open system Floquet theorem agree well with the exact dynamics in the high-frequency limit. It may find applications in quantum engineering with systems subject to decoherence.
Mlakar, Jernej; Zorman, Jerneja Videčnik; Matičič, Mojca; Vrabec, Matej; Alibegović, Armin; Popović, Mara
2016-02-01
Primary angiitis of the central nervous system is a rare condition, usually with an insidious onset. There is a wide variety of histological types (granulomatous, lymphocytic or necrotizing vasculitis) and types of vessel involved (arteries, veins or both). Most cases are idiopathic. We describe a first case of idiopathic granulomatous central nervous system phlebitis with additional limited involvement of the heart and lung, exclusively affecting small and medium sized veins in a 22-year-old woman, presenting as a sub acute headache. The reasons for this peculiar limitation of inflammation to the veins and the involvement of the heart and lungs are unknown.
The Digital Morphological Sampling Theorem
NASA Astrophysics Data System (ADS)
Haralick, Robert M.; Zhuang, Xinhua; Lin, Charlotte; Lee, James
1988-02-01
There are potential industrial applications for any methodology which inherently reduces processing time and cost and yet produces results sufficiently close to the result of full processing. It is for this reason that a morphological sampling theorem is important. The morphological sampling theorem described in this paper states: (1) how a digital image must be morphologically filtered before sampling in order to preserve the relevant information after sampling; (2) to what precision an appropriately morphologically filtered image can be reconstructed after sampling; and (3) the relationship between morphologically operating before sampling and the more computationally efficient scheme of morphologically operating on the sampled image with a sampled structuring element. The digital sampling theorem is developed first for the case of binary morphology and then it is extended to gray scale morphology through the use of the umbra homomorphism theorems.
Factor and Remainder Theorems: An Appreciation
ERIC Educational Resources Information Center
Weiss, Michael
2016-01-01
The high school curriculum sometimes seems like a disconnected collection of topics and techniques. Theorems like the factor theorem and the remainder theorem can play an important role as a conceptual "glue" that holds the curriculum together. These two theorems establish the connection between the factors of a polynomial, the solutions…
MEASURABLE UTILITY AND THE MEASURABLE CHOICE THEOREM.
Three theorems are proved that are useful in mathematical treatments of economic models with a continuum of economic agents . The first, called the...measurable. Both these theorems generalize known theorems on these subjects. The third theorem treats a situation in which the set of economic agents forms
Comparison theorems for causal diamonds
NASA Astrophysics Data System (ADS)
Berthiere, Clément; Gibbons, Gary; Solodukhin, Sergey N.
2015-09-01
We formulate certain inequalities for the geometric quantities characterizing causal diamonds in curved and Minkowski spacetimes. These inequalities involve the redshift factor which, as we show explicitly in the spherically symmetric case, is monotonic in the radial direction, and it takes its maximal value at the center. As a by-product of our discussion we rederive Bishop's inequality without assuming the positivity of the spatial Ricci tensor. We then generalize our considerations to arbitrary, static and not necessarily spherically symmetric, asymptotically flat spacetimes. In the case of spacetimes with a horizon our generalization involves the so-called domain of dependence. The respective volume, expressed in terms of the duration measured by a distant observer compared with the volume of the domain in Minkowski spacetime, exhibits behaviors which differ if d =4 or d >4 . This peculiarity of four dimensions is due to the logarithmic subleading term in the asymptotic expansion of the metric near infinity. In terms of the invariant duration measured by a comoving observer associated with the diamond we establish an inequality which is universal for all d . We suggest some possible applications of our results including comparison theorems for entanglement entropy, causal set theory, and fundamental limits on computation.
Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes
Woolgar, Eric; Wylie, William
2016-02-15
We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.
The universality of the Carnot theorem
NASA Astrophysics Data System (ADS)
Gonzalez-Ayala, Julian; Angulo-Brown, F.
2013-03-01
It is common in many thermodynamics textbooks to illustrate the Carnot theorem through the use of diverse state equations for gases, paramagnets, and other simple thermodynamic systems. As is well known, the universality of the Carnot efficiency is easily demonstrated in a temperature-entropy diagram, which means that ηC is independent of the working substance. In this paper we remark that the universality of the Carnot theorem goes beyond conventional state equations, and is fulfilled by gas state equations that do not correspond to an ideal gas in the dilution limit, namely V → ∞. Some of these unconventional state equations have certain thermodynamic ‘anomalies’ that nonetheless do not forbid them from obeying the Carnot theorem. We discuss how this very general behaviour arises from Maxwell relations, which are connected with a geometrical property expressed through preserving area transformations. A rule is proposed to calculate the Maxwell relations associated with a thermodynamic system by using the preserving area relationships. In this way it is possible to calculate the number of possible preserving area mappings by giving the number of possible Jacobian identities between all pairs of thermodynamic variables included in the corresponding Gibbs equation. This paper is intended for undergraduates and specialists in thermodynamics and related areas.
More on soft theorems: Trees, loops, and strings
NASA Astrophysics Data System (ADS)
Bianchi, Massimo; He, Song; Huang, Yu-tin; Wen, Congkao
2015-09-01
We study soft theorems in a broader context, their universality in effective field theories and string theory, as well as continue the analysis of their fate at loop level. In effective field theories with F3 and R3 interactions, the soft theorems are not modified. However, for gravity theories with R2ϕ interactions, the sub-subleading order soft graviton theorem, which is beyond what is implied by the extended Bondi, van der Burg, Metzner, and Sachs symmetry, requires modifications at tree level for nonsupersymmetric theories and at loop level for N ≤4 supergravity due to anomalies. For open and closed superstrings at finite α', via explicit calculation for lower-point examples as well as world sheet operator product expansion analysis for arbitrary multiplicity, we show that scattering amplitudes satisfy the same soft theorem as their field-theory counterpart. This is no longer true for closed bosonic or heterotic strings due to the presence of R2ϕ interactions. We also consider loop corrections to gauge theories in the planar limit, where we show that tree-level soft gluon theorems are respected at the integrand level for 1 ≤N ≤4 SYM. Finally, we discuss the fate of soft theorems for finite loop amplitudes in pure Yang-Mills theory and gravity.
Randall B. Heiligmann; Jeffery S. Ward
1993-01-01
The effects of diameter-limit cutting on the future species composition and development of 60-80 year-old upland oak stands were studied in southern Ohio. Four treatments, 11-inch diameter-limit cut, 14-inch diameter-limit cut with selective thinning, 14-inch diameter-limit cut with low thinning, and uncut control were evaluated on medium oak sites (black oak site...
Distributed Online Judge System for Interactive Theorem Provers
NASA Astrophysics Data System (ADS)
Mizuno, Takahisa; Nishizaki, Shin-ya
2014-03-01
In this paper, we propose a new software design of an online judge system for interactive theorem proving. The distinctive feature of this architecture is that our online judge system is distributed on the network and especially involves volunteer computing. In volunteers' computers, network bots (software robots) are executed and donate computational resources to the central host of the online judge system. Our proposed design improves fault tolerance and security. We gave an implementation to two different styles of interactive theorem prover, Coq and ACL2, and evaluated our proposed architecture. From the experiment on the implementation, we concluded that our architecture is efficient enough to be used practically.
Aurora B suppresses microtubule dynamics and limits central spindle size by locally activating KIF4A
Nunes Bastos, Ricardo; Gandhi, Sapan R.; Baron, Ryan D.; Gruneberg, Ulrike; Nigg, Erich A.
2013-01-01
Anaphase central spindle formation is controlled by the microtubule-stabilizing factor PRC1 and the kinesin KIF4A. We show that an MKlp2-dependent pool of Aurora B at the central spindle, rather than global Aurora B activity, regulates KIF4A accumulation at the central spindle. KIF4A phosphorylation by Aurora B stimulates the maximal microtubule-dependent ATPase activity of KIF4A and promotes its interaction with PRC1. In the presence of phosphorylated KIF4A, microtubules grew more slowly and showed long pauses in growth, resulting in the generation of shorter PRC1-stabilized microtubule overlaps in vitro. Cells expressing only mutant forms of KIF4A lacking the Aurora B phosphorylation site overextended the anaphase central spindle, demonstrating that this regulation is crucial for microtubule length control in vivo. Aurora B therefore ensures that suppression of microtubule dynamic instability by KIF4A is restricted to a specific subset of microtubules and thereby contributes to central spindle size control in anaphase. PMID:23940115
Ferromagnetism beyond Lieb's theorem
NASA Astrophysics Data System (ADS)
Costa, Natanael C.; Mendes-Santos, Tiago; Paiva, Thereza; Santos, Raimundo R. dos; Scalettar, Richard T.
2016-10-01
The noninteracting electronic structures of tight-binding models on bipartite lattices with unequal numbers of sites in the two sublattices have a number of unique features, including the presence of spatially localized eigenstates and flat bands. When a uniform on-site Hubbard interaction U is turned on, Lieb proved rigorously that at half-filling (ρ =1 ) the ground state has a nonzero spin. In this paper we consider a "CuO2 lattice" (also known as "Lieb lattice," or as a decorated square lattice), in which "d orbitals" occupy the vertices of the squares, while "p orbitals" lie halfway between two d orbitals; both d and p orbitals can accommodate only up to two electrons. We use exact determinant quantum Monte Carlo (DQMC) simulations to quantify the nature of magnetic order through the behavior of correlation functions and sublattice magnetizations in the different orbitals as a function of U and temperature; we have also calculated the projected density of states, and the compressibility. We study both the homogeneous (H) case, Ud=Up , originally considered by Lieb, and the inhomogeneous (IH) case, Ud≠Up . For the H case at half-filling, we found that the global magnetization rises sharply at weak coupling, and then stabilizes towards the strong-coupling (Heisenberg) value, as a result of the interplay between the ferromagnetism of like sites and the antiferromagnetism between unlike sites; we verified that the system is an insulator for all U . For the IH system at half-filling, we argue that the case Up≠Ud falls under Lieb's theorem, provided they are positive definite, so we used DQMC to probe the cases Up=0 ,Ud=U and Up=U ,Ud=0 . We found that the different environments of d and p sites lead to a ferromagnetic insulator when Ud=0 ; by contrast, Up=0 leads to to a metal without any magnetic ordering. In addition, we have also established that at density ρ =1 /3 , strong antiferromagnetic correlations set in, caused by the presence of one fermion on each
Wakefield, Ewan D; Phillips, Richard A; Matthiopoulos, Jason
2014-03-07
Animal populations are frequently limited by the availability of food or of habitat. In central-place foragers, the cost of accessing these resources is distance-dependent rather than uniform in space. However, in seabirds, a widely studied exemplar of this paradigm, empirical population models have hitherto ignored this cost. In part, this is because non-independence among colonies makes it difficult to define population units. Here, we model the effects of both resource availability and accessibility on populations of a wide-ranging, pelagic seabird, the black-browed albatross Thalassarche melanophris. Adopting a multi-scale approach, we define regional populations objectively as spatial clusters of colonies. We consider two readily quantifiable proxies of resource availability: the extent of neritic waters (the preferred foraging habitat) and net primary production (NPP). We show that the size of regional albatross populations has a strong dependence, after weighting for accessibility, on habitat availability and to a lesser extent, NPP. Our results provide indirect support for the hypothesis that seabird populations are regulated from the bottom-up by food availability during the breeding season, and also suggest that the spatio-temporal predictability of food may be limiting. Moreover, we demonstrate a straightforward, widely applicable method for estimating resource limitation in populations of central-place foragers.
Wakefield, Ewan D.; Phillips, Richard A.; Matthiopoulos, Jason
2014-01-01
Animal populations are frequently limited by the availability of food or of habitat. In central-place foragers, the cost of accessing these resources is distance-dependent rather than uniform in space. However, in seabirds, a widely studied exemplar of this paradigm, empirical population models have hitherto ignored this cost. In part, this is because non-independence among colonies makes it difficult to define population units. Here, we model the effects of both resource availability and accessibility on populations of a wide-ranging, pelagic seabird, the black-browed albatross Thalassarche melanophris. Adopting a multi-scale approach, we define regional populations objectively as spatial clusters of colonies. We consider two readily quantifiable proxies of resource availability: the extent of neritic waters (the preferred foraging habitat) and net primary production (NPP). We show that the size of regional albatross populations has a strong dependence, after weighting for accessibility, on habitat availability and to a lesser extent, NPP. Our results provide indirect support for the hypothesis that seabird populations are regulated from the bottom-up by food availability during the breeding season, and also suggest that the spatio-temporal predictability of food may be limiting. Moreover, we demonstrate a straightforward, widely applicable method for estimating resource limitation in populations of central-place foragers. PMID:24430849
Nambu-Goldstone theorem and spin-statistics theorem
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
2016-05-01
On December 19-21 in 2001, we organized a yearly workshop at Yukawa Institute for Theoretical Physics in Kyoto on the subject of “Fundamental Problems in Field Theory and their Implications”. Prof. Yoichiro Nambu attended this workshop and explained a necessary modification of the Nambu-Goldstone theorem when applied to non-relativistic systems. At the same workshop, I talked on a path integral formulation of the spin-statistics theorem. The present essay is on this memorable workshop, where I really enjoyed the discussions with Nambu, together with a short comment on the color freedom of quarks.
Formulation of Liouville's theorem for grand ensemble molecular simulations
NASA Astrophysics Data System (ADS)
Delle Site, Luigi
2016-02-01
Liouville's theorem in a grand ensemble, that is for situations where a system is in equilibrium with a reservoir of energy and particles, is a subject that, to our knowledge, has not been explicitly treated in literature related to molecular simulation. Instead, Liouville's theorem, a central concept for the correct employment of molecular simulation techniques, is implicitly considered only within the framework of systems where the total number of particles is fixed. However, the pressing demand of applied science in treating open systems leads to the question of the existence and possible exact formulation of Liouville's theorem when the number of particles changes during the dynamical evolution of the system. The intention of this paper is to stimulate a debate about this crucial issue for molecular simulation.
Time dependent electromagnetic fields and 4-dimensional Stokes' theorem
NASA Astrophysics Data System (ADS)
Andosca, Ryan; Singleton, Douglas
2016-11-01
Stokes' theorem is central to many aspects of physics—electromagnetism, the Aharonov-Bohm effect, and Wilson loops to name a few. However, the pedagogical examples and research work almost exclusively focus on situations where the fields are time-independent so that one need only deal with purely spatial line integrals (e.g., ∮ A . d x ) and purely spatial area integrals (e.g., ∫ ( ∇ × A ) . d a = ∫ B . d a ). Here, we address this gap by giving some explicit examples of how Stokes' theorem plays out with time-dependent fields in a full 4-dimensional spacetime context. We also discuss some unusual features of Stokes' theorem with time-dependent fields related to gauge transformations and non-simply connected topology.
NASA Astrophysics Data System (ADS)
Lampart, Jonas; Lewin, Mathieu
2015-12-01
We prove a generalized version of the RAGE theorem for N-body quantum systems. The result states that only bound states of systems with {0 ≤slant n ≤slant N} particles persist in the long time average. The limit is formulated by means of an appropriate weak topology for many-body systems, which was introduced by the second author in a previous work, and is based on reduced density matrices. This topology is connected to the weak-* topology of states on the algebras of canonical commutation or anti-commutation relations, and we give a formulation of our main result in this setting.
Four theorems on the psychometric function.
May, Keith A; Solomon, Joshua A
2013-01-01
In a 2-alternative forced-choice (2AFC) discrimination task, observers choose which of two stimuli has the higher value. The psychometric function for this task gives the probability of a correct response for a given stimulus difference, Δx. This paper proves four theorems about the psychometric function. Assuming the observer applies a transducer and adds noise, Theorem 1 derives a convenient general expression for the psychometric function. Discrimination data are often fitted with a Weibull function. Theorem 2 proves that the Weibull "slope" parameter, β, can be approximated by β(Noise) x β(Transducer), where β(Noise) is the β of the Weibull function that fits best to the cumulative noise distribution, and β(Transducer) depends on the transducer. We derive general expressions for β(Noise) and β(Transducer), from which we derive expressions for specific cases. One case that follows naturally from our general analysis is Pelli's finding that, when d' ∝ (Δx)(b), β ≈ β(Noise) x b. We also consider two limiting cases. Theorem 3 proves that, as sensitivity improves, 2AFC performance will usually approach that for a linear transducer, whatever the actual transducer; we show that this does not apply at signal levels where the transducer gradient is zero, which explains why it does not apply to contrast detection. Theorem 4 proves that, when the exponent of a power-function transducer approaches zero, 2AFC performance approaches that of a logarithmic transducer. We show that the power-function exponents of 0.4-0.5 fitted to suprathreshold contrast discrimination data are close enough to zero for the fitted psychometric function to be practically indistinguishable from that of a log transducer. Finally, Weibull β reflects the shape of the noise distribution, and we used our results to assess the recent claim that internal noise has higher kurtosis than a Gaussian. Our analysis of β for contrast discrimination suggests that, if internal noise is stimulus
New double soft emission theorems
NASA Astrophysics Data System (ADS)
Cachazo, Freddy; He, Song; Yuan, Ellis Ye
2015-09-01
We study the behavior of the tree-level S-matrix of a variety of theories as two particles become soft. By analogy with the recently found subleading soft theorems for gravitons and gluons, we explore subleading terms in double soft emissions. We first consider double soft scalar emissions and find subleading terms that are controlled by the angular momentum operator acting on hard particles. The order of the subleading theorems depends on the presence or not of color structures. Next we obtain a compact formula for the leading term in a double soft photon emission. The theories studied are a special Galileon, Dirac-Born-Infeld, Einstein-Maxwell-Scalar, nonlinear sigma model and Yang-Mills-Scalar. We use the recently found Cachazo-He-Yuan representation of these theories in order to give a simple proof of the leading order part of all these theorems.
Soft theorems in superstring theory
NASA Astrophysics Data System (ADS)
Sen, Ashoke
2017-06-01
We use insights from superstring field theory to prove the subleading soft graviton theorem for tree amplitudes of (compactified) heterotic and type II string theories for arbitrary number of finite energy NS (NSNS) sector external states but only one soft graviton. We also prove the leading soft graviton theorem in these theories for arbitrary number of external soft gravitons. In our analysis there is no restriction on the mass and spin of the finite energy external states. This method can also be used to give a proof of the subleading soft graviton theorem for tree amplitudes in quantum field theories coupled to gravity with generic interactions. We discuss the technical issue involved in extending this analysis to loop amplitudes of superstring theory including Ramond sector external states, and its possible resolution.
Doryńska, Agnieszka; Pajak, Andrzej; Kubinova, Ruzena; Malyutina, Sofia; Tamosiunas, Abdonas; Pikhart, Hynek; Peasey, Anne; Nikitin, Yuri; Marmot, Michael; Bobak, Martin
2012-11-01
to investigate functional limitations and their association with socioeconomic factors in four Central and Eastern European populations. a cross-sectional study of random population samples in Novosibirsk (Russia), Krakow (Poland), Kaunas (Lithuania) and six Czech towns participating in the HAPIEE study. Functional limitations (classified into tertiles of the SF-36 physical functioning subscale), socioeconomic circumstances and health behaviours were available for 34,431 subjects aged 45-69 years. the proportion of subjects in the worst tertile of the functional limitations score (≤80% of the maximum score) ranged from 21% of the men in Kaunas to 48% in Krakow women. In multivariate ordered logistic regression, functional limitations were strongly inversely associated with education and positively with material deprivation and with being economically inactive. Functional limitations were more common in male smokers and less common in alcohol drinkers. Socioeconomic characteristics explained some of the differences in functional limitations between populations. Health behaviours explained some of the differences between social groups in both genders and between populations in women. unexpectedly, functional limitations were not most common in the sample from Russia, the country with the highest mortality rates. All socioeconomic measures were strongly associated with functional limitations and made some contribution towards explaining differences in limitations between populations.
Long-term assessment of financial maturity, diameter-limit selection in the central Appalachians
Thomas M. Schuler; David W. McGill
2007-01-01
Financial maturity, diameter-limit (FMDL) selection was proposed more than three decades ago as a replacement for diameter-limit cutting. FMDL incorporates financial maturity guidelines for individual trees, high-priority removal of poorquality trees, and guidelines for residual basal area. We provide the first long-term assessment of this practice after more than...
Quantum cryptography without Bell's theorem
NASA Astrophysics Data System (ADS)
Bennett, Charles H.; Brassard, Gilles; Mermin, N. David
1992-02-01
Ekert has described a cryptographic scheme in which Einstein-Podolsky-Rosen (EPR) pairs of particles are used to generate identical random numbers in remote places, while Bell's theorem certifies that the particles have not been measured in transit by an eavesdropper. We describe a related but simpler EPR scheme and, without invoking Bell's theorem, prove it secure against more general attacks, including substitution of a fake EPR source. Finally we show our scheme is equivalent to the original 1984 key distribution scheme of Bennett and Brassard, which uses single particles instead of EPR pairs.
Berends, Inez E; Reitsma, Pieter
2005-10-01
In two studies it is examined whether lateral presentation of words in remedial practice for reading disabled children has additional effects to central presentation. The effect of limited exposure duration (LED) is also studied as a possible factor in inducing higher level decoding processes or increased processing speed of words. Two groups of Dutch reading disabled children (n1 = 25, mean age = 9;8 years and n2 = 36, mean age = 7;1 years) repeatedly practiced reading words presented in the left, right or the central visual field. The results show that all children improved substantially both in reading speed and accuracy, which demonstrates the importance of repetitive practice in reading to attain fluency in reading disabled children. Further analysis demonstrated that neither site of presentation nor limited exposure duration added significantly to the training results. These findings do not corroborate neuropsychological theories suggesting a special role for lateral presentations.
A low upper mass limit for the central black hole in the late-type galaxy NGC 4414
NASA Astrophysics Data System (ADS)
Thater, S.; Krajnović, D.; Bourne, M. A.; Cappellari, M.; de Zeeuw, T.; Emsellem, E.; Magorrian, J.; McDermid, R. M.; Sarzi, M.; van de Ven, G.
2017-01-01
We present our mass estimate of the central black hole in the isolated spiral galaxy NGC 4414. Using natural guide star adaptive optics assisted observations with the Gemini Near-Infrared Integral Field Spectrometer (NIFS) and the natural seeing Gemini Multi-Object Spectrographs-North (GMOS), we derived two-dimensional stellar kinematic maps of NGC 4414 covering the central 1.5 arcsec and 10 arcsec, respectively, at a NIFS spatial resolution of 0.13 arcsec. The kinematic maps reveal a regular rotation pattern and a central velocity dispersion dip down to around 105 km s-1. We constructed dynamical models using two different methods: Jeans anisotropic dynamical modeling and axisymmetric Schwarzschild modeling. Both modeling methods give consistent results, but we cannot constrain the lower mass limit and only measure an upper limit for the black hole mass of MBH = 1.56 × 106M⊙ (at 3σ level) which is at least 1σ below the recent MBH-σe relations. Further tests with dark matter, mass-to-light ratio variation and different light models confirm that our results are not dominated by uncertainties. The derived upper limit mass is not only below the MBH-σe relation, but is also five times lower than the lower limit black hole mass anticipated from the resolution limit of the sphere of influence. This proves that via high quality integral field data we are now able to push black hole measurements down to at least five times less than the resolution limit. The reduced data cubes (FITS files) are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/597/A18
Pine (Pinus sylvestris L. ) tree-limit surveillance during recent decades, central Sweden
Kullman, L. )
1993-02-01
The altitudinal tree-limit of Scots pine (Pinus sylvestris L.) has been surveyed at the population level since the early- and mid-1970s in the Swedish Scandes. Elevational tree-limit advance was recorded for the majority of sites, despite statistically stable, although highly fluctuating climate with clusters of exceptionally cold winters and many relatively cool summers. The new tree-limit derived from pines established in the late 1950s. Tree-limit rise was concurrent with net population decline for the period 1972 to 1991, mainly as a result of failing regeneration. The main factor of individual vitality depression and mortality was deduced to be winter desiccation. The progressive tree-limit has a tendency for slow upslope advance during periods of climatic stability, even if punctuated by shorter events of unfavorable climate. Pine tree-limit dynamics is suggested to be a complex of climate/age/disturbance interactions. The tree-limit may decline altitudinally mainly in response to secular climate cooling, which makes it best suited for surveying sustained climatic trends and analogous paleoclimatic reconstruction. 51 refs., 12 figs., 1 tabs.
Generalized energy measurements and modified transient quantum fluctuation theorems.
Watanabe, Gentaro; Venkatesh, B Prasanna; Talkner, Peter
2014-05-01
Determining the work which is supplied to a system by an external agent provides a crucial step in any experimental realization of transient fluctuation relations. This, however, poses a problem for quantum systems, where the standard procedure requires the projective measurement of energy at the beginning and the end of the protocol. Unfortunately, projective measurements, which are preferable from the point of view of theory, seem to be difficult to implement experimentally. We demonstrate that, when using a particular type of generalized energy measurements, the resulting work statistics is simply related to that of projective measurements. This relation between the two work statistics entails the existence of modified transient fluctuation relations. The modifications are exclusively determined by the errors incurred in the generalized energy measurements. They are universal in the sense that they do not depend on the force protocol. Particularly simple expressions for the modified Crooks relation and Jarzynski equality are found for Gaussian energy measurements. These can be obtained by a sequence of sufficiently many generalized measurements which need not be Gaussian. In accordance with the central limit theorem, this leads to an effective error reduction in the individual measurements and even yields a projective measurement in the limit of infinite repetitions.
The Variation Theorem Applied to H-2+: A Simple Quantum Chemistry Computer Project
ERIC Educational Resources Information Center
Robiette, Alan G.
1975-01-01
Describes a student project which requires limited knowledge of Fortran and only minimal computing resources. The results illustrate such important principles of quantum mechanics as the variation theorem and the virial theorem. Presents sample calculations and the subprogram for energy calculations. (GS)
The Variation Theorem Applied to H-2+: A Simple Quantum Chemistry Computer Project
ERIC Educational Resources Information Center
Robiette, Alan G.
1975-01-01
Describes a student project which requires limited knowledge of Fortran and only minimal computing resources. The results illustrate such important principles of quantum mechanics as the variation theorem and the virial theorem. Presents sample calculations and the subprogram for energy calculations. (GS)
Tribal Minor NSR Synthetic Minor Limit Application Form in EPA's South Central Region
This Tribal Minor NSR application form should be used to notify the EPA Region 6 Tribal NSR Permitting Program of requested synthetic minor emission limits associated with a new source general application form.
Merlo, Rion; Witzgall, Bob; Yu, William; Ohlinger, Kurt; Ramberg, Steve; De Las Casas, Carla; Henneman, Seppi; Parker, Denny
2015-12-01
The Sacramento Regional County Sanitation District (District) must be compliant with stringent nitrogen limits by 2021 that the existing treatment facilities cannot meet. An 11-month pilot study was conducted to confirm that these limits could be met with an air activated sludge biological nutrient removal (BNR) process. The pilot BNR treated an average flow of 946 m(3)/d and demonstrated that it could reliably meet the ammonia limit, but that external carbon addition may be necessary to satisfy the nitrate limit. The BNR process performed well throughout the 11 months of operation with good settleability, minimal nocardioform content, and high quality secondary effluent. The BNR process was operated at a minimum pH of 6.4 with no noticeable impact to nitrification rates. Increased secondary sludge production was observed during rainfall events and is attributed to a change in wastewater influent characteristics.
Generalized Pump-restriction Theorem
Sinitsyn, Nikolai A; Chernyak, Vladimir Y
2008-01-01
We formulate conditions under which periodic modulations of parameters on a finite graph with stochastic transitions among its nodes do not lead to overall pump currents through any given link. Our theorem unifies previously known results with the new ones and provides a universal approach to explore futher restrictions on stochastic pump effect in non-adiabatically driven systems with detailed balance.
Discovering the Inscribed Angle Theorem
ERIC Educational Resources Information Center
Roscoe, Matt B.
2012-01-01
Learning to play tennis is difficult. It takes practice, but it also helps to have a coach--someone who gives tips and pointers but allows the freedom to play the game on one's own. Learning to act like a mathematician is a similar process. Students report that the process of proving the inscribed angle theorem is challenging and, at times,…
Expanding the Interaction Equivalency Theorem
ERIC Educational Resources Information Center
Rodriguez, Brenda Cecilia Padilla; Armellini, Alejandro
2015-01-01
Although interaction is recognised as a key element for learning, its incorporation in online courses can be challenging. The interaction equivalency theorem provides guidelines: Meaningful learning can be supported as long as one of three types of interactions (learner-content, learner-teacher and learner-learner) is present at a high level. This…
NASA Astrophysics Data System (ADS)
Chambers, Chris M.; Moss, Ian G.
1994-08-01
A generalization of Price's theorem is given for application to inflationary cosmologies. Namely, we show that on a Schwarzschild-de Sitter background there are no static solutions to the wave or gravitational perturbation equations for modes with angular momentum greater than their intrinsic spin.
Angle Defect and Descartes' Theorem
ERIC Educational Resources Information Center
Scott, Paul
2006-01-01
Rene Descartes lived from 1596 to 1650. His contributions to geometry are still remembered today in the terminology "Descartes' plane". This paper discusses a simple theorem of Descartes, which enables students to easily determine the number of vertices of almost every polyhedron. (Contains 1 table and 2 figures.)
Discovering the Inscribed Angle Theorem
ERIC Educational Resources Information Center
Roscoe, Matt B.
2012-01-01
Learning to play tennis is difficult. It takes practice, but it also helps to have a coach--someone who gives tips and pointers but allows the freedom to play the game on one's own. Learning to act like a mathematician is a similar process. Students report that the process of proving the inscribed angle theorem is challenging and, at times,…
Arriving at the Pythagorean Theorem.
ERIC Educational Resources Information Center
Jaramillo, James; Brown, Jonathan Caius
This lesson plan uses group activity and manipulative materials to teach English-speaking students (ages 15-16) of diverse ethnic backgrounds an operatonal understanding of the Pythagorean Theorem. It is based on theories of constructivism and holism and includes teacher instructions, discussion questions, a retrospective vision, and an ancillary…
Limited irrigation of corn-based no-till crop rotations in West Central Great Plains
USDA-ARS?s Scientific Manuscript database
Due to numerous alternatives in crop sequence and changes in crop yield and price, finding the most profitable crop rotation for an area is a continuous research challenge. The objective of this study was to evaluate 1-, 2-, 3-, and 4-yr limited irrigation corn (Zea mays L.)-based crop rotations for...
Limited irrigation of corn-based no-till crop rotations in west central Great Plains.
USDA-ARS?s Scientific Manuscript database
Identifying the most profitable crop rotation for an area is a continuous research challenge. The objective of this study was to evaluate 2, 3, and 4 yr. limited irrigation corn (Zea mays L.) based crop rotations for grain yield, available soil water, crop water productivity, and profitability in co...
Pythagorean Theorem Proofs: Connecting Interactive Websites
ERIC Educational Resources Information Center
Lin, Cheng-Yao
2007-01-01
There are over 400 proofs of the Pythagorean Theorem. Some are visual proofs, others are algebraic. This paper features several proofs of the Pythagorean Theorem in different cultures--Greek, Chinese, Hindu and American. Several interactive websites are introduced to explore ways to prove this beautiful theorem. (Contains 8 figures.)
A Fundamental Theorem on Particle Acceleration
Xie, Ming
2003-05-01
A fundamental theorem on particle acceleration is derived from the reciprocity principle of electromagnetism and a rigorous proof of the theorem is presented. The theorem establishes a relation between acceleration and radiation, which is particularly useful for insightful understanding of and practical calculation about the first order acceleration in which energy gain of the accelerated particle is linearly proportional to the accelerating field.
A note on generalized Weyl's theorem
NASA Astrophysics Data System (ADS)
Zguitti, H.
2006-04-01
We prove that if either T or T* has the single-valued extension property, then the spectral mapping theorem holds for B-Weyl spectrum. If, moreover T is isoloid, and generalized Weyl's theorem holds for T, then generalized Weyl's theorem holds for f(T) for every . An application is given for algebraically paranormal operators.
Generalizations of Ptolemy and Brahmagupta Theorems
ERIC Educational Resources Information Center
Ayoub, Ayoub B.
2007-01-01
The Greek astronomer Ptolemy of Alexandria (second century) and the Indian mathematician Brahmagupta (sixth century) each have a significant theorem named after them. Both theorems have to do with cyclic quadrilaterals. Ptolemy's theorem states that: In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of two…
Generalizations of Ptolemy and Brahmagupta Theorems
ERIC Educational Resources Information Center
Ayoub, Ayoub B.
2007-01-01
The Greek astronomer Ptolemy of Alexandria (second century) and the Indian mathematician Brahmagupta (sixth century) each have a significant theorem named after them. Both theorems have to do with cyclic quadrilaterals. Ptolemy's theorem states that: In a cyclic quadrilateral, the product of the diagonals is equal to the sum of the products of two…
Khalfin's Theorem and Neutral Mesons Subsystem
NASA Astrophysics Data System (ADS)
Urbanowski, Krzysztof
2009-01-01
The consequences of Khalfin's Theorem are discussed. we find, eg., that diagonal matrix elements of the exact effective Hamiltonian for the neutral meson complex can not be equal if CPT symmetry holds and CP symmetry is violated. Within a given model we examine numerically the Khalfin's Theorem and show in a graphic form how the Khalfin's Theorem works.
An implicit sampling theorem for bounded bandlimited functions
NASA Technical Reports Server (NTRS)
Bar-David, I.
1974-01-01
A rigorous proof of the 'strong bias tone' scheme is embodied in the implicit sampling theorem. The representation of signals that are sample functions of possible nonstationary random processes being of principal interest, the proof could not directly invoke results from classical analysis, which depend on the existence of the Fourier transform of the function under consideration; rather, it is based on Zakai's (1965) theorem on the series expansion of functions, band-limited under a suitably extended definition. A practical circuit that restores an approximate version of the signal from its sine-wave-crossings is presented and possible improvements to it are discussed.
Sardiñas, Hillary S; Tom, Kathleen; Ponisio, Lauren Catherine; Rominger, Andrew; Kremen, Claire
2016-03-01
The delivery of ecosystem services by mobile organisms depends on the distribution of those organisms, which is, in turn, affected by resources at local and landscape scales. Pollinator-dependent crops rely on mobile animals like bees for crop production, and the spatial relationship between floral resources and nest location for these central-place foragers influences the delivery of pollination services. Current models that map pollination coverage in agricultural regions utilize landscape-level estimates of floral availability and nesting incidence inferred from expert opinion, rather than direct assessments. Foraging distance is often derived from proxies of bee body size, rather than direct measurements of foraging that account for behavioral responses to floral resource type and distribution. The lack of direct measurements of nesting incidence and foraging distances may lead to inaccurate mapping of pollination services. We examined the role of local-scale floral resource presence from hedgerow plantings on nest incidence of ground-nesting bees in field margins and within monoculture, conventionally managed sunflower fields in California's Central Valley. We tracked bee movement into fields using fluorescent powder. We then used these data to simulate the distribution of pollination services within a crop field. Contrary to expert opinion, we found that ground-nesting native bees nested both in fields and edges, though nesting rates declined with distance into field. Further, we detected no effect of field-margin floral enhancements on nesting. We found evidence of an exponential decay rate of bee movement into fields, indicating that foraging predominantly occurred in less than 1% of medium-sized bees' predicted typical foraging range. Although we found native bees nesting within agricultural fields, their restricted foraging movements likely centralize pollination near nest sites. Our data thus predict a heterogeneous distribution of pollination services
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is
Band limited emission with central frequency around 2 Hz accompanying powerful cyclones
NASA Technical Reports Server (NTRS)
Troitskaia, V. A.; Shepetnov, K. S.; Dvobnia, B. D.
1992-01-01
It has been found that powerful cyclones are proceeded, accompanied and followed by narrow band electromagnetic emission with central frequency around 2 Hz. It is shown that the signal from this emission is unique and clearly distinguishable from known types of magnetic pulsations, spectra of local thunderstorms, and signals from industrial sources. This emission was first observed during an unusually powerful cyclone with tornadoes in the western European part of the Soviet Union, which passed by the observatory of Borok from south to north-east. The emission has been confirmed by analysis of similar events in Antarctica. The phenomenon described presents a new aspect of interactions of processes in the lower atmosphere and the ionosphere.
Saoithín: A Theorem Prover for UTP
NASA Astrophysics Data System (ADS)
Butterfield, Andrew
Saoithín is a theorem prover developed to support the Unifying Theories of Programming (UTP) framework. Its primary design goal was to support the higher-order logic, alphabets, equational reasoning and "programs as predicates" style that is prevalent in much of the UTP literature, from the seminal work by Hoare & He [HH98] onwards. This paper describes the key features of the theorem prover, with an emphasis on the underlying foundations, and how these affect the design and implementation choices. These key features include: a formalisation of a UTP Theory; support for common proof strategies; sophisticated goal/law matching ; and user-defined language constructs. A simple theory of designs with some proof extracts is used to illustrate the above features. The theorem prover has been used with undergraduate students and we discuss some of those experiences. The paper then concludes with a discussion of current limitations and planned improvements to the tool.
Nakagawa, Shunsuke; Shinkoda, Yuichi; Hazeki, Daisuke; Imamura, Mari; Okamoto, Yasuhiro; Kawakami, Kiyoshi; Kawano, Yoshifumi
2016-07-01
Central diabetes insipidus (CDI) and relapse are frequently seen in multifocal Langerhans cell histiocytosis (LCH). We present two females with multifocal LCH who developed CDI 9 and 5 years after the initial diagnosis, respectively, as a relapse limited to the pituitary stalk. Combination chemotherapy with cytarabine reduced the mass in the pituitary stalk. Although CDI did not improve, there has been no anterior pituitary hormone deficiency (APHD), neurodegenerative disease in the central nervous system (ND-CNS) or additional relapse for 2 years after therapy. It was difficult to predict the development of CDI in these cases. CDI might develop very late in patients with multifocal LCH, and therefore strict follow-up is necessary, especially with regard to symptoms of CDI such as polydipsia and polyuria. For new-onset CDI with LCH, chemotherapy with cytarabine might be useful for preventing APHD and ND-CNS.
Level reduction and the quantum threshold theorem
NASA Astrophysics Data System (ADS)
Aliferis, Panagiotis (Panos)
Computers have led society to the information age revolutionizing central aspects of our lives from production and communication to education and entertainment. There exist, however, important problems which are intractable with the computers available today and, experience teaches us, will remain so even with the more advanced computers we can envision for tomorrow.Quantum computers promise speedups to some of these important but classically intractable problems. Simulating physical systems, a problem of interest in a diverse range of areas from testing physical theories to understanding chemical reactions, and solving number factoring, a problem at the basis of cryptographic protocols that are used widely today on the internet, are examples of applications for which quantum computers, when built, will offer a great advantage over what is possible with classical computer technology.The construction of a quantum computer of sufficient scale to solve interesting problems is, however, especially challenging. The reason for this is that, by its very nature, operating a quantum computer will require the coherent control of the quantum state of a very large number of particles. Fortunately, the theory of quantum error correction and fault-tolerant quantum computation gives us confidence that such quantum states can be created, can be stored in memory and can also be manipulated provided the quantum computer can be isolated to a sufficient degree from sources of noise.One of the central results in the theory of fault-tolerant quantum computation, the quantum threshold theorem shows that a noisy quantum computer can accurately and efficiently simulate any ideal quantum computation provided that noise is weakly correlated and its strength is below a critical value known as the quantum accuracy threshold. This thesis provides a simpler and more transparent non-inductive proof of this theorem based on the concept of level reduction. This concept is also used in proving the
Complex virial theorem and complex scaling
Junker, B.R.
1983-06-01
We present the simple generalization to complex energies of the normal global real scaling used for bound-state calculations to produce a variational energy which satisfies the virial theorem. We show that in two limiting cases, one or the other of which is almost always p satisfied in all calculations, the virially stabilized complex energy is sensitive to only the real part or the imaginary part of the complex virial expression. We then compute the virial expression for a number of wave functions for the 1s2s/sup 2/ /sup 2/S He/sup -/, 1s2s2p /sup 2/P/sup o/ He/sup -/, and 1s/sup 2/2s/sup 2/kp /sup 2/P/sup o/ Be/sup -/ resonances and the corresponding virially stabilized resonance energies. In all calculations one of the limiting cases was applicable.
The de Finetti theorem for test spaces
NASA Astrophysics Data System (ADS)
Barrett, Jonathan; Leifer, Matthew
2009-03-01
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical and quantum de Finetti theorems are obtained as special cases. By working in a test space framework, the common features that are responsible for the existence of these theorems are elucidated. In addition, the test space framework is general enough to imply a de Finetti theorem for classical processes. We conclude by discussing the ways in which our assumptions may fail, leading to probabilistic models that do not have a de Finetti theorem.
Generalized Bloch theorem and chiral transport phenomena
NASA Astrophysics Data System (ADS)
Yamamoto, Naoki
2015-10-01
Bloch theorem states the impossibility of persistent electric currents in the ground state of nonrelativistic fermion systems. We extend this theorem to generic systems based on the gauged particle number symmetry and study its consequences on the example of chiral transport phenomena. We show that the chiral magnetic effect can be understood as a generalization of the Bloch theorem to a nonequilibrium steady state, similarly to the integer quantum Hall effect. On the other hand, persistent axial currents are not prohibited by the Bloch theorem and they can be regarded as Pauli paramagnetism of relativistic matter. An application of the generalized Bloch theorem to quantum time crystals is also discussed.
Restriction limits and main drivers of fruit production in palm in central Amazonia
NASA Astrophysics Data System (ADS)
Freitas, Cintia; Costa, Flávia R. C.; Barbosa, Carlos Eduardo; Cintra, Renato
2016-11-01
Adult plants incapable of producing viable offspring inflate our perception of the size of population distribution. We propose that species occurrence is limited to a subset of the environmental gradient and that it changes as ontogenetic development progresses. Moreover, fruit production is associated with site-specific environmental conditions. We sampled 2988 adult individuals from nine palm species in 30 plots (40 × 250 m) and used a larger data set including 42 other plots distributed along a continuous topo-edaphic gradient in a terra firme forest near Manaus, Brazil. Five out of nine palm species were more restricted to a sub-section of the topo-edaphic gradient in the adult-size phase. More specifically, reproductive individuals of species Attalea attaleoides and A. microcarpa had even more restricted distributions than adult-sized, non-reproductive plants. Successive environmental filtering and competition probably acting through selective mortality led to increasing habitat restriction, with reproductive adults being restricted to a smaller part of the region than juveniles and adults. Water availability and nutrients limited both the ability to produce fruits and the amount of fruit production. Previous studies have reported stronger habitat associations for older plants than for seedlings or juveniles, but we show here that some species are more restricted at their reproductive stage. Plant specializations to local conditions may be more common than currently acknowledged, and a significant portion of individuals in a population might represent sinks. Such strong environmental limitations of reproductive plants should also be considered in management of species with economic value and in conservation planning.
Wu, Gregory F; Shindler, Kenneth S; Allenspach, Eric J; Stephen, Tom L; Thomas, Hannah L; Mikesell, Robert J; Cross, Anne H; Laufer, Terri M
2011-02-01
Experimental autoimmune encephalomyelitis (EAE), a model for the human disease multiple sclerosis (MS), is dependent upon the activation and effector functions of autoreactive CD4 T cells. Multiple interactions between CD4 T cells and major histocompatibility class II (MHCII)+ antigen presenting cells (APCs) must occur in both the periphery and central nervous system (CNS) to elicit autoimmunity. The identity of the MHCII+ APCs involved throughout this process remains in question. We investigated which APC in the periphery and CNS mediates disease using transgenic mice with MHCII expression restricted to dendritic cells (DCs). MHCII expression restricted to DCs results in normal susceptibility to peptide-mediated EAE. Indeed, radiation-sensitive bone marrow-derived DCs were sufficient for all APC functions during peptide-induced disease. However, DCs alone were inefficient at promoting disease after immunization with the myelin protein myelin oligodendrocyte glycoprotein (MOG), even in the presence of MHCII-deficient B cells. Consistent with a defect in disease induction following protein immunization, antigen presentation by DCs alone was incapable of mediating spontaneous optic neuritis. These results indicate that DCs are capable of perpetuating CNS-targeted autoimmunity when antigens are readily available, but other APCs are required to efficiently initiate pathogenic cognate CD4 T cell responses.
Evidence-based evaluation of information: the centrality and limitations of systematic reviews.
Järvholm, Bengt; Bohlin, Ingemar
2014-03-01
This introductory paper considers the value and limitations of the methodology of systematic reviews especially according to the evidence-based movement. It explains some terms and organisations producing systematic reviews. It also discusses controversies. The first concerns the criteria by which the quality of individual studies is assessed, the second the possible effects of the affiliation of some reviewers, and the third the value of formalisation of procedure (i.e. the tensions between formal tools and professional judgments). The article contrasts the evidence-based formalism with other formalisms as those by the Intergovernmental Panel on Climate Change and the International Agency for Research on Cancer. It discusses systematic reviews in social science where interventions are complex, difficult to blind, and depend on context. Systematic reviews in working life research are often focusing on prevention. The formal evidence-based process may devaluate or disregard findings from mechanistic and observational studies. Hence such reviews may falsely conclude that existing knowledge about the risk of the factor is limited or nonexistent.
IL-27 limits central nervous system viral clearance by promoting IL-10 and enhances demyelination.
de Aquino, Maria Teresa P; Kapil, Parul; Hinton, David R; Phares, Timothy W; Puntambekar, Shweta S; Savarin, Carine; Bergmann, Cornelia C; Stohlman, Stephen A
2014-07-01
IL-27 is a pleiotropic member of the IL-6 and IL-12 cytokine family composed of the IL-27p28 and the EBV-induced gene 3. IL-27 and its receptor mRNA are both upregulated in the CNS during acute encephalomyelitis induced by the JHM strain of mouse hepatitis virus (JHMV) and sustained during viral persistence. Contributions of IL-27 to viral pathogenesis were evaluated by infection of IL-27Rα-chain-deficient (IL-27Rα(-/-)) mice. The absence of IL-27 signaling accelerated virus control within the CNS associated with increased IFN-γ secreting virus-specific CD4+ and CD8+ T cells. Abrogation of IL-27 signaling did not affect virus-specific CD8+ T cell-mediated IL-10 production or cytolytic activity or Foxp3+ regulatory T cell populations. However, IL-10 production by virus-specific CD4+ T cells was reduced significantly. Despite increased T cell-mediated antiviral function in IL-27Rα(-/-) mice, the virus persisted in the CNS at similar levels as in wild-type mice. Nevertheless, IL-27Rα(-/-) mice exhibited decreased clinical disease during persistence, coincident with less severe demyelination, the hallmark tissue damage associated with JHMV infection. Overall, these data demonstrate that in contrast to viral infections at other sites, IL-27 does not play a proinflammatory role during JHMV-induced encephalomyelitis. Rather, it limits CNS inflammation and impairs control of CNS virus replication via induction of IL-10 in virus-specific CD4+ T cells. Furthermore, in contrast to its protective role in limiting CNS autoimmunity and preventing immunopathology, these data define a detrimental role of IL-27 in promoting demyelination by delaying viral control. Copyright © 2014 by The American Association of Immunologists, Inc.
IL-27 Limits Central Nervous System Viral Clearance by Promoting IL-10 and Enhances Demyelination
de Aquino, Maria Teresa P.; Kapil, Parul; Hinton, David R.; Phares, Timothy W.; Puntambekar, Shweta S.; Savarin, Carine; Bergmann, Cornelia C.
2014-01-01
IL-27 is a pleiotropic member of the IL-6 and IL-12 cytokine family composed of the IL-27p28 and the EBV-induced gene 3. IL-27 and its receptor mRNA are both upregulated in the CNS during acute encephalomyelitis induced by the JHM strain of mouse hepatitis virus (JHMV) and sustained during viral persistence. Contributions of IL-27 to viral pathogenesis were evaluated by infection of IL-27Rα-chain–deficient (IL-27Rα−/−) mice. The absence of IL-27 signaling accelerated virus control within the CNS associated with increased IFN-γ secreting virus-specific CD4+ and CD8+ T cells. Abrogation of IL-27 signaling did not affect virus-specific CD8+ T cell–mediated IL-10 production or cytolytic activity or Foxp3+ regulatory T cell populations. However, IL-10 production by virus-specific CD4+ T cells was reduced significantly. Despite increased T cell–mediated antiviral function in IL-27Rα−/− mice, the virus persisted in the CNS at similar levels as in wild-type mice. Nevertheless, IL-27Rα−/− mice exhibited decreased clinical disease during persistence, coincident with less severe demyelination, the hallmark tissue damage associated with JHMV infection. Overall, these data demonstrate that in contrast to viral infections at other sites, IL-27 does not play a proinflammatory role during JHMV-induced encephalomyelitis. Rather, it limits CNS inflammation and impairs control of CNS virus replication via induction of IL-10 in virus-specific CD4+ T cells. Furthermore, in contrast to its protective role in limiting CNS autoimmunity and preventing immunopathology, these data define a detrimental role of IL-27 in promoting demyelination by delaying viral control. PMID:24890725
Equivalence theorem of uncertainty relations
NASA Astrophysics Data System (ADS)
Li, Jun-Li; Qiao, Cong-Feng
2017-01-01
We present an equivalence theorem to unify the two classes of uncertainty relations, i.e. the variance-based ones and the entropic forms, showing that the entropy of an operator in a quantum system can be built from the variances of a set of commutative operators. This means that an uncertainty relation in the language of entropy may be mapped onto a variance-based one, and vice versa. Employing the equivalence theorem, alternative formulations of entropic uncertainty relations are obtained for the qubit system that are stronger than the existing ones in the literature, and variance-based uncertainty relations for spin systems are reached from the corresponding entropic uncertainty relations.
c-Theorem for disordered systems
NASA Astrophysics Data System (ADS)
Gurarie, V.
1999-05-01
We find an analog of Zamolodchikov's c-theorem for disordered two-dimensional non-interacting systems in their supersymmetric field theory representation. We show that the energy momentum tensor of such field theories must be a part of a supermultiplet, and that a new parameter b can be introduced with the help of that multiplet. b flows along the renormalization group trajectories much like the central charge for unitary two-dimensional field theories. While it has not been established if this flow is irreversible, that is, if b always flows down to lower values, it does so for all the cases worked out so far. b gives a new way to label different conformal field theories for disordered systems whose central charge is always 0. b turns out to be related to the central extension of a certain algebra, a generalization of the Virasoro algebra, which we show may be present at the critical points of these theories. b is also related to the finite size corrections of the physical free energy of disordered systems. We discuss possible applications by computing b for two-dimensional Dirac fermions with random gauge potential, in other words, for U(1∣1) Kac-Moody algebra.
Uniqueness Theorem for Black Objects
Rogatko, Marek
2010-06-23
We shall review the current status of uniqueness theorem for black objects in higher dimensional spacetime. At the beginning we consider static charged asymptotically flat spacelike hypersurface with compact interior with both degenerate and non-degenerate components of the event horizon in n-dimensional spacetime. We gave some remarks concerning partial results in proving uniqueness of stationary axisymmetric multidimensional solutions and winding numbers which can uniquely characterize the topology and symmetry structure of black objects.
Carbon balance indicates a time limit for cultivation of organic soils in central Switzerland
NASA Astrophysics Data System (ADS)
Paul, Sonja; Ammann, Christof; Alewell, Christine; Leifeld, Jens
2016-04-01
Peatlands serve as important carbon sinks. Globally, more than 30% of the soil organic carbon is stored in organic soils, although they cover only 3% of the land surface. The agricultural use of organic soils usually requires drainage thereby transforming these soils from a net carbon sink into a net source. Currently, about 2 to 3 Gt CO2 are emitted world-wide from degrading organic soils (Joosten 2011; Parish et al. 2008) which is ca. 5% of the total anthropogenic emissions. Besides these CO2 emissions, the resulting subsidence of drained peat soils during agricultural use requires that drainage system are periodically renewed and finally to use pumping systems after progressive subsidence. In Switzerland, the Seeland region is characterised by fens which are intensively used for agriculture since 1900. The organic layer is degrading and subsequently getting shallower and the underlying mineral soil, as lake marl or loam, is approaching the surface. The questions arises for how long and under which land use practises and costs these soils can be cultivated in the near future. The study site was under crop rotation until 2009 when it was converted to extensively used grassland with the water regime still being regulated. The soil is characterised by a degraded organic horizon of 40 to 70 cm. Since December 2014 we are measuring the carbon exchange of this grassland using the Eddy-Covariance method. For 2015, the carbon balance indicates that the degraded fen is a strong carbon source, with approximately 500 g C m-2 a-1. The carbon balance is dominated by CO2 emissions and harvest. Methane emissions are negligible. With the gained emission factors different future scenarios are evaluated for the current cultivation practise of organic soils in central Switzerland. Joosten, H., 2011: Neues Geld aus alten Mooren: Über die Erzeugung von Kohlenstoffzertifikaten aus Moorwiedervernässungen. Telma Beiheft 4, 183-202. Parish, F., A. Sirin, D. Charman, H. Joosten, T
Tschoep, Hendrik; Gibon, Yves; Carillo, Petronia; Armengaud, Patrick; Szecowka, Marek; Nunes-Nesi, Adriano; Fernie, Alisdair R; Koehl, Karin; Stitt, Mark
2009-03-01
We have established a simple soil-based experimental system that allows a small and sustained restriction of growth of Arabidopsis by low nitrogen (N). Plants were grown in a large volume of a peat-vermiculite mix that contained very low levels of inorganic N. As a control, inorganic N was added in solid form to the peat-vermiculite mix, or plants were grown in conventional nutrient-rich solids. The low N growth regime led to a sustained 20% decrease of the relative growth rate over a period of 2 weeks, resulting in a two- to threefold decrease in biomass in 35- to 40-day-old plants. Plants in the low N regime contained lower levels of nitrate, lower nitrate reductase activity, lower levels of malate, fumarate and other organic acids and slightly higher levels of starch, as expected from published studies of N-limited plants. However, their rosette protein content was unaltered, and total and many individual amino acid levels increased compared with N-replete plants. This metabolic phenotype reveals that Arabidopsis responds adaptively to low N by decreasing the rate of growth, while maintaining the overall protein content, and maintaining or even increasing the levels of many amino acids.
Limitations of selective deltamethrin application for triatomine control in central coastal Ecuador
2011-01-01
Background This year-long study evaluated the effectiveness of a strategy involving selective deltamethrin spraying and community education for control of Chagas disease vectors in domestic units located in rural communities of coastal Ecuador. Results Surveys for triatomines revealed peridomestic infestation with Rhodnius ecuadoriensis and Panstrongylus howardi, with infestation indices remaining high during the study (13%, 17%, and 10%, at initial, 6-month, and 12-month visits, respectively), which indicates a limitation of this strategy for triatomine population control. Infestation was found 6 and 12 months after spraying with deltamethrin. In addition, a large number of previously vector-free domestic units also were found infested at the 6- and 12-month surveys, which indicates new infestations by sylvatic triatomines. The predominance of young nymphs and adults suggests new infestation events, likely from sylvatic foci. In addition, infection with Trypanosoma cruzi was found in 65%, 21% and 29% at initial, 6-month and 12-month visits, respectively. All parasites isolated (n = 20) were identified as TcI. Conclusion New vector control strategies need to be devised and evaluated for reduction of T. cruzi transmission in this region. PMID:21332985
A global conformal extension theorem for perfect fluid Bianchi space-times
Luebbe, Christian Tod, Paul
2008-12-15
A global extension theorem is established for isotropic singularities in polytropic perfect fluid Bianchi space-times. When an extension is possible, the limiting behaviour of the physical space-time near the singularity is analysed.
Geldenhuys, C; Dramowski, A; Jenkins, A; Bekker, A
2017-08-25
The rate of central-line-associated bloodstream infection (CLABSI) in South African (SA) public sector neonatal intensive care units (NICUs) is unknown. Tygerberg Children's Hospital (TCH), Cape Town, introduced a neonatal CLABSI surveillance and prevention programme in August 2012. To describe CLABSI events and identify risk factors for development of CLABSI in a resource-limited NICU. A retrospective case-control study was conducted using prospectively collected NICU CLABSI events matched to four randomly selected controls, sampled from the NICU registry between 9 August 2012 and 31 July 2014. Clinical data and laboratory records were reviewed to identify possible risk factors, using stepwise forward logistic regression analysis. A total of 706 central lines were inserted in 530 neonates during the study period. Nineteen CLABSI events were identified, with a CLABSI rate of 5.9/1 000 line days. CLABSI patients were of lower gestational age (28 v. 34 weeks; p=0.003), lower median birth weight (1 170 g v. 1 975 g; p=0.014), had longer catheter dwell times (>4 days) (odds ratio (OR) 5.1 (95% confidence interval (CI) 1.0 - 25.4); p=0.04) and were more likely to have had surgery during their NICU stay (OR 3.5 (95% CI 1.26 - 10); p=0.01). Significant risk factors for CLABSI were length of stay >30 days (OR 20.7 (95% CI 2.1 - 203.2); p=0.009) and central-line insertion in the operating theatre (OR 8.1 (95% CI 1.2 - 54.7); p=0.03). Gram-negative pathogens predominated (12/22; 54%), with most isolates (10/12; 83%) exhibiting multidrug resistance. The TCH NICU CLABSI rate is similar to that reported from resource-limited settings, but exceeds that of high-income countries. Prolonged NICU stay and central-line insertion in the operating theatre were important risk factors for CLABSI development. Intensified neonatal staff training regarding CLABSI maintenance bundle elements and hand hygiene are key to reducing CLABSI rates.
Maleki Seifar, R.; ten Pierick, A.; van Helmond, W.; Pieterse, M. M.; Heijnen, J. J.
2016-01-01
ABSTRACT Ammonium is the most common N source for yeast fermentations. Although its transport and assimilation mechanisms are well documented, there have been only a few attempts to measure the in vivo intracellular concentration of ammonium and assess its impact on gene expression. Using an isotope dilution mass spectrometry (IDMS)-based method, we were able to measure the intracellular ammonium concentration in N-limited aerobic chemostat cultivations using three different N sources (ammonium, urea, and glutamate) at the same growth rate (0.05 h−1). The experimental results suggest that, at this growth rate, a similar concentration of intracellular (IC) ammonium, about 3.6 mmol NH4+/literIC, is required to supply the reactions in the central N metabolism, independent of the N source. Based on the experimental results and different assumptions, the vacuolar and cytosolic ammonium concentrations were estimated. Furthermore, we identified a futile cycle caused by NH3 leakage into the extracellular space, which can cost up to 30% of the ATP production of the cell under N-limited conditions, and a futile redox cycle between Gdh1 and Gdh2 reactions. Finally, using shotgun proteomics with protein expression determined relative to a labeled reference, differences between the various environmental conditions were identified and correlated with previously identified N compound-sensing mechanisms. IMPORTANCE In our work, we studied central N metabolism using quantitative approaches. First, intracellular ammonium was measured under different N sources. The results suggest that Saccharomyces cerevisiae cells maintain a constant NH4+ concentration (around 3 mmol NH4+/literIC), independent of the applied nitrogen source. We hypothesize that this amount of intracellular ammonium is required to obtain sufficient thermodynamic driving force. Furthermore, our calculations based on thermodynamic analysis of the transport mechanisms of ammonium suggest that ammonium is not equally
A Perron-Frobenius Type of Theorem for Quantum Operations
NASA Astrophysics Data System (ADS)
Lagro, Matthew; Yang, Wei-Shih; Xiong, Sheng
2017-08-01
We define a special class of quantum operations we call Markovian and show that it has the same spectral properties as a corresponding Markov chain. We then consider a convex combination of a quantum operation and a Markovian quantum operation and show that under a norm condition its spectrum has the same properties as in the conclusion of the Perron-Frobenius theorem if its Markovian part does. Moreover, under a compatibility condition of the two operations, we show that its limiting distribution is the same as the corresponding Markov chain. We apply our general results to partially decoherent quantum random walks with decoherence strength 0 ≤ p ≤ 1 . We obtain a quantum ergodic theorem for partially decoherent processes. We show that for 0 < p ≤ 1 , the limiting distribution of a partially decoherent quantum random walk is the same as the limiting distribution for the classical random walk.
A Perron-Frobenius Type of Theorem for Quantum Operations
NASA Astrophysics Data System (ADS)
Lagro, Matthew; Yang, Wei-Shih; Xiong, Sheng
2017-10-01
We define a special class of quantum operations we call Markovian and show that it has the same spectral properties as a corresponding Markov chain. We then consider a convex combination of a quantum operation and a Markovian quantum operation and show that under a norm condition its spectrum has the same properties as in the conclusion of the Perron-Frobenius theorem if its Markovian part does. Moreover, under a compatibility condition of the two operations, we show that its limiting distribution is the same as the corresponding Markov chain. We apply our general results to partially decoherent quantum random walks with decoherence strength 0 ≤ p ≤ 1. We obtain a quantum ergodic theorem for partially decoherent processes. We show that for 0 < p ≤ 1, the limiting distribution of a partially decoherent quantum random walk is the same as the limiting distribution for the classical random walk.
Fluctuation theorem for partially masked nonequilibrium dynamics
NASA Astrophysics Data System (ADS)
Shiraishi, Naoto; Sagawa, Takahiro
2015-01-01
We establish a generalization of the fluctuation theorem for partially masked nonequilibrium dynamics. We introduce a partial entropy production with a subset of all possible transitions, and show that the partial entropy production satisfies the integral fluctuation theorem. Our result reveals the fundamental properties of a broad class of autonomous as well as nonautonomous nanomachines. In particular, our result gives a unified fluctuation theorem for both autonomous and nonautonomous Maxwell's demons, where mutual information plays a crucial role. Furthermore, we derive a fluctuation-dissipation theorem that relates nonequilibrium stationary current to two kinds of equilibrium fluctuations.
Scattering theorems for dyadic chiral fields
NASA Astrophysics Data System (ADS)
Athanasiadis, Christodoulos; Gotopoulos, Stavros
2004-06-01
A time-harmonic plane dyadic electromagnetic field is scattered by a chiral body in a chiral environment. The body is either a perfect conductor or a dielectric. The incident field is a linear combination of left-circularly polarized and right-circularly polarized dyadic electromagnetic fields, each of which has a different wave number. We prove reciprocity and scattering theorems in dyadic form, which incorporate as special cases the corresponding known theorems for vector electromagnetic waves. Specializing to the same direction of incidence and observation in the general scattering theorems we obtain forward scattering theorems.
On Liouville's theorem in fluid mechanics
NASA Astrophysics Data System (ADS)
Morrison, P. J.; Bouchet, F.; Thalabard, S.; Zaboronski, O. V.
2011-11-01
Since the early work of Burgers it has been known that discretizations of fluid models possess a version of Liouville's theorem on conservation of phase space volume. In fact, spectral representations of two-dimensional turbulence are known to have a detailed version of this theorem. The existence of such Liouville theorems led many (e.g. Burgers, Lee, Kraichnan and Montgomery) to consider various statistical mechanical approaches to turbulence. We show how this theorem arises naturally from the Hamiltonian structure of inviscid fluid equations.
Cosmological perturbations and the Weinberg theorem
Akhshik, Mohammad; Firouzjahi, Hassan; Jazayeri, Sadra E-mail: firouz@ipm.ir
2015-12-01
The celebrated Weinberg theorem in cosmological perturbation theory states that there always exist two adiabatic scalar modes in which the comoving curvature perturbation is conserved on super-horizon scales. In particular, when the perturbations are generated from a single source, such as in single field models of inflation, both of the two allowed independent solutions are adiabatic and conserved on super-horizon scales. There are few known examples in literature which violate this theorem. We revisit the theorem and specify the loopholes in some technical assumptions which violate the theorem in models of non-attractor inflation, fluid inflation, solid inflation and in the model of pseudo conformal universe.
The matching theorems and coincidence theorems for generalized R-KKM mapping in topological spaces
NASA Astrophysics Data System (ADS)
Huang, Jianhua
2005-12-01
In this paper we present some new matching theorems with open cover and closed cover by using the generalized R-KKM theorems [L. Deng, X. Xia, Generalized R-KKM theorem in topological space and their applications, J. Math. Anal. Appl. 285 (2003) 679-690] in the topological spaces with property (H). As applications, some coincidence theorems are established in topological spaces. Our results extend and generalize some known results.
INTERPOLATION THEOREMS FOR THE SPACES L_{p,q}
NASA Astrophysics Data System (ADS)
Ovchinnikov, V. I.
1989-02-01
A sharp or optimal interpolation theorem is proved for the Lorentz spaces L_{p,q}, generalizing the Marcinkiewicz theorem and refining the Riesz-Thorin theorem and the Stein-Weiss theorem. This theorem extends to the spaces \\overline{X}_{\\theta,p} of the real method constructed from any Banach pair; thus it extends also to Besov spaces.Bibliography: 12 titles.
Uniqueness theorems in bioluminescence tomography.
Wang, Ge; Li, Yi; Jiang, Ming
2004-08-01
Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed in the University of Iowa. While the forward imaging model is described by the well-known diffusion equation, the inverse problem is to recover an internal bioluminescent source distribution subject to Cauchy data. Our primary goal in this paper is to establish the solution uniqueness for BLT under practical constraints despite the ill-posedness of the inverse problem in the general case. After a review on the inverse source literature, we demonstrate that in the general case the BLT solution is not unique by constructing the set of all the solutions to this inverse problem. Then, we show the uniqueness of the solution in the case of impulse sources. Finally, we present our main theorem that solid/hollow ball sources can be uniquely determined up to nonradiating sources. For better readability, the exact conditions for and rigorous proofs of the theorems are given in the Appendices. Further research directions are also discussed.
An extension of Newton's apsidal precession theorem
NASA Astrophysics Data System (ADS)
Valluri, S. R.; Yu, P.; Smith, G. E.; Wiegert, P. A.
2005-04-01
Newton's apsidal precession theorem in Proposition 45 of Book I of the `Principia' has great mathematical, physical, astronomical and historical interest. The lunar theory and the precession of the perihelion of the planet Mercury are but two examples of the applications of this theorem. We have examined the precession of orbits under varying force laws as measured by the apsidal angle θ(N, e), where N is the index for the centripetal force law, for varying eccentricity e. The paper derives a general function for the apsidal angle, dependent only on e and N as the potential is spherically symmetric. Further, we explore approximate ways of the solution of this equation, in the neighbourhood of N= 2 which happens to be the case of greatest historical interest. Exact solutions are derived where they are possible. The first derivatives ∂θ/∂N and ∂θ/∂h[where h(N, e) is the angular momentum] are analytically expressed in the neighbourhood of N= 2 (case of the inverse square law). The value of ∂θ/∂N is computed numerically as well for 1 <=N < 3. The resulting integrals are interesting improper integrals with singularities at both limits. Some of the integrals, especially for N= 2, can be given in closed form in terms of generalized hypergeometric functions which are reducible in terms of algebraic and logarithmic functions. No evidence was found for isolated cases of zero precession as e was increased. The N= 1 case of the logarithmic potential is also briefly discussed in view of its interest for the dynamics of eccentric orbits and its relevance to realistic galaxy models. The possibility of apsidal precession was also examined for a few cases of high-eccentricity asteroids and extrasolar planets. We find that these systems may provide interesting new laboratories for studies of gravity.
2017-01-01
Seed dispersal permits the colonization of favorable habitats and generation of new populations, facilitating escape from habitats that are in decline. There is little experimental evidence of the factors that limit epiphyte dispersion towards their hosts. In a tropical dry forest in central Mexico, we monitored the phenology of dispersion of epiphyte species of the genus Tillandsia; we tested experimentally whether precipitation could cause failures in seed dispersal and whether seed capture differs among vertical strata and between host species with high (Bursera copallifera) and low (Conzattia multiflora) epiphyte loads. With the exception of one species that presents late dispersion and low abundance, all of the species disperse prior to the onset of the rainy season. However, early rains immobilize the seeds, affecting up to 24% of the fruits in species with late dispersion. We observed that Tillandsia seeds reach both Bursera and Conzattia hosts, but found that adherence to the host is 4–5 times higher in Bursera. Furthermore, seeds liberated from Bursera travel shorter distances and up to half may remain within the same crown, while the highest seed capture takes place in the upper strata of the trees. We conclude that dispersion of Tillandsia seeds is limited by early rains and by the capture of seeds within the trees where populations concentrate. This pattern of capture also helps to explain the high concentrations of epiphytes in certain hosts, while trees with few epiphytes can be simultaneously considered deficient receivers and efficient exporters of seeds. PMID:28158320
Victoriano-Romero, Elizabeth; Valencia-Díaz, Susana; Toledo-Hernández, Víctor Hugo; Flores-Palacios, Alejandro
2017-01-01
Seed dispersal permits the colonization of favorable habitats and generation of new populations, facilitating escape from habitats that are in decline. There is little experimental evidence of the factors that limit epiphyte dispersion towards their hosts. In a tropical dry forest in central Mexico, we monitored the phenology of dispersion of epiphyte species of the genus Tillandsia; we tested experimentally whether precipitation could cause failures in seed dispersal and whether seed capture differs among vertical strata and between host species with high (Bursera copallifera) and low (Conzattia multiflora) epiphyte loads. With the exception of one species that presents late dispersion and low abundance, all of the species disperse prior to the onset of the rainy season. However, early rains immobilize the seeds, affecting up to 24% of the fruits in species with late dispersion. We observed that Tillandsia seeds reach both Bursera and Conzattia hosts, but found that adherence to the host is 4-5 times higher in Bursera. Furthermore, seeds liberated from Bursera travel shorter distances and up to half may remain within the same crown, while the highest seed capture takes place in the upper strata of the trees. We conclude that dispersion of Tillandsia seeds is limited by early rains and by the capture of seeds within the trees where populations concentrate. This pattern of capture also helps to explain the high concentrations of epiphytes in certain hosts, while trees with few epiphytes can be simultaneously considered deficient receivers and efficient exporters of seeds.
Parrish, Karen E.; Cen, Ling; Murray, James; Calligaris, David; Kizilbash, Sani; Mittapalli, Rajendar K.; Carlson, Brett L.; Schroeder, Mark A.; Sludden, Julieann; Boddy, Alan V.; Agar, Nathalie Y.R.; Curtin, Nicola J.; Elmquist, William F.; Sarkaria, Jann N.
2015-01-01
Poly (ADP-ribose) polymerase (PARP) inhibition can enhance the efficacy of temozolomide (TMZ) and prolong survival in orthotopic glioblastoma (GBM) xenografts. The aim of this study was to evaluate the combination of the PARP inhibitor rucaparib with TMZ and to correlate pharmacokinetic and pharmacodynamic studies with efficacy in patient-derived GBM xenograft models. The combination of rucaparib with TMZ was highly effective in vitro in short-term explant cultures derived from GBM12, and similarly, the combination of rucaparib and TMZ (dosed for 5 days every 28 days × 3 cycles) significantly prolonged the time to tumor regrowth by 40% in heterotopic xenografts. In contrast, the addition of rucaparib had no impact on the efficacy of TMZ in GBM12 or GBM39 orthotopic models. Using Madin-Darby canine kidney (MDCK) II cells stably expressing murine BCRP1 or human MDR1, cell accumulation studies demonstrated that rucaparib is transported by both transporters. Consistent with the influence of these efflux pumps on central nervous system drug distribution, Mdr1a/b−/−Bcrp1−/− knockout mice had a significantly higher brain to plasma ratio for rucaparib (1.61 ± 0.25) than wild-type mice (0.11 ± 0.08). A pharmacokinetic and pharmacodynamic evaluation after a single dose confirmed limited accumulation of rucaparib in the brain associated with substantial residual PARP enzymatic activity. Similarly, matrix-assisted laser desorption/ionization mass spectrometric imaging demonstrated significantly enhanced accumulation of drug in flank tumor compared to normal brain or orthotopic tumors. Collectively, these results suggest that limited drug delivery into brain tumors may significantly limit the efficacy of rucaparib combined with TMZ in GBM. PMID:26438157
A Physical Proof of the Pythagorean Theorem
ERIC Educational Resources Information Center
Treeby, David
2017-01-01
What proof of the Pythagorean theorem might appeal to a physics teacher? A proof that involved the notion of mass would surely be of interest. While various proofs of the Pythagorean theorem employ the circumcenter and incenter of a right-angled triangle, we are not aware of any proof that uses the triangle's center of mass. This note details one…
The Classical Version of Stokes' Theorem Revisited
ERIC Educational Resources Information Center
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
Euler and the Fundamental Theorem of Algebra.
ERIC Educational Resources Information Center
Duham, William
1991-01-01
The complexity of the proof of the Fundamental Theorem of Algebra makes it inaccessible to lower level students. Described are more understandable attempts of proving the theorem and a historical account of Euler's efforts that relates the progression of the mathematical process used and indicates some of the pitfalls encountered. (MDH)
Bring the Pythagorean Theorem "Full Circle"
ERIC Educational Resources Information Center
Benson, Christine C.; Malm, Cheryl G.
2011-01-01
Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…
A Note on Morley's Triangle Theorem
ERIC Educational Resources Information Center
Mueller, Nancy; Tikoo, Mohan; Wang, Haohao
2012-01-01
In this note, we offer a proof of a variant of Morley's triangle theorem, when the exterior angles of a triangle are trisected. We also offer a generalization of Morley's theorem when angles of an "n"-gon are "n"-sected. (Contains 9 figures.)
A note on Morley's triangle theorem
NASA Astrophysics Data System (ADS)
Mueller, Nancy; Tikoo, Mohan; Wang, Haohao
2012-06-01
In this note, we offer a proof of a variant of Morley's triangle theorem, when the exterior angles of a triangle are trisected. We also offer a generalization of Morley's theorem when angles of an n-gon are n-sected.
Bring the Pythagorean Theorem "Full Circle"
ERIC Educational Resources Information Center
Benson, Christine C.; Malm, Cheryl G.
2011-01-01
Middle school mathematics generally explores applications of the Pythagorean theorem and lays the foundation for working with linear equations. The Grade 8 Curriculum Focal Points recommend that students "apply the Pythagorean theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and…
TAUBERIAN THEOREMS FOR MATRIX REGULAR VARIATION
MEERSCHAERT, M. M.; SCHEFFLER, H.-P.
2013-01-01
Karamata’s Tauberian theorem relates the asymptotics of a nondecreasing right-continuous function to that of its Laplace-Stieltjes transform, using regular variation. This paper establishes the analogous Tauberian theorem for matrix-valued functions. Some applications to time series analysis are indicated. PMID:24644367
The Pythagorean Theorem: I. The finite case
Kadison, Richard V.
2002-01-01
The Pythagorean Theorem and variants of it are studied. The variations evolve to a formulation in terms of noncommutative, conditional expectations on von Neumann algebras that displays the theorem as the basic result of noncommutative, metric, Euclidean Geometry. The emphasis in the present article is finite dimensionality, both “discrete” and “continuous.” PMID:11929992
General Theorems about Homogeneous Ellipsoidal Inclusions
ERIC Educational Resources Information Center
Korringa, J.; And Others
1978-01-01
Mathematical theorems about the properties of ellipsoids are developed. Included are Poisson's theorem concerning the magnetization of a homogeneous body of ellipsoidal shape, the polarization of a dielectric, the transport of heat or electricity through an ellipsoid, and other problems. (BB)
The Classical Version of Stokes' Theorem Revisited
ERIC Educational Resources Information Center
Markvorsen, Steen
2008-01-01
Using only fairly simple and elementary considerations--essentially from first year undergraduate mathematics--we show how the classical Stokes' theorem for any given surface and vector field in R[superscript 3] follows from an application of Gauss' divergence theorem to a suitable modification of the vector field in a tubular shell around the…
A Note on Morley's Triangle Theorem
ERIC Educational Resources Information Center
Mueller, Nancy; Tikoo, Mohan; Wang, Haohao
2012-01-01
In this note, we offer a proof of a variant of Morley's triangle theorem, when the exterior angles of a triangle are trisected. We also offer a generalization of Morley's theorem when angles of an "n"-gon are "n"-sected. (Contains 9 figures.)
Using Pictures to Enhance Students' Understanding of Bayes' Theorem
ERIC Educational Resources Information Center
Trafimow, David
2011-01-01
Students often have difficulty understanding algebraic proofs of statistics theorems. However, it sometimes is possible to prove statistical theorems with pictures in which case students can gain understanding more easily. I provide examples for two versions of Bayes' theorem.
Using Pictures to Enhance Students' Understanding of Bayes' Theorem
ERIC Educational Resources Information Center
Trafimow, David
2011-01-01
Students often have difficulty understanding algebraic proofs of statistics theorems. However, it sometimes is possible to prove statistical theorems with pictures in which case students can gain understanding more easily. I provide examples for two versions of Bayes' theorem.
The Euler Line and Nine-Point-Circle Theorems.
ERIC Educational Resources Information Center
Eccles, Frank M.
1999-01-01
Introduces the Euler line theorem and the nine-point-circle theorem which emphasize transformations and the power of functions in a geometric concept. Presents definitions and proofs of theorems. (ASK)
Carnot{close_quote}s theorem as Noether{close_quote}s theorem for thermoacoustic engines
Smith, E. |
1998-09-01
Onset in thermoacoustic engines, the transition to spontaneous self-generation of oscillations, is studied here as both a dynamical critical transition and a limiting heat engine behavior. The critical transition is interesting because it occurs for both dissipative and conservative systems, with common scaling properties. When conservative, the stable oscillations above the critical point also implement a reversible engine cycle satisfying Carnot{close_quote}s theorem, a universal conservation law for entropy flux. While criticality in equilibrium systems is naturally associated with symmetries and universal conservation laws, these are usually exploited with global minimization principles, which dynamical critical systems may not have if dissipation is essential to their criticality. Acoustic heat engines furnish an example connecting equilibrium methods with dynamical and possibly even dissipative critical transitions: A reversible engine is shown to map, by a change of variables, to an equivalent system in apparent thermal equilibrium; a Noether symmetry in the equilibrium field theory implies Carnot{close_quote}s theorem for the engine. Under the same association, onset is shown to be a process of spontaneous symmetry breaking and the scaling of the quality factor predicted for both the reversible {ital and irreversible} engines is shown to arise from the Ginzburg-Landau description of the broken phase. {copyright} {ital 1998} {ital The American Physical Society}
On the Theorem of Correspondence.
Krøjgaard, Peter
2017-03-01
In a recent paper, Mammen (Integrative Psychological and Behavioral Science, 50, 196-233, 2016a) brought novel arguments into the discussion concerning the importance of being able to single out and track objects through space and time. Mammen offered a formal account of two basic, yet distinct, ways in which we as human beings encounter objects in the real world, that is, sense and choice categories. In this paper I discuss aspects of his theory and in particular the Theorem of Correspondence. I shall attempt to argue that Mammen's formal account is indeed a novel and powerful analytical generic tool allowing us to see the important relevance in different domains of being able to establish choice categories. Meanwhile, I will attempt to show that evidence from the so-called multiple object tracking studies -- even though these use highly artificial stimuli -- provide compelling evidence in support of Mammen's formal account.
Singlet and triplet instability theorems
Yamada, Tomonori; Hirata, So
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree–Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree–Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree–Fock-theory-based explanations of Hund’s rule, a singlet instability in Jahn–Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Singlet and triplet instability theorems
NASA Astrophysics Data System (ADS)
Yamada, Tomonori; Hirata, So
2015-09-01
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
Singlet and triplet instability theorems.
Yamada, Tomonori; Hirata, So
2015-09-21
A useful definition of orbital degeneracy—form-degeneracy—is introduced, which is distinct from the usual energy-degeneracy: Two canonical spatial orbitals are form-degenerate when the energy expectation value in the restricted Hartree-Fock (RHF) wave function is unaltered upon a two-electron excitation from one of these orbitals to the other. Form-degenerate orbitals tend to have isomorphic electron densities and occur in the highest-occupied and lowest-unoccupied molecular orbitals (HOMOs and LUMOs) of strongly correlated systems. Here, we present a mathematical proof of the existence of a triplet instability in a real or complex RHF wave function of a finite system in the space of real or complex unrestricted Hartree-Fock wave functions when HOMO and LUMO are energy- or form-degenerate. We also show that a singlet instability always exists in a real RHF wave function of a finite system in the space of complex RHF wave functions, when HOMO and LUMO are form-degenerate, but have nonidentical electron densities, or are energy-degenerate. These theorems provide Hartree-Fock-theory-based explanations of Hund's rule, a singlet instability in Jahn-Teller systems, biradicaloid electronic structures, and a triplet instability during some covalent bond breaking. They also suggest (but not guarantee) the spontaneous formation of a spin density wave (SDW) in a metallic solid. The stability theory underlying these theorems extended to a continuous orbital-energy spectrum proves the existence of an oscillating (nonspiral) SDW instability in one- and three-dimensional homogeneous electron gases, but only at low densities or for strong interactions.
NASA Astrophysics Data System (ADS)
Söderberg, Per G.; Malmberg, Filip; Sandberg-Melin, Camilla
2017-02-01
The present study aimed to elucidate if comparison of angular segments of Pigment epithelium central limit- Inner limit of the retina Minimal Distance, measured over 2π radians in the frontal plane (PIMD-2π) between visits of a patient, renders sufficient precision for detection of loss of nerve fibers in the optic nerve head. An optic nerve head raster scanned cube was captured with a TOPCON 3D OCT 2000 (Topcon, Japan) device in one early to moderate stage glaucoma eye of each of 13 patients. All eyes were recorded at two visits less than 1 month apart. At each visit, 3 volumes were captured. Each volume was extracted from the OCT device for analysis. Then, angular PIMD was segmented three times over 2π radians in the frontal plane, resolved with a semi-automatic algorithm in 500 equally separated steps, PIMD-2π. It was found that individual segmentations within volumes, within visits, within subjects can be phase adjusted to each other in the frontal plane using cross-correlation. Cross correlation was also used to phase adjust volumes within visits within subjects and visits to each other within subjects. Then, PIMD-2π for each subject was split into 250 bundles of 2 adjacent PIMDs. Finally, the sources of variation for estimates of segments of PIMD-2π were derived with analysis of variance assuming a mixed model. The variation among adjacent PIMDS was found very small in relation to the variation among segmentations. The variation among visits was found insignificant in relation to the variation among volumes and the variance for segmentations was found to be on the order of 20 % of that for volumes. The estimated variances imply that, if 3 segmentations are averaged within a volume and at least 10 volumes are averaged within a visit, it is possible to estimate around a 10 % reduction of a PIMD-2π segment from baseline to a subsequent visit as significant. Considering a loss rate for a PIMD-2π segment of 23 μm/yr., 4 visits per year, and averaging 3
Posterior Probability and Fluctuation Theorem in Stochastic Processes
NASA Astrophysics Data System (ADS)
Ohkubo, Jun
2009-12-01
A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via Bayes’ theorem. In conventional fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when suitable assumptions are employed.
Droessler, T.D.
1992-03-01
The proposed research will quantify white spruce growth and document its latitudinal stability at the tree limit in the central Brooks Range over the life span of the living trees. The goal is to link tree growth and tree position to summer temperature and precipitation. Historical records from 1929 to 1938 from work by Robert Marshall have been used to identify tree limit sites and provide information to interpret the present location of the tree limit.
Chidambaram, Swathi; Nair, M Nathan; Krishnan, Shyam Sundar; Cai, Ling; Gu, Weiling; Vasudevan, Madabushi Chakravarthy
2015-12-01
Postoperative central nervous system infections (PCNSIs) are rare but serious complications after neurosurgery. The purpose of this study was to examine the prevalence and causative pathogens of PCNSIs at a modernized, resource-limited neurosurgical center in South Asia. A retrospective analysis was conducted of the medical records of all 363 neurosurgical cases performed between June 1, 2012, and June 30, 2013, at a neurosurgical center in South Asia. Data from all operative neurosurgical cases during the 13-month period were included. Cerebrospinal fluid (CSF) analysis indicated that 71 of the 363 surgical cases had low CSF glucose or CSF leukocytosis. These 71 cases were categorized as PCNSIs. The PCNSIs with positive CSF cultures (9.86%) all had gram-negative bacteria with Pseudomonas aeruginosa (n = 5), Escherichia coli (n = 1), or Klebsiella pneumoniae (n = 1). The data suggest a higher rate of death (P = 0.031), a higher rate of CSF leak (P < 0.001), and a higher rate of cranial procedures (P < 0.001) among the infected patients and a higher rate of CSF leak among the patients with culture-positive infections (P = 0.038). This study summarizes the prevalence, causative organism of PCNSI, and antibiotic usage for all of the neurosurgical cases over a 13-month period in a modernized yet resource-limited neurosurgical center located in South Asia. The results from this study highlight the PCNSI landscape in an area of the world that is often underreported in the neurosurgical literature because of the paucity of clinical neurosurgical research undertaken there. This study shows an increasing prevalence of gram-negative organisms in CSF cultures from PCNSIs, which supports a trend in the recent literature of increasing gram-negative bacillary meningitis. Copyright © 2015 Elsevier Inc. All rights reserved.
Quantum-mechanical diffraction theory of light from a small hole: Extinction-theorem approach
NASA Astrophysics Data System (ADS)
Jung, Jesper; Keller, Ole
2015-07-01
In a recent paper [Phys. Rev. A 90, 043830 (2014), 10.1103/PhysRevA.90.043830] it was shown that the so-called aperture response tensor is the central concept in the microscopic quantum theory of light diffraction from a small hole in a flat screen. It was further shown that the quantum mechanical theory of diffraction only requires a preknowledge of the incident field plus the electronic properties of identical screens with and without a hole. Starting from the quantum mechanical expression for the linear conductivity tensor, we study the related causal conductivity tensor paying particular attention to diamagnetic electron dynamics. Using a nonlocal-potential separation assumption, we present a calculation of the diamagnetic causal surface conductivity for a jellium quantum-well screen using a two-dimensional Hartree-Fock model. In the diamagnetic case the difference between the light-unperturbed electron densities for screens with (n0) and without (n∞0) holes are the primary quantities for the diffraction theory. In a central part (Sec. IV) of this article we determine n0 via a quantum-mechanical two-dimensional extinction-theorem approach related to elastic electron scattering from a hole with an electronic selvedge. For heuristic purposes we illustrate aspects of the extinction-theorem theory by applying the approach for an infinitely high potential barrier to the vacuum hole. Finally, we calculate and discuss the aperture response tensor in the small hole limit and in the zeroth-order Born approximation. Our final result for the aperture response tensor establishes the bridge to the anisotropic electric dipole polarizability tensor of the hole. It turns out that the effective optical aperture (hole) size relates closely to the extension of the relevant electronic wave functions scattered from the hole.
Testability of the Pusey-Barrett-Rudolph Theorem
NASA Astrophysics Data System (ADS)
Halataei, Seyyed Mohammad Hassan
2014-03-01
Pusey, Barrett, and Rudolph (PBR) proved a mathematically neat theorem which assesses the reality of the quantum state. They proposed a test such that if any pair of quantum states could pass it, then for small deviation in the probabilities of measurement outcomes, ɛ, from the predicted quantum probabilities, one can conclude that the physical state λ ``is normally closely associated with only one of the two quantum states.'' While the mathematics of their theorem is correct, the physical conclusion is incomplete. In this talk, I present an argument which greatly limits the conclusion one can draw from even a successful PBR test. Specifically, I show that the physical state can be associated with several quantum states and, thus, the reality of quantum states cannot be deduced. This work was supported by the MacArthur Professorship endowed by the John D. and Catherine T. MacArthur Foundation at the University of Illinois.
Sampling Theorem in Terms of the Bandwidth and Sampling Interval
NASA Technical Reports Server (NTRS)
Dean, Bruce H.
2011-01-01
An approach has been developed for interpolating non-uniformly sampled data, with applications in signal and image reconstruction. This innovation generalizes the Whittaker-Shannon sampling theorem by emphasizing two assumptions explicitly (definition of a band-limited function and construction by periodic extension). The Whittaker- Shannon sampling theorem is thus expressed in terms of two fundamental length scales that are derived from these assumptions. The result is more general than what is usually reported, and contains the Whittaker- Shannon form as a special case corresponding to Nyquist-sampled data. The approach also shows that the preferred basis set for interpolation is found by varying the frequency component of the basis functions in an optimal way.
Fan beam image reconstruction with generalized Fourier slice theorem.
Zhao, Shuangren; Yang, Kang; Yang, Kevin
2014-01-01
For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N
The Lax-Onsager regression `theorem' revisited
NASA Astrophysics Data System (ADS)
Lax, Melvin
2000-05-01
It is stated by Ford and O'Connell in this festschrift issue and elsewhere that "there is no quantum regression theorem" although Lax "obtained a formula for correlation in a driven quantum system that has come to be called the quantum regression theorem". This produces a puzzle: "How can it be that a non-existent theorem gives correct results?" Clarification will be provided in this paper by a description of the Lax procedure, with a quantitative estimate of the error for a damped harmonic oscillator based on expressions published in the 1960's.
Kato type operators and Weyl's theorem
NASA Astrophysics Data System (ADS)
Duggal, B. P.; Djordjevic, S. V.; Kubrusly, Carlos
2005-09-01
A Banach space operator T satisfies Weyl's theorem if and only if T or T* has SVEP at all complex numbers [lambda] in the complement of the Weyl spectrum of T and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity. If T* (respectively, T) has SVEP and T is Kato type at all [lambda] which are isolated eigenvalues of T of finite algebraic multiplicity (respectively, T is Kato type at all [lambda][set membership, variant]iso[sigma](T)), then T satisfies a-Weyl's theorem (respectively, T* satisfies a-Weyl's theorem).
Cosmological singularity theorems and black holes
NASA Astrophysics Data System (ADS)
Vilenkin, Alexander; Wall, Aron C.
2014-03-01
An extension of Penrose's singularity theorem is proved for spacetimes where black holes are allowed to form from nonsingular initial data. With standard assumptions about the spacetime, and assuming the existence of a trapped surface which lies outside of black hole horizons and is not completely surrounded by horizons, we show that the spacetime region outside (or on) the horizons must contain singularities. If the trapped surface is surrounded by horizons, we show that the horizons divide spacetime into causally disconnected pieces. Unlike the original Penrose theorem, our theorems provide some information about the location of singularities. We illustrate how they can be used to rule out some cosmological scenarios.
[Count on your beliefs. Bayes' theorem in diagnosis].
Taube, A; Malmquist, J
2001-06-13
Bayesian analysis of data finds increasing use in medical statistics, diagnostic evaluation and decision analysis. The central element in bayesian analysis is a set of mathematical rules for integrated evaluation of prior knowledge and new information. In many situations this approach has superior ability to deliver dependable updated knowledge and to provide an optimal probability basis for decisions. This article (the first of two) presents Bayes' theorem and its application in diagnostic work. It is explained how likelihood ratios of diagnostic tests interact with the outcome of such tests in the conversion of initial information (prior odds) to enhanced information (posterior odds).
Kohn's theorem and Newton-Hooke symmetry for Hill's equations
NASA Astrophysics Data System (ADS)
Zhang, P. M.; Gibbons, G. W.; Horvathy, P. A.
2012-02-01
Hill’s equations, which first arose in the study of the Earth-Moon-Sun system, admit the two-parameter centrally extended Newton-Hooke symmetry without rotations. This symmetry allows us to extend Kohn’s theorem about the center-of-mass decomposition. Particular light is shed on the problem using Duval’s “Bargmann” framework. The separation of the center-of-mass motion into that of a guiding center and relative motion is derived by a generalized chiral decomposition.
ERIC Educational Resources Information Center
Andrich, David; Marais, Ida; Humphry, Stephen
2012-01-01
Andersen (1995, 2002) proves a theorem relating variances of parameter estimates from samples and subsamples and shows its use as an adjunct to standard statistical analyses. The authors show an application where the theorem is central to the hypothesis tested, namely, whether random guessing to multiple choice items affects their estimates in the…
ERIC Educational Resources Information Center
Andrich, David; Marais, Ida; Humphry, Stephen
2012-01-01
Andersen (1995, 2002) proves a theorem relating variances of parameter estimates from samples and subsamples and shows its use as an adjunct to standard statistical analyses. The authors show an application where the theorem is central to the hypothesis tested, namely, whether random guessing to multiple choice items affects their estimates in the…
NASA Astrophysics Data System (ADS)
Lützgendorf, N.; Kissler-Patig, M.; Gebhardt, K.; Baumgardt, H.; Noyola, E.; Jalali, B.; de Zeeuw, P. T.; Neumayer, N.
2012-06-01
Context. Globular clusters are an excellent laboratory for stellar population and dynamical research. Recent studies have shown that these stellar systems are not as simple as previously assumed. With multiple stellar populations as well as outer rotation and mass segregation they turn out to exhibit high complexity. This includes intermediate-mass black holes (IMBHs) which are proposed to sit at the centers of some massive globular clusters. Today's high angular resolution ground based spectrographs allow velocity-dispersion measurements at a spatial resolution comparable to the radius of influence for plausible IMBH masses, and to detect changes in the inner velocity-dispersion profile. Together with high quality photometric data from HST, it is possible to constrain black-hole masses by their kinematic signatures. Aims: We determine the central velocity-dispersion profile of the globular cluster NGC 2808 using VLT/FLAMES spectroscopy. In combination with HST/ACS data our goal is to probe whether this massive cluster hosts an IMBH at its center and constrain the cluster mass to light ratio as well as its total mass. Methods: We derive a velocity-dispersion profile from integral field spectroscopy in the center and Fabry Perot data for larger radii. High resolution HST data are used to obtain the surface brightness profile. Together, these data sets are compared to dynamical models with varying parameters such as mass to light ratio profiles and black-hole masses. Results: Using analytical Jeans models in combination with variable M/LV profiles from N-body simulations we find that the best fit model is a no black hole solution. After applying various Monte Carlo simulations to estimate the uncertainties, we derive an upper limit of the back hole mass of MBH < 1 × 104 M⊙ (with 95% confidence limits) and a global mass-to-light ratio of M/LV = (2.1 ± 0.2) M⊙/L⊙. Based on observations collected at the European Organization for Astronomical Research in the
Duality Theorems in Ergodic Transport
NASA Astrophysics Data System (ADS)
Lopes, Artur O.; Mengue, Jairo K.
2012-11-01
We analyze several problems of Optimal Transport Theory in the setting of Ergodic Theory. In a certain class of problems we consider questions in Ergodic Transport which are generalizations of the ones in Ergodic Optimization. Another class of problems is the following: suppose σ is the shift acting on Bernoulli space X={1,2,…, d}ℕ, and, consider a fixed continuous cost function c: X× X→ℝ. Denote by Π the set of all Borel probabilities π on X× X, such that, both its x and y marginals are σ-invariant probabilities. We are interested in the optimal plan π which minimizes ∫ c dπ among the probabilities in Π. We show, among other things, the analogous Kantorovich Duality Theorem. We also analyze uniqueness of the optimal plan under generic assumptions on c. We investigate the existence of a dual pair of Lipschitz functions which realizes the present dual Kantorovich problem under the assumption that the cost is Lipschitz continuous. For continuous costs c the corresponding results in the Classical Transport Theory and in Ergodic Transport Theory can be, eventually, different. We also consider the problem of approximating the optimal plan π by convex combinations of plans such that the support projects in periodic orbits.
ALGEBRAIC DEPENDENCE THEOREMS ON COMPLEX PSEUDOCONCAVE SPACES
The notion of pseudoconcave space is introduced and classical theorems on algebraic dependence of meromorphic functions are extended for this new class of spaces and for sections in a coherent sheaf. (Author)
Structure theorem for Vaisman completely solvable solvmanifolds
NASA Astrophysics Data System (ADS)
Sawai, Hiroshi
2017-04-01
Locally conformal Kähler manifold is said to be a Vaisman manifold if the Lee form is parallel with respect to the Riemannian metric. In this paper, we have the structure theorem for Vaisman completely solvable solvmanifolds.
Sahoo- and Wayment-Type Integral Mean Value Theorems
ERIC Educational Resources Information Center
Tiryaki, Aydin; Cakmak, Devrim
2010-01-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…
Sahoo- and Wayment-Type Integral Mean Value Theorems
ERIC Educational Resources Information Center
Tiryaki, Aydin; Cakmak, Devrim
2010-01-01
In this article, by using Rolle's theorem, we establish some results related to the mean value theorem for integrals. Our results are different from the set of integral mean value theorems which are given by Wayment ["An integral mean value theorem", Math. Gazette 54 (1970), pp. 300-301] and Sahoo ["Some results related to the integral mean value…
Fishman, S.; Soffer, A.
2016-07-15
We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.
The Great Emch Closure Theorem and a combinatorial proof of Poncelet's Theorem
NASA Astrophysics Data System (ADS)
Avksentyev, E. A.
2015-11-01
The relations between the classical closure theorems (Poncelet's, Steiner's, Emch's, and the zigzag theorems) and some of their generalizations are discussed. It is known that Emch's Theorem is the most general of these, while the others follow as special cases. A generalization of Emch's Theorem to pencils of circles is proved, which (by analogy with the Great Poncelet Theorem) can be called the Great Emch Theorem. It is shown that the Great Emch and Great Poncelet Theorems are equivalent and can be derived one from the other using elementary geometry, and also that both hold in the Lobachevsky plane as well. A new closure theorem is also obtained, in which the construction of closure is slightly more involved: closure occurs on a variable circle which is tangent to a fixed pair of circles. In conclusion, a combinatorial proof of Poncelet's Theorem is given, which deduces the closure principle for an arbitrary number of steps from the principle for three steps using combinatorics and number theory. Bibliography: 20 titles.
A Physical Proof of the Pythagorean Theorem
NASA Astrophysics Data System (ADS)
Treeby, David
2017-02-01
What proof of the Pythagorean theorem might appeal to a physics teacher? A proof that involved the notion of mass would surely be of interest. While various proofs of the Pythagorean theorem employ the circumcenter and incenter of a right-angled triangle, we are not aware of any proof that uses the triangle's center of mass. This note details one such proof. Though far from the most elegant approach, we believe it to be novel.
A Converse of Fermat's Little Theorem
ERIC Educational Resources Information Center
Bruckman, P. S.
2007-01-01
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…
A Converse of Fermat's Little Theorem
ERIC Educational Resources Information Center
Bruckman, P. S.
2007-01-01
As the name of the paper implies, a converse of Fermat's Little Theorem (FLT) is stated and proved. FLT states the following: if p is any prime, and x any integer, then x[superscript p] [equivalent to] x (mod p). There is already a well-known converse of FLT, known as Lehmer's Theorem, which is as follows: if x is an integer coprime with m, such…
Littlewood-Paley Theorem for Schrodinger Operators
2006-07-26
26 JUL 2006 2. REPORT TYPE 3. DATES COVERED 00-00-2006 to 00-00-2006 4. TITLE AND SUBTITLE Littlewood -Paley theorem for Schrodinger operators...associated with H are well defined. We further give a Littlewood -Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes...unclassified c THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18 LITTLEWOOD -PALEY THEOREM FOR SCHRÖDINGER
Joanny, Fanny; Löhr, Sascha J Z; Engleitner, Thomas; Lell, Bertrand; Mordmüller, Benjamin
2014-06-14
Proper malaria diagnosis depends on the detection of asexual forms of Plasmodium spp. in the blood. Thick blood smear microscopy is the accepted gold standard of malaria diagnosis and is widely implemented. Surprisingly, diagnostic performance of this method is not well investigated and many clinicians in African routine settings base treatment decisions independent of microscopy results. This leads to overtreatment and poor management of other febrile diseases. Implementation of quality control programmes is recommended, but requires sustained funding, external logistic support and constant training and supervision of the staff. This study describes an easily applicable method to assess the performance of thick blood smear microscopy by determining the limit of blank and limit of detection. These two values are representative of the diagnostic quality and allow the correct discrimination between positive and negative samples. Standard-conform methodology was applied and adapted to determine the limit of blank and the limit of detection of two thick blood smear microscopy methods (WHO and Lambaréné method) in a research centre in Lambaréné, Gabon. Duplicates of negative and low parasitaemia thick blood smears were read by several microscopists. The mean and standard deviation of the results were used to calculate the limit of blank and subsequently the limit of detection. The limit of blank was 0 parasites/μL for both methods. The limit of detection was 62 and 88 parasites/μL for the Lambaréné and WHO method, respectively. With a simple, back-of-the-envelope calculation, the performance of two malaria microscopy methods can be measured. These results are specific for each diagnostic unit and cannot be generalized but implementation of a system to control microscopy performance can improve confidence in parasitological results and thereby strengthen malaria control.
2014-01-01
Background Proper malaria diagnosis depends on the detection of asexual forms of Plasmodium spp. in the blood. Thick blood smear microscopy is the accepted gold standard of malaria diagnosis and is widely implemented. Surprisingly, diagnostic performance of this method is not well investigated and many clinicians in African routine settings base treatment decisions independent of microscopy results. This leads to overtreatment and poor management of other febrile diseases. Implementation of quality control programmes is recommended, but requires sustained funding, external logistic support and constant training and supervision of the staff. This study describes an easily applicable method to assess the performance of thick blood smear microscopy by determining the limit of blank and limit of detection. These two values are representative of the diagnostic quality and allow the correct discrimination between positive and negative samples. Methods Standard-conform methodology was applied and adapted to determine the limit of blank and the limit of detection of two thick blood smear microscopy methods (WHO and Lambaréné method) in a research centre in Lambaréné, Gabon. Duplicates of negative and low parasitaemia thick blood smears were read by several microscopists. The mean and standard deviation of the results were used to calculate the limit of blank and subsequently the limit of detection. Results The limit of blank was 0 parasites/μL for both methods. The limit of detection was 62 and 88 parasites/μL for the Lambaréné and WHO method, respectively. Conclusion With a simple, back-of-the-envelope calculation, the performance of two malaria microscopy methods can be measured. These results are specific for each diagnostic unit and cannot be generalized but implementation of a system to control microscopy performance can improve confidence in parasitological results and thereby strengthen malaria control. PMID:24929248
Fractional Stochastic Differential Equations Satisfying Fluctuation-Dissipation Theorem
NASA Astrophysics Data System (ADS)
Li, Lei; Liu, Jian-Guo; Lu, Jianfeng
2017-09-01
We propose in this work a fractional stochastic differential equation (FSDE) model consistent with the over-damped limit of the generalized Langevin equation model. As a result of the `fluctuation-dissipation theorem', the differential equations driven by fractional Brownian noise to model memory effects should be paired with Caputo derivatives, and this FSDE model should be understood in an integral form. We establish the existence of strong solutions for such equations and discuss the ergodicity and convergence to Gibbs measure. In the linear forcing regime, we show rigorously the algebraic convergence to Gibbs measure when the `fluctuation-dissipation theorem' is satisfied, and this verifies that satisfying `fluctuation-dissipation theorem' indeed leads to the correct physical behavior. We further discuss possible approaches to analyze the ergodicity and convergence to Gibbs measure in the nonlinear forcing regime, while leave the rigorous analysis for future works. The FSDE model proposed is suitable for systems in contact with heat bath with power-law kernel and subdiffusion behaviors.
The Nekhoroshev Theorem and Long-Term Stabilities in the Solar System
NASA Astrophysics Data System (ADS)
Guzzo, M.
2015-06-01
The Nekhoroshev theorem has been often indicated in the last decades as the reference theorem for explaining the dynamics of several systems which are stable in the long-term. The Solar System dynamics provides a wide range of possible and useful applications. In fact, despite the complicated models which are used to numerically integrate realistic Solar System dynamics as accurately as possible, when the integrated solutions are chaotic the reliability of the numerical integrations is limited, and a theoretical long-term stability analysis is required. After the first formulation of Nekhoroshev's theorem in 1977, many theoretical improvements have been achieved. On the one hand, alternative proofs of the theorem itself led to consistent improvements of the stability estimates; on the other hand, the extensions which were necessary to apply the theorem to the systems of interest for Solar System Dynamics, in particular concerning the removal of degeneracies and the implementation of computer assisted proofs, have been developed. In this review paper we discuss some of the motivations and the results which have made Nekhoroshev's theorem a reference stability result for many applications in the Solar System dynamics.
Conditioned Limit Theorems for Some Null Recurrent Markov Processes
1976-08-01
this conlus ion is the lolloing Suppos I in Pt > t 0 for all (t - nd (iv) hold X10 I J -or each is arN > mtv ,x is an inureas tip function of St hen (v...Diffusion Processes and Their Sample Paths, Springer-Verlag, second printing, (1973). 39. Jacobsen , M., Splitting times for Markov processes and a
NASA Astrophysics Data System (ADS)
Chavanis, Pierre-Henri; Sire, Clément
2006-06-01
We derive the virial theorem appropriate to the generalized Smoluchowski-Poisson (GSP) system describing self-gravitating Brownian particles in an overdamped limit. We extend previous works by considering the case of an unbounded domain and an arbitrary equation of state. We use the virial theorem to study the diffusion (evaporation) of an isothermal Brownian gas above the critical temperature Tc in dimension d=2 and show how the effective diffusion coefficient and the Einstein relation are modified by self-gravity. We also study the collapse at T=Tc and show that the central density increases logarithmically with time instead of exponentially in a bounded domain. Finally, for d>2 , we show that the evaporation of the system is essentially a pure diffusion slightly slowed down by self-gravity. We also study the linear dynamical stability of stationary solutions of the GSP system representing isolated clusters of particles and investigate the influence of the equation of state and of the dimension of space on the dynamical stability of the system.
NASA Astrophysics Data System (ADS)
Young, Eliot F.; Olkin, Catherine B.; Young, Leslie A.; Howell, Robert R.; French, Richard G.
2014-11-01
We report a new analysis of occultation lightcurves observed in 2007 (from Mt John Observatory) and 2011 (from San Pedro Martir Observatory). In both cases, lightcurves were observed simultaneously in two wavelengths, and in the 2007 case, a double-peaked central flash was observed. In contrast to the wavelength-dependent opacities reported by Elliot et al. (Nature 2003; 424:165) in 2002, we see no evidence for an opacity source in Pluto's atmosphere that has greater extinction at shorter wavelengths. From the separation of the peaks in the 2007 central flash lightcurves, we find the oblateness of Pluto's atmosphere (equatorial vs. polar radii of pressure contours near R = 1215 km) of 1.03 ± 0.002. If this oblateness were caused solely by zonal winds, the wind speed at the equator would have to be 206 km/s; an alternative explanation is that the equatorial bulge is caused by warmer temperatures above the equator than the poles. Finally, the amplitudes of the central flash peaks are very sensitive to the surface pressure. If that pressure is driven by the vapor pressure of nitrogen ice, then the ice temperature of 42 ± 2 K reported by Tryka et al. (Icarus 1994; 212:513) is too high and produces central flash amplitudes that are much too bright. We find that the observed central flash peak amplitudes are consistent with nitrogen ice temperatures near 37 K, closer to the alpha-beta transition temperature (35.6 K) of nitrogen ice.
Topological interpretation of the Luttinger theorem
NASA Astrophysics Data System (ADS)
Seki, Kazuhiro; Yunoki, Seiji
2017-08-01
Based solely on the analytical properties of the single-particle Green's function of fermions at finite temperatures, we show that the generalized Luttinger theorem inherently possesses topological aspects. The topological interpretation of the generalized Luttinger theorem can be introduced because (i) the Luttinger volume is represented as the winding number of the single-particle Green's function and, thus, (ii) the deviation of the theorem, expressed with a ratio between the interacting and noninteracting single-particle Green's functions, is also represented as the winding number of this ratio. The formulation based on the winding number naturally leads to two types of the generalized Luttinger theorem. Exploring two examples of single-band translationally invariant interacting electrons, i.e., simple metal and Mott insulator, we show that the first type falls into the original statement for Fermi liquids given by Luttinger, where poles of the single-particle Green's function appear at the chemical potential, while the second type corresponds to the extended one for nonmetallic cases with no Fermi surface such as insulators and superconductors generalized by Dzyaloshinskii, where zeros of the single-particle Green's function appear at the chemical potential. This formulation also allows us to derive a sufficient condition for the validity of the Luttinger theorem of the first type by applying the Rouche's theorem in complex analysis as an inequality. Moreover, we can rigorously prove in a nonperturbative manner, without assuming any detail of a microscopic Hamiltonian, that the generalized Luttinger theorem of both types is valid for generic interacting fermions as long as the particle-hole symmetry is preserved. Finally, we show that the winding number of the single-particle Green's function can also be associated with the distribution function of quasiparticles, and therefore the number of quasiparticles is equal to the Luttinger volume. This implies that
Ergodic theorem, ergodic theory, and statistical mechanics
Moore, Calvin C.
2015-01-01
This perspective highlights the mean ergodic theorem established by John von Neumann and the pointwise ergodic theorem established by George Birkhoff, proofs of which were published nearly simultaneously in PNAS in 1931 and 1932. These theorems were of great significance both in mathematics and in statistical mechanics. In statistical mechanics they provided a key insight into a 60-y-old fundamental problem of the subject—namely, the rationale for the hypothesis that time averages can be set equal to phase averages. The evolution of this problem is traced from the origins of statistical mechanics and Boltzman's ergodic hypothesis to the Ehrenfests' quasi-ergodic hypothesis, and then to the ergodic theorems. We discuss communications between von Neumann and Birkhoff in the Fall of 1931 leading up to the publication of these papers and related issues of priority. These ergodic theorems initiated a new field of mathematical-research called ergodic theory that has thrived ever since, and we discuss some of recent developments in ergodic theory that are relevant for statistical mechanics. PMID:25691697
Anti-Bell - Refutation of Bell's theorem
NASA Astrophysics Data System (ADS)
Barukčić, Ilija
2012-12-01
In general, Albert Einstein as one of "the founding fathers of quantum mechanics" had some problems to accept especially the Copenhagen dominated interpretation of quantum mechanics. Einstein's dissatisfaction with Copenhagen's interpretation of quantum mechanics, the absence of locality and causality within the Copenhagen dominated quantum mechanics lead to the well known Einstein, Podolsky and Rosen thought experiment. According to Einstein et al., the Copenhagen dominated quantum mechanics cannot be regarded as a complete physical theory. The Einstein, Podolsky and Rosen thought experiment was the origin of J. S. Bell's publication in 1964; known as Bell's theorem. Meanwhile, some dramatic violations of Bell's inequality (by so called Bell test experiments) have been reported which is taken as an empirical evidence against local realism and causality at quantum level and as positive evidence in favor of the Copenhagen dominated quantum mechanics. Thus far, Quantum mechanics is still regarded as a "strictly" non-local theory. The purpose of this publication is to refute Bell's original theorem. Thus far, if we accept Bell's theorem as correct, we must accept that +0> = +1. We can derive a logical contradiction out of Bell's theorem, Bell's theorem is refuted.
Generalized parametric down conversion, many particle interferometry, and Bell's theorem
NASA Technical Reports Server (NTRS)
Choi, Hyung Sup
1992-01-01
A new field of multi-particle interferometry is introduced using a nonlinear optical spontaneous parametric down conversion (SPDC) of a photon into more than two photons. The study of SPDC using a realistic Hamiltonian in a multi-mode shows that at least a low conversion rate limit is possible. The down converted field exhibits many stronger nonclassical phenomena than the usual two photon parametric down conversion. Application of the multi-particle interferometry to a recently proposed many particle Bell's theorem on the Einstein-Podolsky-Rosen problem is given.
Dai-Freed theorem and topological phases of matter
NASA Astrophysics Data System (ADS)
Yonekura, Kazuya
2016-09-01
We describe a physics derivation of theorems due to Dai and Freed about the Atiyah-Patodi-Singer eta-invariant which is important for anomalies and topological phases of matter. This is done by studying a massive fermion. The key role is played by the wave function of the ground state in the Hilbert space of the fermion in the large mass limit. The ground state takes values in the determinant line bundle and has nontrivial Berry phases which characterize the low energy topological phases.
A Program Certification Assistant Based on Fully Automated Theorem Provers
NASA Technical Reports Server (NTRS)
Denney, Ewen; Fischer, Bernd
2005-01-01
We describe a certification assistant to support formal safety proofs for programs. It is based on a graphical user interface that hides the low-level details of first-order automated theorem provers while supporting limited interactivity: it allows users to customize and control the proof process on a high level, manages the auxiliary artifacts produced during this process, and provides traceability between the proof obligations and the relevant parts of the program. The certification assistant is part of a larger program synthesis system and is intended to support the deployment of automatically generated code in safety-critical applications.
Stojak, Joanna; McDevitt, Allan D; Herman, Jeremy S; Kryštufek, Boris; Uhlíková, Jitka; Purger, Jenő J; Lavrenchenko, Leonid A; Searle, Jeremy B; Wójcik, Jan M
2016-01-01
The common vole (Microtus arvalis) has been a model species of small mammal for studying end-glacial colonization history. In the present study we expanded the sampling from central and eastern Europe, analyzing contemporary genetic structure to identify the role of a potential 'northern glacial refugium', i.e. a refugium at a higher latitude than the traditional Mediterranean refugia. Altogether we analyzed 786 cytochrome b (cytb) sequences (representing mitochondrial DNA; mtDNA) from the whole of Europe, adding 177 new sequences from central and eastern Europe, and we conducted analyses on eight microsatellite loci for 499 individuals (representing nuclear DNA) from central and eastern Europe, adding data on 311 new specimens. Our new data fill gaps in the vicinity of the Carpathian Mountains, the potential northern refugium, such that there is now dense sampling from the Balkans to the Baltic Sea. Here we present evidence that the Eastern mtDNA lineage of the common vole was present in the vicinity of this Carpathian refugium during the Last Glacial Maximum and the Younger Dryas. The Eastern lineage expanded from this refugium to the Baltic and shows low cytb nucleotide diversity in those most northerly parts of the distribution. Analyses of microsatellites revealed a similar pattern but also showed little differentiation between all of the populations sampled in central and eastern Europe.
Stojak, Joanna; McDevitt, Allan D.; Herman, Jeremy S.; Kryštufek, Boris; Uhlíková, Jitka; Purger, Jenő J.; Lavrenchenko, Leonid A.; Searle, Jeremy B.; Wójcik, Jan M.
2016-01-01
The common vole (Microtus arvalis) has been a model species of small mammal for studying end-glacial colonization history. In the present study we expanded the sampling from central and eastern Europe, analyzing contemporary genetic structure to identify the role of a potential ‘northern glacial refugium’, i.e. a refugium at a higher latitude than the traditional Mediterranean refugia. Altogether we analyzed 786 cytochrome b (cytb) sequences (representing mitochondrial DNA; mtDNA) from the whole of Europe, adding 177 new sequences from central and eastern Europe, and we conducted analyses on eight microsatellite loci for 499 individuals (representing nuclear DNA) from central and eastern Europe, adding data on 311 new specimens. Our new data fill gaps in the vicinity of the Carpathian Mountains, the potential northern refugium, such that there is now dense sampling from the Balkans to the Baltic Sea. Here we present evidence that the Eastern mtDNA lineage of the common vole was present in the vicinity of this Carpathian refugium during the Last Glacial Maximum and the Younger Dryas. The Eastern lineage expanded from this refugium to the Baltic and shows low cytb nucleotide diversity in those most northerly parts of the distribution. Analyses of microsatellites revealed a similar pattern but also showed little differentiation between all of the populations sampled in central and eastern Europe. PMID:27992546
USDA-ARS?s Scientific Manuscript database
The era of expanding irrigated agriculture in the central high plains has come to an end, and we are likely entering a period of contraction. Contraction has begun in Colorado where the state estimates that current consumptive use exceeds sustainable supplies by about 10%. Groundwater pumping has ...
Republication of: A theorem on Petrov types
NASA Astrophysics Data System (ADS)
Goldberg, J. N.; Sachs, R. K.
2009-02-01
This is a republication of the paper “A Theorem on Petrov Types” by Goldberg and Sachs, Acta Phys. Pol. 22 (supplement), 13 (1962), in which they proved the Goldberg-Sachs theorem. The article has been selected for publication in the Golden Oldies series of General Relativity and Gravitation. Typographical errors of the original publication were corrected by the editor. The paper is accompanied by a Golden Oldie Editorial containing an editorial note written by Andrzej Krasiński and Maciej Przanowski and Goldberg’s brief autobiography. The editorial note explains some difficult parts of the proof of the theorem and discusses the influence of results of the paper on later research.
Perkins, R. J. Bellan, P. M.
2015-02-15
Action integrals are often used to average a system over fast oscillations and obtain reduced dynamics. It is not surprising, then, that action integrals play a central role in the Hellmann-Feynman theorem of classical mechanics, which furnishes the values of certain quantities averaged over one period of rapid oscillation. This paper revisits the classical Hellmann-Feynman theorem, rederiving it in connection to an analogous theorem involving the time-averaged evolution of canonical coordinates. We then apply a modified version of the Hellmann-Feynman theorem to obtain a new result: the magnetic flux enclosed by one period of gyro-motion of a charged particle in a non-uniform magnetic field. These results further demonstrate the utility of the action integral in regards to obtaining orbit-averaged quantities and the usefulness of this formalism in characterizing charged particle motion.
An invariance theorem in acoustic scattering theory
NASA Astrophysics Data System (ADS)
Ha-Duong, T.
1996-10-01
Karp's theorem states that if the far-field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle is invariant under the group of orthogonal transformations in 0266-5611/12/5/007/img1 (rotations in 0266-5611/12/5/007/img2), then the scatterer is a sphere (circle). The theorem is generalized to the case where the invariant group of the far field pattern is only a subgroup of the orthogonal group, and for a class of mixed boundary conditions.
At math meetings, enormous theorem eclipses fermat.
Cipra, B
1995-02-10
Hardly a word was said about Fermat's Last Theorem at the joint meetings of the American Mathematical Society and the Mathematical Association of America, held this year from 4 to 7 January in San Francisco. For Andrew Wiles's proof, no news is good news: There are no reports of mistakes. But mathematicians found plenty of other topics to discuss. Among them: a computational breakthrough in the study of turbulent diffusion and progress in slimming down the proof of an important result in group theory, whose original size makes checking the proof of Fermat's Last Theorem look like an afternoon's pastime.
Asymptotic symmetries and subleading soft graviton theorem
NASA Astrophysics Data System (ADS)
Campiglia, Miguel; Laddha, Alok
2014-12-01
Motivated by the equivalence between the soft graviton theorem and Ward identities for the supertranslation symmetries belonging to the Bondi, van der Burg, Metzner and Sachs (BMS) group, we propose a new extension (different from the so-called extended BMS) of the BMS group that is a semidirect product of supertranslations and Diff(S2) . We propose a definition for the canonical generators associated with the smooth diffeomorphisms and show that the resulting Ward identities are equivalent to the subleading soft graviton theorem of Cachazo and Strominger.
Federal Register 2010, 2011, 2012, 2013, 2014
2010-07-02
... requirements of the LLP is intended to provide a limited opportunity for entry level vessel operators to... sufficient, amount of participation in the Pacific cod fishery to indicate some level of dependence on...
Note on the theorems of Bjerknes and Crocco
NASA Technical Reports Server (NTRS)
Theodorsen, Theodore
1946-01-01
The theorems of Bjerknes and Crocco are of great interest in the theory of flow around airfoils at Mach numbers near and above unity. A brief note shows how both theorems are developed by short vector transformations.
Szabo, B. J.; Lindsey, D.A.
1986-01-01
Analysis of three travertine samples from the southeast side of The Park (central Montana) yield an average uranium-thorium age of 73 000 yr. Another sample from the west side of The Park is 320 000 yr old. These results indicate that travertine deposits may have formed at several intervals. The surface beneath The Park travertine is older than about 320 000 yr. Number 2 pediment gravels that contain travertine downslope from the oldest dated sample may be younger than about 320 000 yr. -Authors
The Viner-Wong Envelope Theorem.
ERIC Educational Resources Information Center
Silberberg, Eugene
1999-01-01
Observes that the envelope theorem, a fundamental tool in duality analysis, is still a puzzle to many people. Argues that the essence of a solution proposed by Paul Samuelson (1947) is also unclear to many people, but can be communicated with a simple cost diagram. Presents and explains the proposed diagram. (DSK)
A non-differentiable Noether's theorem
NASA Astrophysics Data System (ADS)
Cresson, Jacky; Greff, Isabelle
2011-02-01
In the framework of the nondifferentiable embedding of Lagrangian systems, defined by Cresson and Greff [non-dierentiable embedding of lagrangian systems and partial dierential equations. Preprint Max-Plank-Institut für Mathematik in den Naturwissenschaften, Leipzig 16, 26 (2010)], we prove a Noether's theorem based on the lifting of one-parameter groups of diffeomorphisms.
The Pythagorean Theorem and the Solid State
ERIC Educational Resources Information Center
Kelly, Brenda S.; Splittgerber, Allan G.
2005-01-01
Packing efficiency and crystal density can be calculated from basic geometric principles employing the Pythagorean theorem, if the unit-cell structure is known. The procedures illustrated have applicability in courses such as general chemistry, intermediate and advanced inorganic, materials science, and solid-state physics.
On Viviani's Theorem and Its Extensions
ERIC Educational Resources Information Center
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
Abel's Theorem Simplifies Reduction of Order
ERIC Educational Resources Information Center
Green, William R.
2011-01-01
We give an alternative to the standard method of reduction or order, in which one uses one solution of a homogeneous, linear, second order differential equation to find a second, linearly independent solution. Our method, based on Abel's Theorem, is shorter, less complex and extends to higher order equations.
Generalized Friedland's theorem for C0-semigroups
NASA Astrophysics Data System (ADS)
Cichon, Dariusz; Jung, Il Bong; Stochel, Jan
2008-07-01
Friedland's characterization of bounded normal operators is shown to hold for infinitesimal generators of C0-semigroups. New criteria for normality of bounded operators are furnished in terms of Hamburger moment problem. All this is achieved with the help of the celebrated Ando's theorem on paranormal operators.
Fixed point theorems and dissipative processes.
NASA Technical Reports Server (NTRS)
Hale, J. K.; Lopes, O.
1973-01-01
Operators of the type considered by Hale et al. (1972) are used to show that under certain conditions there is a fixed point in a dissipative map within a Banach space. The conditions required for the existence of this fixed point are discussed in detail. Several fixed point theorems are formulated and proved.
Student Research Project: Goursat's Other Theorem
ERIC Educational Resources Information Center
Petrillo, Joseph
2009-01-01
In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…
Codimension- p Paley-Wiener theorems
NASA Astrophysics Data System (ADS)
Yang, Yan; Qian, Tao; Sommen, Frank
2007-04-01
We obtain the generalized codimension- p Cauchy-Kovalevsky extension of the exponential function e^{i
An extension theorem for conformal gauge singularities
NASA Astrophysics Data System (ADS)
Lübbe, Christian; Tod, Paul
2009-11-01
We analyze conformal gauge, or isotropic, singularities in cosmological models in general relativity. Using the calculus of tractors, we find conditions in terms of tractor curvature for a local extension of the conformal structure through a cosmological singularity and prove a local extension theorem along a congruence of timelike conformal geodesics.
The Binomial Theorem Tastes the Rainbow.
ERIC Educational Resources Information Center
Cuff, Carolyn K.
1998-01-01
Discusses the commercial for Skittles candies and asks the question "How many flavor combinations can you find?" Focuses on the modeling for a Skittles exercise which includes a brief outline of the mathematical modeling process. Guides students in the use of the binomial theorem and Pascal's triangle in this activity. (ASK)
Fundamental Theorems of Algebra for the Perplexes
ERIC Educational Resources Information Center
Poodiak, Robert; LeClair, Kevin
2009-01-01
The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…
Tennis Rackets and the Parallel Axis Theorem
ERIC Educational Resources Information Center
Christie, Derek
2014-01-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
The soft photon theorem for bremsstrahlung
Heller, L.
1990-01-01
We review this theorem and discuss the possible importance of the second term in the expansion of the cross section in powers of the photon momentum, especially for radiation from particle coming from the decay of resonances. 10 refs., 4 figs.
Ptolemy's Theorem and Familiar Trigonometric Identities.
ERIC Educational Resources Information Center
Bidwell, James K.
1993-01-01
Integrates the sum, difference, and multiple angle identities into an examination of Ptolemy's Theorem, which states that the sum of the products of the lengths of the opposite sides of a quadrilateral inscribed in a circle is equal to the product of the lengths of the diagonals. (MDH)
Reflection theorem for Lorentz-Minkowski spaces
NASA Astrophysics Data System (ADS)
Lee, Nam-Hoon
2016-07-01
We generalize the reflection theorem of the Lorentz-Minkowski plane to that of the Lorentz-Minkowski spaces of higher dimensions. As a result, we show that an isometry of the Lorentz-Minkowski spacetime is a composition of at most 5 reflections.
An Ordinary but Surprisingly Powerful Theorem
ERIC Educational Resources Information Center
Sultan, Alan
2009-01-01
Being a mathematician, the author started to wonder if there are any theorems in mathematics that seem very ordinary on the outside, but when applied, have surprisingly far reaching consequences. The author thought about this and came up with the following unlikely candidate which follows immediately from the definition of the area of a rectangle…
The Pythagorean Theorem and the Solid State
ERIC Educational Resources Information Center
Kelly, Brenda S.; Splittgerber, Allan G.
2005-01-01
Packing efficiency and crystal density can be calculated from basic geometric principles employing the Pythagorean theorem, if the unit-cell structure is known. The procedures illustrated have applicability in courses such as general chemistry, intermediate and advanced inorganic, materials science, and solid-state physics.
Student Research Project: Goursat's Other Theorem
ERIC Educational Resources Information Center
Petrillo, Joseph
2009-01-01
In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Edouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of…
Fundamental Theorems of Algebra for the Perplexes
ERIC Educational Resources Information Center
Poodiak, Robert; LeClair, Kevin
2009-01-01
The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…
On Viviani's Theorem and Its Extensions
ERIC Educational Resources Information Center
Abboud, Elias
2010-01-01
Viviani's theorem states that the sum of distances from any point inside an equilateral triangle to its sides is constant. Here, in an extension of this result, we show, using linear programming, that any convex polygon can be divided into parallel line segments on which the sum of the distances to the sides of the polygon is constant. Let us say…
Ptolemy's Theorem and Familiar Trigonometric Identities.
ERIC Educational Resources Information Center
Bidwell, James K.
1993-01-01
Integrates the sum, difference, and multiple angle identities into an examination of Ptolemy's Theorem, which states that the sum of the products of the lengths of the opposite sides of a quadrilateral inscribed in a circle is equal to the product of the lengths of the diagonals. (MDH)
Tennis Rackets and the Parallel Axis Theorem
ERIC Educational Resources Information Center
Christie, Derek
2014-01-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
Tennis Rackets and the Parallel Axis Theorem
NASA Astrophysics Data System (ADS)
Christie, Derek
2014-04-01
This simple experiment uses an unusual graph straightening exercise to confirm the parallel axis theorem for an irregular object. Along the way, it estimates experimental values for g and the moment of inertia of a tennis racket. We use Excel to find a 95% confidence interval for the true values.
An Elementary Proof of Pick's Theorem.
ERIC Educational Resources Information Center
Pullman, Howard W.
1979-01-01
Pick's Theorem, a statement of the relationship between the area of a polygonal region on a lattice and its interior and boundary lattice points, is familiar to those whose students have participated in activities and discovery lessons using the geoboard. The proof presented, although rather long, is well within the grasp of the average geometry…
Applications of square-related theorems
NASA Astrophysics Data System (ADS)
Srinivasan, V. K.
2014-04-01
The square centre of a given square is the point of intersection of its two diagonals. When two squares of different side lengths share the same square centre, there are in general four diagonals that go through the same square centre. The Two Squares Theorem developed in this paper summarizes some nice theoretical conclusions that can be obtained when two squares of different side lengths share the same square centre. These results provide the theoretical basis for two of the constructions given in the book of H.S. Hall and F.H. Stevens , 'A Shorter School Geometry, Part 1, Metric Edition'. In page 134 of this book, the authors present, in exercise 4, a practical construction which leads to a verification of the Pythagorean theorem. Subsequently in Theorems 29 and 30, the authors present the standard proofs of the Pythagorean theorem and its converse. In page 140, the authors present, in exercise 15, what amounts to a geometric construction, whose verification involves a simple algebraic identity. Both the constructions are of great importance and can be replicated by using the standard equipment provided in a 'geometry toolbox' carried by students in high schools. The author hopes that the results proved in this paper, in conjunction with the two constructions from the above-mentioned book, would provide high school students an appreciation of the celebrated theorem of Pythagoras. The diagrams that accompany this document are based on the free software GeoGebra. The author formally acknowledges his indebtedness to the creators of this free software at the end of this document.
A Simple Geometrical Derivation of the Spatial Averaging Theorem.
ERIC Educational Resources Information Center
Whitaker, Stephen
1985-01-01
The connection between single phase transport phenomena and multiphase transport phenomena is easily accomplished by means of the spatial averaging theorem. Although different routes to the theorem have been used, this paper provides a route to the averaging theorem that can be used in undergraduate classes. (JN)
Extending the Principal Axis Theorem to Fields Other than R.
ERIC Educational Resources Information Center
Friedberg, Stephen H.
1990-01-01
That the principal axis theorem does not extend to any finite field is demonstrated. Presented are four examples that illustrate the difficulty in extending the principal axis theorem to fields other than the field of real numbers. Included are a theorem and proof that uses only a simple counting argument. (KR)
Extending the Principal Axis Theorem to Fields Other than R.
ERIC Educational Resources Information Center
Friedberg, Stephen H.
1990-01-01
That the principal axis theorem does not extend to any finite field is demonstrated. Presented are four examples that illustrate the difficulty in extending the principal axis theorem to fields other than the field of real numbers. Included are a theorem and proof that uses only a simple counting argument. (KR)
The essence of the generalized Newton binomial theorem
NASA Astrophysics Data System (ADS)
Liu, Cheng-shi
2010-10-01
Under the frame of the homotopy analysis method, Liao gives a generalized Newton binomial theorem and thinks it as a rational base of his theory. In the paper, we prove that the generalized Newton binomial theorem is essentially the usual Newton binomial expansion at another point. Our result uncovers the essence of generalized Newton binomial theorem as a key of the homotopy analysis method.
Using Dynamic Geometry to Explore Non-Traditional Theorems
ERIC Educational Resources Information Center
Wares, Arsalan
2010-01-01
The purpose of this article is to provide examples of "non-traditional" theorems that can be explored in a dynamic geometry environment by university and high school students. These theorems were encountered in the dynamic geometry environment. The author believes that teachers can ask their students to construct proofs for these theorems. The…
New Erdős-Kac Type Theorems for Signed Measures on Square-Free Integers
NASA Astrophysics Data System (ADS)
Avdeeva, Maria; Li, Dong; Sinai, Yakov G.
2013-11-01
We consider a family of signed measures supported on the set of square-free numbers. We prove some local limit theorems for the prime divisor counting function ω(n) and establish new Erdős-Kac type results.
Fluctuation theorem applied to the Nosé-Hoover thermostated Lorentz gas.
Gilbert, Thomas
2006-03-01
We present numerical evidence supporting the validity of the Gallavotti-Cohen fluctuation theorem applied to the driven Lorentz gas with Nosé-Hoover thermostating. It is moreover argued that the asymptotic form of the fluctuation formula is independent of the amplitude of the driving force in the limit where it is small.
Fluctuation theorem applied to the Nosé-Hoover thermostated Lorentz gas
NASA Astrophysics Data System (ADS)
Gilbert, Thomas
2006-03-01
We present numerical evidence supporting the validity of the Gallavotti-Cohen fluctuation theorem applied to the driven Lorentz gas with Nosé-Hoover thermostating. It is moreover argued that the asymptotic form of the fluctuation formula is independent of the amplitude of the driving force in the limit where it is small.
NASA Astrophysics Data System (ADS)
Commins, Eugene D.; Jackson, J. David; Demille, David P.
2007-06-01
In most experimental searches for the electron electric dipole moment, one searches for a linear Stark effect in a paramagnetic atom or molecule and interprets the result in terms of the electric dipole moment of the unpaired valence electron(s). Schiff's theorem states that in the limit of nonrelativistic quantum mechanics, there can be no linear Stark effect to first order in the electric dipole moment. Sandars has shown that Schiff's theorem is not applicable when special relativity is taken into account. We give a heuristic explanation for this relativistic effect, which corrects a widespread misconception in the literature.
NASA Astrophysics Data System (ADS)
McRae, S. M.; Vrscay, E. R.
1992-09-01
The classical hypervirial and Hellmann-Feynman theorems are used to formulate a "perturbation theory without Fourier series" that can be used to generate canonical series expansions for the energies of perturbed periodic orbits for separable classical Hamiltonians. Here, the method is applied to one-dimensional anharmonic oscillators and radial Kepler problems. In all cases, the classical series for energies and expectation values are seen to correspond to the expansions associated with their quantum mechanical counterparts through an appropriate action preserving classical limit. This "action fixing" is inherent in the classical Hellmann-Feynman theorem applied to periodic orbits.
Tails of Polynomials of Random Variables and Stable Limits for Nonconventional Sums
NASA Astrophysics Data System (ADS)
Kifer, Yuri; Varadhan, S. R. S.
2017-02-01
First, we obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails. Then we derive stable limit theorems for sums of the form sum _{Nt≥n≥1}Fbig (X_{q_1(n)},ldots ,X_{q_ℓ (n)}big ) where F is a polynomial, q_i(n) is either n-1+i or ni and X_n,n≥0 is a sequence of independent identically distributed random variables with heavy tails. Our results can be viewed as an extension to the heavy tails case of the nonconventional functional central limit theorem from Kifer and Varadhan (Ann Probab 42:649-688, 2014).
Invisibility and cloaking structures as weak or strong solutions of Devaney-Wolf theorem.
Labate, Giuseppe; Matekovits, Ladislau
2016-08-22
Inspired by a general theorem on non-radiating sources demonstrated by Devaney and Wolf, a unified theory for invisible and cloaking structures is here proposed. By solving Devaney-Wolf theorem in the quasi-static limit, a weak solution is obtained, demonstrating the existence of Anapole modes, Mantle Cloaking and Plasmonic Cloaking. Beyond the quasi-static regime, a strong solution of Devaney-Wolf theorem can be formulated, predicting general non-scattering devices based on directional invisibility, Transformation Optics, neutral inclusions and refractive index continuity. Both weak and strong solutions are analytically demonstrated to depend on the concept of contrast, mathematically defined as a normalized difference between constitutive parameters (or wave-impedance property) of a material and its surrounding background.
Sparse image reconstruction on the sphere: implications of a new sampling theorem.
McEwen, Jason D; Puy, Gilles; Thiran, Jean-Philippe; Vandergheynst, Pierre; Van De Ville, Dimitri; Wiaux, Yves
2013-06-01
We study the impact of sampling theorems on the fidelity of sparse image reconstruction on the sphere. We discuss how a reduction in the number of samples required to represent all information content of a band-limited signal acts to improve the fidelity of sparse image reconstruction, through both the dimensionality and sparsity of signals. To demonstrate this result, we consider a simple inpainting problem on the sphere and consider images sparse in the magnitude of their gradient. We develop a framework for total variation inpainting on the sphere, including fast methods to render the inpainting problem computationally feasible at high resolution. Recently a new sampling theorem on the sphere was developed, reducing the required number of samples by a factor of two for equiangular sampling schemes. Through numerical simulations, we verify the enhanced fidelity of sparse image reconstruction due to the more efficient sampling of the sphere provided by the new sampling theorem.
A generalization of Bertrand's theorem to surfaces of revolution
Zagryadskii, Oleg A; Kudryavtseva, Elena A; Fedoseev, Denis A
2012-08-31
We prove a generalization of Bertrand's theorem to the case of abstract surfaces of revolution that have no 'equators'. We prove a criterion for exactly two central potentials to exist on this type of surface (up to an additive and a multiplicative constant) for which all bounded orbits are closed and there is a bounded nonsingular noncircular orbit. We prove a criterion for the existence of exactly one such potential. We study the geometry and classification of the corresponding surfaces with the aforementioned pair of potentials (gravitational and oscillatory) or unique potential (oscillatory). We show that potentials of the required form do not exist on surfaces that do not belong to any of the classes described. Bibliography: 33 titles.
Bailey, David H.; Misiurewicz, Michal
2005-12-31
A real number alpha is said to be b-normal if every m-long string of digits appears in the base-b expansion of alpha with limiting frequency b-m. We prove that alpha is b-normal if and only if it possesses no base-b ''hot spot''. In other words, alpha is b-normal if and only if there is no real number y such that smaller and smaller neighborhoods of y are visited by the successive shifts of the base-b expansion of alpha with larger and larger frequencies, relative to the lengths of these neighborhoods
Quantum Stratonovich calculus and the quantum Wong-Zakai theorem
NASA Astrophysics Data System (ADS)
Gough, John
2006-11-01
We extend the Itō-to-Stratonovich analysis or quantum stochastic differential equations, introduced by Gardiner and Collett for emission (creation), absorption (annihilation) processes, to include scattering (conservation) processes. Working within the framework of quantum stochastic calculus, we define Stratonovich calculus as an algebraic modification of the Itō one and give conditions for the existence of Stratonovich time-ordered exponentials. We show that conversion formula for the coefficients has a striking resemblance to Green's function formulas from standard perturbation theory. We show that the calculus conveniently describes the Markov limit of regular open quantum dynamical systems in much the same way as in the Wong-Zakai approximation theorems of classical stochastic analysis. We extend previous limit results to multiple-dimensions with a proof that makes use of diagrammatic conventions.
Quantum Stratonovich calculus and the quantum Wong-Zakai theorem
Gough, John
2006-11-15
We extend the Ito(bar sign)-to-Stratonovich analysis or quantum stochastic differential equations, introduced by Gardiner and Collett for emission (creation), absorption (annihilation) processes, to include scattering (conservation) processes. Working within the framework of quantum stochastic calculus, we define Stratonovich calculus as an algebraic modification of the Ito(bar sign) one and give conditions for the existence of Stratonovich time-ordered exponentials. We show that conversion formula for the coefficients has a striking resemblance to Green's function formulas from standard perturbation theory. We show that the calculus conveniently describes the Markov limit of regular open quantum dynamical systems in much the same way as in the Wong-Zakai approximation theorems of classical stochastic analysis. We extend previous limit results to multiple-dimensions with a proof that makes use of diagrammatic conventions.
NASA Astrophysics Data System (ADS)
Izmailov, Ramil; Potapov, Alexander A.; Filippov, Alexander I.; Ghosh, Mithun; Nandi, Kamal K.
2015-04-01
We investigate the stability of circular material orbits in the analytic galactic metric recently derived by Harko et al., Mod. Phys. Lett. A29, 1450049 (2014). It turns out that stability depends more strongly on the dark matter central density ρ0 than on other parameters of the solution. This property then yields an upper limit on ρ0 for each individual galaxy, which we call here ρ 0 upper, such that stable circular orbits are possible only when the constraint ρ 0<= ρ 0 upper is satisfied. This is our new result. To approximately quantify the upper limit, we consider as a familiar example our Milky Way galaxy that has a projected dark matter radius RDM 180 kpc and find that ρ 0 upper ˜ 2.37× 1011 M⊙ kpc-3. This limit turns out to be about four orders of magnitude larger than the latest data on central density ρ0 arising from the fit to the Navarro-Frenk-White (NFW) and Burkert density profiles. Such consistency indicates that the Eddington-inspired Born-Infeld (EiBI) solution could qualify as yet another viable alternative model for dark matter.
Ferretti, G; Antonutto, G; Denis, C; Hoppeler, H; Minetti, A E; Narici, M V; Desplanches, D
1997-01-01
1. The effects of bed rest on the cardiovascular and muscular parameters which affect maximal O2 consumption (VO2,max) were studied. The fractional limitation of VO2,max imposed by these parameters after bed rest was analysed. 2. The VO2,max, by standard procedure, and the maximal cardiac output (Qmax), by the pulse contour method, were measured during graded cyclo-ergometric exercise on seven subjects before and after a 42-day head-down tilt bed rest. Blood haemoglobin concentration ([Hb]) and arterialized blood gas analysis were determined at the highest work load. 3. Muscle fibre types, oxidative enzyme activities, and capillary and mitochondrial densities were measured on biopsy samples from the vastus lateralis muscle before and at the end of bed rest. The measure of muscle cross-sectional area (CSA) by NMR imaging at the level of biopsy site allowed computation of muscle oxidative capacity and capillary length. 4. The VO2,max was reduced after bed rest (-16.6%). The concomitant decreases in Qmax (-30.8%), essentially due to a change in stroke volume, and in [Hb] led to a huge decrease in O2 delivery (-39.7%). 5. Fibre type distribution was unaffected by bed rest. The decrease in fibre area corresponded to the significant reduction in muscle CSA (-17%). The volume density of mitochondria was reduced after bed rest (-16.6%), as were the oxidative enzyme activities (-11%). The total mitochondrial volume was reduced by 28.5%. Capillary density was unchanged. Total capillary length was 22.2% lower after bed rest, due to muscle atrophy. 6. The interaction between these muscular and cardiovascular changes led to a smaller reduction in VO2,max than in cardiovascular O2 transport. Yet the latter appears to play the greatest role in limiting VO2,max after bed rest (> 70% of overall limitation), the remaining fraction being shared between peripheral O2 diffusion and utilization. PMID:9218227
Craft, Kathleen J; Ashley, Mary V; Koenig, Walter D
2002-11-01
Many oak species are interfertile, and morphological and genetic evidence for hybridization is widespread. Here we use DNA microsatellite markers to characterize hybridization between two closely related oak species in a mixed stand in central coastal California, Quercus lobata (valley oak) and Q. douglasii (blue oak) (Fagaceae). Genotypes from four microsatellite loci indicate that many alleles are shared between the two species. However, each species harbors unique alleles, and allele frequencies differ significantly. A Bayesian analysis of genetic structure in the stand identified two highly differentiated genetic clusters, essentially corresponding to species assignment based on morphology. Data from the four loci were sufficient to assign all 135 trees to one of the two species. In addition, five putative hybrid individuals having intermediate morphologies could be assigned genetically to one or the other species, and all but one had low probability of hybrid ancestry. Overally, only six (4.6%) trees showed >0.05 probability of hybrid ancestry, in all cases their probabilities for nonhybrid ancestry were substantially higher. We conclude that adult hybrids of Q. douglasii × Q. lobata are rare at this site and plasticity in morphological characters may lead to overestimates of hybridization among Quercus species.
Baur, Hannes
2015-01-01
Abstract Two new species, Pteromalus briani sp. n. and Pteromalus janstai sp. n., with unusual characters are described from the Central Plateau and the Alps in Switzerland, respectively. Pteromalus briani sp. n. is remarkable in that it has the metatibia quite abruptly expanded before the middle. This type of modification of the hind tibia is unique within the Pteromalidae and probably also the entire Chalcidoidea. It is also very rare in other parasitic wasps, where it is suspected to be associated with pheromone glands. The species is a gregarious endoparasitoid of pupae of Vanessa atalanta (Linnaeus) and Aglais urticae (Linnaeus), two common butterflies (Lepidoptera: Nymphalidae) in Europe. It is furthermore a koinobiont parasitoid ovipositing in an early larval stage of the host. The other species, Pteromalus janstai sp. n., shows a flattened mesosoma. A dorsoventrally depressed body is a unique feature within the genus Pteromalus, but known from a number species in unrelated genera and subfamilies. The two records demonstrate that it is possible to discover entirely new species with extraordinary characters even in one of the taxonomically most thoroughly explored parts of the world. PMID:26261432
Baur, Hannes
2015-01-01
Two new species, Pteromalusbriani sp. n. and Pteromalusjanstai sp. n., with unusual characters are described from the Central Plateau and the Alps in Switzerland, respectively. Pteromalusbriani sp. n. is remarkable in that it has the metatibia quite abruptly expanded before the middle. This type of modification of the hind tibia is unique within the Pteromalidae and probably also the entire Chalcidoidea. It is also very rare in other parasitic wasps, where it is suspected to be associated with pheromone glands. The species is a gregarious endoparasitoid of pupae of Vanessaatalanta (Linnaeus) and Aglaisurticae (Linnaeus), two common butterflies (Lepidoptera: Nymphalidae) in Europe. It is furthermore a koinobiont parasitoid ovipositing in an early larval stage of the host. The other species, Pteromalusjanstai sp. n., shows a flattened mesosoma. A dorsoventrally depressed body is a unique feature within the genus Pteromalus, but known from a number species in unrelated genera and subfamilies. The two records demonstrate that it is possible to discover entirely new species with extraordinary characters even in one of the taxonomically most thoroughly explored parts of the world.
Cekanaviciute, Egle; Dietrich, Hans K; Axtell, Robert C; Williams, Aaron M; Egusquiza, Riann; Wai, Karen M; Koshy, Anita A; Buckwalter, Marion S
2014-07-01
The balance between controlling infection and limiting inflammation is particularly precarious in the brain because of its unique vulnerability to the toxic effects of inflammation. Astrocytes have been implicated as key regulators of neuroinflammation in CNS infections, including infection with Toxoplasma gondii, a protozoan parasite that naturally establishes a chronic CNS infection in mice and humans. In CNS toxoplasmosis, astrocytes are critical to controlling parasite growth. They secrete proinflammatory cytokines and physically encircle parasites. However, the molecular mechanisms used by astrocytes to limit neuroinflammation during toxoplasmic encephalitis have not yet been identified. TGF-β signaling in astrocytes is of particular interest because TGF-β is universally upregulated during CNS infection and serves master regulatory and primarily anti-inflammatory functions. We report in this study that TGF-β signaling is activated in astrocytes during toxoplasmic encephalitis and that inhibition of astrocytic TGF-β signaling increases immune cell infiltration, uncouples proinflammatory cytokine and chemokine production from CNS parasite burden, and increases neuronal injury. Remarkably, we show that the effects of inhibiting astrocytic TGF-β signaling are independent of parasite burden and the ability of GFAP(+) astrocytes to physically encircle parasites. Copyright © 2014 by The American Association of Immunologists, Inc.
Bosonization Theorem and a Model of High-Tc Superconductor.
NASA Astrophysics Data System (ADS)
Ren, Hai-Cang
1996-03-01
For a purely fermionic system on a lattice, there exists a different, but well defined system on the same lattice, consisting both of bona fide fermions and bosons with an interaction depending on a parameter G characterizing on-site repulsion between particles(R. Friedberg, T. D. Lee and H. C. Ren, Phys. Rev. B50, 10190 (1994).). The energy spectrum and the scattering matrix of the former are identical to those in the finite-energy sector of the latter in the hard-core limit, G→∞. This theorem is particularly useful for the description of a fermionic system whose low-lying spectrum consists of bosonic resonances. We argue that the high-Tc superconductors belong to this category and the long-range order in the superphase can be identified with the condensation of resonance bosons. A short coherence length, results from μSR experiments, measurements of the Hall number and the anomalous behavior of H_c2 near T=0 can be understood in terms of this resonance-boson model(R. Friedberg, T. D. Lee and H. C. Ren, Phys. Rev. B42, 4122 (1990).). We have also examined the possibility of a bosonic d-wave resonance(O.Tchernyshyov, A.S.Blaer and H.Ren, in the current Proceedings.). In this case, the bosonization theorem predicts coexistence of an s-wave bosonic condensate and a d-wave gap parameter for fermions.
Formal reasoning about systems biology using theorem proving
Hasan, Osman; Siddique, Umair; Tahar, Sofiène
2017-01-01
System biology provides the basis to understand the behavioral properties of complex biological organisms at different levels of abstraction. Traditionally, analysing systems biology based models of various diseases have been carried out by paper-and-pencil based proofs and simulations. However, these methods cannot provide an accurate analysis, which is a serious drawback for the safety-critical domain of human medicine. In order to overcome these limitations, we propose a framework to formally analyze biological networks and pathways. In particular, we formalize the notion of reaction kinetics in higher-order logic and formally verify some of the commonly used reaction based models of biological networks using the HOL Light theorem prover. Furthermore, we have ported our earlier formalization of Zsyntax, i.e., a deductive language for reasoning about biological networks and pathways, from HOL4 to the HOL Light theorem prover to make it compatible with the above-mentioned formalization of reaction kinetics. To illustrate the usefulness of the proposed framework, we present the formal analysis of three case studies, i.e., the pathway leading to TP53 Phosphorylation, the pathway leading to the death of cancer stem cells and the tumor growth based on cancer stem cells, which is used for the prognosis and future drug designs to treat cancer patients. PMID:28671950
Generalized virial theorem in Palatini f(R) gravity
Sefiedgar, A. S.; Atazadeh, K.; Sepangi, H. R.
2009-09-15
We use the collision-free Boltzmann equation in Palatini f(R) gravity to derive the virial theorem within the context of the Palatini approach. It is shown that the virial mass is proportional to certain geometrical terms appearing in the Einstein field equations which contributes to gravitational energy and that such geometric mass can be attributed to the virial mass discrepancy in a cluster of galaxies. We then derive the velocity dispersion relation for clusters, followed by the metric tensor components inside the cluster as well as the f(R) Lagrangian in terms of the observational parameters. Since these quantities may also be obtained experimentally, the f(R) virial theorem is a convenient tool to test the viability of f(R) theories in different models. Finally, we discuss the limitations of our approach in light of the cosmological averaging used and questions that have been raised in the literature against such averaging procedures in the context of the present work.
Revisiting MHD stability comparison theorems: Some surprising new results
NASA Astrophysics Data System (ADS)
Cerfon, Antoine; Freidberg, Jeffrey
2009-05-01
The classic MHD stability comparison theorems (Kruskal-Oberman, Rosenbluth-Rostoker) show that ideal MHD yields the most stringent stability limits according to the hierarchy δWCGL>δWKIN>δWMHD. This has long justified the use of ideal MHD for conservative predictions of MHD stability boundaries. We reexamine these theorems, with the following conclusions:(1) It is crucial to distinguish between ergodic and closed field line systems.(2) It is essential to account for resonant particles in the kinetic MHD model.(3) For ergodic systems the original kinetic MHD analysis over-estimates stability: δWKIN>δWMHD. Our new result predicts δWKIN=δWMHD.(4) For closed line systems plasma compressibility effects become important, and resonant particle effects vanish. Both the original and new analysis predict δWKIN>δWMHD. However, using a Vlasov-Fluid model with Vlasov ions and fluid electrons we show that both δWKIN and δWMHD, while mathematically correct, yield the wrong physical result. The V-F model shows that at marginal stability the compressibility stabilization term vanishes identically! For ergodic systems, marginal stability is always incompressible, so δWKIN=δWMHD=δWVF. For compressible modes in closed line systems, however, perpendicular resonant particle effects cancel the stabilizing effect of plasma compressibility predicted by ideal and kinetic MHD: δWKIN>δWMHD>δWVF.
NASA Astrophysics Data System (ADS)
Gottwald, Georg A.; Wormell, J. P.; Wouters, Jeroen
2016-09-01
Using a sensitive statistical test we determine whether or not one can detect the breakdown of linear response given observations of deterministic dynamical systems. A goodness-of-fit statistics is developed for a linear statistical model of the observations, based on results for central limit theorems for deterministic dynamical systems, and used to detect linear response breakdown. We apply the method to discrete maps which do not obey linear response and show that the successful detection of breakdown depends on the length of the time series, the magnitude of the perturbation and on the choice of the observable. We find that in order to reliably reject the assumption of linear response for typical observables sufficiently large data sets are needed. Even for simple systems such as the logistic map, one needs of the order of 106 observations to reliably detect the breakdown with a confidence level of 95 %; if less observations are available one may be falsely led to conclude that linear response theory is valid. The amount of data required is larger the smaller the applied perturbation. For judiciously chosen observables the necessary amount of data can be drastically reduced, but requires detailed a priori knowledge about the invariant measure which is typically not available for complex dynamical systems. Furthermore we explore the use of the fluctuation-dissipation theorem (FDT) in cases with limited data length or coarse-graining of observations. The FDT, if applied naively to a system without linear response, is shown to be very sensitive to the details of the sampling method, resulting in erroneous predictions of the response.
NASA Astrophysics Data System (ADS)
Thomas, R. Q.; Kellner, J. R.; Peart, D. R.
2005-12-01
Logistical constraints on sample size and spatial scale limit individual-based field research on tropical trees. With remote sensing data, we may escape these limitations if fates of individuals can be tracked rigorously. We assessed the potential of readily available, commercial satellite data (QuickBird, 0.7 m pixels) obtained in 2003, to track the fate of individual crowns (> 40 m height) in tropical rain forest at La Selva, Costa Rica. The positions and shapes of these crowns in 1997 had been established using small-footprint LiDAR data with field verification. We focused first on a subset (n=180) of trees monitored in the field over the period 1997-2003. For the 60% of those trees whose crown positions and shapes could be tracked with confidence in the satellite image, we correctly recorded all 3 actual deaths. But we also incorrectly assigned 4 additional deaths to living individuals, due to the abundance of dark pixels in their crown areas. For the 40% of field-monitored trees for which our tracking in the satellite data was less confident (due to lack of image clarity), we correctly identified the one real death event, but incorrectly assigned 6 additional deaths to living trees. Thus, for the field-monitored trees, we grossly overestimated mortality in the satellite image (by 350%). Although currently available high resolution satellite imagery was not adequate for reliable monitoring of individuals, even for the largest forest trees, time series satellite data, rather than time series LiDAR to satellite data, might provide unbiased estimates of overall tree mortality rates if errors compensate. Satellite data may be also be useful as a labor and time saving complement to fieldwork on individual forest trees.
Generalized reciprocity theorem for semiconductor devices
NASA Technical Reports Server (NTRS)
Misiakos, K.; Lindholm, F. A.
1985-01-01
A reciprocity theorem is presented that relates the short-circuit current of a device, induced by a carrier generation source, to the minority-carrier Fermi level in the dark. The basic relation is general under low injection. It holds for three-dimensional devices with position dependent parameters (energy gap, electron affinity, mobility, etc.), and for transient or steady-state conditions. This theorem allows calculation of the internal quantum efficiency of a solar cell by using the analysis of the device in the dark. Other applications could involve measurements of various device parameters, interfacial surface recombination velocity at a polcrystalline silicon emitter contact, for rexample, by using steady-state or transient photon or mass-particle radiation.
A Geometrical Approach to Bell's Theorem
NASA Technical Reports Server (NTRS)
Rubincam, David Parry
2000-01-01
Bell's theorem can be proved through simple geometrical reasoning, without the need for the Psi function, probability distributions, or calculus. The proof is based on N. David Mermin's explication of the Einstein-Podolsky-Rosen-Bohm experiment, which involves Stern-Gerlach detectors which flash red or green lights when detecting spin-up or spin-down. The statistics of local hidden variable theories for this experiment can be arranged in colored strips from which simple inequalities can be deduced. These inequalities lead to a demonstration of Bell's theorem. Moreover, all local hidden variable theories can be graphed in such a way as to enclose their statistics in a pyramid, with the quantum-mechanical result lying a finite distance beneath the base of the pyramid.
About the Stokes decomposition theorem of waves
NASA Astrophysics Data System (ADS)
Lacaze, B.
2011-06-01
The Stokes decomposition theorem deals with the electrical field E→=X,Y of a light beam. The theorem asserts that a beam can be viewed as the sum of two differently polarized parts. This result was recently discussed for light in the frame of the unified theory of coherence. We study the general case of an electromagnetic wave which can be in radio, radar, communications, or light. We assume stationary components with any power spectrum and finite or infinite bandwidth. We show that an accurate definition of polarization and unpolarization is a key parameter which rules the set of solutions of the problem. When dealing with a "strong definition" of unpolarization, the problem is treated in the frame of stationary processes and linear invariant filters. When dealing with a "weak definition", solutions are given by elementary properties of bidimensional random variables.
Thermodynamics of biochemical networks and duality theorems.
De Martino, Daniele
2013-05-01
One interesting yet difficult computational issue has recently been posed in biophysics in regard to the implementation of thermodynamic constraints to complex networks. Biochemical networks of enzymes inside cells are among the most efficient, robust, differentiated, and flexible free-energy transducers in nature. How is the second law of thermodynamics encoded for these complex networks? In this article it is demonstrated that for chemical reaction networks in the steady state the exclusion (presence) of closed reaction cycles makes possible (impossible) the definition of a chemical potential vector. Interestingly, this statement is encoded in one of the key results in combinatorial optimization, i.e., the Gordan theorem of the alternatives. From a computational viewpoint, the theorem reveals that calculating a reaction's free energy and identifying infeasible loops in flux states are dual problems whose solutions are mutually exclusive, and this opens the way for efficient and scalable methods to perform the energy balance analysis of large-scale biochemical networks.
NASA Astrophysics Data System (ADS)
Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.
2016-09-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. Lastly, we further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
Construction of momentum theorem using cross moments
NASA Astrophysics Data System (ADS)
Hahm, T. S.; Wang, Lu; Diamond, P. H.
2009-11-01
Charney-Drazin theorem has been extended to Hasegawa Wakatani system for zonal flow problem in magnetic fusion [P.H. Diamond, et al., Plasma Phys. Control. Fusion 50, 124018 (2008)]. For this model, the guiding center density is the potential vorticity and zonal flow is influenced by the particle flux. In this work we construct momentum theorems in terms of a hierarchy of cross moments
Lesovik, G B; Lebedev, A V; Sadovskyy, I A; Suslov, M V; Vinokur, V M
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy.
A torus bifurcation theorem with symmetry
NASA Technical Reports Server (NTRS)
Vangils, S. A.; Golubitsky, M.
1989-01-01
Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.
Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; ...
2016-09-12
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. Lastly, we further demonstrate that the typicalmore » evolution of energy-isolated quantum systems occurs with non-diminishing entropy.« less
Lanford's Theorem and the Emergence of Irreversibility
NASA Astrophysics Data System (ADS)
Uffink, Jos; Valente, Giovanni
2015-04-01
It has been a longstanding problem to show how the irreversible behaviour of macroscopic systems can be reconciled with the time-reversal invariance of these same systems when considered from a microscopic point of view. A result by Lanford (Dynamical systems, theory and applications, 1975, Asterisque 40:117-137, 1976, Physica 106A:70-76, 1981) shows that, under certain conditions, the famous Boltzmann equation, describing the irreversible behaviour of a dilute gas, can be obtained from the time-reversal invariant Hamiltonian equations of motion for the hard spheres model. Here, we examine how and in what sense Lanford's theorem succeeds in deriving this remarkable result. Many authors have expressed different views on the question which of the ingredients in Lanford's theorem is responsible for the emergence of irreversibility. We claim that these interpretations miss the target. In fact, we argue that there is no time-asymmetric ingredient at all.
Fluctuation theorem for constrained equilibrium systems.
Gilbert, Thomas; Dorfman, J Robert
2006-02-01
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as isokinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless, finite-time averages of the phase-space contraction rate have nontrivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states. Moreover, we show that these fluctuations are distributed according to a Gaussian curve for long enough times. Three different systems are considered here: namely, (i) a fluid composed of particles interacting with Lennard-Jones potentials, (ii) a harmonic oscillator with Nosé-Hoover thermostatting, and (iii) a simple hyperbolic two-dimensional map.
Fluctuation theorem for constrained equilibrium systems
NASA Astrophysics Data System (ADS)
Gilbert, Thomas; Dorfman, J. Robert
2006-02-01
We discuss the fluctuation properties of equilibrium chaotic systems with constraints such as isokinetic and Nosé-Hoover thermostats. Although the dynamics of these systems does not typically preserve phase-space volumes, the average phase-space contraction rate vanishes, so that the stationary states are smooth. Nevertheless, finite-time averages of the phase-space contraction rate have nontrivial fluctuations which we show satisfy a simple version of the Gallavotti-Cohen fluctuation theorem, complementary to the usual fluctuation theorem for nonequilibrium stationary states and appropriate to constrained equilibrium states. Moreover, we show that these fluctuations are distributed according to a Gaussian curve for long enough times. Three different systems are considered here: namely, (i) a fluid composed of particles interacting with Lennard-Jones potentials, (ii) a harmonic oscillator with Nosé-Hoover thermostatting, and (iii) a simple hyperbolic two-dimensional map.
Luttinger theorem and imbalanced Fermi systems
NASA Astrophysics Data System (ADS)
Pieri, Pierbiagio; Strinati, Giancarlo Calvanese
2017-04-01
The proof of the Luttinger theorem, which was originally given for a normal Fermi liquid with equal spin populations formally described by the exact many-body theory at zero temperature, is here extended to an approximate theory given in terms of a "conserving" approximation also with spin imbalanced populations. The need for this extended proof, whose underlying assumptions are here spelled out in detail, stems from the recent interest in superfluid trapped Fermi atoms with attractive inter-particle interaction, for which the difference between two spin populations can be made large enough that superfluidity is destroyed and the system remains normal even at zero temperature. In this context, we will demonstrate the validity of the Luttinger theorem separately for the two spin populations for any "Φ-derivable" approximation, and illustrate it in particular for the self-consistent t-matrix approximation.
Lesovik, G. B.; Lebedev, A. V.; Sadovskyy, I. A.; Suslov, M. V.; Vinokur, V. M.
2016-01-01
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. PMID:27616571
Fluctuation-Dissipation Theorem for Metastable Systems
NASA Astrophysics Data System (ADS)
Báez, G.; Larralde, H.; Leyvraz, F.; Méndez-Sánchez, R. A.
2003-04-01
We show that an appropriately defined fluctuation-dissipation theorem, connecting generalized susceptibilities and time correlation functions, is valid for times shorter than the nucleation time of the metastable state of Markovian systems satisfying detailed balance. This is done by assuming that such systems can be described by a superposition of the ground and first excited states of the master equation. We corroborate our results numerically for the metastable states of a two-dimensional Ising model.
Asynchronous networks: modularization of dynamics theorem
NASA Astrophysics Data System (ADS)
Bick, Christian; Field, Michael
2017-02-01
Building on the first part of this paper, we develop the theory of functional asynchronous networks. We show that a large class of functional asynchronous networks can be (uniquely) represented as feedforward networks connecting events or dynamical modules. For these networks we can give a complete description of the network function in terms of the function of the events comprising the network: the modularization of dynamics theorem. We give examples to illustrate the main results.
Infinite flag varieties and conjugacy theorems
Peterson, Dale H.; Kac, Victor G.
1983-01-01
We study the orbit of a highest-weight vector in an integrable highest-weight module of the group G associated to a Kac-Moody algebra [unk](A). We obtain applications to the geometric structure of the associated flag varieties and to the algebraic structure of [unk](A). In particular, we prove conjugacy theorems for Cartan and Borel subalgebras of [unk](A), so that the Cartan matrix A is an invariant of [unk](A). PMID:16593298
Tests of the lattice index theorem
Jordan, Gerald; Hoellwieser, Roman; Faber, Manfried; Heller, Urs M.
2008-01-01
We investigate the lattice index theorem and the localization of the zero modes for thick classical center vortices. For nonorientable spherical vortices, the index of the overlap Dirac operator differs from the topological charge although the traces of the plaquettes deviate only by a maximum of 1.5% from trivial plaquettes. This may be related to the fact that even in Landau gauge some links of these configuration are close to the nontrivial center elements.
Volume integral theorem for exotic matter
Nandi, Kamal Kanti; Zhang Yuanzhong; Kumar, K.B. Vijaya
2004-12-15
We answer an important question in general relativity about the volume integral theorem for exotic matter by suggesting an exact integral quantifier for matter violating Averaged Null Energy Condition (ANEC). It is checked against some well-known static, spherically symmetric traversable wormhole solutions of general relativity with a sign reversed kinetic term minimally coupled scalar field. The improved quantifier is consistent with the principle that traversable wormholes can be supported by arbitrarily small quantities of exotic matter.
New electromagnetic memories and soft photon theorems
NASA Astrophysics Data System (ADS)
Mao, Pujian; Ouyang, Hao; Wu, Jun-Bao; Wu, Xiaoning
2017-06-01
In this paper, we present a new type of electromagnetic memory. It is a "magnetic" type, or B mode, radiation memory effect. Rather than a residual velocity, we find a position displacement of a charged particle induced by the B mode radiation with memory. We find two types of electromagnetic displacement (ordinary and null). We also show that the null electromagnetic memory formulas are nothing but a Fourier transformation of soft photon theorems.
Spontaneously broken spacetime symmetries and Goldstone's theorem.
Low, Ian; Manohar, Aneesh V
2002-03-11
Goldstone's theorem states that there is a massless mode for each broken symmetry generator. It has been known for a long time that the naive generalization of this counting fails to give the correct number of massless modes for spontaneously broken spacetime symmetries. We explain how to get the right count of massless modes in the general case, and discuss examples involving spontaneously broken Poincaré and conformal invariance.
[Objectivity of BSE symptoms using Bayes theorem].
Hässig, M; Urech Hässig, B; Knubben-Schweizer, G
2011-12-01
In clinical epidemiology the Bayes theorem finds ever more use to render clinical acting more objective. It is shown that unusual examinations of BSE (bovine spongiform encephalopathy) as noise producing with ladle covers may quite objectively be evaluated. With the help of the likelihood ratio computed thereby, also a ranking of importance (clinical utility) of symptoms can be provided. The single most important symptom for BSE is photosensibility.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
Haag's Theorem and Parameterized Quantum Field Theory
NASA Astrophysics Data System (ADS)
Seidewitz, Edwin
2017-01-01
``Haag's theorem is very inconvenient; it means that the interaction picture exists only if there is no interaction''. In traditional quantum field theory (QFT), Haag's theorem states that any field unitarily equivalent to a free field must itself be a free field. But the derivation of the Dyson series perturbation expansion relies on the use of the interaction picture, in which the interacting field is unitarily equivalent to the free field, but which must still account for interactions. So, the usual derivation of the scattering matrix in QFT is mathematically ill defined. Nevertheless, perturbative QFT is currently the only practical approach for addressing realistic scattering, and it has been very successful in making empirical predictions. This success can be understood through an alternative derivation of the Dyson series in a covariant formulation of QFT using an invariant, fifth path parameter in addition to the usual four position parameters. The parameterization provides an additional degree of freedom that allows Haag's Theorem to be avoided, permitting the consistent use of a form of interaction picture in deriving the Dyson expansion. The extra symmetry so introduced is then broken by the choice of an interacting vacuum.
Theorem Proving In Higher Order Logics
NASA Technical Reports Server (NTRS)
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
Limits for the central production of Theta+ and Xi(--)pentaquarks in 920-GeV pA collisions.
Abt, I; Adams, M; Agari, M; Albrecht, H; Aleksandrov, A; Amaral, V; Amorim, A; Aplin, S J; Aushev, V; Bagaturia, Y; Balagura, V; Bargiotti, M; Barsukova, O; Bastos, J; Batista, J; Bauer, C; Bauer, Th S; Belkov, A; Belkov, Ar; Belotelov, I; Bertin, A; Bobchenko, B; Böcker, M; Bogatyrev, A; Bohm, G; Bräuer, M; Bruinsma, M; Bruschi, M; Buchholz, P; Buran, T; Carvalho, J; Conde, P; Cruse, C; Dam, M; Danielsen, K M; Danilov, M; Castro, S De; Deppe, H; Dong, X; Dreis, H B; Egorytchev, V; Ehret, K; Eisele, F; Emeliyanov, D; Essenov, S; Fabbri, L; Faccioli, P; Feuerstack-Raible, M; Flammer, J; Fominykh, B; Funcke, M; Garrido, Ll; Giacobbe, B; Gläss, J; Goloubkov, D; Golubkov, Y; Golutvin, A; Golutvin, I; Gorbounov, I; Gorisek, A; Gouchtchine, O; Goulart, D C; Gradl, S; Gradl, W; Grimaldi, F; Groth-Jensen, J; Guilitsky, Yu; Hansen, J D; Hernández, J M; Hofmann, W; Hott, T; Hulsbergen, W; Husemann, U; Igonkina, O; Ispiryan, M; Jagla, T; Jiang, C; Kapitza, H; Karabekyan, S; Karpenko, N; Keller, S; Kessler, J; Khasanov, F; Kiryushin, Yu; Klinkby, E; Knöpfle, K T; Kolanoski, H; Korpar, S; Krauss, C; Kreuzer, P; Krizan, P; Krücker, D; Kupper, S; Kvaratskheliia, T; Lanyov, A; Lau, K; Lewendel, B; Lohse, T; Lomonosov, B; Männer, R; Masciocchi, S; Massa, I; Matchikhilian, I; Medin, G; Medinnis, M; Mevius, M; Michetti, A; Mikhailov, Yu; Mizuk, R; Muresan, R; Zur Nedden, M; Negodaev, M; Nörenberg, M; Nowak, S; Núñez Pardo de Vera, M T; Ouchrif, M; Ould-Saada, F; Padilla, C; Peralta, D; Pernack, R; Pestotnik, R; Piccinini, M; Pleier, M A; Poli, M; Popov, V; Pose, A; Pose, D; Prystupa, S; Pugatch, V; Pylypchenko, Y; Pyrlik, J; Reeves, K; Ressing, D; Rick, H; Riu, I; Robmann, P; Rostovtseva, I; Rybnikov, V; Sánchez, F; Sbrizzi, A; Schmelling, M; Schmidt, B; Schreiner, A; Schröder, H; Schwartz, A J; Schwarz, A S; Schwenninger, B; Schwingenheuer, B; Sciacca, F; Semprini-Cesari, N; Shuvalov, S; Silva, L; Smirnov, K; Sözüer, L; Solunin, S; Somov, A; Somov, S; Spengler, J; Spighi, R; Spiridonov, A; Stanovnik, A; Staric, M; Stegmann, C; Subramania, H S; Symalla, M; Tikhomirov, I; Titov, M; Tsakov, I; Uwer, U; van Eldik, C; Vassiliev, Yu; Villa, M; Vitale, A; Vukotic, I; Wahlberg, H; Walenta, A H; Walter, M; Wang, J J; Wegener, D; Werthenbach, U; Wolters, H; Wurth, R; Wurz, A; Zaitsev, Yu; Zavertyaev, M; Zech, G; Zeuner, T; Zhelezov, A; Zheng, Z; Zimmermann, R; Zivko, T; Zoccoli, A
2004-11-19
We have searched for Theta+(1540) and Xi(--)(1862) pentaquark candidates in proton-induced reactions on C, Ti, and W targets at midrapidity and square root of s = 41.6 GeV. In 2 x 10(8) inelastic events we find no evidence for narrow (sigma approximately 5 MeV) signals in the Theta+ --> pK0(S) and Xi(--) --> Xi- pi- channels; our 95% C.L. upper limits (UL) for the inclusive production cross section times branching fraction B dsigma/dy/(y approximately 0) are (4-16) mub/N for a Theta+ mass between 1521 and 1555 MeV, and 2.5 mub/N for the Xi(--). The UL of the yield ratio of Theta+/Lambda(1520) < (3-12)% is significantly lower than model predictions. Our UL of B Xi(--)/Xi(1530)0 < 4% is at variance with the results that have provided the first evidence for the Xi(--).
Noncrossing theorem for the ground ensembles of systems with noninteger particle numbers
NASA Astrophysics Data System (ADS)
Sagvolden, Espen
2006-08-01
That the external potential vext(r⃗) of a system of electrons is determined uniquely by the ground-state density is one of the central statements of the first Hohenberg-Kohn theorem. It is known that the validity of this statement extends to densities n(r⃗) with noninteger particle number [i.e., n(r⃗) integrates to a number that is not an integer] if the functional derivative of Ts[n(r⃗)]+U[n(r⃗)]+Exc[n(r⃗)] exists or (without relying on the existence of functional derivatives) if the ground-state energy is a strictly convex function of the particle number. In the present article, a proof that relies neither on the existence of the above functional derivative nor on the strict convexity of the ground-state energy is presented. The fact that the density determines the external potential leads to a noncrossing theorem for ground-state densities. The noncrossing theorem produces knowledge as to what the integer-particle-number ground-state densities of a system cannot be. The noncrossing theorem produces inequalities that the functional derivatives of the exchange-correlation energy functional Exc[n(r⃗)] and the noninteracting kinetic energy functional Ts[n(r⃗)] must fulfill.
Towards a no-lose theorem for naturalness
NASA Astrophysics Data System (ADS)
Curtin, David; Saraswat, Prashant
2016-03-01
We derive a phenomenological no-lose theorem for naturalness up to the TeV scale, which applies when quantum corrections to the Higgs mass from top quarks are canceled by perturbative beyond Standard Model (BSM) particles (top partners) of similar multiplicity due to to some symmetry. Null results from LHC searches already seem to disfavor such partners if they are colored. Any partners with SM charges and ˜TeV masses will be exhaustively probed by the LHC and a future 100 TeV collider. Therefore, we focus on neutral top partners. While these arise in twin Higgs theories, we analyze neutral top partners as model-independently as possible using effective field theory and simplified model methods. We classify all perturbative neutral top partner structures in order to compute their irreducible low-energy signatures at proposed future lepton and hadron colliders, as well as the irreducible tunings suffered in each scenario. Central to our theorem is the assumption that SM-charged BSM states appear in the UV completion of neutral naturalness, which is the case in all known examples. Direct production at the 100 TeV collider then allows this scale to be probed at the ˜10 TeV level. We find that proposed future colliders probe any such scenario of naturalness with tuning of 10% or better. This provides very strong model-independent motivation for both new lepton and hadron colliders, which in tandem act as discovery machines for general naturalness. We put our results in context by discussing other possibilities for naturalness, including "swarms" of top partners, inherently nonperturbative or exotic physics, or theories without SM-charged states in the UV completion. Realizing a concrete scenario which avoids our arguments while still lacking experimental signatures remains an open model-building challenge.
3D Image Reconstructions and the Nyquist-Shannon Theorem
NASA Astrophysics Data System (ADS)
Ficker, T.; Martišek, D.
2015-09-01
Fracture surfaces are occasionally modelled by Fourier's two-dimensional series that can be converted into digital 3D reliefs mapping the morphology of solid surfaces. Such digital replicas may suffer from various artefacts when processed inconveniently. Spatial aliasing is one of those artefacts that may devalue Fourier's replicas. According to the Nyquist-Shannon sampling theorem the spatial aliasing occurs when Fourier's frequencies exceed the Nyquist critical frequency. In the present paper it is shown that the Nyquist frequency is not the only critical limit determining aliasing artefacts but there are some other frequencies that intensify aliasing phenomena and form an infinite set of points at which numerical results abruptly and dramatically change their values. This unusual type of spatial aliasing is explored and some consequences for 3D computer reconstructions are presented.
A Converse of the Mean Value Theorem Made Easy
ERIC Educational Resources Information Center
Mortici, Cristinel
2011-01-01
The aim of this article is to discuss some results about the converse mean value theorem stated by Tong and Braza [J. Tong and P. Braza, "A converse of the mean value theorem", Amer. Math. Monthly 104(10), (1997), pp. 939-942] and Almeida [R. Almeida, "An elementary proof of a converse mean-value theorem", Internat. J. Math. Ed. Sci. Tech. 39(8)…
The van Cittert-Zernike theorem for electromagnetic fields.
Ostrovsky, Andrey S; Martínez-Niconoff, Gabriel; Martínez-Vara, Patricia; Olvera-Santamaría, Miguel A
2009-02-02
The van Cittert-Zernike theorem, well known for the scalar optical fields, is generalized for the case of vector electromagnetic fields. The deduced theorem shows that the degree of coherence of the electromagnetic field produced by the completely incoherent vector source increases on propagation whereas the degree of polarization remains unchanged. The possible application of the deduced theorem is illustrated by an example of optical simulation of partially coherent and partially polarized secondary source with the controlled statistical properties.
Borsuk-Ulam theorem in infinite-dimensional Banach spaces
NASA Astrophysics Data System (ADS)
Gel'man, B. D.
2002-02-01
The well-known classical Borsuk-Ulam theorem has a broad range of applications to various problems. Its generalization to infinite-dimensional spaces runs across substantial difficulties because its statement is essentially finite-dimensional. A result established in the paper is a natural generalization of the Borsuk-Ulam theorem to infinite-dimensional Banach spaces. Applications of this theorem to various problems are discussed.
Extending Bell's Theorem: Ruling out Paramater Independent Hidden Variable Theories
NASA Astrophysics Data System (ADS)
Leegwater, G. J.
2016-03-01
Bell's Theorem may well be the best known result in the foundations of quantum mechanics. Here, it is presented as stating that for any hidden variable theory the combination of the conditions Parameter Independence, Outcome Independence, Source Independence and Compatibility with Quantum Theory leads to a contradiction. Based on work by Roger Colbeck and Renato Renner, an extension of Bell's Theorem is considered. In this extension the theorem is strengthened by replacing Outcome Independence by a strictly weaker condition.
A Converse of the Mean Value Theorem Made Easy
ERIC Educational Resources Information Center
Mortici, Cristinel
2011-01-01
The aim of this article is to discuss some results about the converse mean value theorem stated by Tong and Braza [J. Tong and P. Braza, "A converse of the mean value theorem", Amer. Math. Monthly 104(10), (1997), pp. 939-942] and Almeida [R. Almeida, "An elementary proof of a converse mean-value theorem", Internat. J. Math. Ed. Sci. Tech. 39(8)…
Geometric fluctuation theorem for a spin-boson system
NASA Astrophysics Data System (ADS)
Watanabe, Kota L.; Hayakawa, Hisao
2017-08-01
We derive an extended fluctuation theorem for geometric pumping of a spin-boson system under periodic control of environmental temperatures by using a Markovian quantum master equation. We obtain the current distribution, the average current, and the fluctuation in terms of the Monte Carlo simulation. To explain the results of our simulation we derive an extended fluctuation theorem. This fluctuation theorem leads to the fluctuation dissipation relations but the absence of the conventional reciprocal relation.
A qualitative approach to Bayes' theorem.
Medow, Mitchell A; Lucey, Catherine R
2011-12-01
While decisions made according to Bayes' theorem are the academic normative standard, the theorem is rarely used explicitly in clinical practice. Yet the principles can be followed without intimidating mathematics. To do so, one can first categorise the prior-probability of the disease being tested for as very unlikely (less likely than 10%), unlikely (10-33%), uncertain (34-66%), likely (67-90%) or very likely (more likely than 90%). Usually, for disorders that are very unlikely or very likely, no further testing is needed. If the prior probability is unlikely, uncertain or likely, a test and a Bayesian-inspired update process incorporating the result can help. A positive result of a good test increases the probability of the disorder by one likelihood category (eg, from uncertain to likely) and a negative test decreases the probability by one category. If testing is needed to escape the extremes of likelihood (eg, a very unlikely but particularly dangerous condition or in the circumstance of population screening, or a very likely condition with a particularly noxious treatment), two tests may be needed to achieve. Negative results of tests with sensitivity ≥99% are sufficient to rule-out a diagnosis; positive results of tests with specificity ≥99% are sufficient to rule-in a diagnosis. This method overcomes some common heuristic errors: ignoring the base rate, probability adjustment errors and order effects. The simplicity of the method, while still adhering to the basic principles of Bayes' theorem, has the potential to increase its application in clinical practice.
Stochastic thermodynamics, fluctuation theorems and molecular machines
NASA Astrophysics Data System (ADS)
Seifert, Udo
2012-12-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Stochastic thermodynamics, fluctuation theorems and molecular machines.
Seifert, Udo
2012-12-01
Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation-dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production.
Penrose's singularity theorem in a Finsler spacetime
NASA Astrophysics Data System (ADS)
Babak Aazami, Amir; Javaloyes, Miguel Angel
2016-01-01
We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to the differences that arise in the Finslerian setting. This activity is supported by the programme 'Young leaders in research' 18942/JLI/13 by Fundación Séneca, Regional Agency for Science and Technology from the Region of Murcia, and by the World Premier International Research Center Initiative (WPI), MEXT, Japan.
Generating Test Templates via Automated Theorem Proving
NASA Technical Reports Server (NTRS)
Kancherla, Mani Prasad
1997-01-01
Testing can be used during the software development process to maintain fidelity between evolving specifications, program designs, and code implementations. We use a form of specification-based testing that employs the use of an automated theorem prover to generate test templates. A similar approach was developed using a model checker on state-intensive systems. This method applies to systems with functional rather than state-based behaviors. This approach allows for the use of incomplete specifications to aid in generation of tests for potential failure cases. We illustrate the technique on the cannonical triangle testing problem and discuss its use on analysis of a spacecraft scheduling system.
Generalizations of Brandl's theorem on Engel length
NASA Astrophysics Data System (ADS)
Quek, S. G.; Wong, K. B.; Wong, P. C.
2013-04-01
Let n < m be positive integers such that [g,nh] = [g,mh] and assume that n and m are chosen minimal with respect to this property. Let gi = [g,n+ih] where i = 1,2,…,m-n. Then π(g,h) = (g1,…,gm-n) is called the Engel cycle generated by g and h. The length of the Engel cycle is m-n. A group G is said to have Engel length r, if all the length of the Engel cycles in G divides r. In this paper we discuss the Brandl's theorem on Engel length and give some of its generalizations.
Reciprocity theorem for smith-purcell configurations
NASA Astrophysics Data System (ADS)
Scarlat, Florea; Facina, M.
2001-06-01
The reciprocity theorem is referred to the equivalence of the obtained relations for the Smith-Purcell radiation, in both cases when the electron beam is propagating forward and backward with respect to the metal grating, respectively. The results of the radiation factor for the Smith-Purcell radiation in the ((theta) , (phi) ) direction generated by relativistic electron beams with energy up to 100 MeV and rectangular perfectly conducting gratings are presented. The results obtained prove the equivalence of the Smith-Purcell radiation field in both cases of propagation for the electron beam.
Nekhoroshev theorem for the periodic Toda lattice.
Henrici, Andreas; Kappeler, Thomas
2009-09-01
The periodic Toda lattice with N sites is globally symplectomorphic to a two parameter family of N-1 coupled harmonic oscillators. The action variables fill out the whole positive quadrant of R(N-1). We prove that in the interior of the positive quadrant as well as in a neighborhood of the origin, the Toda Hamiltonian is strictly convex and therefore Nekhoroshev's theorem applies on (almost) all parts of phase space (2000 Mathematics Subject Classification: 37J35, 37J40, 70H06).
No-cloning theorem on quantum logics
Miyadera, Takayuki; Imai, Hideki
2009-10-15
This paper discusses the no-cloning theorem in a logicoalgebraic approach. In this approach, an orthoalgebra is considered as a general structure for propositions in a physical theory. We proved that an orthoalgebra admits cloning operation if and only if it is a Boolean algebra. That is, only classical theory admits the cloning of states. If unsharp propositions are to be included in the theory, then a notion of effect algebra is considered. We proved that an atomic Archimedean effect algebra admitting cloning operation is a Boolean algebra. This paper also presents a partial result, indicating a relation between the cloning on effect algebras and hidden variables.
Index Theorem for Topological Excitations on R^3 \\times S^1 and Chern-Simons Theory
Poppitz, Erich; Unsal, Mithat
2008-12-12
We derive an index theorem for the Dirac operator in the background of various topological excitations on an R{sup 3} x S{sup 1} geometry. The index theorem provides more refined data than the APS index for an instanton on R{sup 4} and reproduces it in decompactification limit. In the R{sup 3} limit, it reduces to the Callias index theorem. The index is expressed in terms of topological charge and the {eta}-invariant associated with the boundary Dirac operator. Neither topological charge nor {eta}-invariant is typically an integer, however, the non-integer parts cancel to give an integer-valued index. Our derivation is based on axial current non-conservation--an exact operator identity valid on any four-manifold--and on the existence of a center symmetric, or approximately center symmetric, boundary holonomy (Wilson line). We expect the index theorem to usefully apply to many physical systems of interest, such as low temperature (large S{sup 1}, confined) phases of gauge theories, center stabilized Yang-Mills theories with vector-like or chiral matter (at S{sup 1} of any size), and supersymmetric gauge theories with supersymmetry-preserving boundary conditions (also at any S{sup 1}). In QCD-like and chiral gauge theories, the index theorem should shed light into the nature of topological excitations responsible for chiral symmetry breaking and the generation of mass gap in the gauge sector. We also show that imposing chirally-twisted boundary condition in gauge theories with fermions induces a Chern-Simons term in the infrared. This suggests that some QCD-like gauge theories should possess components with a topological Chern-Simons phase in the small S{sup 1} regime.
Index theorem for topological excitations on R3 × S1 and Chern-Simons theory
NASA Astrophysics Data System (ADS)
Poppitz, Erich; Ünsal, Mithat
2009-03-01
We derive an index theorem for the Dirac operator in the background of various topological excitations on an R3 × S1 geometry. The index theorem provides more refined data than the APS index for an instanton on R4 and reproduces it in decompactification limit. In the R3 limit, it reduces to the Callias index theorem. The index is expressed in terms of topological charge and the η-invariant associated with the boundary Dirac operator. Neither topological charge nor η-invariant is typically an integer, however, the non-integer parts cancel to give an integer-valued index. Our derivation is based on axial current non-conservation — an exact operator identity valid on any four-manifold — and on the existence of a center symmetric, or approximately center symmetric, boundary holonomy (Wilson line). We expect the index theorem to usefully apply to many physical systems of interest, such as low temperature (large S1, confined) phases of gauge theories, center stabilized Yang-Mills theories with vector-like or chiral matter (at S1 of any size), and supersymmetric gauge theories with supersymmetry-preserving boundary conditions (also at any S1). In QCD-like and chiral gauge theories, the index theorem should shed light into the nature of topological excitations responsible for chiral symmetry breaking and the generation of mass gap in the gauge sector. We also show that imposing chirally-twisted boundary condition in gauge theories with fermions induces a Chern-Simons term in the infrared. This suggests that some QCD-like gauge theories should possess components with a topological Chern-Simons phase in the small S1 regime.
Brigham-Grette, J.; Gualtieri, L.M.; Glushkova, O.Y.; Hamilton, T.D.; Mostoller, D.; Kotov, A.
2003-01-01
The Pekulney Mountains and adjacent Tanyurer River valley are key regions for examining the nature of glaciation across much of northeast Russia. Twelve new cosmogenic isotope ages and 14 new radiocarbon ages in concert with morphometric analyses and terrace stratigraphy constrain the timing of glaciation in this region of central Chukotka. The Sartan Glaciation (Last Glacial Maximum) was limited in extent in the Pekulney Mountains and dates to ???20,000 yr ago. Cosmogenic isotope ages > 30,000 yr as well as non-finite radiocarbon ages imply an estimated age no younger than the Zyryan Glaciation (early Wisconsinan) for large sets of moraines found in the central Tanyurer Valley. Slope angles on these loess-mantled ridges are less than a few degrees and crest widths are an order of magnitude greater than those found on the younger Sartan moraines. The most extensive moraines in the lower Tanyurer Valley are most subdued implying an even older, probable middle Pleistocene age. This research provides direct field evidence against Grosswald's Beringian ice-sheet hypothesis. ?? 2003 Elsevier Science (USA). All rights reserved.
NASA Astrophysics Data System (ADS)
Boyce, H.; Lützgendorf, N.; van der Marel, R. P.; Baumgardt, H.; Kissler-Patig, M.; Neumayer, N.; de Zeeuw, P. T.
2017-09-01
We constrain the possible presence of a central black hole (BH) in the center of the Large Magellanic Cloud. This requires spectroscopic measurements over an area of the order of a square degree, due to the poorly known position of the kinematic center. Such measurements are now possible with the impressive field of view of the Multi Unit Spectroscopic Explorer (MUSE) on the ESO Very Large Telescope. We used the Calcium Triplet (∼850 nm) spectral lines in many short-exposure MUSE pointings to create a two-dimensional integrated-light line-of-sight velocity map from the ∼ {10}8 individual spectra, taking care to identify and remove Galactic foreground populations. The data reveal a clear velocity gradient at an unprecedented spatial resolution of 1 arcmin2. We fit kinematic models to arrive at a 3σ upper-mass limit of {10}7.1 {M}ȯ for any central BH—consistent with the known scaling relations for supermassive black holes and their host systems. This adds to the growing body of knowledge on the presence of BHs in low-mass and dwarf galaxies, and their scaling relations with host-galaxy properties, which can shed light on theories of BH growth and host system interaction.
The Poincaré-Hopf Theorem for line fields revisited
NASA Astrophysics Data System (ADS)
Crowley, Diarmuid; Grant, Mark
2017-07-01
A Poincaré-Hopf Theorem for line fields with point singularities on orientable surfaces can be found in Hopf's 1956 Lecture Notes on Differential Geometry. In 1955 Markus presented such a theorem in all dimensions, but Markus' statement only holds in even dimensions 2 k ≥ 4. In 1984 Jänich presented a Poincaré-Hopf theorem for line fields with more complicated singularities and focussed on the complexities arising in the generalized setting. In this expository note we review the Poincaré-Hopf Theorem for line fields with point singularities, presenting a careful proof which is valid in all dimensions.
Fluctuation theorem in dynamical systems with quenched disorder
NASA Astrophysics Data System (ADS)
Drocco, Jeffrey; Olson Reichhardt, Cynthia; Reichhardt, Charles
2010-03-01
We demonstrate that the fluctuation theorem of Gallavotti and Cohen can be used to characterize far from equilibrium dynamical nonthermal systems in the presence of quenched disorder where strong fluctuations or crackling noise occur. By observing the frequency of entropy-destroying trajectories, we show that the theorem holds in specific dynamical regimes near the threshold for motion, indicating that these systems might be ideal candidates for understanding what types of nonthermal fluctuations could be used in constructing generalized fluctuation theorems. We also discuss how the theorem could be tested with global or local probes in systems such as superconducting vortices, magnetic domain walls, stripe phases, Coulomb glasses and earthquake models.
Schaefers, J; Cools, M; De Waele, K; Gies, I; Beauloye, V; Lysy, P; Francois, I; Beckers, D; De Schepper, J
2017-08-01
Despite lymphocytic or autoimmune infundibuloneurohypophysitis (INH) is an increasingly recognized aetiology in children with central diabetes insipidus (CDI); clinical data on epidemiology (clinical evolution, predisposing factors, complications), diagnosis and management of this entity are limited and mostly based on published case reports. The aim of this study was to gain a broader insight in the natural history of this disease by analysing the clinical presentation, radiological pituitary stalk changes, associated autoimmunity and hormonal deficiencies in children with CDI and a self-limiting or transient stalk thickening (ST), diagnosed as autoimmune infundibuloneurohypophysitis, during the last 15 years in four Belgian university hospitals. The medical files of nine CDI patients with a ST at initial presentation and no signs of Langerhans cell histiocytosis or germinoma at presentation and/or during follow-up of more than 1.5 years were reviewed. Age at presentation ranged from 3 to 14 years. Two patients had a positive family history of autoimmunity. Three children presented with associated growth failure, two with nausea and one with long-standing headache. Median maximal diameter of the stalk was 4.6 mm (2.7-10 mm). Four patients had extra-pituitary brain anomalies, such as cysts. One patient had central hypothyroidism, and another had a partial growth hormone deficiency at diagnosis. Within a mean follow-up of 5.4 (1.5-15) years, stalk thickening remained unchanged in two patients, regressed in one and normalized in six children. CDI remained in all, while additional pituitary hormone deficiencies developed in only one patient. In this series of children INH with CDI as initial presentation, CDI was permanent and infrequently associated with anterior pituitary hormone deficiencies, despite a frequent association with nonstalk cerebral lesions. © 2017 The Authors. Clinical Endocrinology Published by John Wiley & Sons Ltd.
Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics
NASA Astrophysics Data System (ADS)
Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.
2008-11-01
In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.
Bell's theorem, inference, and quantum transactions
NASA Astrophysics Data System (ADS)
Garrett, A. J. M.
1990-04-01
Bell's theorem is expounded as an analysis in Bayesian inference. Assuming the result of a spin measurement on a particle is governed by a causal variable internal (hidden, “local”) to the particle, one learns about it by making a spin measurement; thence about the internal variable of a second particle correlated with the first; and from there predicts the probabilistic result of spin measurements on the second particle. Such predictions are violated by experiment: locality/causality fails. The statistical nature of the observations rules out signalling; acausal, superluminal, or otherwise. Quantum mechanics is irrelevant to this reasoning, although its correct predictions of experiment imply that it has a nonlocal/acausal interpretation. Cramer's new transactional interpretation, which incorporates this feature by adapting the Wheeler-Feynman idea of advanced and retarded processes to the quantum laws, is advocated. It leads to an invaluable way of envisaging quantum processes. The usual paradoxes melt before this, and one, the “delayed choice” experiment, is chosen for detailed inspection. Nonlocality implies practical difficulties in influencing hidden variables, which provides a very plausible explanation for why they have not yet been found; from this standpoint, Bell's theorem reinforces arguments in favor of hidden variables.
De Finetti Theorem on the CAR Algebra
NASA Astrophysics Data System (ADS)
Crismale, Vitonofrio; Fidaleo, Francesco
2012-10-01
The symmetric states on a quasi local C*-algebra on the infinite set of indices J are those invariant under the action of the group of the permutations moving only a finite, but arbitrary, number of elements of J. The celebrated De Finetti Theorem describes the structure of the symmetric states (i.e. exchangeable probability measures) in classical probability. In the present paper we extend the De Finetti Theorem to the case of the CAR algebra, that is for physical systems describing Fermions. Namely, after showing that a symmetric state is automatically even under the natural action of the parity automorphism, we prove that the compact convex set of such states is a Choquet simplex, whose extremal (i.e. ergodic w.r.t. the action of the group of permutations previously described) are precisely the product states in the sense of Araki-Moriya. In order to do that, we also prove some ergodic properties naturally enjoyed by the symmetric states which have a self-containing interest.
On the inversion of Fueter's theorem
NASA Astrophysics Data System (ADS)
Dong, Baohua; Kou, Kit Ian; Qian, Tao; Sabadini, Irene
2016-10-01
The well known Fueter theorem allows to construct quaternionic regular functions or monogenic functions with values in a Clifford algebra defined on open sets of Euclidean space R n + 1, starting from a holomorphic function in one complex variable or, more in general, from a slice hyperholomorphic function. Recently, the inversion of this theorem has been obtained for odd values of the dimension n. The present work extends the result to all dimensions n by using the Fourier multiplier method. More precisely, we show that for any axially monogenic function f defined in a suitable open set in R n + 1, where n is a positive integer, we can find a slice hyperholomorphic function f → such that f =Δ (n - 1) / 2 f →. Both the even and the odd dimensions are treated with the same, viz., the Fourier multiplier, method. For the odd dimensional cases the result obtained by the Fourier multiplier method coincides with the existing result obtained through the pointwise differential method.
Equipartition theorem and the dynamics of liquids
Levashov, Valentin A.; Egami, Takeshi; Aga, Rachel S; Morris, James R
2008-01-01
In liquids, phonons have a very short lifetime and the total potential energy does not depend linearly on temperature. Thus it may appear that atomic vibrations in liquids cannot be described by the harmonic-oscillator model and that the equipartition theorem for the potential energy is not upheld. In this paper we show that the description of the local atomic dynamics in terms of the atomic-level stresses provides such a description, satisfying the equipartition theorem. To prove this point we carried out molecular-dynamics simulations with several pairwise potentials, including the Lennard-Jones potential, the modified Johnson potential, and the repulsive part of the Johnson potential, at various particle number densities. In all cases studied the total self-energy of the atomic-level stresses followed the (3/2)kBT law. From these results we suggest that the concept of local atomic stresses can provide description of thermodynamic properties of glasses and liquids on the basis of harmonic atomistic excitations. An example of application of this approach to the description of the glass transition temperature in metallic glasses is discussed.
Miserev, D. S. E-mail: erazorheader@gmail.com
2016-06-15
The problem of localized states in 1D systems with a relativistic spectrum, namely, graphene stripes and carbon nanotubes, is studied analytically. The bound state as a superposition of two chiral states is completely described by their relative phase, which is the foundation of the variable phase method (VPM) developed herein. Based on our VPM, we formulate and prove the relativistic Levinson theorem. The problem of bound states can be reduced to the analysis of closed trajectories of some vector field. Remarkably, the Levinson theorem appears as the Poincaré index theorem for these closed trajectories. The VPM equation is also reduced to the nonrelativistic and semiclassical limits. The limit of a small momentum p{sub y} of transverse quantization is applicable to an arbitrary integrable potential. In this case, a single confined mode is predicted.
Yin, Hai-wei; Kong, Fan-hua; Luo, Zhen-dong; Yan, Wei-jiao; Sun, Chang-feng; Xu, Feng
2013-08-01
The suitability assessment of regional construction land is one of the important prerequisites for the spatial arrangement in regional planning, and also, the important foundation for the reasonable utilization of regional land resources. With the support of GIS, and by using the regional comprehensive strength and spatial accessibility analysis and the eco-environmental sensitivity analysis, this paper quantitatively analyzed the development potential and its ecological limitation of the central and southern parts of Hebei Province. Besides, based on the cost-benefit analysis, the potential-limitation model was accordingly developed, and the three land suitability scenarios under different developmental concepts were captured through the interaction matrix. The results indicated that both the comprehensive strength and the development potential of the study area showed a primacy distribution pattern, and presented an obvious pole-axis spatial pattern. The areas with higher eco-environmental sensitivity were mainly distributed in the west regions, while those with lower eco-environmental sensitivity were in the east regions. Regional economic development concept had important effects on the regional ecological security pattern and urban growth. The newly developed principles and methods for the land suitability assessment in this paper could not only scientifically realize the spatial grid of regional development potential and capture the future land development trend and spatial distribution, but also provide scientific basis and effective ways for urban and regional planning to realize region 'smart growth' and 'smart conservation'.
Cueto-Rojas, H F; Maleki Seifar, R; Ten Pierick, A; van Helmond, W; Pieterse M, M; Heijnen, J J; Wahl, S A
2016-09-16
Ammonium is the most common N-source for yeast fermentations. Although, its transport and assimilation mechanisms are well documented, there have been only few attempts to measure the in vivo intracellular concentration of ammonium and assess its impact on gene expression. Using an isotope dilution mass spectrometry (IDMS)-based method we were able to measure the intracellular ammonium concentration in N-limited aerobic chemostat cultivations using three different N-sources (ammonium, urea and glutamate) at the same growth rate (0.05 h(-1)). The experimental results suggest that, at this growth rate, a similar concentration of intracellular ammonium, about 3.6 mmol NH4(+)/LIC, is required to supply the reactions in the central N-metabolism independent of the N-source. Based on the experimental results and different assumptions, the vacuolar and cytosolic ammonium concentrations were estimated. Furthermore, we identified a futile cycle caused by NH3 leakage to the extracellular space, which can cost up to 30% of the ATP production of the cell under N-limited conditions, and a futile redox cycle between reactions Gdh1 and Gdh2. Finally, using shotgun proteomics with labeled reference-relative protein expression, differences between the various environmental conditions were identified and correlated with previously identified N-compound sensing mechanisms.
Estimating Filtering Errors Using the Peano Kernel Theorem
Jerome Blair
2009-02-20
The Peano Kernel Theorem is introduced and a frequency domain derivation is given. It is demonstrated that the application of this theorem yields simple and accurate formulas for estimating the error introduced into a signal by filtering it to reduce noise.
Leaning on Socrates to Derive the Pythagorean Theorem
ERIC Educational Resources Information Center
Percy, Andrew; Carr, Alistair
2010-01-01
The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the…
Solving boundary-value electrostatics problems using Green's reciprocity theorem
NASA Astrophysics Data System (ADS)
Hu, Ben Yu-Kuang
2001-12-01
Formal solutions to electrostatics boundary-value problems are derived using Green's reciprocity theorem. This method provides a more transparent interpretation of the solutions than the standard Green's function derivation. An energy-based argument for the reciprocity theorem is also presented.
Unique Factorization and the Fundamental Theorem of Arithmetic
ERIC Educational Resources Information Center
Sprows, David
2017-01-01
The fundamental theorem of arithmetic is one of those topics in mathematics that somehow "falls through the cracks" in a student's education. When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like "every natural number can be broken down into a…
When 95% Accurate Isn't: Exploring Bayes's Theorem
ERIC Educational Resources Information Center
CadwalladerOlsker, Todd D.
2011-01-01
Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…
Systematic Approaches to Experimentation: The Case of Pick's Theorem
ERIC Educational Resources Information Center
Papadopoulos, Ioannis; Iatridou, Maria
2010-01-01
In this paper two 10th graders having an accumulated experience on problem-solving ancillary to the concept of area confronted the task to find Pick's formula for a lattice polygon's area. The formula was omitted from the theorem in order for the students to read the theorem as a problem to be solved. Their working is examined and emphasis is…
On Euler's Theorem for Homogeneous Functions and Proofs Thereof.
ERIC Educational Resources Information Center
Tykodi, R. J.
1982-01-01
Euler's theorem for homogenous functions is useful when developing thermodynamic distinction between extensive and intensive variables of state and when deriving the Gibbs-Duhem relation. Discusses Euler's theorem and thermodynamic applications. Includes six-step instructional strategy for introducing the material to students. (Author/JN)
Group Theoretical Interpretation of von Neumann's Theorem on Composite Systems.
ERIC Educational Resources Information Center
Bergia, S.; And Others
1979-01-01
Shows that von Neumann's mathematical theorem on composite systems acquires a transparent physical meaning with reference to a suitable physical example; a composite system in a state of definite angular momentum. Gives an outline of the theorem, and the results are restated in Dirac's notation, thus generalizing von Neumann's results which were…
Generalizations of Karp's theorem to elastic scattering theory
NASA Astrophysics Data System (ADS)
Tuong, Ha-Duong
Karp's theorem states that if the far field pattern corresponding to the scattering of a time-harmonic acoustic plane wave by a sound-soft obstacle in R2 is invariant under the group of rotations, then the scatterer is a circle. The theorem is generalized to the elastic scattering problems and the axisymmetric scatterers in R3.
Three Lectures on Theorem-proving and Program Verification
NASA Technical Reports Server (NTRS)
Moore, J. S.
1983-01-01
Topics concerning theorem proving and program verification are discussed with particlar emphasis on the Boyer/Moore theorem prover, and approaches to program verification such as the functional and interpreter methods and the inductive assertion approach. A history of the discipline and specific program examples are included.
Discovering Theorems in Abstract Algebra Using the Software "GAP"
ERIC Educational Resources Information Center
Blyth, Russell D.; Rainbolt, Julianne G.
2010-01-01
A traditional abstract algebra course typically consists of the professor stating and then proving a sequence of theorems. As an alternative to this classical structure, the students could be expected to discover some of the theorems even before they are motivated by classroom examples. This can be done by using a software system to explore a…
Group Theoretical Interpretation of von Neumann's Theorem on Composite Systems.
ERIC Educational Resources Information Center
Bergia, S.; And Others
1979-01-01
Shows that von Neumann's mathematical theorem on composite systems acquires a transparent physical meaning with reference to a suitable physical example; a composite system in a state of definite angular momentum. Gives an outline of the theorem, and the results are restated in Dirac's notation, thus generalizing von Neumann's results which were…
When 95% Accurate Isn't: Exploring Bayes's Theorem
ERIC Educational Resources Information Center
CadwalladerOlsker, Todd D.
2011-01-01
Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…
A new generalized Wick theorem in conformal field theory
NASA Astrophysics Data System (ADS)
Takagi, T.
2017-08-01
We describe a new generalized Wick theorem for interacting fields in two-dimensional conformal field theory and briefly discuss its relation to the Borcherds identity and its derivation by an analytic method. We give examples of calculating operator product expansions using the generalized Wick theorem including fermionic fields.
Interactive Theorem Finding through Continuous Variation of Geometric Configurations.
ERIC Educational Resources Information Center
Schumann, Heinz
1991-01-01
Described and evaluated are microcomputers as a tool for construction in geometry education and heuristic theorem finding through interactive continuous variation of geometric configurations. Numerous examples of theorem finding processes are provided using the prototype graphics system CABRI-Geometer. (MDH)
Unique Factorization and the Fundamental Theorem of Arithmetic
ERIC Educational Resources Information Center
Sprows, David
2017-01-01
The fundamental theorem of arithmetic is one of those topics in mathematics that somehow "falls through the cracks" in a student's education. When asked to state this theorem, those few students who are willing to give it a try (most have no idea of its content) will say something like "every natural number can be broken down into a…
On the Weighted Mean Value Theorem for Integrals
ERIC Educational Resources Information Center
Polezzi, M.
2006-01-01
The Mean Value Theorem for Integrals is a powerful tool, which can be used to prove the Fundamental Theorem of Calculus, and to obtain the average value of a function on an interval. On the other hand, its weighted version is very useful for evaluating inequalities for definite integrals. This article shows the solutions on applying the weighted…
Fürst, Thomas; Ouattara, Mamadou; Silué, Kigbafori D; N'Goran, Dje N; Adiossan, Lukas G; Bogoch, Isaac I; N'Guessan, Yao; Koné, Siaka; Utzinger, Jürg; N'Goran, Eliézer K
2014-01-01
Schistosomiasis and soil-transmitted helminthiasis are two high-burden neglected tropical diseases. In highly endemic areas, control efforts emphasize preventive chemotherapy. However, as morbidity, infection, and transmission begin to decrease, more targeted treatment is likely to become more cost-effective, provided that comparatively cheap diagnostic methods with reasonable accuracy are available. Adults were administered an anamnestic questionnaire in mid-2010 during a cross-sectional epidemiological survey in the Taabo health demographic surveillance system in south-central Côte d'Ivoire. Questions pertaining to risk factors and signs and symptoms for schistosomiasis and soil-transmitted helminthiasis were included. The individuals' helminth infection status and their belonging to three different anthelmintic treatment groups were compared with the questionnaire results (i) to inform the local health authorities about the epidemiological and clinical footprint of locally prevailing helminthiases, and (ii) to explore the scope and limits of an anamnestic questionnaire as monitoring tool, which eventually could help guiding the control of neglected tropical diseases in control-induced low-endemicity settings. Our study sample consisted of 195 adults (101 males, 94 females). We found prevalences of hookworm, Trichuris trichiura, Schistosoma haematobium, and Schistosoma mansoni of 39.0%, 2.7%, 2.1%, and 2.1%, respectively. No Ascaris lumbricoides infection was found. Helminth infection intensities were generally very low. Seven, 74 and 79 participants belonged to three different treatment groups. Multivariable logistic regression models revealed statistically significant (p<0.05) associations between some risk factors, signs, and symptoms, and the different helminth infections and treatment groups. However, the risk factors, signs, and symptoms showed weak diagnostic properties. The generally low prevalence and intensity of helminth infection in this part of
Flores, Noemí; Olvera, Maricela; Sigala, Juan Carlos; Gosset, Guillermo; Morett, Enrique; Bolívar, Francisco
2009-01-01
The phosphoenolpyruvate: carbohydrate transferase system (PTS) transports glucose in Escherichia coli. Previous work demonstrated that strains lacking PTS, such as PB11, grow slow on glucose. PB11 has a reduced expression of glycolytic, and upregulates poxB and acs genes as compared to the parental strain JM101, when growing on glucose. The products of the latter genes are involved in the production of AcetylCoA. Inactivation of rpoS that codes for the RNA polymerase σ38 subunit, reduces further (50%) growth of PB11, indicating that σ38 plays a central role in the expression of central metabolism genes in slowly growing cells. In fact, transcription levels of glycolytic genes is reduced in strain PB11rpoS− as compared to PB11. In this report we studied the role of σ70 and σ38 in the expression of the complete glycolytic pathway and poxB and acs genes in certain PTS− strains and their rpoS− derivatives. We determined the transcription start sites (TSSs) and the corresponding promoters, in strains JM101, PB11, its derivative PB12 that recovered its growth capacity, and in their rpoS− derivatives, by 5′RACE and pyrosequencing. In all these genes the presence of sequences resembling σ38 recognition sites allowed the proposition that they could be transcribed by both sigma factors, from overlapping putative promoters that initiate transcription at the same site. Fourteen new TSSs were identified in seventeen genes. Besides, more than 30 putative promoters were proposed and we confirmed ten previously reported. In vitro transcription experiments support the functionality of putative dual promoters. Alternatives that could also explain lower transcription levels of the rpoS− derivatives are discussed. We propose that the presence if real, of both σ70 and σ38 dependent promoters in all glycolytic genes and operons could allow a differential transcription of these central metabolism genes by both sigma subunits as an adaptation response to carbon
The virial theorem for the polarizable continuum model
Cammi, R.
2014-02-28
The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.
NASA Astrophysics Data System (ADS)
Kamann, S.; Wisotzki, L.; Roth, M. M.; Gerssen, J.; Husser, T.-O.; Sandin, C.; Weilbacher, P.
2014-06-01
We used the PMAS integral field spectrograph to obtain large sets of radial velocities in the central regions of three northern Galactic globular clusters: M3, M13, and M92. By applying the novel technique of crowded field 3D spectroscopy, we measured radial velocities for about 80 stars within the central ~10″ of each cluster. These are by far the largest spectroscopic datasets obtained in the innermost parts of these clusters up to now. To obtain kinematical data across the whole extent of the clusters, we complement our data with measurements available in the literature. We combine our velocity measurements with surface brightness profiles to analyse the internal dynamics of each cluster using spherical Jeans models, and investigate whether our data provide evidence for an intermediate-mass black hole in any of the clusters. The surface brightness profiles reveal that all three clusters are consistent with a core profile, although shallow cusps cannot be excluded. We find that spherical Jeans models with a constant mass-to-light ratio provide a good overall representation of the kinematical data. A massive black hole is required in none of the three clusters to explain the observed kinematics. Our 1σ (3σ) upper limits are 5300 M⊙ (12 000 M⊙) for M3, 8600 M⊙ (13 000 M⊙) for M13, and 980 M⊙ (2700 M⊙) for M92. A puzzling circumstance is the existence of several potential high velocity stars in M3 and M13, as their presence can account for the majority of the discrepancies that we find in our mass limits compared to M92. Based on observations collected at the Centro Astronómico Hispano-Alemán (CAHA) at Calar Alto, operated jointly by the Max-Planck Institut für Astronomie and the Instituto de Astrofísica de Andalucía (CSIC).Appendices are available in electronic form at http://www.aanda.orgTables D.1 to D.6 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc
Theorem Proving in Intel Hardware Design
NASA Technical Reports Server (NTRS)
O'Leary, John
2009-01-01
For the past decade, a framework combining model checking (symbolic trajectory evaluation) and higher-order logic theorem proving has been in production use at Intel. Our tools and methodology have been used to formally verify execution cluster functionality (including floating-point operations) for a number of Intel products, including the Pentium(Registered TradeMark)4 and Core(TradeMark)i7 processors. Hardware verification in 2009 is much more challenging than it was in 1999 - today s CPU chip designs contain many processor cores and significant firmware content. This talk will attempt to distill the lessons learned over the past ten years, discuss how they apply to today s problems, outline some future directions.
The Birkhoff theorem and string clouds
NASA Astrophysics Data System (ADS)
Bronnikov, K. A.; Kim, S.-W.; Skvortsova, M. V.
2016-10-01
We consider spherically symmetric space-times in GR under the unconventional assumptions that the spherical radius r is either a constant or has a null gradient in the (t, x) subspace orthogonal to the symmetry spheres (i.e., {(\\partial r)}2 = 0). It is shown that solutions to the Einstein equations with r={const} contain an extra (fourth) spatial or temporal Killing vector and thus satisfy the Birkhoff theorem under an additional physically motivated condition that the tangential pressure is functionally related to the energy density. This leads to solutions that directly generalize the Bertotti-Robinson, Nariai and Plebanski-Hacyan solutions. Under similar conditions, solutions with {(\\partial r)}2 = 0 but r\
Walking Through the Impulse-Momentum Theorem
NASA Astrophysics Data System (ADS)
Haugland, Ole Anton
2013-02-01
Modern force platforms are handy tools for investigating forces during human motion. Earlier they were very expensive and were mostly used in research laboratories. But now even platforms that can measure in two directions are quite affordable. In this work we used the PASCO 2-Axis Force Platform. The analysis of the data can serve as a nice illustration of qualitative or quantitative use of the impulse-momentum theorem p - p0 = ∫t0t Fdt = I. The most common use of force platforms is to study the force from the base during the push-off period of a vertical jump. I think this is an activity of great value, and I would recommend it. The use of force platforms in teaching is well documented in research literature.1-4
A Stochastic Tikhonov Theorem in Infinite Dimensions
Buckdahn, Rainer Guatteri, Giuseppina
2006-03-15
The present paper studies the problem of singular perturbation in the infinite-dimensional framework and gives a Hilbert-space-valued stochastic version of the Tikhonov theorem. We consider a nonlinear system of Hilbert-space-valued equations for a 'slow' and a 'fast' variable; the system is strongly coupled and driven by linear unbounded operators generating a C{sub 0}-semigroup and independent cylindrical Brownian motions. Under well-established assumptions to guarantee the existence and uniqueness of mild solutions, we deduce the required stability of the system from a dissipativity condition on the drift of the fast variable. We avoid differentiability assumptions on the coefficients which would be unnatural in the infinite-dimensional framework.
Extended Ehrenfest theorem with radiative corrections
NASA Astrophysics Data System (ADS)
de la Peña, L.; Cetto, A. M.; Valdés-Hernández, A.
2015-10-01
A set of basic evolution equations for the mean values of dynamical variables is obtained from the Fokker-Planck equation applied to the general problem of a particle subject to a random force. The specific case of stochastic electrodynamics is then considered, in which the random force is due to the zero-point radiation field. Elsewhere it has been shown that when this system reaches a state of energy balance, it becomes controlled by an equation identical to Schrödinger’s, if the radiationless approximation is made. The Fokker-Planck equation was shown to lead to the Ehrenfest theorem under such an approximation. Here we show that when the radiative terms are not neglected, an extended form of the Ehrenfest equation is obtained, from which follow, among others, the correct formulas for the atomic lifetimes and the (nonrelativistic) Lamb shift.
Elementary theorems regarding blue isocurvature perturbations
NASA Astrophysics Data System (ADS)
Chung, Daniel J. H.; Yoo, Hojin
2015-04-01
Blue CDM-photon isocurvature perturbations are attractive in terms of observability and may be typical from the perspective of generic mass relations in supergravity. We present and apply three theorems useful for blue isocurvature perturbations arising from linear spectator scalar fields. In the process, we give a more precise formula for the blue spectrum associated with the axion model of Kasuya and Kawasaki [Axion Isocurvature Fluctuations with Extremely Blue Spectrum, Phys. Rev. D 80, 023516 (2009).], which can in a parametric corner give a factor of O (10 ) correction. We explain how a conserved current associated with Peccei-Quinn symmetry plays a crucial role and explicitly plot several example spectra including the breaks in the spectra. We also resolve a little puzzle arising from a naive multiplication of isocurvature expression that sheds light on the gravitational imprint of the adiabatic perturbations on the fields responsible for blue isocurvature fluctuations.
On the decoupling theorem for vacuum metastability
NASA Astrophysics Data System (ADS)
Patel, Hiren H.; Radovčić, Branimir
2017-10-01
In this paper, we numerically study the impact heavy field degrees of freedom have on vacuum metastability in a toy model, with the aim of better understanding how the decoupling theorem extends to semiclassical processes. We observe that decoupling applies to partial amplitudes associated with fixed final state field configurations emerging from the tunneling processes, characterized by a scale such as the inverse radius of a spherically symmetric bubble, and not directly on the total lifetime (as determined by the ;bounce;). More specifically, tunneling amplitudes for bubbles with inverse radii smaller than the scale of the heavier fields are largely insensitive to their presence, while those for bubbles with inverse radii larger than that scale may be significantly modified.
Differential diagnosis in immunohistochemistry with Bayes theorem.
Vollmer, Robin T
2009-05-01
When immunohistochemical stains that are specific for specific tumor diagnoses do not yield diagnostic results, we often turn to less specific immunohistochemical stains and consider the resulting lists of possible tumor types. Typically, such lists are ordered according to tumor sensitivities for the stains. In probability terminology, sensitivity is the conditional probability of a positive stain given a specific tumor. Yet, the most useful probability to know is the probability of a specific tumor diagnosis, given a set of staining results. Bayes theorem provides this probability. To illustrate its use for differential diagnosis, I apply it here to the situation of carcinomas of uncertain primary site and use the information provided by stains for cytokeratin 7 and cytokeratin 20.
Splitting theorem for Z2n -supermanifolds
NASA Astrophysics Data System (ADS)
Covolo, Tiffany; Grabowski, Janusz; Poncin, Norbert
2016-12-01
Smooth Z2n -supermanifolds have been introduced and studied recently. The corresponding sign rule is given by the 'scalar product' of the involved Z2n -degrees. It exhibits interesting changes in comparison with the sign rule using the parity of the total degree. With the new rule, nonzero degree even coordinates are not nilpotent, and even (resp., odd) coordinates do not necessarily commute (resp., anticommute) pairwise. The classical Batchelor-Gawȩdzki theorem says that any smooth supermanifold is diffeomorphic to the 'superization' ΠE of a vector bundle E. It is also known that this result fails in the complex analytic category. Hence, it is natural to ask whether an analogous statement goes through in the category of Z2n -supermanifolds with its local model made of formal power series. We give a positive answer to this question.
A Fubini Theorem for Iterated Stochastic Integrals.
1978-02-01
part icular , for 0 < t1 < t 2 , ( 2 . 2 ) f(t 1 .t2) E f(t1 ,t 2) + J ~ (t 1 ,t ,t2)d~~(T) where ~Gt 1 , i ,t ) is 3(t 1 ,T)—measurable , a.e. I...formally exists and is given by f0(t1,t2 )dt 1 — f(t 1 ,t2 )dB (t1) So that f~ is simply the negative of the diffusion part of it. We now make the following...and the functions {~ p :n = 1,2,...) are as in Theorem 2.A. And g is defined analogously.a,n b In part icular , t t II (t 1,t2) 2 = F
Robbing the Bank with a Theorem Prover
NASA Astrophysics Data System (ADS)
Youn, Paul; Adida, Ben; Bond, Mike; Clulow, Jolyon; Herzog, Jonathan; Lin, Amerson; Rivest, Ronald L.; Anderson, Ross
In this work, we present the first automated analysis of security application programming interfaces (security APIs). In particular, we analyze the API of the IBM 4758 CCA, a hardware security module for banking networks. Adapting techniques from formal analyses of security protocols, we model the API purely according its specification and assuming ideal encryption primitives. We then use the automated theorem-prover Otter to analyze this model, combining its standard reasoning strategies with novel techniques of our own (also presented here). In this way, we derive not only all published API-level attacks against the 4758 CCA, but an extension to these attacks as well. Thus, this work represents the first step toward fully-automated, rigorous analyses of security APIs.
Quantum violation of fluctuation-dissipation theorem
NASA Astrophysics Data System (ADS)
Shimizu, Akira; Fujikura, Kyota
2017-02-01
We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems, even if measurements are made in an ideal way that emulates classical ideal measurements as closely as possible. This is a genuine quantum effect that survives on a macroscopic scale. We also show that the state realized during measurements of temporal equilibrium fluctuations is a ‘squeezed equilibrium state’, which is macroscopically identical to the pre-measurement equilibrium state but is squeezed by the measurement. It is a time-evolving state, in which macrovariables fluctuate and relax. We also explain some of subtle but important points, careless treatments of which often lead to unphysical results, of the linear response theory.
NASA Astrophysics Data System (ADS)
Gong, Zongping; Quan, H. T.
2015-07-01
By taking full advantage of the dynamic property imposed by the detailed balance condition, we derive a new refined unified fluctuation theorem (FT) for general stochastic thermodynamic systems. This FT involves the joint probability distribution functions of the final phase-space point and a thermodynamic variable. Jarzynski equality, Crooks fluctuation theorem, and the FTs of heat as well as the trajectory entropy production can be regarded as special cases of this refined unified FT, and all of them are generalized to arbitrary initial distributions. We also find that the refined unified FT can easily reproduce the FTs for processes with the feedback control, due to its unconventional structure that separates the thermodynamic variable from the choices of initial distributions. Our result is heuristic for further understanding of the relations and distinctions between all kinds of FTs and might be valuable for studying thermodynamic processes with information exchange.
On the Lehmann-Filhés theorem as a consequence of one theorem of Ostrogradsky.
NASA Astrophysics Data System (ADS)
Shirmin, G. I.
It is shown that the so-called Lehmann-Filh´es theorem playing the role of a groundwork in the "method of incomplete integral" of dynamical problems solving is a simple consequence of one theorem of Russian academician M. V. Ostrogradsky. The appropriate proof of that is contained in his famous paper "The Memoir on Differential Equations of the isoperimetric Problem" having been reported to the Russian Academy of Sciences on the 29-th of November 1848. So it is prooved that on the basis of the above mentioned method the priority belongs to M. V. Ostrogradsky who published his results more than half a century earlier than the same was made by Lehmann-Filhés (1904).
Merits and qualms of work fluctuations in classical fluctuation theorems
NASA Astrophysics Data System (ADS)
Deng, Jiawen; Tan, Alvis Mazon; Hänggi, Peter; Gong, Jiangbin
2017-01-01
Work is one of the most basic notions in statistical mechanics, with work fluctuation theorems being one central topic in nanoscale thermodynamics. With Hamiltonian chaos commonly thought to provide a foundation for classical statistical mechanics, here we present general salient results regarding how (classical) Hamiltonian chaos generically impacts on nonequilibrium work fluctuations. For isolated chaotic systems prepared with a microcanonical distribution, work fluctuations are minimized and vanish altogether in adiabatic work protocols. For isolated chaotic systems prepared at an initial canonical distribution at inverse temperature β , work fluctuations depicted by the variance of e-β W are also minimized by adiabatic work protocols. This general result indicates that, if the variance of e-β W diverges for an adiabatic work protocol, it diverges for all nonadiabatic work protocols sharing the same initial and final Hamiltonians. Such divergence is hence not an isolated event and thus greatly impacts on the efficiency of using Jarzynski's equality to simulate free-energy differences. Theoretical results are illustrated in a Sinai model. Our general insights shall boost studies in nanoscale thermodynamics and are of fundamental importance in designing useful work protocols.
Merits and qualms of work fluctuations in classical fluctuation theorems.
Deng, Jiawen; Tan, Alvis Mazon; Hänggi, Peter; Gong, Jiangbin
2017-01-01
Work is one of the most basic notions in statistical mechanics, with work fluctuation theorems being one central topic in nanoscale thermodynamics. With Hamiltonian chaos commonly thought to provide a foundation for classical statistical mechanics, here we present general salient results regarding how (classical) Hamiltonian chaos generically impacts on nonequilibrium work fluctuations. For isolated chaotic systems prepared with a microcanonical distribution, work fluctuations are minimized and vanish altogether in adiabatic work protocols. For isolated chaotic systems prepared at an initial canonical distribution at inverse temperature β, work fluctuations depicted by the variance of e^{-βW} are also minimized by adiabatic work protocols. This general result indicates that, if the variance of e^{-βW} diverges for an adiabatic work protocol, it diverges for all nonadiabatic work protocols sharing the same initial and final Hamiltonians. Such divergence is hence not an isolated event and thus greatly impacts on the efficiency of using Jarzynski's equality to simulate free-energy differences. Theoretical results are illustrated in a Sinai model. Our general insights shall boost studies in nanoscale thermodynamics and are of fundamental importance in designing useful work protocols.
Precise Calibration of the Virial Theorem from Hubble Volume Cluster Catalogs
NASA Astrophysics Data System (ADS)
Evrard, A. E.; Horikawa, T.; Virgo Consortium Collaboration
2000-10-01
The Hubble Volume project of the Virgo Consortium has created 109 particle N-body simulations of large-scale structure formation in ΛCDM and τCDM cosmologies with resolution sufficient to define a virtual Coma cluster with 500 particles. Light-cone survey output from the simulations provide synthetic sky surveys of the dark matter distribution in very large cosmic volumes, ~ 1010 h-3 Mpc3. Cluster catalogs derived from the surveys contain 100,000 to 500,000 clusters with masses exceeding 5 x 1013 h-1 Msun and redshifts extending to z ~ 2. We analyse in detail the virial relation between dark matter mass MΔ c and velocity dispersion σ . We find a unified calibration of the relation in the form H(z) MΔ c = A σ p for which the amplitude A and slope p are independent of cosmology and/or epoch (H(z) is the Hubble parameter at redshift z). This holds for clusters whose properties are defined within a spherical region encompassing a fixed density contrast Δ c (typically 200) with respect to the critical density. Other definitions of clusters require a redshift dependent amplitude A(z). The scatter in σ at fixed H(z) M about the mean relation is small ( ~ 6%) and positively skewed. Subdividing the population into two classes --- `parents' and `children' --- we identify the minority child component as the source of the skewness and infer that the children are merger debris that has not yet been fully incorporated into the parent population. For the parents alone, the probability distribution function of the velocity dispersion residuals is very well modeled by a Gaussian distribution, suggesting a central limit theorem interpretation. The accuracy of the calibration will be addressed by examining Virgo simulations with higher mass resolution and smaller volumes. Connections to obervable measures --- cluster X-ray temperature and galaxy velocity dispersion --- will be briefly discussed.
From the necessary to the possible: the genesis of the spin-statistics theorem
NASA Astrophysics Data System (ADS)
Blum, Alexander
2014-12-01
The spin-statistics theorem, which relates the intrinsic angular momentum of a single particle to the type of quantum statistics obeyed by a system of many such particles, is one of the central theorems in quantum field theory and the physics of elementary particles. It was first formulated in 1939/40 by Wolfgang Pauli and his assistant Markus Fierz. This paper discusses the developments that led up to this first formulation, starting from early attempts in the late 1920s to explain why charged matter particles obey Fermi-Dirac statistics, while photons obey Bose-Einstein statistics. It is demonstrated how several important developments paved the way from such general philosophical musings to a general (and provable) theorem, most notably the use of quantum field theory, the discovery of new elementary particles, and the generalization of the notion of spin. It is also discussed how the attempts to prove a spin-statistics connection were driven by Pauli from formal to more physical arguments, culminating in Pauli's 1940 proof. This proof was a major success for the beleaguered theory of quantum field theory and the methods Pauli employed proved essential for the renaissance of quantum field theory and the development of renormalization techniques in the late 1940s.
Generalized Optical Theorem Detection in Random and Complex Media
NASA Astrophysics Data System (ADS)
Tu, Jing
The problem of detecting changes of a medium or environment based on active, transmit-plus-receive wave sensor data is at the heart of many important applications including radar, surveillance, remote sensing, nondestructive testing, and cancer detection. This is a challenging problem because both the change or target and the surrounding background medium are in general unknown and can be quite complex. This Ph.D. dissertation presents a new wave physics-based approach for the detection of targets or changes in rather arbitrary backgrounds. The proposed methodology is rooted on a fundamental result of wave theory called the optical theorem, which gives real physical energy meaning to the statistics used for detection. This dissertation is composed of two main parts. The first part significantly expands the theory and understanding of the optical theorem for arbitrary probing fields and arbitrary media including nonreciprocal media, active media, as well as time-varying and nonlinear scatterers. The proposed formalism addresses both scalar and full vector electromagnetic fields. The second contribution of this dissertation is the application of the optical theorem to change detection with particular emphasis on random, complex, and active media, including single frequency probing fields and broadband probing fields. The first part of this work focuses on the generalization of the existing theoretical repertoire and interpretation of the scalar and electromagnetic optical theorem. Several fundamental generalizations of the optical theorem are developed. A new theory is developed for the optical theorem for scalar fields in nonhomogeneous media which can be bounded or unbounded. The bounded media context is essential for applications such as intrusion detection and surveillance in enclosed environments such as indoor facilities, caves, tunnels, as well as for nondestructive testing and communication systems based on wave-guiding structures. The developed scalar
NASA Astrophysics Data System (ADS)
Crisanti, A.; Sarracino, A.; Zannetti, M.
2017-05-01
We study analytically the probability distribution of the heat released by an ensemble of harmonic oscillators to the thermal bath, in the nonequilibrium relaxation process following a temperature quench. We focus on the asymmetry properties of the heat distribution in the nonstationary dynamics, in order to study the forms taken by the fluctuation theorem as the number of degrees of freedom is varied. After analyzing in great detail the cases of one and two oscillators, we consider the limit of a large number of oscillators, where the behavior of fluctuations is enriched by a condensation transition with a nontrivial phase diagram, characterized by reentrant behavior. Numerical simulations confirm our analytical findings. We also discuss and highlight how concepts borrowed from the study of fluctuations in equilibrium under symmetry-breaking conditions [Gaspard, J. Stat. Mech. (2012) P08021, 10.1088/1742-5468/2012/08/P08021] turn out to be quite useful in understanding the deviations from the standard fluctuation theorem.
Fürst, Thomas; Ouattara, Mamadou; Silué, Kigbafori D.; N’Goran, Dje N.; Adiossan, Lukas G.; Bogoch, Isaac I.; N’Guessan, Yao; Koné, Siaka; Utzinger, Jürg; N’Goran, Eliézer K.
2013-01-01
Background Schistosomiasis and soil-transmitted helminthiasis are two high-burden neglected tropical diseases. In highly endemic areas, control efforts emphasize preventive chemotherapy. However, as morbidity, infection, and transmission begin to decrease, more targeted treatment is likely to become more cost-effective, provided that comparatively cheap diagnostic methods with reasonable accuracy are available. Methodology Adults were administered an anamnestic questionnaire in mid-2010 during a cross-sectional epidemiological survey in the Taabo health demographic surveillance system in south-central Côte d’Ivoire. Questions pertaining to risk factors and signs and symptoms for schistosomiasis and soil-transmitted helminthiasis were included. The individuals’ helminth infection status and their belonging to three different anthelmintic treatment groups were compared with the questionnaire results (i) to inform the local health authorities about the epidemiological and clinical footprint of locally prevailing helminthiases, and (ii) to explore the scope and limits of an anamnestic questionnaire as monitoring tool, which eventually could help guiding the control of neglected tropical diseases in control-induced low-endemicity settings. Principal Findings Our study sample consisted of 195 adults (101 males, 94 females). We found prevalences of hookworm, Trichuris trichiura, Schistosoma haematobium, and Schistosoma mansoni of 39.0%, 2.7%, 2.1%, and 2.1%, respectively. No Ascaris lumbricoides infection was found. Helminth infection intensities were generally very low. Seven, 74 and 79 participants belonged to three different treatment groups. Multivariable logistic regression models revealed statistically significant (p<0.05) associations between some risk factors, signs, and symptoms, and the different helminth infections and treatment groups. However, the risk factors, signs, and symptoms showed weak diagnostic properties. Conclusions/Significance The generally
Convolution theorems: partitioning the space of integral transforms
NASA Astrophysics Data System (ADS)
Lindsey, Alan R.; Suter, Bruce W.
1999-03-01
Investigating a number of different integral transforms uncovers distinct patterns in the type of translation convolution theorems afforded by each. It is shown that transforms based on separable kernels (aka Fourier, Laplace and their relatives) have a form of the convolution theorem providing for a transform domain product of the convolved functions. However, transforms based on kernels not separable in the function and transform variables mandate a convolution theorem of a different type; namely in the transform domain the convolution becomes another convolution--one function with the transform of the other.
Fluctuation theorem for Hamiltonian systems: Le Chatelier's principle.
Evans, D J; Searles, D J; Mittag, E
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
Fluctuation theorem for Hamiltonian Systems: Le Chatelier's principle
NASA Astrophysics Data System (ADS)
Evans, Denis J.; Searles, Debra J.; Mittag, Emil
2001-05-01
For thermostated dissipative systems, the fluctuation theorem gives an analytical expression for the ratio of probabilities that the time-averaged entropy production in a finite system observed for a finite time takes on a specified value compared to the negative of that value. In the past, it has been generally thought that the presence of some thermostating mechanism was an essential component of any system that satisfies a fluctuation theorem. In the present paper, we point out that a fluctuation theorem can be derived for purely Hamiltonian systems, with or without applied dissipative fields.
Quantum voting and violation of Arrow's impossibility theorem
NASA Astrophysics Data System (ADS)
Bao, Ning; Yunger Halpern, Nicole
2017-06-01
We propose a quantum voting system in the spirit of quantum games such as the quantum prisoner's dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's impossibility theorem. Arrow's theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's theorem. A quantum version of majority rule, we show, violates this quantum Arrow conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.
Criterium for the index theorem on the lattice
NASA Astrophysics Data System (ADS)
Bicudo, Pedro
2003-04-01
We study how far the Index Theorem can be extrapolated from the continuum to finite lattices with finite topological charge densities. To examine how the Wilson action approximates the Index theorem, we specialize in the lattice version of the Schwinger model. We propose a new criterion for solutions of the Ginsparg-Wilson Relation constructed with the Wilson action. We conclude that the Neuberger action is the simplest one that maximally complies with the Index Theorem, and that its best parameter in d = 2 is m0 = 1.1 ± 0.1.
Criterium for the Index Theorem on the Lattice
NASA Astrophysics Data System (ADS)
Bicudo, Pedro
2003-08-01
We study how far the Index Theorem can be extrapolated from the continuum to finite lattices with finite topological charge densities. To examine how the Wilson action approximates the Index theorem, we specialize in the lattice version of the Schwinger model. We propose a new criterion for solutions of the Ginsparg-Wilson Relation constructed with the Wilson action. We conclude that the Neuberger action is the simplest one that maximally complies with the Index Theorem, and that its best parameter in d = 2 is m0 = 1.1 ± 0.1.
An Almost Sure Ergodic Theorem for Quasistatic Dynamical Systems
NASA Astrophysics Data System (ADS)
Stenlund, Mikko
2016-09-01
We prove an almost sure ergodic theorem for abstract quasistatic dynamical systems, as an attempt of taking steps toward an ergodic theory of such systems. The result at issue is meant to serve as a working counterpart of Birkhoff's ergodic theorem which fails in the quasistatic setup. It is formulated so that the conditions, which essentially require sufficiently good memory-loss properties, could be verified in a straightforward way in physical applications. We also introduce the concept of a physical family of measures for a quasistatic dynamical system. These objects manifest themselves, for instance, in numerical experiments. We then illustrate the use of the theorem by examples.
Saludes, P; Proença, L; Gruartmoner, G; Enseñat, L; Pérez-Madrigal, A; Espinal, C; Mesquida, J
2016-11-10
Central venous-to-arterial carbon dioxide difference (PcvaCO2) has demonstrated its prognostic value in critically ill patients suffering from shock, and current expert recommendations advocate for further resuscitation interventions when PcvaCO2 is elevated. PcvaCO2 combination with arterial-venous oxygen content difference (PcvaCO2/CavO2) seems to enhance its performance when assessing anaerobic metabolism. However, the fact that PCO2 values might be altered by changes in blood O2 content (the Haldane effect), has been presented as a limitation of PCO2-derived variables. The present study aimed at exploring the impact of hyperoxia on PcvaCO2 and PcvaCO2/CavO2 during the early phase of shock. Prospective interventional study. Ventilated patients suffering from shock within the first 24 h of ICU admission. Patients requiring FiO2 ≥ 0.5 were excluded. At inclusion, simultaneous arterial and central venous blood samples were collected. Patients underwent a hyperoxygenation test (5 min of FiO2 100%), and arterial and central venous blood samples were repeated. Oxygenation and CO2 variables were calculated at both time points. Twenty patients were studied. The main cause of shock was septic shock (70%). The hyperoxygenation trial increased oxygenation parameters in arterial and venous blood, whereas PCO2 only changed at the venous site. Resulting PcvaCO2 and PcvaCO2/CavO2 significantly increased [6.8 (4.9, 8.1) vs. 7.6 (6.7, 8.5) mmHg, p 0.001; and 1.9 (1.4, 2.2) vs. 2.3 (1.8, 3), p < 0.001, respectively]. Baseline PcvaCO2, PcvaCO2/CavO2 and ScvO2 correlated with the magnitude of PO2 augmentation at the venous site within the trial (ρ -0.46, p 0.04; ρ 0.6, p < 0.01; and ρ 0.7, p < 0.001, respectively). Increased PcvaCO2/CavO2 values were associated with higher mortality in our sample [1.46 (1.21, 1.89) survivors vs. 2.23 (1.86, 2.8) non-survivors, p < 0.01]. PcvaCO2 and PcvaCO2/CavO2 are influenced by oxygenation changes not related to flow. Elevated
Caprioli, Riccardo; Cargini, Daniele; Marcacci, Maurilia; Cammà, Cesare; Giansante, Carla; Ferri, Nicola
2013-03-26
Crayfish plague, caused by the oomycete Aphanomyces astaci, is a serious disease of European freshwater crayfish and has eliminated entire populations in several European countries. In September 2011, mortality was observed among the Austropotamobius pallipes population of a river basin in the Abruzzi region (central Italy), and A. astaci DNA was detected by PCR in dead crayfish. A systematic survey was carried out to evaluate the spread and the effects of the plague in the river basin. The source of the outbreak remained unknown since North American crayfish species, which frequently act as subclinical carriers of the infection, were not detected in the area. The A. pallipes population disappeared from a river stretch of ~1 km, where A. astaci infection was detected in dead crayfish. However, apparently unaffected crayfish were still present upstream of that area as well as in a tributary that joined the brook in the apparently depopulated stretch. A. astaci infection was not detected in dead individuals collected in the upstream area and tributary. A follow-up visit conducted in the following season showed the presence of A. pallipes in the river stretch hit by the plague. In this outbreak, the spread of the infection could have been limited by a low density of the crayfish population and by the geographic conformation of the river basin, which includes a dense network of small tributaries, characterized by high flow velocity and low water temperature. In this particular setting, crayfish plague outbreaks can remain undetected. This underlines the importance of active monitoring programs aimed at the prompt recognition of both episodes of mortality and the presence of non-indigenous crayfish species.
NASA Astrophysics Data System (ADS)
Gaines, K.; Meinzer, F. C.; Duffy, C.; Thomas, E.; Eissenstat, D. M.
2014-12-01
Water uptake and retention by trees affects their ability to cope with drought, as well as influences ground water recharge and stream flow. Historically, water has not often been limiting in Eastern U.S. forests. As a result, very little work has been done to understand the basics of timing of water use by vegetation in these systems. As droughts are projected to increase in length and severity in future decades, this focus is increasingly important, particularly for informing hydrologic models. We used deuterium tracer and sap flux techniques to study tree water transport on a forested ridge top with shallow soil in central Pennsylvania. Three trees of each of the species, Acer saccharum, Carya tomentosa, Quercus prinus, and Quercus rubrum were accessed by tree climbing and scaffolding towers. We hypothesized that contrasting vessel size of the tree species would affect the efficiency of water transport (tracer velocity) and contrasting tree size would affect tracer storage as estimated by tracer residence times. Trees were injected with deuterated water in July 2012. Leaves were sampled 15 times over 35 days, initially daily for the first week, then at regular intervals afterwards. The tracer arrived in the canopy of the study trees between 1 and 7 days after injection, traveling at a velocity of 2 to 19 m d-1. The tracer residence time was between 7 and 33 days. Although there was variation in tracer velocity and residence time in individual trees, there were no significant differences among wood types or species (P>0.05). The general patterns in timing of water use were similar to other studies on angiosperm trees in tropical and arid ecosystems. There was no evidence of longer residence times in the larger trees. Sap flux-based estimates of sap velocity were much lower than tracer estimates, which was consistent with other studies. Levels of sap flux and midday water potential measurements suggested that the trees were water-stressed. We observed relatively
On soft limits of inflationary correlation functions
Assassi, Valentin; Baumann, Daniel; Green, Daniel E-mail: dbaumann@damtp.cam.ac.uk
2012-11-01
Soft limits of inflationary correlation functions are both observationally relevant and theoretically robust. Various theorems can be proven about them that are insensitive to detailed model-building assumptions. In this paper, we re-derive several of these theorems in a universal way. Our method makes manifest why soft limits are such an interesting probe of the spectrum of additional light fields during inflation. We illustrate these abstract results with a detailed case study of the soft limits of quasi-single-field inflation.
On soft limits of inflationary correlation functions
NASA Astrophysics Data System (ADS)
Assassi, Valentin; Baumann, Daniel; Green, Daniel
2012-11-01
Soft limits of inflationary correlation functions are both observationally relevant and theoretically robust. Various theorems can be proven about them that are insensitive to detailed model-building assumptions. In this paper, we re-derive several of these theorems in a universal way. Our method makes manifest why soft limits are such an interesting probe of the spectrum of additional light fields during inflation. We illustrate these abstract results with a detailed case study of the soft limits of quasi-single-field inflation.
Luttinger's theorem, superfluid vortices and holography
NASA Astrophysics Data System (ADS)
Iqbal, Nabil; Liu, Hong
2012-10-01
Strongly coupled field theories with gravity duals can be placed at finite density in two ways: electric field flux emanating from behind a horizon, or bulk charged fields outside of the horizon that explicitly source the density. We discuss field-theoretical observables that are sensitive to this distinction. If the charged fields are fermionic, we discuss a modified Luttinger's theorem that holds for holographic systems, in which the sum of boundary theory Fermi surfaces counts only the charge outside of the horizon. If the charged fields are bosonic, we show that the resulting superfluid phase may be characterized by the coefficient of the transverse Magnus force on a moving superfluid vortex, which again is sensitive only to the charge outside of the horizon. For holographic systems, these observables provide a field-theoretical way to distinguish how much charge is held by a dual horizon, but they may be useful in more general contexts as measures of deconfined (i.e. ‘fractionalized’) charge degrees of freedom.
Digital superresolution and the generalized sampling theorem
NASA Astrophysics Data System (ADS)
Prasad, Sudhakar
2007-02-01
The technique of reconstructing a higher-resolution (HR) image of size ML×ML by digitally processing L×L subpixel-shifted lower-resolution (LR) copies of it, each of size M×M, has now become well established. This particular digital superresolution problem is analyzed from the standpoint of the generalized sampling theorem. It is shown both theoretically and by computer simulation that the choice of regularly spaced subpixel shifts for the LR images tends to maximize the robustness and minimize the error of reconstruction of the HR image. In practice, since subpixel-level control of LR image shifts may be nearly impossible to achieve, however, a more likely scenario, which is also discussed, is one involving random subpixel shifts. It is shown that without reasonably tight bounds on the range of random shifts, the reconstruction is likely to fail in the presence of even small amounts of noise unless either reliable prior information or additional data are available.
On the Spin-Statistics Theorem
NASA Astrophysics Data System (ADS)
Peshkin, Murray
2002-05-01
M.V. Berry and J.M. Robbins* (B) have explained the spin-statistics theorem (SST) within nonrelativistic quantum mechanics (QM), without using relativity or field theory. For two identical spinless particles, their starting point is a coordinate space which consists of unordered pairs r,r' where r and r' represent two points in space, not particle labels. The point r,r' is the point r',r\\. That has topological consequences for the 6D configuration space and for the wave functions |r,r'>. More generally, spin variables are appended and there are N vectors. B gave a beautiful mathematical analysis to go from there to the usual SST under stated assumptions of QM. They also explored alternative assumptions that give unusual results but that may not be physical. I seek additional insight by recasting B's analysis into a form that emphasizes the relative orbital angular momenta of pairs of particles. I report here on the spinless case, where boson statistics emerges in a transparent way. This approach appears to exclude unusual possibilities. Work supported by U.S. DOE contract W-31-109-ENG-38. *Proc. R. Soc. Lond. A 453, 1771 (1997).
Negative probabilities, Fine's theorem, and linear positivity
NASA Astrophysics Data System (ADS)
Halliwell, J. J.; Yearsley, J. M.
2013-02-01
Many situations in quantum theory and other areas of physics lead to quasiprobabilities which seem to be physically useful but can be negative. The interpretation of such objects is not at all clear. In this paper, we show that quasiprobabilities naturally fall into two qualitatively different types, according to whether their non-negative marginals can or cannot be matched to a non-negative probability. The former type of quasiprobabilities, which we call viable, are qualitatively similar to true probabilities, but the latter type, which we call nonviable, may not have a sensible interpretation. Determining the existence of a probability matching given marginals is a nontrivial question in general. In simple examples, Fine's theorem indicates that inequalities of the Bell and Clauser-Horne-Shimony-Holt (CHSH) types provide criteria for its existence, and these examples are considered in detail. Our results have consequences for the linear positivity condition of Goldstein and Page in the context of the histories approach to quantum theory. Although it is a very weak condition for the assignment of probabilities, it fails in some important cases where our results indicate that probabilities clearly exist. We speculate that our method, of matching probabilities to a given set of marginals, provides a general method of assigning probabilities to histories and we show that it passes the Diósi test for the statistical independence of subsystems.
The Pythagorean Theorem and the Solid State
NASA Astrophysics Data System (ADS)
Kelly, Brenda S.; Splittgerber, Allen G.
2005-05-01
Solid-state parameters such as radius ratios, packing efficiencies, and crystal densities may be calculated for various crystal structures from basic Euclidean geometry relating to the Pythagorean theorem of right triangles. Because simpler cases are often discussed in the standard inorganic chemistry texts, this article only presents calculations for closest-packed A-type lattices (one type of particle) and several compound AB lattices (A and B particles) including sodium chloride, cesium chloride, zinc blende (sphalerite), wurtzite, and fluorite. For A-type metallic crystals, the use of recommended values of atomic radii results in calculated densities within 1% of observed values. For AB lattices, assuming ionic crystals, the use of recommended values of ionic radii results in density determinations that are usually but not always close to observed values. When there is covalent character to the bonding, the use of covalent radii results in calculated densities that correlate well with observed values. If interionic or interatomic spacings are used, the calculated densities are always close to the observed values. As indicated by a survey of the standard inorganic texts, these calculations are generally not presented. However, as an illustration of the application of simple mathematical principles to the study of chemistry, discussion of the methods presented in this manuscript may be of value in classroom presentations pertaining to the solid state.
Chaotic hypothesis: Onsager reciprocity and fluctuation-dissipation theorem
Gallavotti, G.
1996-09-01
It is shown that the chaoticity hypothesis recently introduced in statistical mechanics, which is analogous to Ruelle`s principle for turbulence, implies the Onsager reciprocity and the fluctuation-dissipation theorem in various reversible models for coexisting transport phenomena.