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
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)
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…
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
"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…
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.
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
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
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).
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…
Nonequilibrium fluctuation theorems in the presence of local heating
NASA Astrophysics Data System (ADS)
Pradhan, Punyabrata; Kafri, Yariv; Levine, Dov
2008-04-01
We study two nonequilibrium work fluctuation theorems, the Crooks theorem and the Jarzynski equality, for a test system coupled to a spatially extended heat reservoir whose degrees of freedom are explicitly modeled. The sufficient conditions for the validity of the theorems are discussed in detail and compared to the case of classical Hamiltonian dynamics. When the conditions are met the fluctuation theorems are shown to hold despite the fact that the immediate vicinity of the test system goes out of equilibrium during an irreversible process. We also study the effect of the coupling to the heat reservoir on the convergence of ⟨exp(-βW)⟩ to its theoretical mean value, where W is the work done on the test system and β is the inverse temperature. It is shown that the larger the local heating, the slower the convergence.
On local-hidden-variable no-go theorems
NASA Astrophysics Data System (ADS)
Methot, A. A.
2006-06-01
The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky, and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimately doomed in 1964 with the work of Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus, we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities, and pseudo-telepathy. A discussion of the similarities and differences will follow.
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.
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.
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).
No-local-broadcasting theorem for multipartite quantum correlations.
Piani, Marco; Horodecki, Paweł; Horodecki, Ryszard
2008-03-07
We prove that the correlations present in a multipartite quantum state have an operational quantum character even if the state is unentangled, as long as it does not simply encode a multipartite classical probability distribution. Said quantumness is revealed by the new task of local broadcasting, i.e., of locally sharing preestablished correlations, which is feasible if and only if correlations are stricly classical. Our operational approach leads to natural definitions of measures for quantumness of correlations. It also reproduces the standard no-broadcasting theorem as a special case.
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…
Local Paley Wiener theorems for functions analytic on unit spheres
NASA Astrophysics Data System (ADS)
Damelin, S. B.; Devaney, A. J.
2007-04-01
The purpose of this paper is to provide new and simplified statements of local Paley-Wiener theorems on the (n - 1)-dimensional unit sphere realized as a subset of n = 2, 3 Euclidean space. More precisely, given a function f:{\\bb C}^n\\to {\\bb C}, n=2,3 , whose restriction to an n - 1 sphere is analytic, we establish necessary and sufficient conditions determining whether f is the Fourier transform of a compactly supported, bounded function F:{\\bb R}^n\\to{\\bb C} . The essence of this investigation is that, because of the local nature of the problem, the mapping f → F is not in general invertible and so the problem cannot be studied via a Fourier integral. Our proofs are new.
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
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.
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).
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…
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…
Signal-locality, uncertainty, and the subquantum H-theorem. II
NASA Astrophysics Data System (ADS)
Valentini, Antony
1991-08-01
In the pilot-wave formulation, signal-locality and the uncertainty principle are shown to be valid only for the equilibrium distribution P=| Ψ| 2 (which arises from the subquantum H-theorem proved earlier). The H-theorem then explains the emergence of effective locality and uncertainty from a deeper nonlocal and deterministic theory. In order to explain the present uneasy “peaceful coexistence” (or “conspiracy”) between relativity and quantum theory, we suggest that a subquantum analogue of Boltzmann's heat death has actually happened in the real universe.
Metric rigidity theorems on Hermitian locally symmetric spaces
Mok, Ngaiming
1986-01-01
Let X = Ω/Γ be a compact quotient of an irreducible bounded symmetric domain Ω of rank ≥2 by a discrete group ω of automorphisms without fixed points. It is well known that the Kähler-Einstein metric g on X carries seminegative curvature (in the sense of Griffiths). I show that any Hermitian metric h on X carrying seminegative curvature must be a constant multiple of g. This can be applied to prove rigidity theorems of holomorphic maps from X into Hermitian manifolds (Y, k) carrying seminegative curvature. These results are also generalized to the case of quotients of finite volume. On the other hand, let (Xc, gc) be an irreducible compact Hermitian symmetric manifold of rank ≥2. Then gc is Kähler and carries semipositive holomorphic bisectional curvature. I prove that any Kähler h on Xc carrying semipositive holomorphic bisectional curvature must be equal to gc up to a constant multiple and up to a biholomorphic transformation of Xc. PMID:16593680
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.
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.
The optical theorem for local source excitation of a particle near a plane interface
NASA Astrophysics Data System (ADS)
Eremin, Yuri; Wriedt, Thomas
2015-11-01
Based on classic Maxwell's theory and the Gauss Theorem we extended the Optical Theorem to the case of a penetrable particle excited by a local source deposited near a plane interface. We demonstrate that the derived Extinction Cross-Section involves the total point source radiating cross-section and some definite integrals responsible for the scattering by the interface. The derived extinction cross-section can be employed to estimate the quantum yield and the optical antenna efficiency without computation of the absorption cross-section.
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
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.
A Local Bifurcation Theorem for Degenerate Elliptic Equations With Radial Symmetry
NASA Astrophysics Data System (ADS)
García-Melián, J.; Sabina de Lis, J.
2002-02-01
In this work we provide local bifurcation results for equations involving the p-Laplacian in balls. We analyze the continua Cn of radial solutions emanating from (λn, p, 0), {λn, p} being the radial eigenvalues of -Δp. First, we show that the only nontrivial solutions close to (λn, p, 0) lie on a continuous curve, thus extending the Crandall-Rabinowitz theorem. Second, it is proved that Cn{(λn, p, 0)} splits into two unbounded connected pieces, characterized by their nodal properties thus sharpening previous results.
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.
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.
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…
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.
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…
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.
THE LOCAL LIMIT OF GLOBAL GYROKINETIC SIMULATIONS
CANDY J; WALTZ RE; DORLAND W
2003-10-01
OAK-B135 Global gyrokinetic simulations of turbulence include physical effects that are not retained in local flux-tube simulations. nevertheless, in the limit of sufficiently small {rho}* (gyroradius compared to system size) it is expected that a local simulation should agree with a global one (at the local simulation radius) since all effects that are dropped in the local simulations are expected to vanish as {rho}* {yields} 0. In this note, global simulations of a well-established test case are indeed shown to recover the flux-tube limit at each radius.
NASA Astrophysics Data System (ADS)
Grzybowski, J. M. V.; Macau, E. E. N.; Yoneyama, T.
2017-05-01
This paper presents a self-contained framework for the stability assessment of isochronal synchronization in networks of chaotic and limit-cycle oscillators. The results were based on the Lyapunov-Krasovskii theorem and they establish a sufficient condition for local synchronization stability of as a function of the system and network parameters. With this in mind, a network of mutually delay-coupled oscillators subject to direct self-coupling is considered and then the resulting error equations are block-diagonalized for the purpose of studying their stability. These error equations are evaluated by means of analytical stability results derived from the Lyapunov-Krasovskii theorem. The proposed approach is shown to be a feasible option for the investigation of local stability of isochronal synchronization for a variety of oscillators coupled through linear functions of the state variables under a given undirected graph structure. This ultimately permits the systematic identification of stability regions within the high-dimensionality of the network parameter space. Examples of applications of the results to a number of networks of delay-coupled chaotic and limit-cycle oscillators are provided, such as Lorenz, Rössler, Cubic Chua's circuit, Van der Pol oscillator and the Hindmarsh-Rose neuron.
Fluctuation limits of a locally regulated population and generalized Langevin equations
NASA Astrophysics Data System (ADS)
Savov, Mladen; Wang, Shi-Dong
2015-06-01
We consider a locally regulated spatial population model introduced by Bolker and Pacala. Based on the deterministic approximation studied by Fournier and Méléard, we prove that the fluctuation theorem holds under some mild moment conditions. The limiting process is shown to be an infinite-dimensional Gaussian process solving a generalized Langevin equation. In particular, we further consider its properties in one dimension case, which is characterized as a time-inhomogeneous Ornstein-Uhlenbeck process.
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.
NASA Astrophysics Data System (ADS)
Conley, Stephen; Faloona, Ian; Mehrotra, Shobhit; Suard, Maxime; Lenschow, Donald H.; Sweeney, Colm; Herndon, Scott; Schwietzke, Stefan; Pétron, Gabrielle; Pifer, Justin; Kort, Eric A.; Schnell, Russell
2017-09-01
Airborne estimates of greenhouse gas emissions are becoming more prevalent with the advent of rapid commercial development of trace gas instrumentation featuring increased measurement accuracy, precision, and frequency, and the swelling interest in the verification of current emission inventories. Multiple airborne studies have indicated that emission inventories may underestimate some hydrocarbon emission sources in US oil- and gas-producing basins. Consequently, a proper assessment of the accuracy of these airborne methods is crucial to interpreting the meaning of such discrepancies. We present a new method of sampling surface sources of any trace gas for which fast and precise measurements can be made and apply it to methane, ethane, and carbon dioxide on spatial scales of ˜ 1000 m, where consecutive loops are flown around a targeted source region at multiple altitudes. Using Reynolds decomposition for the scalar concentrations, along with Gauss's theorem, we show that the method accurately accounts for the smaller-scale turbulent dispersion of the local plume, which is often ignored in other average mass balance
methods. With the help of large eddy simulations (LES) we further show how the circling radius can be optimized for the micrometeorological conditions encountered during any flight. Furthermore, by sampling controlled releases of methane and ethane on the ground we can ascertain that the accuracy of the method, in appropriate meteorological conditions, is often better than 10 %, with limits of detection below 5 kg h-1 for both methane and ethane. Because of the FAA-mandated minimum flight safe altitude of 150 m, placement of the aircraft is critical to preventing a large portion of the emission plume from flowing underneath the lowest aircraft sampling altitude, which is generally the leading source of uncertainty in these measurements. Finally, we show how the accuracy of the method is strongly dependent on the number of sampling loops
Resolution limits of ultrafast ultrasound localization microscopy
NASA Astrophysics Data System (ADS)
Desailly, Yann; Pierre, Juliette; Couture, Olivier; Tanter, Mickael
2015-11-01
As in other imaging methods based on waves, the resolution of ultrasound imaging is limited by the wavelength. However, the diffraction-limit can be overcome by super-localizing single events from isolated sources. In recent years, we developed plane-wave ultrasound allowing frame rates up to 20 000 fps. Ultrafast processes such as rapid movement or disruption of ultrasound contrast agents (UCA) can thus be monitored, providing us with distinct punctual sources that could be localized beyond the diffraction limit. We previously showed experimentally that resolutions beyond λ/10 can be reached in ultrafast ultrasound localization microscopy (uULM) using a 128 transducer matrix in reception. Higher resolutions are theoretically achievable and the aim of this study is to predict the maximum resolution in uULM with respect to acquisition parameters (frequency, transducer geometry, sampling electronics). The accuracy of uULM is the error on the localization of a bubble, considered a point-source in a homogeneous medium. The proposed model consists in two steps: determining the timing accuracy of the microbubble echo in radiofrequency data, then transferring this time accuracy into spatial accuracy. The simplified model predicts a maximum resolution of 40 μm for a 1.75 MHz transducer matrix composed of two rows of 64 elements. Experimental confirmation of the model was performed by flowing microbubbles within a 60 μm microfluidic channel and localizing their blinking under ultrafast imaging (500 Hz frame rate). The experimental resolution, determined as the standard deviation in the positioning of the microbubbles, was predicted within 6 μm (13%) of the theoretical values and followed the analytical relationship with respect to the number of elements and depth. Understanding the underlying physical principles determining the resolution of superlocalization will allow the optimization of the imaging setup for each organ. Ultimately, accuracies better than the size
Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Wu, Yu-Chun; Wu, Chunfeng; Ye, Xiang-Jun; Żukowski, Marek; Kwek, L C
2015-06-25
We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum entanglement (this is not so without this condition). This result leads to an enhanced version of Gisin's theorem (originally: all pure entangled states violate local realism). Local realism is violated by all mixed states with the above steering property. The new class of states allows one e.g. to perform three party secret sharing with just pairs of entangled qubits, instead of three qubit entanglements (which are currently available with low fidelity). This significantly increases the feasibility of having high performance versions of such protocols. Finally, we discuss some possible applications.
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.
Restructuring local distribution services: Possibilities and limitations
Duann, D.J.
1994-08-01
The restructuring of local distribution services is now the focus of the natural gas industry. It is the last major step in the ``reconstitution`` of the natural gas industry and a critical clement in realizing the full benefits of regulatory and market reforms that already have taken place in the wellhead and interstate markets. It could also be the most important regulatory initiative for most end-use customers because they are affected directly by the costs and reliability of distribution services. Several factors contribute to the current emphasis on distribution service restructuring. They include the unbundling and restructuring of upstream markets, a realization of the limitations of supply-side options (such as gas procurement oversight), and the increased diversity and volatility of gas demand facing local distribution companies. Local distribution service is not one but a series of activities that start with commodity gas procurement and extend to transportation, load balancing, storage, and metering and billing of services provided. There are also considerable differences in the economies of scale and scope associated with these various activities. Thus, a mixture of supply arrangements (such as a competitive market or a monopoly) is required for the most efficient delivery of local distribution services. A distinction must be made between the supply of commodity gas and the provision of a bundled distribution service. This distinction and identification of the best supply arrangements for various distribution service components are the most critical factors in developing appropriate restructuring policies. For most state public utility commissions the criteria for service restructuring should include pursuing the economies of scale and scope in gas distribution, differentiating and matching gas service reliability and quality with customer requirements, and controlling costs associated with the search, negotiation, and contracting of gas services.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Lu, Deyu
The adiabatic-connection fluctuation-dissipation theorem (ACFDT) is a formal theoretical framework to treat van der Waals (vdW) dispersion interactions. Under the random phase approximation (RPA), it yields the correct asymptotic behavior at large distances, but the short-range correlation is overestimated. It has been demonstrated that non-local exchange-correlation kernels can systematically correct the errors of RPA for homogenous electron gas. However, direct extension of non-local kernels derived from the electron gas model to inhomogeneous systems raises several issues. In addition to the high computational expense, the non-local kernels worsen the rare gas dimer binding curve as compared to RPA. In this study, we propose a quasi-local approximation of the non-local kernel in order to address these issues. This research used resources of the Center for Functional Nanomaterials, which is a U.S. DOE Office of Science Facility, at Brookhaven National Laboratory under Contract No. DE-SC0012704.
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).
NASA Astrophysics Data System (ADS)
Webb, G. M.; Dasgupta, B.; McKenzie, J. F.; Hu, Q.; Zank, G. P.
2014-03-01
Conservation laws in ideal gas dynamics and magnetohydrodynamics (MHD) associated with fluid relabeling symmetries are derived using Noether's first and second theorems. Lie dragged invariants are discussed in terms of the MHD Casimirs. A nonlocal conservation law for fluid helicity applicable for a non-barotropic fluid involving Clebsch variables is derived using Noether's theorem, in conjunction with a fluid relabeling symmetry and a gauge transformation. A nonlocal cross helicity conservation law involving Clebsch potentials, and the MHD energy conservation law are derived by the same method. An Euler-Poincaré variational approach is also used to derive conservation laws associated with fluid relabeling symmetries using Noether's second theorem.
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)
Limits on the local dark matter density
NASA Astrophysics Data System (ADS)
Garbari, Silvia; Read, Justin I.; Lake, George
2011-09-01
We revisit systematics in determining the local dark matter density ρdm from the vertical motion of stars in the solar neighbourhood. Using a simulation of a Milky Way like galaxy, we determine the data quality required to detect ρdm at its expected local value. We introduce a new method for recovering ρdm that uses moments of the Jeans equations, combined with a Markov chain Monte Carlo technique, to marginalize over the unknown parameters. Given sufficiently good data, we show that our method can recover the correct local dark matter density even in the face of disc inhomogeneities, non-isothermal tracers and a non-separable distribution function. We illustrate the power of our technique by applying it to Hipparcos data. We first make the assumption that the A- and F-star tracer populations are isothermal. This recovers ρdm= 0.003+0.009- 0.007 M⊙ pc-3 (ρdm= 0.11+0.34- 0.27 GeV cm-3, with 90 per cent confidence), consistent with previous determinations. However, the vertical dispersion profile of these tracers is poorly known. If we assume instead a non-isothermal profile similar to that of the blue disc stars from SDSS DR-7 recently measured, we obtain a fit with a very similar χ2 value, but with ρdm= 0.033+0.008- 0.009 M⊙ pc-3 (ρdm= 1.25+0.30- 0.34 GeV cm-3 with 90 per cent confidence). This highlights that it is vital to measure the vertical dispersion profile of the tracers to recover an unbiased estimate of ρdm.
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.
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
ERIC Educational Resources Information Center
Makagon, A.; Weron, A.
1976-01-01
Salehi and Scheidt have derived several Wold-Cramer concordance theorems for q-variate stationary processes over discrete groups. This paper characterizes the concordance of the Wold decomposition with respect to families arising in the interpolation problem and the Cramer decomposition for non-full-rank q-variate stationary processes over certain…
ERIC Educational Resources Information Center
Makagon, A.; Weron, A.
1976-01-01
Salehi and Scheidt have derived several Wold-Cramer concordance theorems for q-variate stationary processes over discrete groups. This paper characterizes the concordance of the Wold decomposition with respect to families arising in the interpolation problem and the Cramer decomposition for non-full-rank q-variate stationary processes over certain…
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
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.
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)
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
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.
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.
Combining local and global limitations of visual search.
Põder, Endel
2017-04-01
There are different opinions about the roles of local interactions and central processing capacity in visual search. This study attempts to clarify the problem using a new version of relevant set cueing. A central precue indicates two symmetrical segments (that may contain a target object) within a circular array of objects presented briefly around the fixation point. The number of objects in the relevant segments, and density of objects in the array were varied independently. Three types of search experiments were run: (a) search for a simple visual feature (color, size, and orientation); (b) conjunctions of simple features; and (c) spatial configuration of simple features (rotated Ts). For spatial configuration stimuli, the results were consistent with a fixed global processing capacity and standard crowding zones. For simple features and their conjunctions, the results were different, dependent on the features involved. While color search exhibits virtually no capacity limits or crowding, search for an orientation target was limited by both. Results for conjunctions of features can be partly explained by the results from the respective features. This study shows that visual search is limited by both local interference and global capacity, and the limitations are different for different visual features.
High local unemployment rates limit work after lung transplantation.
Nau, Michael; Shrider, Emily A; Tobias, Joseph D; Hayes, Don; Tumin, Dmitry
2016-10-01
Most lung transplant (LTx) recipients recover sufficient functional status to resume working, yet unemployment is common after LTx. Weak local labor markets may limit employment opportunities for LTx recipients. United Network for Organ Sharing data on first-time LTx recipients 18-60 years old who underwent transplant between 2010 and 2014 were linked to American Community Survey data on unemployment rates at the ZIP Code level. Multivariable competing-risks regression modeled the influence of dichotomous (≥8%) and continuous local unemployment rates on employment after LTx, accounting for the competing risk of mortality. For comparison, analyses were duplicated in a cohort of heart transplant (HTx) recipients who underwent transplant during the same period. The analysis included 3,897 LTx and 5,577 HTx recipients. Work after LTx was reported by 300 (16.3%) residents of low-unemployment areas and 244 (11.9%) residents of high-unemployment areas (p < 0.001). Multivariable analysis of 3,626 LTx recipients with complete covariate data found that high local unemployment rates limited employment after LTx (sub-hazard ratio = 0.605; 95% confidence interval = 0.477, 0.768; p < 0.001), conditional on not working before transplant. Employment after HTx was higher compared with employment after LTx, and not associated with local unemployment rates in multivariable analyses. LTx recipients of working age exhibit exceptionally low employment rates. High local unemployment rates exacerbate low work participation after LTx, and may discourage job search in this population. Copyright © 2016 International Society for Heart and Lung Transplantation. Published by Elsevier Inc. All rights reserved.
Chen, Jing-Ling; Su, Hong-Yi; Xu, Zhen-Peng; Wu, Yu-Chun; Wu, Chunfeng; Ye, Xiang-Jun; Żukowski, Marek; Kwek, L. C.
2015-01-01
We demonstrate here that for a given mixed multi-qubit state if there are at least two observers for whom mutual Einstein-Podolsky-Rosen steering is possible, i.e. each observer is able to steer the other qubits into two different pure states by spontaneous collapses due to von Neumann type measurements on his/her qubit, then nonexistence of local realistic models is fully equivalent to quantum entanglement (this is not so without this condition). This result leads to an enhanced version of Gisin’s theorem (originally: all pure entangled states violate local realism). Local realism is violated by all mixed states with the above steering property. The new class of states allows one e.g. to perform three party secret sharing with just pairs of entangled qubits, instead of three qubit entanglements (which are currently available with low fidelity). This significantly increases the feasibility of having high performance versions of such protocols. Finally, we discuss some possible applications. PMID:26108704
Shivanandan, Arun; Unnikrishnan, Jayakrishnan; Radenovic, Aleksandra
2015-01-01
Single Molecule Localization Microscopy techniques like PhotoActivated Localization Microscopy, with their sub-diffraction limit spatial resolution, have been popularly used to characterize the spatial organization of membrane proteins, by means of quantitative cluster analysis. However, such quantitative studies remain challenged by the techniques’ inherent sources of errors such as a limited detection efficiency of less than 60%, due to incomplete photo-conversion, and a limited localization precision in the range of 10 – 30nm, varying across the detected molecules, mainly depending on the number of photons collected from each. We provide analytical methods to estimate the effect of these errors in cluster analysis and to correct for them. These methods, based on the Ripley’s L(r) – r or Pair Correlation Function popularly used by the community, can facilitate potentially breakthrough results in quantitative biology by providing a more accurate and precise quantification of protein spatial organization. PMID:25794150
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.
Local resolution-limit-free Potts model for community detection.
Ronhovde, Peter; Nussinov, Zohar
2010-04-01
We report on an exceptionally accurate spin-glass-type Potts model for community detection. With a simple algorithm, we find that our approach is at least as accurate as the best currently available algorithms and robust to the effects of noise. It is also competitive with the best currently available algorithms in terms of speed and size of solvable systems. We find that the computational demand often exhibits superlinear scaling O(L1.3) where L is the number of edges in the system, and we have applied the algorithm to synthetic systems as large as 40 x 10(6) nodes and over 1 x 10(9) edges. A previous stumbling block encountered by popular community detection methods is the so-called "resolution limit." Being a "local" measure of community structure, our Potts model is free from this resolution-limit effect, and it further remains a local measure on weighted and directed graphs. We also address the mitigation of resolution-limit effects for two other popular Potts models.
Value and limitations of seizure semiology in localizing seizure onset.
So, Elson L
2006-08-01
Seizure semiology has been the foundation of clinical diagnosis of seizure disorders. This article discusses the value and the limitations of behavioral features of seizure episodes in localizing seizure onset. Studies have shown that some semiologic features of seizures are highly accurate in the hemispheric lateralization and lobar localization of seizures. There is good agreement between blinded reviewers in lateralizing video-recorded seizures in temporal lobe and extratemporal lobe epilepsies. However, seizure semiology alone should not be used to determine the site of seizure onset. Each semiologic feature may falsely localize seizure onset. Seizure semiology in some patients may signify the site of seizure propagation rather than origination. Moreover, seizure semiology may not be as reliable in multifocal epilepsies as it is in unifocal epilepsies. Many semiologic features of seizures of adults are often missing in seizures of children. Seizure semiology should be analyzed and integrated with EEG and neuroimaging data to localize the seizure focus. A sample of the recorded seizures should be shown to the patient's relatives or friends to verify that it is representative of habitual seizures.
Local versus basin-scale limitation of marine nitrogen fixation
Weber, Thomas; Deutsch, Curtis
2014-01-01
Nitrogen (N) fixation by diazotrophic plankton is the primary source of this crucial nutrient to the ocean, but the factors limiting its rate and distribution are controversial. According to one view, the ecological niche of diazotrophs is primarily controlled by the ocean through internally generated N deficits that suppress the growth of their competitors. A second view posits an overriding limit from the atmosphere, which restricts diazotrophs to regions where dust deposition satisfies their high iron (Fe) requirement, thus separating N sources from sinks at a global scale. Here we use multiple geochemical signatures of N2 fixation to show that the Fe limitation of diazotrophs is strong enough to modulate the regional distribution of N2 fixation within ocean basins—particularly the Fe-poor Pacific—but not strong enough to influence its partition between basins, which is instead governed by rates of N loss. This scale-dependent limitation of N2 fixation reconciles local observations of Fe stress in diazotroph communities with an inferred spatial coupling of N sources and sinks. Within this regime of intermediate Fe control, the oceanic N reservoir would respond only weakly to enhanced dust fluxes during glacial climates, but strongly to the reduced fluxes hypothesized under anthropogenic climate warming. PMID:24889607
Local versus basin-scale limitation of marine nitrogen fixation.
Weber, Thomas; Deutsch, Curtis
2014-06-17
Nitrogen (N) fixation by diazotrophic plankton is the primary source of this crucial nutrient to the ocean, but the factors limiting its rate and distribution are controversial. According to one view, the ecological niche of diazotrophs is primarily controlled by the ocean through internally generated N deficits that suppress the growth of their competitors. A second view posits an overriding limit from the atmosphere, which restricts diazotrophs to regions where dust deposition satisfies their high iron (Fe) requirement, thus separating N sources from sinks at a global scale. Here we use multiple geochemical signatures of N2 fixation to show that the Fe limitation of diazotrophs is strong enough to modulate the regional distribution of N2 fixation within ocean basins--particularly the Fe-poor Pacific--but not strong enough to influence its partition between basins, which is instead governed by rates of N loss. This scale-dependent limitation of N2 fixation reconciles local observations of Fe stress in diazotroph communities with an inferred spatial coupling of N sources and sinks. Within this regime of intermediate Fe control, the oceanic N reservoir would respond only weakly to enhanced dust fluxes during glacial climates, but strongly to the reduced fluxes hypothesized under anthropogenic climate warming.
Exponential Localization of Photons
NASA Astrophysics Data System (ADS)
Bialynicki-Birula, Iwo
1998-06-01
It is shown that photons can be localized in space with an exponential falloff of the energy density and photodetection rates. The limits of localization are determined by the fundamental Paley-Wiener theorem. A direct mathematical connection between the spatial localization of photons and the decay in time of quantum mechanical systems is established.
Limits of localized control in extended nonlinear systems
NASA Astrophysics Data System (ADS)
Handel, Andreas
We investigate the limits of localized linear control in spatially extended, nonlinear systems. Spatially extended, nonlinear systems can be found in virtually every field of engineering and science. An important category of such systems are fluid flows. Fluid flows play an important role in many commercial applications, for instance in the chemical, pharmaceutical and food-processing industries. Other important fluid flows include air- or water flows around cars, planes or ships. In all these systems, it is highly desirable to control the flow of the respective fluid. For instance control of the air flow around an airplane or car leads to better fuel-economy and reduced noise production. Usually, it is impossible to apply control everywhere. Consider an airplane: It would not be feasibly to cover the whole body of the plane with control units. Instead, one can place the control units at localized regions, such as points along the edge of the wings, spaced as far apart from each other as possible. These considerations lead to an important question: For a given system, what is the minimum number of localized controllers that still ensures successful control? Too few controllers will not achieve control, while using too many leads to unnecessary expenses and wastes resources. To answer this question, we study localized control in a class of model equations. These model equations are good representations of many real fluid flows. Using these equations, we show how one can design localized control that renders the system stable. We study the properties of the control and derive several expressions that allow us to determine the limits of successful control. We show how the number of controllers that are needed for successful control depends on the size and type of the system, as well as the way control is implemented. We find that especially the nonlinearities and the amount of noise present in the system play a crucial role. This analysis allows us to determine under
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.
Local and Global Limits on Visual Processing in Schizophrenia
Tibber, Marc S.; Anderson, Elaine J.; Bobin, Tracy; Carlin, Patricia; Shergill, Sukhwinder S.; Dakin, Steven C.
2015-01-01
Schizophrenia has been linked to impaired performance on a range of visual processing tasks (e.g. detection of coherent motion and contour detection). It has been proposed that this is due to a general inability to integrate visual information at a global level. To test this theory, we assessed the performance of people with schizophrenia on a battery of tasks designed to probe voluntary averaging in different visual domains. Twenty-three outpatients with schizophrenia (mean age: 40±8 years; 3 female) and 20 age-matched control participants (mean age 39±9 years; 3 female) performed a motion coherence task and three equivalent noise (averaging) tasks, the latter allowing independent quantification of local and global limits on visual processing of motion, orientation and size. All performance measures were indistinguishable between the two groups (ps>0.05, one-way ANCOVAs), with one exception: participants with schizophrenia pooled fewer estimates of local orientation than controls when estimating average orientation (p = 0.01, one-way ANCOVA). These data do not support the notion of a generalised visual integration deficit in schizophrenia. Instead, they suggest that distinct visual dimensions are differentially affected in schizophrenia, with a specific impairment in the integration of visual orientation information. PMID:25689281
Local and global limits on visual processing in schizophrenia.
Tibber, Marc S; Anderson, Elaine J; Bobin, Tracy; Carlin, Patricia; Shergill, Sukhwinder S; Dakin, Steven C
2015-01-01
Schizophrenia has been linked to impaired performance on a range of visual processing tasks (e.g. detection of coherent motion and contour detection). It has been proposed that this is due to a general inability to integrate visual information at a global level. To test this theory, we assessed the performance of people with schizophrenia on a battery of tasks designed to probe voluntary averaging in different visual domains. Twenty-three outpatients with schizophrenia (mean age: 40±8 years; 3 female) and 20 age-matched control participants (mean age 39±9 years; 3 female) performed a motion coherence task and three equivalent noise (averaging) tasks, the latter allowing independent quantification of local and global limits on visual processing of motion, orientation and size. All performance measures were indistinguishable between the two groups (ps>0.05, one-way ANCOVAs), with one exception: participants with schizophrenia pooled fewer estimates of local orientation than controls when estimating average orientation (p = 0.01, one-way ANCOVA). These data do not support the notion of a generalised visual integration deficit in schizophrenia. Instead, they suggest that distinct visual dimensions are differentially affected in schizophrenia, with a specific impairment in the integration of visual orientation information.
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
OVII and Temperature Limits on the Local Hot Bubble
NASA Astrophysics Data System (ADS)
Pirtle, Robert; Petre, N.; McCammon, D.; Morgan, K.; Sauter, P.; Clavadetscher, K.; Fujimoto, R.; Hagihara, T.; Masui, K.; Mitsuda, K.; Takei, Y.; Wang, Q. D.; Yamasaki, N. Y.; Yao, Y.; Yoshino, T.
2013-01-01
The observed ¼-keV (ROSAT R12 band) X-ray background originates largely in a region of hot ionized gas roughly 100 pc in extent surrounding the Sun known as the Local Hot Bubble (LHB). The observed flux is quite uniform at low latitudes (|b| < 30°), but there a several large areas at intermediate and high latitudes that are enhanced by factors of 2 - 3. Charge exchange between highly charged ions in the Solar wind and interstellar neutral H and He moving through interplanetary space might provide a very roughly isotropic contribution about equal to the low- latitude flux (Koutroumpa et al. 2008), but cannot produce the enhancements. Correlations with the interstellar absorbing column show that some of these bright regions are apparently due to clumps of hot gas in the Galactic halo, while many of them show no correlation and must be due to extensions of the LHB (Kuntz & Snowden 2000, Bellm & Vaillancourt 2005). Global fits of simple plasma emission spectra give temperatures near 1.0 x 106 K for both LHB and halo emission, but the possibility of a substantial contamination by charge exchange could distort this result in unknown ways. Thermal excitation of O VII is strongly temperature dependent in this range, so we have tried to correlate O VII fluxes measured with Suzaku with variations in ¼-keV intensity from the ROSAT R12 band map to determine the temperature. We take eleven O VII intensity measurements from Yoshino et al. (2009), one from Masui et al. (2009), and an additional eighteen from archival Suzaku pointings and correlate these with the R12 band local and halo intensities as separated by Kunzt & Snowden (2000). The lack of detectable correlation in both cases strongly limits any O VII production by the material producing the enhancements, and upper limits to the temperatures are set. This work was supported in part by the National Science Foundation's REU program through NSF Award AST-1004881 and by NASA grant NNX09AF09G. *present address: Department
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.
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.
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.
Limits on the OVII Emission from the Local Hot Bubble
NASA Astrophysics Data System (ADS)
Jaeckel, Felix T; Li, Yaqiong; Morgan, Kelsey; Petre, Natalia; Sauter, Patrick; McCammon, Dan
2014-06-01
Constraining the properties of the gas in the local hot-bubble (LHB) is important for the understanding of the interstellar medium surrounding the sun. Much information about its energetic state is embedded in the observations of the low-energy diffuse X-ray background. From molecular-cloud shadowing observations (Galeazzi et al. 2006, R. Smith et al. 2007, Henley et al. 2007) it is known that a significant fraction of the 0.57keV OVII X-ray flux originates locally (< ~300 pc).To investigate the origin of this OVII emission, we analyze the correlation between OVII flux (extracted from Suzaku observations cleaned of point sources) against the local fraction of the ROSAT ¼ keV emission (R12 band), as separated from the distant (hot halo/extragalactic) component by Snowden (1998) and Kuntz (2000).Observations were selected to avoid galactic in-plane emission and features of other large-scale ISM structures. After correcting OVII flux for the more distant latitude-dependent emission, we find that it is essentially uncorrelated with the local ¼ keV emission, implying that the local hot bubble is not the source of the observed OVII emission. The lack of OVII emission further precludes temperatures above ~1E6K for the LHB gas (assuming collisional equilibrium models with solar abundance).
Local land-atmosphere feedbacks limit irrigation demand
NASA Astrophysics Data System (ADS)
Decker, Mark; Ma, Shaoxiu; Pitman, Andy
2017-05-01
Irrigation is known to influence regional climate but most studies forecast and simulate irrigation with offline (i.e. land only) models. Using south eastern Australia as a test bed, we demonstrate that irrigation demand is fundamentally different between land only and land-atmosphere simulations. While irrigation only has a small impact on maximum temperature, the semi-arid environment experiences near surface moistening in coupled simulations over the irrigated regions, a feedback that is prevented in offline simulations. In land only simulations that neglect the local feedbacks, the simulated irrigation demand is 25% higher and the standard deviation of the mean irrigation rate is 60% smaller. These local-scale irrigation-driven feedbacks are not resolved in coarse-resolution climate models implying that use of these tools will overestimate irrigation demand. Future studies of irrigation demand must therefore account for the local land-atmosphere interactions by using coupled frameworks, at a spatial resolution that captures the key feedbacks.
Local Area Networks in Education: Overview, Applications, and Current Limitations.
ERIC Educational Resources Information Center
Piele, Philip K.
Local area networks (LAN) are privately owned communication systems that connect multivendor devices at high speed. As microcomputers become more common in schools, user interest in sharing information, software, and peripherals will increase. A basic understanding of the operation of all LAN's can be gained by knowing four elements: media,…
Local Longitudinal Microwave Instability Limits During Bunch Rotation
Ng, K. Y.
2012-10-23
Bunch width compression can be accomplished by rf rotating an elongated bunch with minimal energy spread. The formation of tails at the two bunch ends produces disconnected regions in many time-advance slices. The stability limits of longitudinal microwave growth for each time-advance slice of the beam will be affected. This effect is studied and the Keil-Schnell stability limits for such time-advance slices are derived. Application is made to the bunch-width compression in the Fermilab Compressor Ring, destined for pion and subsequently muon production
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…
Local Revenues for Schools: Limits and Options in California
ERIC Educational Resources Information Center
Perry, Mary; Edwards, Brian
2009-01-01
With K-12 schools representing the single largest expenditure in the state budget, education funding has been a central issue throughout the chaos that has recently characterized California's budget process. School districts throughout California have endured deep cuts in state funding, and more cuts are looming. But state law severely limits the…
49 CFR 174.2 - Limitation on actions by states, local governments, and Indian tribes.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 49 Transportation 2 2013-10-01 2013-10-01 false Limitation on actions by states, local governments... REGULATIONS CARRIAGE BY RAIL General Requirements § 174.2 Limitation on actions by states, local governments, and Indian tribes. Sections 5125 and 20106 of Title 49, United States Code, limit the authority of...
Quantum-limited estimation of continuous spontaneous localization
NASA Astrophysics Data System (ADS)
McMillen, S.; Brunelli, M.; Carlesso, M.; Bassi, A.; Ulbricht, H.; Paris, M. G. A.; Paternostro, M.
2017-01-01
We apply the formalism of quantum estimation theory to extract information about potential collapse mechanisms of the continuous spontaneous localization (CSL) form. In order to estimate the strength with which the field responsible for the CSL mechanism couples to massive systems, we consider the optomechanical interaction between a mechanical resonator and a cavity field. Our estimation strategy passes through the probing of either the state of the oscillator or that of the electromagnetic field that drives its motion. In particular, we concentrate on all-optical measurements, such as homodyne and heterodyne measurements. We also compare the performances of such strategies with those of a spin-assisted optomechanical system, where the estimation of the CSL parameter is performed through time-gated spinlike measurements.
NASA Astrophysics Data System (ADS)
Mund, Jens; Rehren, Karl-Henning; Schroer, Bert
2017-10-01
The problem of accounting for the quantum degrees of freedom in passing from massive higher-spin potentials to massless ones, and the inverse problem of ;fattening; massless tensor potentials of helicity ±h to their massive s = | h | counterparts, are solved - in a perfectly ghost-free approach - using ;string-localized fields;. This approach allows to overcome the Weinberg-Witten impediment against the existence of massless | h | ≥ 2 energy-momentum tensors, and to qualitatively and quantitatively resolve the van Dam-Veltman-Zakharov discontinuity concerning, e.g., very light gravitons, in the limit m → 0.
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 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,…
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.
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.
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
Local superconducting coupling in the strong-localization limit of ultrathin granular metal films
Haviland, D. B.; Jaeger, H. M.; Orr, B. G.; Goldman, A. M.
1989-07-01
The onset of fluctuations into the superconducting state, as identified bythe appearance of a local minimum in the resistance versus temperature, isfound to be coincident with the characteristic activation energy ofnormal-state conduction falling to a value of the order of the superconductingenergy gap of the material at /ital T/=0. The model of conduction used isvariable-range hopping with a Coulomb gap, appropriate to granular metals.
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.
Bradetich, Ryan; Dearien, Jason A; Grussling, Barry Jakob; Remaley, Gavin
2013-11-05
The present disclosure provides systems and methods for remote device management. According to various embodiments, a local intelligent electronic device (IED) may be in communication with a remote IED via a limited bandwidth communication link, such as a serial link. The limited bandwidth communication link may not support traditional remote management interfaces. According to one embodiment, a local IED may present an operator with a management interface for a remote IED by rendering locally stored templates. The local IED may render the locally stored templates using sparse data obtained from the remote IED. According to various embodiments, the management interface may be a web client interface and/or an HTML interface. The bandwidth required to present a remote management interface may be significantly reduced by rendering locally stored templates rather than requesting an entire management interface from the remote IED. According to various embodiments, an IED may comprise an encryption transceiver.
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.
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…
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
Reaching the ultimate performance limit given by non-local effects in BOTDA sensors
NASA Astrophysics Data System (ADS)
Dominguez-Lopez, Alejandro; Yang, Zhisheng; Soto, Marcelo A.; Angulo-Vinuesa, Xabier; Martin-Lopez, S.; Thevenaz, Luc; Gonzalez-Herraez, Miguel
2015-09-01
Non-local effects have been traditionally identified as one of the most limiting factors of the performance of Brillouin optical time-domain analyzers. These phenomena, directly linked with the energy gained/lost by the pump pulse, limit the probe power and ultimately the SNR of the system. Several solutions have been proposed, although none offers the possibility to increase the probe power until its limit, the onset of amplified spontaneous Brillouin scattering. In this work, we propose a technique that avoids non-local effects and permits to set the probe power at its maximum, reaching a 100 km sensing distance with 2 meter resolution.
NASA Astrophysics Data System (ADS)
Bongu, Sudhakara Reddy; Bisht, Prem B.; Namboodiri, Raman C. K.; Nayak, Pranati; Ramaprabhu, Sundara; Kelly, Thomas J.; Fallon, Colm; Costello, John T.
2014-08-01
The Pauli blocking limit and optical limiting threshold have been found to be modified following silver-nanoparticle decoration of functionalized hydrogen induced exfoliated graphene. Femtosecond Z-scan experiments have been used to measure the Pauli blocking range, optical limiting threshold, and the third order nonlinear susceptibility (χ(3)) values. The observed results have been explained by modified band structure of graphene in the presence of silver nanoparticles and their localized surface plasmon resonances.
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.
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
Automatic localization of cochlear implant electrodes in CTs with a limited intensity range
NASA Astrophysics Data System (ADS)
Zhao, Yiyuan; Dawant, Benoit M.; Noble, Jack H.
2017-02-01
Cochlear implants (CIs) are neural prosthetics for treating severe-to-profound hearing loss. Our group has developed an image-guided cochlear implant programming (IGCIP) system that uses image analysis techniques to recommend patientspecific CI processor settings to improve hearing outcomes. One crucial step in IGCIP is the localization of CI electrodes in post-implantation CTs. Manual localization of electrodes requires time and expertise. To automate this process, our group has proposed automatic techniques that have been validated on CTs acquired with scanners that produce images with an extended range of intensity values. However, there are many clinical CTs acquired with a limited intensity range. This limitation complicates the electrode localization process. In this work, we present a pre-processing step for CTs with a limited intensity range and extend the methods we proposed for full intensity range CTs to localize CI electrodes in CTs with limited intensity range. We evaluate our method on CTs of 20 subjects implanted with CI arrays produced by different manufacturers. Our method achieves a mean localization error of 0.21mm. This indicates our method is robust for automatic localization of CI electrodes in different types of CTs, which represents a crucial step for translating IGCIP from research laboratory to clinical use.
Plasmonic localized heating beyond the diffraction limit via magnetic polariton excitation
NASA Astrophysics Data System (ADS)
Alshehri, Hassan; Ying, Xiaoyan; Wang, Hao; Wang, Liping
2016-09-01
Optical localized heating in the nanoscale has recently attracted great attention due to its unique small hot spot size with high energy. However, the hot spot size is conventionally constrained by the diffraction limit. Plasmonic localized heating can provide solutions to this limitation in nanoscale patterning, cancer treatment, and data storage. Plasmonic approaches to overcome the diffraction limit in hot spot size have mainly utilized the excitation of surface plasmon or localized surface plasmon resonance. However, achieving plasmonic localized heating by the excitation of magnetic polariton has not been researched extensively yet. In this work, we numerically investigated the optical response of a nanoscale metamaterial composed of a gold nanowire array and a gold film separated by an ultrathin polymer spacer using ANSYS High Frequency Structural Simulator. A strong absorption peak at the wavelength of 760 nm was exhibited, and the underlying physical mechanism for the strong absorption was verified via the local electromagnetic field distribution to be magnetic resonance excitation. An inductor-capacitor circuit model was used to predict the magnetic resonance wavelength and compare with the numerical results for varied geometrical parameters. Volume loss density due to the strong local optical energy confinement was transferred as heat generation to an ANSYS thermal solver to obtain the local temperature profile. The steady state temperature profile shows an average temperature of 145 °C confined in a local area as small as 33 nm within the spacer, with a full-width at half-maximum of 50 nm along the x-direction. Moreover, the temperature rise from ambient drops to half its maximum value at a distance of 5 nm from the top of the spacer along the z-direction. This clearly demonstrates plasmonic localized heating beyond the diffraction limit via magnetic polariton excitation. Furthermore, the transient temperature profile shows that the system reached
One-dimensional three-state quantum walks: Weak limits and localization
NASA Astrophysics Data System (ADS)
Ko, Chul Ki; Segawa, Etsuo; Yoo, Hyun Jae
2016-11-01
We investigate one-dimensional three-state quantum walks. We find a formula for the moments of the weak limit distribution via a vacuum expectation of powers of a self-adjoint operator. We use this formula to fully characterize the localization of three-state quantum walks in one dimension. The localization is also characterized by investing the eigenvectors of the evolution operator for the quantum walk. As a byproduct we clarify the concepts of localization differently used in the literature. We also study the continuous part of the limit distribution. For typical examples we show that the continuous part is the same kind as that of two-state quantum walks. We provide with explicit expressions for the density of the weak limits of some three-state quantum walks.
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
The use of food imports to overcome local limits to growth
NASA Astrophysics Data System (ADS)
Porkka, Miina; Guillaume, Joseph H. A.; Siebert, Stefan; Schaphoff, Sibyll; Kummu, Matti
2017-04-01
There is a fundamental tension between population growth and carrying capacity, i.e., the population that could potentially be supported using the resources and technologies available at a given time. When population growth outpaces improvements in food production locally, food imports can avoid local limits and allow growth to continue. This import strategy is central to the debate on food security with continuing rapid growth of the world population. This highlights the importance of a quantitative global understanding of where the strategy is implemented, whether it has been successful, and what drivers are involved. We present an integrated quantitative analysis to answer these questions at sub-national and national scale for 1961-2009, focusing on water as the key limiting resource and accounting for resource and technology impacts on local carrying capacity. According to the sub-national estimates, food imports have nearly universally been used to overcome local limits to growth, affecting 3.0 billion people—81% of the population that is approaching or already exceeded local carrying capacity. This strategy is successful in 88% of the cases, being highly dependent on economic purchasing power. In the unsuccessful cases, increases in imports and local productivity have not kept pace with population growth, leaving 460 million people with insufficient food. Where the strategy has been successful, food security of 1.4 billion people has become dependent on imports. Whether or not this dependence on imports is considered desirable, it has policy implications that need to be taken into account.
Ai, Dexiecuo; Desjardins-Proulx, Philippe; Chu, Chengjin; Wang, Gang
2012-01-01
Repeatability of community composition has been a critical aspect for community structure, which is closely associated with community stability, predictability, conservation biology and ecological restoration. It has been shown that both immigration and local dispersal limitation can affect the community composition in both neutral and niche model. Hence, we use a spatially explicit individual-based model to investigate the potential influence of immigration rate and strength of local dispersal limitation on repeatability in both neutral and niche models. Similarity measures are used to quantify repeatability. We examine the repeatability of community composition among replicate communities (which means the same community repeats many times), and between niche and neutral replicate communities. We find the correlation between repeatability and immigration rate is positive in the neutral model and an inverted unimodal in the niche model. The correlation between repeatability and local dispersal distance is positive in the niche model and negative in the neutral model. High repeatability between niche communities and neutral communities is observed with high immigration rates or when high local dispersal distance appears in the niche model or low local dispersal distance in the neutral model. Our results show that repeatability of community composition is not only dependent on the types of community models (niche vs. neutrality) but also strongly determined by immigration rates and local dispersal limitation.
Jeudy, Christian; Ruffel, Sandrine; Freixes, Sandra; Tillard, Pascal; Santoni, Anne Lise; Morel, Sylvain; Journet, Etienne-Pascal; Duc, Gérard; Gojon, Alain; Lepetit, Marc; Salon, Christophe
2010-02-01
Adaptation of Medicago truncatula to local nitrogen (N) limitation was investigated to provide new insights into local and systemic N signaling. The split-root technique allowed a characterization of the local and systemic responses of NO(3)(-) or N(2)-fed plants to localized N limitation. (15)N and (13)C labeling were used to monitor plant nutrition. Plants expressing pMtENOD11-GUS and the sunn-2 hypernodulating mutant were used to unravel mechanisms involved in these responses. Unlike NO(3)(-)-fed plants, N(2)-fixing plants lacked the ability to compensate rapidly for a localized N limitation by up-regulating the N(2)-fixation activity of roots supplied elsewhere with N. However they displayed a long-term response via a growth stimulation of pre-existing nodules, and the generation of new nodules, likely through a decreased abortion rate of early nodulation events. Both these responses involve systemic signaling. The latter response is abolished in the sunn mutant, but the mutation does not prevent the first response. Local but also systemic regulatory mechanisms related to plant N status regulate de novo nodule development in Mt, and SUNN is required for this systemic regulation. By contrast, the stimulation of nodule growth triggered by systemic N signaling does not involve SUNN, indicating SUNN-independent signaling.
New limits on the violation of local position invariance of gravity
NASA Astrophysics Data System (ADS)
Shao, Lijing; Wex, Norbert
2013-08-01
Within the parameterized post-Newtonian (PPN) formalism, there could be an anisotropy of local gravity induced by an external matter distribution, even for a fully conservative metric theory of gravity. It reflects the breakdown of the local position invariance of gravity and, within the PPN formalism, is characterized by the Whitehead parameter ξ. We present three different kinds of observation, from the Solar system and radio pulsars, to constrain it. The most stringent limit comes from recent results on the extremely stable pulse profiles of solitary millisecond pulsars, that gives |\\hat{\\xi }| < 3.9 \\times 10^{-9} (95% CL), where the hat denotes the strong-field generalization of ξ. This limit is six orders of magnitude more constraining than the current best limit from superconducting gravimeter experiments. It can be converted into an upper limit of ˜4 × 10-16 on the spatial anisotropy of the gravitational constant. Communicated by C M Will
Plasmonic local heating beyond diffraction limit by the excitation of magnetic polariton
NASA Astrophysics Data System (ADS)
Alshehri, Hassan; Wang, Hao; Ma, Yanchao; Wang, Liping
2015-08-01
In recent years, optical local heating in the nanoscale has attracted great attention due to its unique features of small hot spot size and high energy density. Plasmonic local heating can provide solutions to several challenges in data storage and cancer treatment. Research conducted in this field to achieve plasmonic local heating has mainly utilized the excitation of localized surface plasmon (LSP) or surface plasmon resonance (SPR). However, achieving plasmonic local heating by the excitation of magnetic polariton (MP) has not been researched extensively yet. We numerically investigate the optical response of a nanostructure composed of a gold nanowire on a gold surface separated by a polymer spacer using the ANSYS High Frequency Structural Simulator (HFSS). The structure exhibits a strong absorption peak at the wavelength of 750 nm, and the underlying physical mechanism is verified by the local electromagnetic field distribution to be the magnetic resonance excitation. By incorporating the volume loss density due to the strong local optical energy confinement as the heat generation, nanoscale temperature distribution within the structure is numerically obtained with a thermal solver after assigning proper boundary conditions. The results show a maximum temperature of 158.5°C confined in a local area on the order of 35 nm within the ultrathin polymer layer, which clearly demonstrates the plasmonic local heating effect beyond diffraction limit by excitation of MP.
Samis, Karen E; López-Villalobos, Adriana; Eckert, Christopher G
2016-11-01
All species have limited geographic distributions; but the ecological and evolutionary mechanisms causing range limits are largely unknown. That many species' geographic range limits are coincident with niche limits suggests limited evolutionary potential of marginal populations to adapt to conditions experienced beyond the range. We provide a test of range limit theory by combining population genetic analysis of microsatellite polymorphisms with a transplant experiment within, at the edge of, and 60 km beyond the northern range of a coastal dune plant. Contrary to expectations, lifetime fitness increased toward the range limit with highest fitness achieved by most populations at and beyond the range edge. Genetic differentiation among populations was strong, with very low, nondirectional gene flow suggesting range limitation via constraints to dispersal. In contrast, however, local adaptation was negligible, and a distance-dependent decline in fitness only occurred for those populations furthest from home when planted beyond the range limit. These results challenge a commonly held assumption that stable range limits match niche limits, but also raise questions about the unique value of peripheral populations in expanding species' geographical ranges.
40 CFR 1400.11 - Limitation on dissemination to State and local government officials.
Code of Federal Regulations, 2010 CFR
2010-07-01
... 40 Protection of Environment 32 2010-07-01 2010-07-01 false Limitation on dissemination to State and local government officials. 1400.11 Section 1400.11 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY AND DEPARTMENT OF JUSTICE ACCIDENTAL RELEASE PREVENTION REQUIREMENTS; RISK MANAGEMENT...
40 CFR 1400.11 - Limitation on dissemination to State and local government officials.
Code of Federal Regulations, 2011 CFR
2011-07-01
... 40 Protection of Environment 33 2011-07-01 2011-07-01 false Limitation on dissemination to State and local government officials. 1400.11 Section 1400.11 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY AND DEPARTMENT OF JUSTICE ACCIDENTAL RELEASE PREVENTION REQUIREMENTS; RISK MANAGEMENT PROGRAMS UNDER THE CLEAN AIR ACT SECTION 112(r)(7)...
40 CFR 1400.11 - Limitation on dissemination to State and local government officials.
Code of Federal Regulations, 2012 CFR
2012-07-01
... 40 Protection of Environment 34 2012-07-01 2012-07-01 false Limitation on dissemination to State and local government officials. 1400.11 Section 1400.11 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY AND DEPARTMENT OF JUSTICE ACCIDENTAL RELEASE PREVENTION REQUIREMENTS; RISK MANAGEMENT PROGRAMS UNDER THE CLEAN AIR ACT SECTION 112(r)(7)...
40 CFR 1400.11 - Limitation on dissemination to State and local government officials.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 40 Protection of Environment 34 2013-07-01 2013-07-01 false Limitation on dissemination to State and local government officials. 1400.11 Section 1400.11 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY AND DEPARTMENT OF JUSTICE ACCIDENTAL RELEASE PREVENTION REQUIREMENTS; RISK MANAGEMENT PROGRAMS UNDER THE CLEAN AIR ACT SECTION 112(r)(7)...
Reflective Optical and Microwave Limiters based on Non-Linear Localized Modes
NASA Astrophysics Data System (ADS)
Makri, Eleana; Ramezani, Hamidreza; Kottos, Tsampikos; Vitebskiy, Ilya
2014-03-01
A limiter is a structure that controls signal transport by allowing the transmission of low intensity signals while blocking signals with excessively high intensity. Existing designs lead to the absorption of excessive high intensity which can cause their overheating and eventually their (self-)destruction. We introduce the concept of reflective limiter which is based on resonance transmission via a non-linear localized mode. Such a limiter does not absorb the high level radiation, but rather reflects it back to space. Importantly, the total reflection occurs within a broad frequency range and for any direction of incidence. The proposed concept can be applied to optical and microwave frequencies.
Limits of slow sound propagation and transparency in lossy, locally resonant periodic structures
NASA Astrophysics Data System (ADS)
Theocharis, G.; Richoux, O.; Romero García, V.; Merkel, A.; Tournat, V.
2014-09-01
We investigate sound propagation in lossy, locally resonant periodic structures by studying an air-filled tube periodically loaded with Helmholtz resonators and taking into account the intrinsic viscothermal losses. In particular, by tuning the resonator with the Bragg gap in this prototypical locally resonant structure, we study the limits and various characteristics of slow sound propagation. While in the lossless case the overlapping of the gaps results in slow-sound-induced transparency of a narrow frequency band surrounded by a strong and broadband gap, the inclusion of the unavoidable losses imposes limits to the slowdown factor and the maximum transmission. Experiments, theory, and finite element simulations have been used for the characterization of acoustic wave propagation by tuning the Helmholtz/Bragg frequencies and the total amount of loss both for infinite and finite lattices. This study contributes to the field of locally resonant acoustic metamaterials and slow sound applications.
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.
Intragrain charge transport in kesterite thin films—Limits arising from carrier localization
Hempel, Hannes; Redinger, Alex; Repins, Ingrid; ...
2016-11-03
Intragrain charge carrier mobilities measured by time-resolved terahertz spectroscopy in state of the art Cu2ZnSn(S,Se)4 kesterite thin films are found to increase from 32 to 140 cm2V-1s-1 with increasing Se content. The mobilities are limited by carrier localization on the nanometer-scale, which takes place within the first 2 ps after carrier excitation. The localization strength obtained from the Drude-Smith model is found to be independent of the excited photocarrier density. This is in accordance with bandgap fluctuations as a cause of the localized transport. Lastly, charge carrier localization is a general issue in the probed kesterite thin films, which weremore » deposited by coevaporation, colloidal inks, and sputtering followed by annealing with varying Se/S contents and yield 4.9%-10.0% efficiency in the completed device.« less
Intragrain charge transport in kesterite thin films—Limits arising from carrier localization
Hempel, Hannes; Redinger, Alex; Repins, Ingrid; Moisan, Camille; Larramona, Gerardo; Dennler, Gilles; Handwerg, Martin; Fischer, Saskia F.; Eichberger, Rainer; Unold, Thomas
2016-11-03
Intragrain charge carrier mobilities measured by time-resolved terahertz spectroscopy in state of the art Cu_{2}ZnSn(S,Se)_{4} kesterite thin films are found to increase from 32 to 140 cm^{2}V^{-1}s^{-1} with increasing Se content. The mobilities are limited by carrier localization on the nanometer-scale, which takes place within the first 2 ps after carrier excitation. The localization strength obtained from the Drude-Smith model is found to be independent of the excited photocarrier density. This is in accordance with bandgap fluctuations as a cause of the localized transport. Lastly, charge carrier localization is a general issue in the probed kesterite thin films, which were deposited by coevaporation, colloidal inks, and sputtering followed by annealing with varying Se/S contents and yield 4.9%-10.0% efficiency in the completed device.
Intragrain charge transport in kesterite thin films—Limits arising from carrier localization
NASA Astrophysics Data System (ADS)
Hempel, Hannes; Redinger, Alex; Repins, Ingrid; Moisan, Camille; Larramona, Gerardo; Dennler, Gilles; Handwerg, Martin; Fischer, Saskia F.; Eichberger, Rainer; Unold, Thomas
2016-11-01
Intragrain charge carrier mobilities measured by time-resolved terahertz spectroscopy in state of the art Cu2ZnSn(S,Se)4 kesterite thin films are found to increase from 32 to 140 cm2 V-1 s-1 with increasing Se content. The mobilities are limited by carrier localization on the nanometer-scale, which takes place within the first 2 ps after carrier excitation. The localization strength obtained from the Drude-Smith model is found to be independent of the excited photocarrier density. This is in accordance with bandgap fluctuations as a cause of the localized transport. Charge carrier localization is a general issue in the probed kesterite thin films, which were deposited by coevaporation, colloidal inks, and sputtering followed by annealing with varying Se/S contents and yield 4.9%-10.0% efficiency in the completed device.
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.
Building local human resources to implement SLMTA with limited donor funding: The Ghana experience
Nkrumah, Bernard; van der Puije, Beatrice; Bekoe, Veronica; Adukpo, Rowland; Kotey, Nii A.; Yao, Katy; Fonjungo, Peter N.; Luman, Elizabeth T.; Duh, Samuel; Njukeng, Patrick A.; Addo, Nii A.; Khan, Fazle N.; Woodfill, Celia J.I.
2016-01-01
Background In 2009, Ghana adopted the Strengthening Laboratory Management Toward Accreditation (SLMTA) programme in order to improve laboratory quality. The programme was implemented successfully with limited donor funding and local human resources. Objectives To demonstrate how Ghana, which received very limited PEPFAR funding, was able to achieve marked quality improvement using local human resources. Method Local partners led the SLMTA implementation and local mentors were embedded in each laboratory. An in-country training-of-trainers workshop was conducted in order to increase the pool of local SLMTA implementers. Three laboratory cohorts were enrolled in SLMTA in 2011, 2012 and 2013. Participants from each cohort attended in a series of three workshops interspersed with improvement projects and mentorship. Supplemental training on internal audit was provided. Baseline, exit and follow-up audits were conducted using the Stepwise Laboratory Quality Improvement Process Towards Accreditation (SLIPTA) checklist. In November 2013, four laboratories underwent official SLIPTA audits by the African Society for Laboratory Medicine (ASLM). Results The local SLMTA team successfully implemented three cohorts of SLMTA in 15 laboratories. Seven out of the nine laboratories that underwent follow-up audits have reached at least one star. Three out of the four laboratories that underwent official ASLM audits were awarded four stars. Patient satisfaction increased from 25% to 70% and sample rejection rates decreased from 32% to 10%. On average, $40 000 was spent per laboratory to cover mentors' salaries, SLMTA training and improvement project support. Conclusion Building in-country capacity through local partners is a sustainable model for improving service quality in resource-constrained countries such as Ghana. Such models promote country ownership, capacity building and the use of local human resources for the expansion of SLMTA. PMID:26937417
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.
Rotationally invariant proof of Bell's theorem without inequalities
Cabello, Adan
2003-03-01
The singlet state of two spin-(3/2) particles allows a proof of Bell's theorem without inequalities with two distinguishing features: any local observable can be regarded as an Einstein-Podolsky-Rosen element of reality, and the contradiction with local realism occurs not only for some specific local observables but for any rotation whereof.
Seizure Semiology: Its Value and Limitations in Localizing the Epileptogenic Zone
Lüders, Hans O.
2012-01-01
Epilepsy surgery has become an important treatment option in patients with medically refractory epilepsy. The ability to precisely localize the epileptogenic zone is crucial for surgical success. The tools available for localization of the epileptogenic zone are limited. Seizure semiology is a simple and cost effective tool that allows localization of the symptomatogenic zone which either overlaps or is in close proximity of the epileptogenic zone. This becomes particularly important in cases of MRI negative focal epilepsy. The ability to video record seizures made it possible to discover new localizing signs and quantify the sensitivity and specificity of others. Ideally the signs used for localization should fulfill these criteria; 1) Easy to identify and have a high inter-rater reliability, 2) It has to be the first or one of the earlier components of the seizure in order to have localizing value. Later symptoms or signs are more likely to be due to ictal spread and may have only a lateralizing value. 3) The symptomatogenic zone corresponding to the recorded ictal symptom has to be clearly defined and well documented. Reproducibility of the initial ictal symptoms with cortical stimulation identifies the corresponding symptomatogenic zone. Unfortunately, however, not all ictal symptoms can be reproduced by focal cortical stimulation. Therefore, the problem the clinician faces is trying to deduce the epileptogenic zone from the seizure semiology. The semiological classification system is particularly useful in this regard. We present the known localizing and lateralizing signs based on this system. PMID:23323131
Seizure semiology: its value and limitations in localizing the epileptogenic zone.
Tufenkjian, Krikor; Lüders, Hans O
2012-12-01
Epilepsy surgery has become an important treatment option in patients with medically refractory epilepsy. The ability to precisely localize the epileptogenic zone is crucial for surgical success. The tools available for localization of the epileptogenic zone are limited. Seizure semiology is a simple and cost effective tool that allows localization of the symptomatogenic zone which either overlaps or is in close proximity of the epileptogenic zone. This becomes particularly important in cases of MRI negative focal epilepsy. The ability to video record seizures made it possible to discover new localizing signs and quantify the sensitivity and specificity of others. Ideally the signs used for localization should fulfill these criteria; 1) Easy to identify and have a high inter-rater reliability, 2) It has to be the first or one of the earlier components of the seizure in order to have localizing value. Later symptoms or signs are more likely to be due to ictal spread and may have only a lateralizing value. 3) The symptomatogenic zone corresponding to the recorded ictal symptom has to be clearly defined and well documented. Reproducibility of the initial ictal symptoms with cortical stimulation identifies the corresponding symptomatogenic zone. Unfortunately, however, not all ictal symptoms can be reproduced by focal cortical stimulation. Therefore, the problem the clinician faces is trying to deduce the epileptogenic zone from the seizure semiology. The semiological classification system is particularly useful in this regard. We present the known localizing and lateralizing signs based on this system.
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.
Evaluation of Forming Limit by the 3 Dimensional Local Bifurcation Theory
Nishimura, Ryuichi; Nakazawa, Yoshiaki; Ito, Koichi; Uemura, Gen; Mori, Naomichi
2007-05-17
A theoretical prediction and evaluation method for the sheet metal formability is developed on the basis of the three-dimensional local bifurcation theory previously proposed by authors. The forming limit diagram represented on the plane defined by the ratio of stress component to work-hardening rate is perfectly independent of plastic strain history. The upper and the lower limit of the sheet formability are indicated by the 3D critical line and the Stoeren-Rice's critical line on this plane, respectively. In order to verify the above mentioned behavior of the proposed forming limit diagram, the experimental research is also conducted. From the standpoint of the mechanical instability theory, a new concept called instability factor is introduced. It represents a degree of acceleration by current stress for developing the local bifurcation mode toward a fracture. The instability factor provides a method to evaluate a forming allowance which is useful to appropriate identification for a forming limit and to optimize the forming condition. The proposed criterion provides not only the moment to initiate the necking but also the local bifurcation mode vector and the direction of necking line.
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
What can local and geographic population limits tell us about distributions?
Sexton, Jason P; Dickman, Erin E
2016-01-01
Understanding the evolutionary and ecological factors that determine plant distributions is of primary importance in botanical research. These factors may vary in predictable ways across different spatial scales, and thus, we can leverage scale to reveal the underlying processes limiting plant distributions. We review various research considerations across local and geographic scales, including the investigation of dispersal and habitat limitation, evolutionary factors, abiotic and biotic factors, and research logistics. We also present two case studies, slender monkeyflower (Mimulus leptaleus) and cut-leaf monkeyflower (Mimulus laciniatus), in the California Sierra Nevada. At a local spatial scale (within 50 m), no seeds were produced from plants sown at sites located just beyond known patches of M. leptaleus, but within the species' geographic range. At a much broader spatial scale (kilometers), at the highest and lowest elevations of the species' range, we found greatly reduced abundance and fecundity in plants sown outside of the geographic range limits of M. laciniatus. These cases illustrate two contrasting spatial scales, yet agree in their illustration of strong habitat limitation. We end by discussing future avenues of research and by suggesting ways botanical researchers can frame their studies to maximize information gained on species requirements, distribution limits, and conservation among varying spatial scales. © 2016 Botanical Society of America.
A locally-blazed ant trail achieves efficient collective navigation despite limited information.
Fonio, Ehud; Heyman, Yael; Boczkowski, Lucas; Gelblum, Aviram; Kosowski, Adrian; Korman, Amos; Feinerman, Ofer
2016-11-05
Any organism faces sensory and cognitive limitations which may result in maladaptive decisions. Such limitations are prominent in the context of groups where the relevant information at the individual level may not coincide with collective requirements. Here, we study the navigational decisions exhibited by Paratrechina longicornis ants as they cooperatively transport a large food item. These decisions hinge on the perception of individuals which often restricts them from providing the group with reliable directional information. We find that, to achieve efficient navigation despite partial and even misleading information, these ants employ a locally-blazed trail. This trail significantly deviates from the classical notion of an ant trail: First, instead of systematically marking the full path, ants mark short segments originating at the load. Second, the carrying team constantly loses the guiding trail. We experimentally and theoretically show that the locally-blazed trail optimally and robustly exploits useful knowledge while avoiding the pitfalls of misleading information.
Effects of hole localization on limiting p-type conductivity in oxide and nitride semiconductors
Lyons, J. L.; Janotti, A.; Van de Walle, C. G.
2014-01-07
We examine how hole localization limits the effectiveness of substitutional acceptors in oxide and nitride semiconductors and explain why p-type doping of these materials has proven so difficult. Using hybrid density functional calculations, we find that anion-site substitutional impurities in AlN, GaN, InN, and ZnO lead to atomic-like states that localize on the impurity atom itself. Substitution with cation-site impurities, on the other hand, triggers the formation of polarons that become trapped on nearest-neighbor anions, generally leading to large ionization energies for these acceptors. Unlike shallow effective-mass acceptors, these two types of deep acceptors couple strongly with the lattice, significantly affecting the optical properties and severely limiting prospects for achieving p-type conductivity in these wide-band-gap materials.
Code of Federal Regulations, 2013 CFR
2013-01-01
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Code of Federal Regulations, 2010 CFR
2010-01-01
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Code of Federal Regulations, 2011 CFR
2011-01-01
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Code of Federal Regulations, 2012 CFR
2012-01-01
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Code of Federal Regulations, 2014 CFR
2014-01-01
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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.
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
How colorful are fruits? Limited color diversity in fleshy fruits on local and global scales.
Stournaras, Kalliope E; Lo, Eugenia; Böhning-Gaese, Katrin; Cazetta, Eliana; Dehling, D Matthias; Schleuning, Matthias; Stoddard, Mary Caswell; Donoghue, Michael J; Prum, Richard O; Schaefer, H Martin
2013-04-01
The colors of fleshy fruits are considered to be a signal to seed-dispersing animals, but their diversity remains poorly understood. Using an avian color space to derive a sensory morphospace for fruit color, we tested four hypotheses of fruit color diversity: fruit colors occupy a limited area of the color space; they are less diverse than flower colors; fruit colors within localities are similar to each other; and fruit color diversity reflects phylogeny. The global fruit color diversity of 948 primarily bird-dispersed plant species and the color diversity of localities were compared with null models of random, unconstrained evolution of fruit color. Fruit color diversity was further compared with the diversity of 1300 flower colors. Tests of phylogenetic effects on fruit color were used to assess the degree of correspondence with phylogeny. Global and local fruit color diversity was limited compared with null models and fruits have achieved only half the color diversity of flowers. Interestingly, we found little indication of phylogenetic conservatism. Constraints resulting from the chemical properties of pigments probably limit global fruit and flower color diversity. Different types of selection on fruits and flowers may further explain the smaller color diversity of fruits.
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)
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
Upper limit of applicability of the local similarity theory in the stable atmospheric boundary layer
NASA Astrophysics Data System (ADS)
Grachev, A. A.; Andreas, E. L.; Fairall, C. W.; Guest, P. S.; Persson, P. O. G.
2012-04-01
The applicability of the classical Monin-Obukhov similarity theory (1954) has been limited by constant flux assumption, which is valid in a narrow range z/L < 0.1 in the stable boundary layer (SBL). Nieuwstadt (1984) extended the range of applicability of the original theory using the local scaling (height-dependent) in place of the surface scaling, but the limits of applicability of the local similarity theory in the SBL have been blurred. Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to clarify this issue. Based on spectral analysis of wind velocity and temperature fluctuations, it is shown that when both gradient Richardson number, Ri, and flux Richardson number, Rf, exceed a "critical value" about 0.2-0.25, inertial subrange associated with a Kolmogorov cascade dies out and vertical turbulent fluxes become small. Some small-scale turbulence survives even in the supercritical regime but this is non-Kolmogorov turbulence and it decays rapidly with further increasing stability. The similarity theory is based on the turbulent fluxes in the high frequency part of the spectra associated with energy-containing/flux-carrying eddies. Spectral densities in this high-frequency band collapse along with the Kolmogorov energy cascade. Therefore, applicability of the local Monin-Obukhov similarity theory in the SBL is limited by inequalities Ri < Ri_cr and Rf < Rf_cr (however, Rf_cr = 0.2-0.25 is a primary threshold). Application of this prerequisite shows that both the flux-profile and flux-variances relationships follow to the classical Monin-Obukhov local z-less predictions after the irrelevant cases have been filtered out.
Overcoming limits set by scarce resources - role of local food production and food imports
NASA Astrophysics Data System (ADS)
Porkka, Miina; Guillaume, Joseph H. A.; Schaphoff, Sibyll; Siebert, Stefan; Gerten, Dieter; Kummu, Matti
2017-04-01
There is a fundamental tension between population growth and carrying capacity, i.e. the population that could potentially be supported using the resources and technologies available at a given time. This makes the assessments of resource use and agricultural productivity central to the debate on future food security. Local carrying capacity can be increased by expanding (e.g. through land conversion and irrigation infrastructure) or intensifying (e.g. through technologies and practices that increase efficiency) the resource use in agriculture. Food imports can be considered another way of overcoming current local limits and continuing growth beyond the local human-carrying capacity. Focusing on water as the key limiting resource, we performed a global assessment of the capacity for food self-sufficiency at sub-national and national scale for 1961-2009, taking into account the availability of both green and blue water as well as technology and management practices affecting water productivity at a given time, and using the hydrology and agriculture model LPJmL as our primary tool. Furthermore, we examined the use of food imports as a strategy to increase carrying capacity in regions where the potential for food self-sufficiency was limited by water availability and productivity. We found that the capacity for food self-sufficiency reduced notably during the study period due to the rapid population growth that outpaced the substantial improvements in water productivity. In 2009 more than a third (2.2 billion people) of the world's population lived in areas where sufficient food production to meet the needs of the population was not possible, and some 800 million people more were approaching this threshold. Food imports have nearly universally been used to overcome these local limits to growth, though the success of this strategy has been highly dependent on economic purchasing power. In the unsuccessful cases, increases in imports and local productivity have not
Ståhl, Agneta; Månsson Lexell, Eva
2017-01-24
Previous research of how people with stroke manage public transport has mainly focused on barriers due to physical limitations whereas the influence of cognitive limitations is scarce. There is also a lack of knowledge of facilitators that can help to overcome these barriers. The aim of this study was to describe facilitators for travelling with public transport, e.g. local buses, among people with mild cognitive limitations after stroke. A multiple case study research design was used, where quantitative and qualitative data were utilized, and analysed according to a mixed methods design. The case descriptions reveal how people with mild cognitive limitations after stroke manage their trips but constantly have to be prepared to solve problems to unexpected events. Personal characteristics and other individual strategies together with support and solutions from society were important facilitators for travelling with bus. This study takes a new approach by specifically describing facilitators for travelling with public transport among people with mild cognitive limitations after stroke. To facilitate participation in society for this particular traveller group, occupational therapists have an important role when new technology and interventions that target bus travels, and other modes of transport are developed.
The Nielsen-Ninomiya theorem, \\renewcommand{\\P}{{{ P}}} \
NASA Astrophysics Data System (ADS)
Chernodub, M. N.
2017-09-01
The Nielsen-Ninomiya theorem implies that any local, Hermitian and translationally invariant lattice action in even-dimensional spacetime possesses an equal number of left- and right-handed chiral fermions. We argue that if one sacrifices the property of Hermiticity while keeping the locality and translation invariance, and imposing invariance of the action under the space-time ( \\renewcommand{\\P}{{{ P}}} \
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.
Rossi, Tuomas P. Sakko, Arto; Puska, Martti J.; Lehtola, Susi; Nieminen, Risto M.
2015-03-07
We present an approach for generating local numerical basis sets of improving accuracy for first-principles nanoplasmonics simulations within time-dependent density functional theory. The method is demonstrated for copper, silver, and gold nanoparticles that are of experimental interest but computationally demanding due to the semi-core d-electrons that affect their plasmonic response. The basis sets are constructed by augmenting numerical atomic orbital basis sets by truncated Gaussian-type orbitals generated by the completeness-optimization scheme, which is applied to the photoabsorption spectra of homoatomic metal atom dimers. We obtain basis sets of improving accuracy up to the complete basis set limit and demonstrate that the performance of the basis sets transfers to simulations of larger nanoparticles and nanoalloys as well as to calculations with various exchange-correlation functionals. This work promotes the use of the local basis set approach of controllable accuracy in first-principles nanoplasmonics simulations and beyond.
Kawamoto, Tatsuro; Kabashima, Yoshiyuki
2015-06-01
Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both un-normalized and normalized Laplacians in sparse graphs. The detectability threshold is the critical point at which the result of the spectral method is completely uncorrelated to the planted partition. We also analyze whether the localization of eigenvectors affects the partitioning performance in the detectable region. We use the replica method, which is often used in the field of spin-glass theory, and focus on the case of bisection. We show that the gap between the estimated threshold for the spectral method and the threshold obtained from Bayesian inference is considerable in sparse graphs, even without eigenvector localization. This gap closes in a dense limit.
NASA Astrophysics Data System (ADS)
Kawamoto, Tatsuro; Kabashima, Yoshiyuki
2015-06-01
Investigating the performance of different methods is a fundamental problem in graph partitioning. In this paper, we estimate the so-called detectability threshold for the spectral method with both un-normalized and normalized Laplacians in sparse graphs. The detectability threshold is the critical point at which the result of the spectral method is completely uncorrelated to the planted partition. We also analyze whether the localization of eigenvectors affects the partitioning performance in the detectable region. We use the replica method, which is often used in the field of spin-glass theory, and focus on the case of bisection. We show that the gap between the estimated threshold for the spectral method and the threshold obtained from Bayesian inference is considerable in sparse graphs, even without eigenvector localization. This gap closes in a dense limit.
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.
Phase space localization for anti-de Sitter quantum mechanics and its zero curvature limit
NASA Technical Reports Server (NTRS)
Elgradechi, Amine M.
1993-01-01
Using techniques of geometric quantization and SO(sub 0)(3,2)-coherent states, a notion of optimal localization on phase space is defined for the quantum theory of a massive and spinning particle in anti-de Sitter space time. It is shown that this notion disappears in the zero curvature limit, providing one with a concrete example of the regularizing character of the constant (nonzero) curvature of the anti-de Sitter space time. As a byproduct a geometric characterization of masslessness is obtained.
Local dissipation limits the dynamics of impacting droplets on smooth and rough substrates
NASA Astrophysics Data System (ADS)
Wang, Yuli; Amberg, Gustav; Carlson, Andreas
2017-03-01
A droplet that impacts onto a solid substrate deforms in a complex dynamics. To extract the principal mechanisms that dominate this dynamics, we deploy numerical simulations based on the phase field method. Direct comparison with experiments suggests that a dissipation local to the contact line limits the droplet spreading dynamics and its scaled maximum spreading radius βmax. By assuming linear response through a drag force at the contact line, our simulations rationalize experimental observations for droplet impact on both smooth and rough substrates, measured through a single contact line friction parameter μf. Moreover, our analysis shows that dissipation at the contact line can limit the dynamics and we describe βmax by the scaling law βmax˜(Reμl/μf) 1 /2 that is a function of the droplet viscosity (μl) and its Reynolds number (Re).
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.
The value of local normal limits in quantitative Thallium-201 CZT MPI SPECT.
Gregoire, Bastien; Pina-Jomir, Géraldine; Bontemps, Laurence; Janier, Marc; Scheiber, Christian
2017-04-01
Considering the distinctive characteristics of CZT detectors, automatic quantification of ischemia using normal limits included with software package may deliver suboptimal results for CAD detection. The present study aims to evaluate the benefits of creating normal limits specific to a local population and laboratory protocol. Two groups were selected from patients who had undergone a CZT MPI. Normal limits were generated with the QPS application based on the population with low likelihood of CAD. Using the vendor-supplied and the population-specific normal limits i-TPD and vessel-specific SDS results obtained for patients who had subsequently undergone coronary angiography were compared with coronary angiography data. A weak correlation was observed for low i-TPD (stress TPD minus rest TPD) and SDS values. Both databases gave similar values for the area under the ROC curve concerning i-TPD (0.75 to 0.74) and SDS results (0.72 to 0.75 for the LAD, 0.62 to 0.64 for the LCx, and 0.63 to 0.67 for the RCA). Sensitivity (60%), specificity (78%), and predictive positive (84%) and negative (52%) values were also similar with a diagnostic and prognostic threshold value. The use of a population-specific created database did not influence the diagnostic value of thallium-201 MPI QPS results using a CZT camera.
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.
Critical properties of the Anderson localization transition and the high-dimensional limit
NASA Astrophysics Data System (ADS)
Tarquini, E.; Biroli, G.; Tarzia, M.
2017-03-01
In this paper we present a thorough study of transport, spectral, and wave-function properties at the Anderson localization critical point in spatial dimensions d =3 , 4, 5, 6. Our aim is to analyze the dimensional dependence and to assess the role of the d →∞ limit provided by Bethe lattices and treelike structures. Our results strongly suggest that the upper critical dimension of Anderson localization is infinite. Furthermore, we find that dU=∞ is a much better starting point compared to dL=2 to describe even three-dimensional systems. We find that critical properties and finite-size scaling behavior approach by increasing d those found for Bethe lattices: the critical state becomes an insulator characterized by Poisson statistics and corrections to the thermodynamics limit become logarithmic in the number N of lattice sites. In the conclusion, we present physical consequences of our results, propose connections with the nonergodic delocalized phase suggested for the Anderson model on infinite-dimensional lattices, and discuss perspectives for future research studies.
A locally-blazed ant trail achieves efficient collective navigation despite limited information
Fonio, Ehud; Heyman, Yael; Boczkowski, Lucas; Gelblum, Aviram; Kosowski, Adrian; Korman, Amos; Feinerman, Ofer
2016-01-01
Any organism faces sensory and cognitive limitations which may result in maladaptive decisions. Such limitations are prominent in the context of groups where the relevant information at the individual level may not coincide with collective requirements. Here, we study the navigational decisions exhibited by Paratrechina longicornis ants as they cooperatively transport a large food item. These decisions hinge on the perception of individuals which often restricts them from providing the group with reliable directional information. We find that, to achieve efficient navigation despite partial and even misleading information, these ants employ a locally-blazed trail. This trail significantly deviates from the classical notion of an ant trail: First, instead of systematically marking the full path, ants mark short segments originating at the load. Second, the carrying team constantly loses the guiding trail. We experimentally and theoretically show that the locally-blazed trail optimally and robustly exploits useful knowledge while avoiding the pitfalls of misleading information. DOI: http://dx.doi.org/10.7554/eLife.20185.001 PMID:27815944
Beamspace fast fully adaptive brain source localization for limited data sequences
NASA Astrophysics Data System (ADS)
Ravan, Maryam
2017-05-01
In the electroencephalogram (EEG) or magnetoencephalogram (MEG) context, brain source localization methods that rely on estimating second order statistics often fail when the observations are taken over a short time interval, especially when the number of electrodes is large. To address this issue, in previous study, we developed a multistage adaptive processing called fast fully adaptive (FFA) approach that can significantly reduce the required sample support while still processing all available degrees of freedom (DOFs). This approach processes the observed data in stages through a decimation procedure. In this study, we introduce a new form of FFA approach called beamspace FFA. We first divide the brain into smaller regions and transform the measured data from the source space to the beamspace in each region. The FFA approach is then applied to the beamspaced data of each region. The goal of this modification is to benefit the correlation sensitivity reduction between sources in different brain regions. To demonstrate the performance of the beamspace FFA approach in the limited data scenario, simulation results with multiple deep and cortical sources as well as experimental results are compared with regular FFA and widely used FINE approaches. Both simulation and experimental results demonstrate that the beamspace FFA method can localize different types of multiple correlated brain sources in low signal to noise ratios more accurately with limited data.
Crop response to localized organic amendment in soils with limiting physical properties
NASA Astrophysics Data System (ADS)
Lordan, Joan; Pascual, Miquel; Fonseca, Francisco; Villar, Josep Maria; Montilla, Victor; Papió, Josep; Rufat, Josep
2013-04-01
This 2-year study evaluated the use of rice husk as a localized organic amendment in a soil with limiting physical properties. The research was conducted in a commercial peach orchard planted in 2011 using a ridge planting system. Six soil and water management treatments were evaluated in 18 experimental units, which were set up in the field using a randomized complete block design. The treatments were compared both in terms of soil physical properties and crop response. Soil amendment with rice husk was the most effective technique. It improved soil conditions (soil infiltration and soil porosity), providing a better soil environment for root activity and thereby resulted in better crop performance. Concerning growth parameters, the amended treatment presented the highest overall values without negatively affecting crop water status. These techniques were suitable for mitigating the effects of soils with limiting physical conditions. Localized applications of amendments, as proposed in this work, imply an important reduction in application rates. It is important to consider an efficient use of by-products since there is a growing interest in industrial and agronomical exploitations.
Maier, Stefan A; Kik, Pieter G; Atwater, Harry A; Meltzer, Sheffer; Harel, Elad; Koel, Bruce E; Requicha, Ari A G
2003-04-01
Achieving control of light-material interactions for photonic device applications at nanoscale dimensions will require structures that guide electromagnetic energy with a lateral mode confinement below the diffraction limit of light. This cannot be achieved by using conventional waveguides or photonic crystals. It has been suggested that electromagnetic energy can be guided below the diffraction limit along chains of closely spaced metal nanoparticles that convert the optical mode into non-radiating surface plasmons. A variety of methods such as electron beam lithography and self-assembly have been used to construct metal nanoparticle plasmon waveguides. However, all investigations of the optical properties of these waveguides have so far been confined to collective excitations, and direct experimental evidence for energy transport along plasmon waveguides has proved elusive. Here we present observations of electromagnetic energy transport from a localized subwavelength source to a localized detector over distances of about 0.5 microm in plasmon waveguides consisting of closely spaced silver rods. The waveguides are excited by the tip of a near-field scanning optical microscope, and energy transport is probed by using fluorescent nanospheres.
Moore, Kara A.; Stanton, Maureen L.
2014-01-01
Adaptation to novel conditions beyond current range boundaries requires the presence of suitable sites within dispersal range, but may be impeded when emigrants encounter poor habitat and sharply different selection pressures. We investigated fine-scale spatial heterogeneity in ecological dynamics and selection at a local population boundary of the annual plant Gilia tricolor. In two years, we planted G. tricolor seeds in core habitat, margin habitat at the edge of the local range, and exterior habitat in order to measure spatial and temporal variation in habitat quality, opportunity for selection, and selection on phenotypic traits. We found a striking decline in average habitat quality with distance from the population core, yet some migrant seeds were successful in suitable, unoccupied microsites at and beyond the range boundary. Total and direct selection on four out of five measured phenotypic traits varied across habitat zones, as well as between years. Moreover, the margin habitat often exerted unique selection pressures that were not intermediate between core and exterior habitats. This study reveals that a combination of ecological and evolutionary forces, including propagule limitation, variation in habitat quality and spatial heterogeneity in phenotypic selection may reduce opportunities for adaptive range expansion, even across a very local population boundary. PMID:24717472
Local and regional controls of phylogenetic structure at the high-latitude range limits of corals.
Sommer, Brigitte; Sampayo, Eugenia M; Beger, Maria; Harrison, Peter L; Babcock, Russ C; Pandolfi, John M
2017-08-30
Understanding how range-edge populations will respond to climate change is an urgent research priority. Here, we used a phylogenetic community ecology approach to examine how ecological and evolutionary processes shape biodiversity patterns of scleractinian corals at their high-latitude range limits in eastern Australia. We estimated phylogenetic signal in seven ecologically important functional traits and conducted tests of phylogenetic structure at local and regional scales using the net relatedness (NRI) and nearest taxon indices (NTI) for the presence/absence and abundance data. Regional tests showed light phylogenetic clustering, indicating that coral species found in this subtropical-to-temperate transition zone are more closely related to each other than are species on the nearby, more northerly Great Barrier Reef. Local tests revealed variable patterns of phylogenetic clustering and overdispersion and higher than expected phylogenetic turnover among sites. In combination, these results are broadly consistent with the hierarchical filtering model, whereby species pass through a regional climatic filter based on their tolerances for marginal conditions and subsequently segregate into local assemblages according to the relative strength of habitat filtering and species interactions. Conservatism of tested traits suggests that corals will likely track their niches with climate change. Nevertheless, high turnover of lineages among sites indicates that range shifts will probably vary among species and highlights the vulnerability and conservation significance of high-latitude reefs. © 2017 The Author(s).
Moore, Kara A; Stanton, Maureen L
2014-01-01
Adaptation to novel conditions beyond current range boundaries requires the presence of suitable sites within dispersal range, but may be impeded when emigrants encounter poor habitat and sharply different selection pressures. We investigated fine-scale spatial heterogeneity in ecological dynamics and selection at a local population boundary of the annual plant Gilia tricolor. In two years, we planted G. tricolor seeds in core habitat, margin habitat at the edge of the local range, and exterior habitat in order to measure spatial and temporal variation in habitat quality, opportunity for selection, and selection on phenotypic traits. We found a striking decline in average habitat quality with distance from the population core, yet some migrant seeds were successful in suitable, unoccupied microsites at and beyond the range boundary. Total and direct selection on four out of five measured phenotypic traits varied across habitat zones, as well as between years. Moreover, the margin habitat often exerted unique selection pressures that were not intermediate between core and exterior habitats. This study reveals that a combination of ecological and evolutionary forces, including propagule limitation, variation in habitat quality and spatial heterogeneity in phenotypic selection may reduce opportunities for adaptive range expansion, even across a very local population boundary.
Limited availability of ZBP1 restricts axonal mRNA localization and nerve regeneration capacity.
Donnelly, Christopher J; Willis, Dianna E; Xu, Mei; Tep, Chhavy; Jiang, Chunsu; Yoo, Soonmoon; Schanen, N Carolyn; Kirn-Safran, Catherine B; van Minnen, Jan; English, Arthur; Yoon, Sung Ok; Bassell, Gary J; Twiss, Jeffery L
2011-09-30
Subcellular localization of mRNAs is regulated by RNA-protein interactions. Here, we show that introduction of a reporter mRNA with the 3'UTR of β-actin mRNA competes with endogenous mRNAs for binding to ZBP1 in adult sensory neurons. ZBP1 is needed for axonal localization of β-actin mRNA, and introducing GFP with the 3'UTR of β-actin mRNA depletes axons of endogenous β-actin and GAP-43 mRNAs and attenuates both in vitro and in vivo regrowth of severed axons. Consistent with limited levels of ZBP1 protein in adult neurons, mice heterozygous for the ZBP1 gene are haploinsufficient for axonal transport of β-actin and GAP-43 mRNAs and for regeneration of peripheral nerve. Exogenous ZBP1 can rescue the RNA transport deficits, but the axonal growth deficit is only rescued if the transported mRNAs are locally translated. These data support a direct role for ZBP1 in transport and translation of mRNA cargos in axonal regeneration in vitro and in vivo.
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.
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.
Spatial resolution limits for the localization of noise sources using direct sound mapping
NASA Astrophysics Data System (ADS)
Fernandez Comesaña, D.; Holland, K. R.; Fernandez-Grande, E.
2016-08-01
One of the main challenges arising from noise and vibration problems is how to identify the areas of a device, machine or structure that produce significant acoustic excitation, i.e. the localization of main noise sources. The direct visualization of sound, in particular sound intensity, has extensively been used for many years to locate sound sources. However, it is not yet well defined when two sources should be regarded as resolved by means of direct sound mapping. This paper derives the limits of the direct representation of sound pressure, particle velocity and sound intensity by exploring the relationship between spatial resolution, noise level and geometry. The proposed expressions are validated via simulations and experiments. It is shown that particle velocity mapping yields better results for identifying closely spaced sound sources than sound pressure or sound intensity, especially in the acoustic near-field.
Non-local meta-conformal invariance in diffusion-limited erosion
NASA Astrophysics Data System (ADS)
Henkel, Malte
2016-12-01
The non-stationary relaxation and physical ageing in the diffusion-limited erosion process (dle) is studied through the exact solution of its Langevin equation, in d spatial dimensions. The dynamical exponent z = 1, the growth exponent β =\\max (0,(1-d)/2) and the ageing exponents a=b=d-1 and {λ }C={λ }R=d are found. In d = 1 spatial dimension, a new representation of the meta-conformal Lie algebra, isomorphic to {sl}(2,{{R}})\\oplus {sl}(2,{{R}}), acts as a dynamical symmetry of the noise-averaged dle Langevin equation. Its infinitesimal generators are non-local in space. The exact form of the full time-space dependence of the two-time response function of dle is reproduced for d = 1 from this symmetry. The relationship to the terrace-step-kink model of vicinal surfaces is discussed.
Localized reversal of the perpendicular velocity in Tore Supra ohmic, L-mode, limited plasmas
NASA Astrophysics Data System (ADS)
Trier, E.; Hennequin, P.; Gürcan, Ö. D.; Sabot, R.; Bucalossi, J.; Guimarães-Filho, Z. O.; Bourdelle, C.; Clairet, F.; Falchetto, G.; Fenzi, C.; Garbet, X.; Maget, P.; Vermare, L.; The Tore Supra Team
2017-04-01
In Tore Supra plasmas, the perpendicular velocity measured by Doppler reflectometry was observed to reverse in a localized zone close to a normalized radius ∼0.5–0.6, changing from a negative value (corresponding to a negative radial electric field E r) to a positive value ({{E}\\text{r}}>0 ). This occurs in L-mode, ohmic plasmas with a negligible external momentum input, a non-circular limited cross-section, and an edge safety factor close to 3. This reversal is favoured by a decrease in the magnetic field, or an increase in density. It is accompanied by a characteristic behaviour of the MHD activity signal, whose amplitude decrease during a ramp-down of the edge safety factor as it approaches {{q}a}∼ 3.1 –3.2. A m/n = 2/1 mode is involved in the mechanism causing these observations.
Metapopulation dynamics override local limits on long-term parasite persistence.
Ram, Karthik; Preisser, Evan L; Gruner, Daniel S; Strong, Donald R
2008-12-01
A simple null model, particularly germane to small and vulnerable organisms such as parasites, is that local conditions set a stage upon which larger-scale dynamics play out. Soil moisture strongly influences survival of entomopathogenic nematodes (EPN), which in turn drive trophic cascades by protecting vegetation from root-feeding herbivores. In this study, we examine the mechanisms responsible for patchy occurrence of an entomopathogenic nematode, Heterorhabditis marelatus, in a California coastal prairie. One hypothesis proposes that biotic factors such as competition and natural enemies could regulate occurrence of EPN populations. We found that fungi and other enemies of EPN, although locally potent, did not explain the patterns of incidence across sites. Abiotic factors also have strong effects on EPN persistence, especially for vulnerable free-living stages. Thus, we tested the hypothesis that patchy occurrence of EPN on a large landscape was driven by differences in soil moisture. Our research uses long-term data on nematode incidence in combination with a landscape-level experiment to demonstrate the lack of a correlation between soil moisture and long-term persistence. A year-long experiment showed EPN mortality was weakly correlated with soil moisture among our study sites. Thirteen years of data, however, showed that colonization rates were highly correlated with long-term persistence. Sites with highest long-term persistence experienced the highest rates of rhizosphere colonization, extinction, and turnover. As a result, we concluded that metapopulation dynamics override limitations set by local and short-term abiotic conditions to determine long-term persistence in this parasite-driven trophic cascade.
Plasmon Waveguides: Balancing Propagation, Localization, and Loss below the Diffraction Limit
NASA Astrophysics Data System (ADS)
Dionne, Jennifer; Sweatlock, Luke; Atwater, Harry; Polman, Albert
2005-03-01
On subwavelength scales, photon-matter interactions are limited by diffraction. Circumventing this diffraction limit is now a principle focus of integrated nanophotonics. Here, we present studies of surface plasmon (SP) waveguides exhibiting both long-range propagation and spatial confinement of light with lateral dimensions of less than 10 percent of the free-space wavelength. Attention is given to characterizing the dispersion relations, mode profiles, wavelength dependent propagation, and energy density decay in metallodielectric waveguides comprised of silicon dioxide/Ag/silicon dioxide and Ag/silicon dioxide/Ag structures with waveguide thicknesses ranging from 12nm-50nm. Numerical dispersion analysis indicates the presence of three distinct SP branches, including the existence of modes in the plasmon bandgap. For bound modes in Ag waveguides, near-IR propagation lengths exceed centimeter scales only at the expense of confinement. However, enhanced propagation is observed at shorter wavelengths despite notable field localization in the metal. Likewise, for silicon dioxide SP waveguides, propagation lengths exceed tens of microns with fields confined to within 30 nanometers of the structure. Applications of both short and long-wavelength plasmons to photonic waveguiding will be discussed, and utilization of such results for integrated plasmonic applications will be explored.
Turbulence, flows and edge localized mode (ELM) dynamics in limiter H-mode plasmas in TEXTOR
NASA Astrophysics Data System (ADS)
Soldatov, S.; Krämer-Flecken, A.; Kantor, M.; Unterberg, B.; Sun, Y.; Van Oost, G.; Reiter, D.; TEXTOR Team
2010-08-01
The turbulence, plasma flow and edge localized mode (ELM) dynamics in the limiter H-mode TEXTOR plasmas are investigated. Properties of both ambient turbulence within 0 < k⊥ < 4.2 cm-1 and coherent modes are studied on the ELM time scale in detail. The turbulence level near the pedestal is shown to evolve several times with the period of ELMs. Within the inter-ELM period the 'silent stage' is found which is characterized by an extremely low (below that for Ohmic plasmas) turbulence level and a phase growth in the reflectometry signal. The silent stage is associated with the quasi-steady state when the pedestal is formed and confinement is improved between two successive ELMs. Quasi-coherent density oscillations near the pedestal region with m ≈ 3, 5, 16 and 38 are measured with correlation reflectometry. Low-m modes are found to reveal the signatures of precursor mode. At first, the radial structure of the rotation shear and radial electric field Er in limiter H-mode in TEXTOR is presented. The characteristic negative electric field well with the sharp gradient ∇Er ≈ 250 V cm-2 at ≈2 cm inside separatrix is resolved. The Er × B rotation profile defines both the resulting plasma rotation in the electron diamagnetic drift direction and a significant rotation shear near the separatrix which exceeds the decorrelation rate of ambient turbulence by several times.
NASA Astrophysics Data System (ADS)
Cartin, Daniel
2015-10-01
At this point in time, there is very little empirical evidence on the likelihood of a space-faring species originating in the biosphere of a habitable world. However, there is a tension between the expectation that such a probability is relatively high (given our own origins on Earth), and the lack of any basis for believing the Solar System has ever been visited by an extraterrestrial colonization effort. From the latter observational fact, this paper seeks to place upper limits on the probability of an interstellar civilization arising on a habitable planet in its stellar system, using a percolation model to simulate the progress of such a hypothetical civilization's colonization efforts in the local Solar neighbourhood. To be as realistic as possible, the actual physical positions and characteristics of all stars within 40 parsecs of the Solar System are used as possible colony sites in the percolation process. If an interstellar civilization is very likely to have such colonization programmes, and they can travel over large distances, then the upper bound on the likelihood of such a species arising per habitable world is of the order of 10-3 on the other hand, if civilizations are not prone to colonize their neighbours, or do not travel very far, then the upper limiting probability is much larger, even of order one.
Multi sensor fusion framework for indoor-outdoor localization of limited resource mobile robots.
Marín, Leonardo; Vallés, Marina; Soriano, Ángel; Valera, Ángel; Albertos, Pedro
2013-10-21
This paper presents a sensor fusion framework that improves the localization of mobile robots with limited computational resources. It employs an event based Kalman Filter to combine the measurements of a global sensor and an inertial measurement unit (IMU) on an event based schedule, using fewer resources (execution time and bandwidth) but with similar performance when compared to the traditional methods. The event is defined to reflect the necessity of the global information, when the estimation error covariance exceeds a predefined limit. The proposed experimental platforms are based on the LEGO Mindstorm NXT, and consist of a differential wheel mobile robot navigating indoors with a zenithal camera as global sensor, and an Ackermann steering mobile robot navigating outdoors with a SBG Systems GPS accessed through an IGEP board that also serves as datalogger. The IMU in both robots is built using the NXT motor encoders along with one gyroscope, one compass and two accelerometers from Hitecnic, placed according to a particle based dynamic model of the robots. The tests performed reflect the correct performance and low execution time of the proposed framework. The robustness and stability is observed during a long walk test in both indoors and outdoors environments.
Multi Sensor Fusion Framework for Indoor-Outdoor Localization of Limited Resource Mobile Robots
Marín, Leonardo; Vallés, Marina; Soriano, Ángel; Valera, Ángel; Albertos, Pedro
2013-01-01
This paper presents a sensor fusion framework that improves the localization of mobile robots with limited computational resources. It employs an event based Kalman Filter to combine the measurements of a global sensor and an inertial measurement unit (IMU) on an event based schedule, using fewer resources (execution time and bandwidth) but with similar performance when compared to the traditional methods. The event is defined to reflect the necessity of the global information, when the estimation error covariance exceeds a predefined limit. The proposed experimental platforms are based on the LEGO Mindstorm NXT, and consist of a differential wheel mobile robot navigating indoors with a zenithal camera as global sensor, and an Ackermann steering mobile robot navigating outdoors with a SBG Systems GPS accessed through an IGEP board that also serves as datalogger. The IMU in both robots is built using the NXT motor encoders along with one gyroscope, one compass and two accelerometers from Hitecnic, placed according to a particle based dynamic model of the robots. The tests performed reflect the correct performance and low execution time of the proposed framework. The robustness and stability is observed during a long walk test in both indoors and outdoors environments. PMID:24152933
Spin groups of super metrics and a theorem of Rogers
NASA Astrophysics Data System (ADS)
Fulp, Ronald
2017-01-01
We derive the canonical forms of super Riemannian metrics and the local isometry groups of such metrics. For certain super metrics we also compute the simply connected covering groups of the local isometry groups and interpret these as local spin groups of the super metric. Super metrics define reductions OSg of the relevant frame bundle. When principal bundles S˜g exist with structure group the simply connected covering group G ˜ of the structure group of OSg , representations of G ˜ define vector bundles associated to S˜g whose sections are "spinor fields" associated with the super metric g . Using a generalization of a Theorem of Rogers, which is itself one of the main results of this paper, we show that for super metrics we call body reducible, each such simply connected covering group G ˜ is a super Lie group with a conventional super Lie algebra as its corresponding super Lie algebra. Some of our results were known to DeWitt (1984) using formal Grassmann series and others were known by Rogers using finitely many Grassmann generators and passing to a direct limit. We work exclusively in the category of G∞ supermanifolds with G∞ mappings. Our supernumbers are infinite series of products of Grassmann generators subject to convergence in the ℓ1 norm introduced by Rogers (1980, 2007).
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.
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.
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.
Local confidence limits for IMRT and VMAT techniques: a study based on TG119 test suite.
Thomas, M; Chandroth, M
2014-03-01
The aim of this study was to generate a local confidence limit (CL) for intensity modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT) techniques used at Waikato Regional Cancer Centre. This work was carried out based on the American Association of Physicists in Medicine (AAPM) Task Group (TG) 119 report. The AAPM TG 119 report recommends CLs as a bench mark for IMRT commissioning and delivery based on its multiple institutions planning and dosimetry comparisons. In this study the locally obtained CLs were compared to TG119 benchmarks. Furthermore, the same bench mark was used to test the capabilities and quality of the VMAT technique in our clinic. The TG 119 test suite consists of two primary and four clinical tests for evaluating the accuracy of IMRT planning and dose delivery systems. Pre defined structure sets contoured on computed tomography images were downloaded from AAPM website and were transferred to a locally designed phantom. For each test case two plans were generated using IMRT and VMAT optimisation. Dose prescriptions and planning objectives recommended by TG119 report were followed to generate the test plans in Eclipse Treatment Planning System. For each plan the point dose measurements were done using an ion chamber at high dose and low dose regions. The planar dose distribution was analysed for percentage of points passing the gamma criteria of 3%/3 mm, for both the composite plan and individual fields of each plan. The CLs were generated based on the results from the gamma analysis and point dose measurements. For IMRT plans, the CLs obtained were (1) from point dose measurements: 2.49% at high dose region and 2.95% for the low dose region (2) from gamma analysis: 2.12% for individual fields and 5.9% for the composite plan. For VMAT plans, the CLs obtained were (1) from point dose measurements: 2.56% at high dose region and 2.6% for the low dose region (2) from gamma analysis: 1.46% for individual fields and 0.8% for
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.
Code of Federal Regulations, 2011 CFR
2011-04-01
... 20 Employees' Benefits 3 2011-04-01 2011-04-01 false Under what limited conditions may a Local...-Stop Operator? 661.310 Section 661.310 Employees' Benefits EMPLOYMENT AND TRAINING ADMINISTRATION, DEPARTMENT OF LABOR STATEWIDE AND LOCAL GOVERNANCE OF THE WORKFORCE INVESTMENT SYSTEM UNDER TITLE I OF...
Code of Federal Regulations, 2012 CFR
2012-04-01
... 20 Employees' Benefits 4 2012-04-01 2012-04-01 false Under what limited conditions may a Local...-Stop Operator? 661.310 Section 661.310 Employees' Benefits EMPLOYMENT AND TRAINING ADMINISTRATION, DEPARTMENT OF LABOR (CONTINUED) STATEWIDE AND LOCAL GOVERNANCE OF THE WORKFORCE INVESTMENT SYSTEM UNDER...
A categorical account of the Hofmann-Mislove theorem
NASA Astrophysics Data System (ADS)
Townsend, Christopher F.
2005-11-01
A categorical account is given of the Hofmann-Mislove theorem, describing the Scott open filters on a frame. The account is stable under an order duality and so is shown to also cover Bunge and Funk's constructive description of the points of the lower power locale.
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.
Racial Isolation, Poverty, and the Limits of Local Control in Oakland
ERIC Educational Resources Information Center
Noguera, Pedro A.
2004-01-01
Historically, schools in the United States have been governed at the local level by elected school boards, and finances have been raised primarily through local property taxes. While local control theoretically allows for greater responsiveness to local concerns, it does not take into account the vast inequality among and between communities in…
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.
Refinement of Representation Theorems for Context-Free Languages
NASA Astrophysics Data System (ADS)
Fujioka, Kaoru
In this paper, we obtain some refinement of representation theorems for context-free languages by using Dyck languages, insertion systems, strictly locally testable languages, and morphisms. For instance, we improved the Chomsky-Schützenberger representation theorem and show that each context-free language L can be represented in the form L = h (D ∩ R), where D is a Dyck language, R is a strictly 3-testable language, and h is a morphism. A similar representation for context-free languages can be obtained, using insertion systems of weight (3, 0) and strictly 4-testable languages.
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)
On the role of sharp chains in the transport theorem
NASA Astrophysics Data System (ADS)
Falach, L.; Segev, R.
2016-03-01
A generalized transport theorem for convecting irregular domains is presented in the setting of Federer's geometric measure theory. A prototypical r-dimensional domain is viewed as a flat r-chain of finite mass in an open set of an n-dimensional Euclidean space. The evolution of such a generalized domain in time is assumed to follow a continuous succession of Lipschitz embedding so that the spatial gradient may be nonexistent in a subset of the domain with zero measure. The induced curve is shown to be continuous with respect to the flat norm and differential with respect to the sharp norm on currents in Rn. A time-dependent property is naturally assigned to the evolving region via the action of an r-cochain on the current associated with the domain. Applying a representation theorem for cochains, the properties are shown to be locally represented by an r-form. Using these notions, a generalized transport theorem is presented.
Towards a novel no-hair theorem for black holes
Hertog, Thomas
2006-10-15
We provide strong numerical evidence for a new no-scalar-hair theorem for black holes in general relativity, which rules out spherical scalar hair of static four-dimensional black holes if the scalar field theory, when coupled to gravity, satisfies the Positive Energy Theorem. This sheds light on the no-scalar-hair conjecture for Calabi-Yau compactifications of string theory, where the effective potential typically has negative regions but where supersymmetry ensures the total energy is always positive. In theories where the scalar tends to a negative local maximum of the potential at infinity, we find the no-scalar-hair theorem holds provided the asymptotic conditions are invariant under the full anti-de Sitter symmetry group.
Basis set limit and systematic errors in local-orbital based all-electron DFT
NASA Astrophysics Data System (ADS)
Blum, Volker; Behler, Jörg; Gehrke, Ralf; Reuter, Karsten; Scheffler, Matthias
2006-03-01
With the advent of efficient integration schemes,^1,2 numeric atom-centered orbitals (NAO's) are an attractive basis choice in practical density functional theory (DFT) calculations of nanostructured systems (surfaces, clusters, molecules). Though all-electron, the efficiency of practical implementations promises to be on par with the best plane-wave pseudopotential codes, while having a noticeably higher accuracy if required: Minimal-sized effective tight-binding like calculations and chemically accurate all-electron calculations are both possible within the same framework; non-periodic and periodic systems can be treated on equal footing; and the localized nature of the basis allows in principle for O(N)-like scaling. However, converging an observable with respect to the basis set is less straightforward than with competing systematic basis choices (e.g., plane waves). We here investigate the basis set limit of optimized NAO basis sets in all-electron calculations, using as examples small molecules and clusters (N2, Cu2, Cu4, Cu10). meV-level total energy convergence is possible using <=50 basis functions per atom in all cases. We also find a clear correlation between the errors which arise from underconverged basis sets, and the system geometry (interatomic distance). ^1 B. Delley, J. Chem. Phys. 92, 508 (1990), ^2 J.M. Soler et al., J. Phys.: Condens. Matter 14, 2745 (2002).
Freezing of tissue-limits for the autoradiographic localization of diffusible substances.
Frederik, P M; Busing, W M
1979-11-01
Frozen thin sections and sections from freeze-dried and embedded tissue are used for the autoradiographic localization of diffusible substances at the electron microscope level. The presence of ice crystals in such sections may limit the autoradiographic resolution. Ice crystals are formed during freezing and may grow during subsequent processing of tissue. The contribution of ice crystal growth to the final image was estimated by measuring the distribution of the ice crystal sizes in freeze-etch replicas and in sections from freeze-dried and embedded tissues. A surface layer (10-15 mu) without visible ice crystals was present in both preparations. Beneath this surface layer the diameter of ice crystals increased towards the interior with the same relationship between crystal size and distance from the surface in the freeze-etch preparation as in the freeze-dry preparation. Ice crystal growth occurring during a much longer time during freeze-drying compared to freeze-etching does not significantly contribute to the final image in the electron microscope. The formation of ice crystals during freezing determines to a large extent the image (and therefore the autoradiographic resolution) of freeze-dry preparations and this probably holds also for thin cryosections of which examples are given.
Localization of Type I Interferon Receptor Limits Interferon-Induced TLR3 in Epithelial Cells
Ciencewicki, Jonathan M.; Brighton, Luisa E.
2009-01-01
Previous studies have shown that influenza infections increase Toll-like receptor 3 (TLR3) expression and that type I interferons (IFNs) may play a role in this response. This study aimed to expand on the role of type I IFNs in the influenza-induced upregulation of TLR3 and determine whether and how the localization of the IFN-α/β receptor (IFNAR) in respiratory epithelial cells could modify IFN-induced responses. Using differentiated primary human airway epithelial cells this study demonstrates that soluble mediators secreted in response to influenza infection upregulate TLR3 expression in naive cells. This response was associated with an upregulation of type I IFNs and stimulation with type I, but not type II, IFNs enhanced TLR3 expression. Interestingly, although influenza infection results in IFN-β release both toward the apical and basolateral sides of the epithelium, TLR3 expression is only enhanced in cells stimulated with IFN-β from the basolateral side. Immunohistochemical analysis demonstrates that IFNAR expression is limited to the basolateral side of differentiated human airway epithelial cells. However, non- or poorly differentiated epithelial cells express IFNAR more toward the apical side. These data demonstrate that restricted expression of the IFNAR in the differentiated airway epithelium presents a potential mechanism of regulating type I IFN-induced TLR3 expression. PMID:19231996
Limits of the measurability of the local quantum electromagnetic-field amplitude
NASA Astrophysics Data System (ADS)
Compagno, G.; Persico, F.
1998-03-01
The precision with which the amplitude of the free electromagnetic field can be measured locally in QED is evaluated by analyzing a well-known gedanken experiment originally proposed by Bohr and Rosenfeld (BR). The analysis is performed by applying standard theoretical techniques familiar in quantum optics. The main result obtained for the precision is significantly different from the generally accepted Bohr-Rosenfeld result. This leads to questioning the widely accepted notion of the compensating field, fostered by these authors. A misconception at the origin of this notion is pointed out by a careful investigation of the self-force acting on the apparatus designed to measure the field. The correct expression for this self-force is found to be at variance with that proposed by Bohr and Rosenfeld and generally accepted. It is argued that, as a consequence of this new expression and in contrast with the generally accepted view, no compensating force of nonelectromagnetic nature is required in order to perform measurements of the quantum field amplitude with any desired accuracy. It is shown that the only limitations to the precision of the measurement, in the BR gedanken experiment, arise from the time-energy uncertainty principle, as well as from the finite dimensions of the measuring apparatus.
Systemic protein delivery by muscle-gene transfer is limited by a local immune response
Wang, Lixin; Dobrzynski, Eric; Schlachterman, Alexander; Cao, Ou; Herzog, Roland W.
2005-01-01
Adeno-associated viral (AAV) vectors have been successfully used for therapeutic expression of systemic transgene products (such as factor IX or erythropoietin) following in vivo administration to skeletal muscle of animal models of inherited hematologic disorders. However, an immune response may be initiated if the transgene product represents a neoantigen. Here, we use ovalbumin (OVA) as a model antigen and demonstrate immune-mediated elimination of expression on muscle-directed AAV-2 gene transfer. Administration to immune competent mice resulted in transient systemic OVA expression. Within 10 days, OVA-specific T-helper cells had been activated in draining lymph nodes, an inflammatory immune response ensued, and OVA-expressing muscle fibers were destroyed by a cytotoxic CD8+ T-cell response. Use of a muscle-specific promoter did not prevent this immune response. Adoptively transferred CD4+ cells transgenic for a T-cell receptor specific to OVA peptide-major histocompatibility complex class II showed antigen-specific, vector dose-dependent proliferation confined to the draining lymph nodes of AAV-OVA–transduced muscle within 5 days after gene transfer and subsequently participated in lymphocytic infiltration of transduced muscle. This study documents that a local immune response limits sustained expression of a secreted protein in muscle gene transfer, a finding that may have consequences for design of clinical protocols. PMID:15713796
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.
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…
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.
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
Optical theorem for multipole sources in wave diffraction theory
NASA Astrophysics Data System (ADS)
Eremin, Yu. A.; Sveshnikov, A. G.
2016-05-01
The optical theorem is generalized to the case of local body excitation by multipole sources. It is found that, to calculate the extinction cross section, it is sufficient to calculate the scattered field derivatives at a single point. It is shown that the Purcell factor, which is a rather important parameter, can be represented in analytic form. The result is generalized to the case of a local scatterer incorporated in a homogeneous halfspace.
Analytical proof of Gisin's theorem for three qubits
Choudhary, Sujit K.; Ghosh, Sibasish; Kar, Guruprasad; Rahaman, Ramij
2010-04-15
Gisin's theorem assures that for any pure bipartite entangled state, there is violation of the inequality of Bell and of Clauser, Horne, Shimony, and Holt, revealing its contradiction with local realistic model. Whether a similar result holds for three-qubit pure entangled states remained unresolved. We show analytically that all three-qubit pure entangled states violate a Bell-type inequality, derived on the basis of local realism, by exploiting the Hardy's nonlocality argument.
Interpretation of the quantum formalism and Bell's theorem
Santos, E. )
1991-02-01
It is argued that quantum mechanics must be interpreted according to the Copenhagen interpretation. Consequently the formalism must be used in a purely operational way. The relation between realism, hidden variables, and the Bell inequalities is discussed. The proof of impossibility of local hidden-variables theories (Bell theorem) is criticized on the basis that the quantum mechanical states violating local realism are not physically realizable states.
NASA Astrophysics Data System (ADS)
Ivanov, Martin; Kotlarski, Sven; Schär, Christoph
2015-04-01
The Swiss CH2011 scenarios provide a portfolio of climate change scenarios for the region of Switzerland, specifically tailored for use in climate impact research. Although widely applied by a variety of end-users, these scenarios are subject to several limitations related to the underlying delta change methodology. Examples are difficulties to appropriately account for changes in the spatio-temporal variability of meteorological fields and for changes in extreme events. The recently launched ELAPSE project (Enhancing local and regional climate change projections for Switzerland) is connected to the EU COST Action VALUE (www.value-cost.eu) and aims at complementing CH2011 by further scenario products, including a bias-corrected version of daily scenarios at the site scale. For this purpose the well-established empirical quantile mapping (QM) methodology is employed. Here, daily temperature and precipitation output of 15 GCM-RCM model chains of the ENSEMBLES project is downscaled and bias-corrected to match observations at weather stations in Switzerland. We consider established QM techniques based on all empirical quantiles or linear interpolation between the empirical percentiles. In an attempt to improve the downscaling of extreme precipitation events, we also apply a parametric approximation of the daily precipitation distribution by a dynamically weighted mixture of a Gamma distribution for the bulk and a Pareto distribution for the right tail for the first time in the context of QM. All techniques are evaluated and intercompared in a cross-validation framework. The statistical downscaling substantially improves virtually all considered distributional and temporal characteristics as well as their spatial distribution. The empirical methods have in general very similar performances. The parametric method does not show an improvement over the empirical ones. Critical sites and seasons are highlighted and discussed. Special emphasis is placed on investigating the
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.
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.
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.
McGarry, Conor K.; Bokrantz, Rasmus; O’Sullivan, Joe M.; Hounsell, Alan R.
2014-10-01
Efficacy of inverse planning is becoming increasingly important for advanced radiotherapy techniques. This study’s aims were to validate multicriteria optimization (MCO) in RayStation (v2.4, RaySearch Laboratories, Sweden) against standard intensity-modulated radiation therapy (IMRT) optimization in Oncentra (v4.1, Nucletron BV, the Netherlands) and characterize dose differences due to conversion of navigated MCO plans into deliverable multileaf collimator apertures. Step-and-shoot IMRT plans were created for 10 patients with localized prostate cancer using both standard optimization and MCO. Acceptable standard IMRT plans with minimal average rectal dose were chosen for comparison with deliverable MCO plans. The trade-off was, for the MCO plans, managed through a user interface that permits continuous navigation between fluence-based plans. Navigated MCO plans were made deliverable at incremental steps along a trajectory between maximal target homogeneity and maximal rectal sparing. Dosimetric differences between navigated and deliverable MCO plans were also quantified. MCO plans, chosen as acceptable under navigated and deliverable conditions resulted in similar rectal sparing compared with standard optimization (33.7 ± 1.8 Gy vs 35.5 ± 4.2 Gy, p = 0.117). The dose differences between navigated and deliverable MCO plans increased as higher priority was placed on rectal avoidance. If the best possible deliverable MCO was chosen, a significant reduction in rectal dose was observed in comparison with standard optimization (30.6 ± 1.4 Gy vs 35.5 ± 4.2 Gy, p = 0.047). Improvements were, however, to some extent, at the expense of less conformal dose distributions, which resulted in significantly higher doses to the bladder for 2 of the 3 tolerance levels. In conclusion, similar IMRT plans can be created for patients with prostate cancer using MCO compared with standard optimization. Limitations exist within MCO regarding conversion of navigated plans to
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.
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.
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 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.
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.
Code of Federal Regulations, 2010 CFR
2010-04-01
... 20 Employees' Benefits 3 2010-04-01 2010-04-01 false Under what limited conditions may a Local Board directly be a provider of core services, intensive services, or training services, or act as a One-Stop Operator? 661.310 Section 661.310 Employees' Benefits EMPLOYMENT AND TRAINING ADMINISTRATION, DEPARTMENT OF LABOR STATEWIDE AND...
Does the Reeh-Schlieder theorem violate relativistic causality?
NASA Astrophysics Data System (ADS)
Valente, Giovanni
2014-11-01
The Reeh-Schlieder theorem is a purely relativistic result in local quantum field theory, which is often regarded as raising a conflict with relativistic causality, namely the requirement that causal processes cannot propagate faster than light. Allegedly, under an operational interpretation, the theorem would entail non-local effects, in that by performing an operation within a region of Minkowski spacetime one could instantaneously change the state of the field over another spacelike separated region. Here, we argue that such a conflict is only apparent. Indeed, a suitable understanding of the notion of local operations helps one dissolve the puzzle. Accordingly, even if one does not exclude superluminal signalling, the latter cannot be controlled, and thus it may not be used to give rise to causal paradoxes. On the other hand, we maintain that relativistic causality is expressed by the axiom of local primitive causality, assuring no superluminal propagation of a field. The Reeh-Schlieder theorem can be shown to be fully consistent with such a condition, and hence it does not imply that matter and energy carried by a quantum field can travel faster than light. Therefore, there is no violation of relativistic causality at all.
Numerous strategies but limited implementation guidance in US local adaptation plans
NASA Astrophysics Data System (ADS)
Woodruff, Sierra C.; Stults, Missy
2016-08-01
Adaptation planning offers a promising approach for identifying and devising solutions to address local climate change impacts. Yet there is little empirical understanding of the content and quality of these plans. We use content analysis to evaluate 44 local adaptation plans in the United States and multivariate regression to examine how plan quality varies across communities. We find that plans draw on multiple data sources to analyse future climate impacts and include a breadth of strategies. Most plans, however, fail to prioritize impacts and strategies or provide detailed implementation processes, raising concerns about whether adaptation plans will translate into on-the-ground reductions in vulnerability. Our analysis also finds that plans authored by the planning department and those that engaged elected officials in the planning process were of higher quality. The results provide important insights for practitioners, policymakers and scientists wanting to improve local climate adaptation planning and action.
The sensitive period for auditory localization in barn owls is limited by age, not by experience.
Knudsen, E I; Knudsen, P F
1986-07-01
Early in life, the barn owl passes through a sensitive period during which it can interpret and make use of abnormal auditory cues for accurate sound localization. This capacity is lost at about 8 weeks of age, just after the head and ears reach adult size (knudsen et al. 1984a). The end of the sensitive period could be triggered either by an age-dependent process or by the exposure of the auditory system to stable or adult-like cues. To distinguish between these alternatives, we subjected baby owls to constant abnormal cues (chronic monaural occlusion) or to frequently changing abnormal cues (alternating monaural occlusion) throughout the sensitive period. In the first group of animals (n = 2), one ear was plugged continuously until 73 or 79 d of age, respectively, and then the earplug was switched to the opposite ear. Although these animals adjusted sound localization accuracy during the initial chronic monaural occlusion, they could not localize sounds at all after the earplug was switched to the opposite ear, and they remained unable to localize sounds as long as the opposite ear remained occluded (7 and 27 weeks, respectively). When the second monaural occlusion was finally removed, both birds localized sounds with errors that were similar to the errors they exhibited immediately after removal of the first monaural occlusion. One bird that was 127-d-old at the time the second earplug was removed corrected its localization error; the other bird, 250-d-old when the second earplug was removed, did not.(ABSTRACT TRUNCATED AT 250 WORDS)
No-go theorems for generalized chameleon field theories.
Wang, Junpu; Hui, Lam; Khoury, Justin
2012-12-14
The chameleon, or generalizations thereof, is a light scalar that couples to matter with gravitational strength, but whose manifestation depends on the ambient matter density. A key feature is that the screening mechanism suppressing its effects in high-density environments is determined by the local scalar field value. Under very general conditions, we prove two theorems limiting its cosmological impact: (i) the Compton wavelength of such a scalar can be at most ~/= 1 MPc at the present cosmic density, which restricts its impact to nonlinear scales; and (ii) the conformal factor relating Einstein- and Jordan-frame scale factors is essentially constant over the last Hubble time, which precludes the possibility of self-acceleration. These results imply that chameleonlike scalar fields have a negligible effect on the linear-scale growth history; theories that invoke a chameleonlike scalar to explain cosmic acceleration rely on a form of dark energy rather than a genuine modified gravity effect. Our analysis applies to a broad class of chameleon, symmetron, and dilaton theories.
Hijacked organic, limited local, faulty fair trade: what's a radical to eat?
Engler, Mark
2012-01-01
Organic farming has been hijacked by big business. Local food can have a larger carbon footprint than products shipped in from overseas. Fair trade doesn't address the real concerns of farmers in the global South. As the food movement has moved from the countercultural fringe to become a mainstream phenomenon, organic, local, and fair trade advocates have been beset by criticism from overt foes and erstwhile allies alike. Now that Starbucks advertises fair trade coffee and Kraft owns Boca soy burgers, it's fair to ask, "What's a radical to eat?"
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.
Limits on Einstein’s Equivalence Principle from the First Localized Fast Radio Burst FRB 150418
NASA Astrophysics Data System (ADS)
Tingay, S. J.; Kaplan, D. L.
2016-04-01
Fast radio bursts (FRBs) have recently been used to place limits on Einstein's Equivalence Principle via observations of time delays between photons of different radio frequencies by Wei et al. These limits on differential post-Newtonian parameters ({{Δ }}γ \\lt 2.52× {10}-8) are the best yet achieved, but they still rely on uncertain assumptions, namely the relative contributions of dispersion and gravitational delays to the observed time delays and the distances to FRBs. Also, very recently, the first FRB host galaxy has likely been identified, providing the first redshift-based distance estimate to FRB 150418. Moreover, consistency between the {{{Ω }}}{{IGM}} estimate from FRB 150418 and {{{Ω }}}{{IGM}}, expected from ΛCDM models and WMAP observations, leads one to conclude that the observed time delay for FRB 150418 is highly dominated by dispersion, with any gravitational delays being small contributors. This points to even tighter limits on Δγ. In this paper, the technique of Wei et al. is applied to FRB 150418 to produce a limit of Δγ < 1-2 × 10-9, approximately an order of magnitude better than previous limits and in line with expectations by Wei et al. for what could be achieved if the dispersive delay is separated from other effects. Future substantial improvements in such limits will depend on accurately determining the contribution of individual ionized components to the total observed time delays for FRBs.
Implementation of a workplace smoking ban in bars: the limits of local discretion.
Montini, Theresa; Bero, Lisa A
2008-12-08
In January 1998, the California state legislature extended a workplace smoking ban to bars. The purpose of this study was to explore the conditions that facilitate or hinder compliance with a smoking ban in bars. We studied the implementation of the smoking ban in bars by interviewing three sets of policy participants: bar employers responsible for complying with the law; local government officials responsible for enforcing the law; and tobacco control activists who facilitated implementation. We transcribed the interviews and did a qualitative analysis of the text. The conditions that facilitated bar owners' compliance with a smoking ban in bars included: if the cost to comply was minimal; if the bars with which they were in competition were in compliance with the smoking ban; and if there was authoritative, consistent, coordinated, and uniform enforcement. Conversely, the conditions that hindered compliance included: if the law had minimal sanctions; if competing bars in the area allowed smoking; and if enforcement was delayed or inadequate. Many local enforcers wished to forfeit their local discretion and believed the workplace smoking ban in bars would be best implemented by a state agency. The potential implication of this study is that, given the complex nature of local politics, smoking bans in bars are best implemented at a broader provincial or national level.
Implementation of a workplace smoking ban in bars: The limits of local discretion
Montini, Theresa; Bero, Lisa A
2008-01-01
Background In January 1998, the California state legislature extended a workplace smoking ban to bars. The purpose of this study was to explore the conditions that facilitate or hinder compliance with a smoking ban in bars. Methods We studied the implementation of the smoking ban in bars by interviewing three sets of policy participants: bar employers responsible for complying with the law; local government officials responsible for enforcing the law; and tobacco control activists who facilitated implementation. We transcribed the interviews and did a qualitative analysis of the text. Results The conditions that facilitated bar owners' compliance with a smoking ban in bars included: if the cost to comply was minimal; if the bars with which they were in competition were in compliance with the smoking ban; and if there was authoritative, consistent, coordinated, and uniform enforcement. Conversely, the conditions that hindered compliance included: if the law had minimal sanctions; if competing bars in the area allowed smoking; and if enforcement was delayed or inadequate. Conclusion Many local enforcers wished to forfeit their local discretion and believed the workplace smoking ban in bars would be best implemented by a state agency. The potential implication of this study is that, given the complex nature of local politics, smoking bans in bars are best implemented at a broader provincial or national level. PMID:19063716
Localization of type I interferon receptor limits interferon-induced TLR-3 in epithelial cells
This study aimed to expand on the role of type I IFNs in the influenza-induced upregulation of TLR3 and determine whether and how the localization of the IFN-alpha/beta receptor (IFNAR) in respiratory epithelial cells could modify IFN-induced responses. Using differentiated prima...
Taking account of local culture: limits to the development of a professional ethos.
Goopy, Suzanne E
2005-06-01
The need to extend the discussion of culture in the study of nursing, combined with an enthusiasm for the possibility of viewing nursing from a new perspective, provides the impetus for this study. Based on fieldwork undertaken in the intensive care unit (RICU) of a major public hospital in Rome (Italy), this paper explores some of the key aspects of the social relations and local staff culture of one particular group of Italian nurses. In a climate of globalization, where the deployment of dominant Anglo-American ideas is difficult to counter, the RICU presents as a setting which challenges the widespread assumptions of universal standards of nursing practice. By building a picture of the working world of these particular nurses, we are assisted in our understanding of nursing practice as a local cultural activity. In exploring the significance of local culture this paper brings into question the universality of the current paradigm of professionalism and professional identity, and emphasizes the value of acknowledging local culture.
Limitations of a localized surface plasmon resonance sensor on Salmonella detection
USDA-ARS?s Scientific Manuscript database
We have designed a localized surface plasmon resonance (LSPR) biosensor to perform the whole cell detection of Salmonella using gold nanoparticls fabricated by oblique angle deposition technique. The LSPR sensor showed a plasmon peak shift due to the Salmonella antigen and anti-Salmonella antibody r...
USDA-ARS?s Scientific Manuscript database
With more sophisticated data compilation and analytical capabilities, the evolution of “big data” analysis has occurred rapidly. We examine the meta-analysis of “big data” representing phosphorus (P) flows and stocks in global agriculture and address the need to consider local nuances of farm operat...
Localization of type I interferon receptor limits interferon-induced TLR-3 in epithelial cells
This study aimed to expand on the role of type I IFNs in the influenza-induced upregulation of TLR3 and determine whether and how the localization of the IFN-alpha/beta receptor (IFNAR) in respiratory epithelial cells could modify IFN-induced responses. Using differentiated prima...
Scientific Data and Its Limits: Rethinking the Use of Evidence in Local Climate Change Policy
ERIC Educational Resources Information Center
Pearce, Warren
2014-01-01
Climate policy is typically seen as informed by scientific evidence that anthropogenic carbon emissions require reducing in order to avoid dangerous consequences. However, agreement on these matters has not translated into effective policy. Using interviews with local authority officials in the UK's East Midlands region, this paper argues that the…
The value, limitations, and challenges of employing local experts in conservation research.
Elbroch, Mark; Mwampamba, Tuyeni H; Santos, Maria J; Zylberberg, Maxine; Liebenberg, Louis; Minye, James; Mosser, Christopher; Reddy, Erin
2011-12-01
Evidence suggests that the involvement of local people in conservation work increases a project's chances of success. Involving citizen scientists in research, however, raises questions about data quality. As a tool to better assess potential participants for conservation projects, we developed a knowledge gradient, K, along which community members occupy different positions on the basis of their experience with and knowledge of a research subject. This gradient can be used to refine the citizen-science concept and allow researchers to differentiate between community members with expert knowledge and those with little knowledge. We propose that work would benefit from the inclusion of select local experts because it would allow researchers to harness the benefits of local involvement while maintaining or improving data quality. We used a case study from the DeHoop Nature Preserve, South Africa, in which we conducted multiple interviews, identified and employed a local expert animal tracker, evaluated the expert's knowledge, and analyzed the data collected by the expert. The expert animal tracker J.J. created his own sampling design and gathered data on mammals. He patrolled 4653 km in 214 days and recorded 4684 mammals. He worked from a central location, and his patrols formed overlapping loops; however, his data proved neither spatially nor temporally autocorrelated. The distinctive data collected by J.J. are consistent with the notion that involving local experts can produce reliable data. We developed a conceptual model to help identify the appropriate participants for a given project on the basis of research budget, knowledge or skills needed, technical literacy requirements, and scope of the project. ©2011 Society for Conservation Biology.
NASA Astrophysics Data System (ADS)
Garg, Anupam Kumar
This thesis consists of a study of the general spin Einstein-Podolsky-Rosen experiment, with a view to seeing how classical behavior is recovered in the infinite -spin limit. In Bohm's version of the experiment, two spin -s particles fly apart in the singlet state. Quantum theory predicts that if the spin of one particle is measured to be m along a direction a, the other will necessarily have a sping of -m along a. Since the spins of the two far apart particles can be measured in an infinitesimal time interval, the requirement of locality suggests that the particles' spins are predetermined along all directions, in defiance of quantum theoretic precepts. It was shown by Bell and by Clauser and Horne that an alternative point of view called local realism which attempts to explain the spin correlations by introducing hidden variables mut be incompatible with the quantitative predictions of quantum theory for spin- 1/2. Chapters II and III of this thesis contain extensions of their arguments to arbitrary spin. It is found that no matter how large the spin gets, quantum mechanics and local realism do not become more compatible, and classical mechanics does not emerge as a smooth infinite-spin limit. Chapter IV gives a general procedure (with several examples) for deciding whether or not a given set of joint distributions for the spins of the two particles is compatible with local realism. In Chapter V it is argued that local realism can emerge in the infinite-spin limit only if limitations in detector resolution (quite unrelated to those imposed by the uncertainty principle) are explicitly included. Some questions stemming from this point of view are answered for spin- 1/2, and a specific model for including detector error is studied for higher spin.
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.
Optimal limits on f{sub NL}{sup local} from WMAP 5-year data
Smith, Kendrick M.; Senatore, Leonardo; Zaldarriaga, Matias E-mail: senatore@ias.edu
2009-09-01
We have applied the optimal estimator for f{sub NL}{sup local} to the 5 year WMAP data. Marginalizing over the amplitude of foreground templates we get −4 < f{sub NL}{sup local} < 80 at 95% CL. Error bars of previous (sub-optimal) analyses are roughly 40% larger than these. The probability that a Gaussian simulation, analyzed using our estimator, gives a result larger in magnitude than the one we find is 7 %. Our pipeline gives consistent results when applied to the three and five year WMAP data releases and agrees well with the results from our own sub-optimal pipeline. We find no evidence of any residual foreground contamination.
NASA Astrophysics Data System (ADS)
Chrétien, N.; Friedt, J.-M.; Martin, G.
2014-06-01
The role of the phase noise of a local oscillator driving a pulsed-mode RADAR used for probing surface acoustic wave sensors is investigated. The echo delay, representative of the acoustic velocity, and hence the physical quantity probed by the sensor, is finely measured as a phase. Considering that the intrinsic oscillator phase fluctuation defines the phase noise measurement resolution, we experimentally and theoretically assess the relation between phase noise, measurement range, and measurand resolution.
Williford, Anna; Comeron, Josep M
2010-01-01
Recent years have witnessed the integration of theoretical advances in population genetics with large-scale analyses of complete genomes, with a growing number of studies suggesting pervasive natural selection that includes frequent deleterious as well as adaptive mutations. In finite populations, however, mutations under selection alter the fate of genetically linked mutations (the so-called Hill-Robertson effect). Here we review the evolutionary consequences of selection at linked sites (linked selection) focusing on its effects on nearby nucleotides in genomic regions with nonreduced recombination. We argue that these local effects of linkage may account for differences in selection intensity among genes. We also show that even high levels of recombination are unlikely to remove all effects of linked selection, causing a reduction in the polymorphism to divergence ratio (r(pd)) at neutral sites. Because a number of methods employed to estimate the magnitude and frequency of adaptive mutations take reduced r(pd) as evidence of positive selection, ignoring local linkage effects may lead to misleading estimates of the proportion of adaptive substitutions and estimates of positive selection. These biases are caused by employing methods that do not account for local variation in the relative effective population size (N(e)) caused by linked selection.
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.
Quantum mechanics vs local realism near the classical limit:A Bell inequality for spin s
Mermin, N.D.
1980-07-15
The quantitative quantum-mechanical analysis of the Einstein-Podolsky-Rosen experiment for correlated particles of arbitrary spin s is shown to contradict a generalized form of Bell's inequality, for suitable orientations of the detectors. As the classical (s ..-->.. infinity ) limit is approached, the range of angles for which the contradiction arises vanishes as 1/s.
49 CFR 179.8 - Limitation on actions by states, local governments, and Indian tribes.
Code of Federal Regulations, 2010 CFR
2010-10-01
... REGULATIONS SPECIFICATIONS FOR TANK CARS Introduction, Approvals and Reports § 179.8 Limitation on actions by... Administration (see 49 CFR parts 200-244), laws, regulations and orders related to railroad safety, including... law, regulation, or order covering the same subject matter as a DOT regulation or order applicable to...
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.
Fujino, Kenji; Obara, Mari; Ikegaya, Tomohito; Tamura, Kenichi
2015-09-01
The rapid accumulation of pre-existing mutations may play major roles in the establishment and shaping of adaptability for local regions in current rice breeding programs. The cultivated rice, Oryza sativa L., which originated from tropical regions, is now grown worldwide due to the concerted efforts of breeding programs. However, the process of establishing local populations and their origins remain unclear. In the present study, we characterized DNA polymorphisms in the rice variety KITAAKE from Hokkaido, one of the northern limits of rice cultivation in the world. Indel polymorphisms were attributed to transposable element-like insertions, tandem duplications, and non-TE deletions as the original mutation events in the NIPPONBARE and KITAAKE genomes. The allele frequencies of the KITAAKE alleles markedly shifted to the current variety types among the local population from Hokkaido in the last two decades. The KITAAKE alleles widely distributed throughout wild rice and cultivated rice over the world. These have accumulated in the local population from Hokkaido via Japanese landraces as the ancestral population of Hokkaido. These results strongly suggested that combinations of pre-existing mutations played a role in the establishment of adaptability. This approach using the re-sequencing of local varieties in unique environmental conditions will be useful as a genetic resource in plant breeding programs in local regions.
Sughiyama, Yuki; Abe, Sumiyoshi
2008-08-01
A nonlinear relaxation process is considered for a macroscopic thermodynamic quantity, generalizing recent work by Taniguchi and Cohen [J. Stat. Phys. 126, 1 (2006)] that was based on the Onsager-Machlup theory. It is found that the fluctuation theorem holds in the nonlinear nonequilibrium regime if the change of entropy characterized by local equilibria is appropriately renormalized. The fluctuation theorem for the ordinary entropy change is recovered in the linear near-equilibrium case.
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.
Non-local rheological properties of granular flows near a jamming limit.
Aranson, I. S.; Tsimring, L. S.; Malloggi, F.; Clement, E.; Materials Science Division; Univ. of California at San Diego; CNRS-ESPCI Univ.
2008-01-01
We study the rheology of sheared granular flows close to a jamming transition. We use the approach of partially fluidized theory (PFT) with a full set of equations extending the thin layer approximation derived previously for the description of the granular avalanches phenomenology. This theory provides a picture compatible with a local rheology at large shear rates [G. D. R. Midi, Eur. Phys. J. E 14, 341 (2004)] and it works in the vicinity of the jamming transition, where a description in terms of a simple local rheology comes short. We investigate two situations displaying important deviations from local rheology. The first one is based on a set of numerical simulations of sheared soft two-dimensional circular grains. The next case describes previous experimental results obtained on avalanches of sandy material flowing down an incline. Both cases display, close to jamming, significant deviations from the now standard Pouliquen's flow rule [O. Pouliquen, Phys. Fluids 11, 542 (1999); 11, 1956 (1999)]. This discrepancy is the hallmark of a strongly nonlocal rheology and in both cases, we relate the empirical results and the outcomes of PFT. The numerical simulations show a characteristic constitutive structure for the fluid part of the stress involving the confining pressure and the material stiffness that appear in the form of an additional dimensionless parameter. This constitutive relation is then used to describe the case of sandy flows. We show a quantitative agreement as far as the effective flow rules are concerned. A fundamental feature is identified in PFT as the existence of a jammed layer developing in the vicinity of the flow arrest that corroborates the experimental findings. Finally, we study the case of solitary erosive granular avalanches and relate the outcome with the PFT analysis.
Thoughts on Limitation in the Use of Acoustic Sensors in RF Breakdown Localization
Le Pimpec, F
2004-08-02
X-band accelerator structures, meeting the Next Linear Collider (NLC) design requirements, have been found to suffer damage due to radio frequency (RF) breakdown when processed to high gradients. Improved understanding of these breakdown events is desirable for the development of structure designs, fabrication procedures, and processing techniques that minimize structure damage. Using an array of acoustic sensors, we have been able to pinpoint the location of individual breakdown events. However, a more accurate localization is required to understand the interaction between the phonon or the sound wave with the OFE copper.
Overcoming non-local effects and Brillouin threshold limitations in Brillouin distributed sensors
NASA Astrophysics Data System (ADS)
Urricelqui, Javier; Ruiz-Lombera, Rubén.; Sagues, Mikel; Mirapeix, Jesús; López-Higuera, José M.; Loayssa, Alayn
2015-09-01
We demonstrate, for the first time to our knowledge, a Brillouin optical time domain analysis sensor that is able to operate with a probe power larger than the Brillouin threshold of the deployed sensing fiber and that is free from detrimental non-local effects. The technique is based on a dual-probe-sideband setup in which a frequency modulation of the probes waves along the fiber is introduced. This makes the frequency of maximum interaction between pump and probes to vary along the fiber, thus mitigating the pump pulse depletion and making it possible to use very large probe power, which brings an improved signal-to-noise ratio in detection.
Strong converse theorems using Rényi entropies
Leditzky, Felix; Datta, Nilanjana; Wilde, Mark M.
2016-08-15
We use a Rényi entropy method to prove strong converse theorems for certain information-theoretic tasks which involve local operations and quantum (or classical) communication between two parties. These include state redistribution, coherent state merging, quantum state splitting, measurement compression with quantum side information, randomness extraction against quantum side information, and data compression with quantum side information. The method we employ in proving these results extends ideas developed by Sharma [preprint http://arxiv.org/abs/1404.5940 [quant-ph] (2014)], which he used to give a new proof of the strong converse theorem for state merging. For state redistribution, we prove the strong converse property for the boundary of the entire achievable rate region in the (e, q)-plane, where e and q denote the entanglement cost and quantum communication cost, respectively. In the case of measurement compression with quantum side information, we prove a strong converse theorem for the classical communication cost, which is a new result extending the previously known weak converse. For the remaining tasks, we provide new proofs for strong converse theorems previously established using smooth entropies. For each task, we obtain the strong converse theorem from explicit bounds on the figure of merit of the task in terms of a Rényi generalization of the optimal rate. Hence, we identify candidates for the strong converse exponents for each task discussed in this paper. To prove our results, we establish various new entropic inequalities, which might be of independent interest. These involve conditional entropies and mutual information derived from the sandwiched Rényi divergence. In particular, we obtain novel bounds relating these quantities, as well as the Rényi conditional mutual information, to the fidelity of two quantum states.
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.
Moon, Sojin; Bannen, Ryan M; Rutkoski, Thomas J; Phillips, George N; Bae, Euiyoung
2014-10-01
Local structural entropy (LSE) is a descriptor for the extent of conformational heterogeneity in short protein sequences that is computed from structural information derived from the Protein Data Bank. Reducing the LSE of a protein sequence by introducing amino acid mutations can result in fewer conformational states and thus a more stable structure, indicating that LSE optimization can be used as a protein stabilization method. Here, we describe a series of LSE optimization experiments designed to stabilize mesophilic and thermophilic adenylate kinases (AKs) and report crystal structures of LSE-optimized AK variants. In the mesophilic AK, thermal stabilization by LSE reduction was effective but limited. Structural analyses of the LSE-optimized mesophilic AK variants revealed a strong correlation between LSE and the apolar buried surface area. Additional mutations designed to introduce noncovalent interactions between distant regions of the polypeptide resulted in further stabilization. Unexpectedly, optimizing the LSE of the thermophilic AK resulted in a decrease in thermal stability. This destabilization was reduced when charged residues were excluded from the possible substitutions during LSE optimization. These observations suggest that stabilization by LSE reduction may result from the optimization of local hydrophobic contacts. The limitations of this process are likely due to ignorance of other interactions that bridge distant regions in a given amino acid sequence. Our results illustrate the effectiveness and limitations of LSE optimization as a protein stabilization strategy and highlight the importance and complementarity of local conformational stability and global interactions in protein thermal stability. © 2014 Wiley Periodicals, Inc.
NASA Astrophysics Data System (ADS)
Ebrahimi, F.; Blackman, E. G.
2016-06-01
For cylindrical differentially rotating plasmas, we study large-scale magnetic field generation from finite amplitude non-axisymmetric perturbations by comparing numerical simulations with quasi-linear analytic theory. When initiated with a vertical magnetic field of either zero or finite net flux, our global cylindrical simulations exhibit the magnetorotational instability (MRI) and large-scale dynamo growth of radially alternating mean fields, averaged over height and azimuth. This dynamo growth is explained by our analytic calculations of a non-axisymmetric fluctuation-induced electromotive force that is sustained by azimuthal shear of the fluctuating fields. The standard `Ω effect' (shear of the mean field by differential rotation) is unimportant. For the MRI case, we express the large-scale dynamo field as a function of differential rotation. The resulting radially alternating large-scale fields may have implications for angular momentum transport in discs and corona. To connect with previous work on large-scale dynamos with local linear shear and identify the minimum conditions needed for large-scale field growth, we also solve our equations in local Cartesian coordinates. We find that large-scale dynamo growth in a linear shear flow without rotation can be sustained by shear plus non-axisymmetric fluctuations - even if not helical, a seemingly previously unidentified distinction. The linear shear flow dynamo emerges as a more restricted version of our more general new global cylindrical calculations.
Experiments with central-limit properties of spatial samples from locally covariant random fields
Barringer, T.H.; Smith, T.E.
1992-01-01
When spatial samples are statistically dependent, the classical estimator of sample-mean standard deviation is well known to be inconsistent. For locally dependent samples, however, consistent estimators of sample-mean standard deviation can be constructed. The present paper investigates the sampling properties of one such estimator, designated as the tau estimator of sample-mean standard deviation. In particular, the asymptotic normality properties of standardized sample means based on tau estimators are studied in terms of computer experiments with simulated sample-mean distributions. The effects of both sample size and dependency levels among samples are examined for various value of tau (denoting the size of the spatial kernel for the estimator). The results suggest that even for small degrees of spatial dependency, the tau estimator exhibits significantly stronger normality properties than does the classical estimator of standardized sample means. ?? 1992.
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.)
Few-view and limited-angle cone-beam megavoltage CT for breast localization in radiation therapy
NASA Astrophysics Data System (ADS)
Yu, Lifeng; Pan, Xiaochuan; Pelizzari, Charles A.; Martel, Mary
2004-05-01
In radiation therapy for breast cancer treatment, information about the external (skin) and internal (lung) boundaries is highly useful for determining the relative locations of the target and lung. In this work, we investigate the feasibility of tomographic reconstruction from few-view and limited-angle cone-beam projections acquired in radiation therapy unit for obtaining critical boundary information. From the few-view and limited-angle projections acquired directly in the treatment machine with an amorphous silicon electronic portal imaging device (EPID), We compared and evaluated the performance of the conventional cone-beam FDK algorithm and an iterative algorithm based upon the maximum-likelihood method for transmission tomography (ML-TR). Preliminary results demonstrated that the ML-TR algorithm is more promising than is the cone-beam FDK algorithm. Useful boundary information for breast localization can be obtained with very few projections in a limited angle range from the reconstruction of ML-TR algorithm.
Spatial distribution of limited resources and local density regulation in juvenile Atlantic salmon.
Finstad, Anders G; Einum, Sigurd; Ugedal, Ola; Forseth, Torbjørn
2009-01-01
1. Spatial heterogeneity of resources may influence competition among individuals and thus have a fundamental role in shaping population dynamics and carrying capacity. In the present study, we identify shelter opportunities as a limiting resource for juvenile Atlantic salmon (Salmo salar L.). Experimental and field studies are combined in order to demonstrate how the spatial distribution of shelters may influence population dynamics on both within and among population scales. 2. In closed experimental streams, fish performance scaled negatively with decreasing shelter availability and increasing densities. In contrast, the fish in open stream channels dispersed according to shelter availability and performance of fish remaining in the streams did not depend on initial density or shelters. 3. The field study confirmed that spatial variation in densities of 1-year-old juveniles was governed both by initial recruit density and shelter availability. Strength of density-dependent population regulation, measured as carrying capacity, increased with decreasing number of shelters. 4. Nine rivers were surveyed for spatial variation in shelter availability and increased shelter heterogeneity tended to decrease maximum observed population size (measured using catch statistics of adult salmon as a proxy). 5. Our studies highlight the importance of small-scale within-population spatial structure in population dynamics and demonstrate that not only the absolute amount of limiting resources but also their spatial arrangement can be an important factor influencing population carrying capacity.
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)
Cosacov, Andrea; Nattero, Julieta; Cocucci, Andrea A.
2008-01-01
Background and Aims Few studies have examined the dynamics of specialist plant–pollinator interactions at a geographical scale. This knowledge is crucial for a more general evolutionary and ecological understanding of specialized plant–pollinator systems. In the present study, variations in pollinator activity, assemblage composition and pollen limitation were explored in the oil-producing species Nierembergia linariifolia (Solanaceae). Methods Pollen limitation in fruit and seed production was analysed by supplementary hand pollination in five wild populations. Pollinator activity and identity were recorded while carrying out supplementary pollination to assess the effect of pollinators on the degree of pollen limitation. In two populations, pollen limitation was discriminated into quantitative and qualitative components by comparing supplementation and hand cross-pollination in fruit set and seed set. The effect of flower number per plant on the number of flowers pollinated per visitor per visit to a plant was examined in one of these populations as a possible cause of low-quality pollination by increasing geitonogamy. Results and Conclusions Although pollen limitation was evident along time and space, differences in magnitude were detected among populations and years that were greatly explained by pollinator activity, which was significantly different across populations. Floral display size had a significant effect on the visitation rate per flower. Limitation by quality clearly affected one population presumably due to a high proportion of geitonogamous pollen. The great inter-population variation in plant–pollinator interaction (both in pollinator assemblages composition and pollinator activity) and fitness consequences, suggests that this system should be viewed as a mosaic of locally selective processes and locally specialized interactions. PMID:18765440
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)
Fine, Dana S.; Sawin, Stephen
2017-01-01
Feynman's time-slicing construction approximates the path integral by a product, determined by a partition of a finite time interval, of approximate propagators. This paper formulates general conditions to impose on a short-time approximation to the propagator in a general class of imaginary-time quantum mechanics on a Riemannian manifold which ensure that these products converge. The limit defines a path integral which agrees pointwise with the heat kernel for a generalized Laplacian. The result is a rigorous construction of the propagator for supersymmetric quantum mechanics, with potential, as a path integral. Further, the class of Laplacians includes the square of the twisted Dirac operator, which corresponds to an extension of N = 1/2 supersymmetric quantum mechanics. General results on the rate of convergence of the approximate path integrals suffice in this case to derive the local version of the Atiyah-Singer index theorem.
NASA Astrophysics Data System (ADS)
Grachev, Andrey A.; Andreas, Edgar L.; Fairall, Christopher W.; Guest, Peter S.; Persson, P. Ola G.
2013-04-01
Measurements of atmospheric turbulence made over the Arctic pack ice during the Surface Heat Budget of the Arctic Ocean experiment (SHEBA) are used to determine the limits of applicability of Monin-Obukhov similarity theory (in the local scaling formulation) in the stable atmospheric boundary layer. Based on the spectral analysis of wind velocity and air temperature fluctuations, it is shown that, when both the gradient Richardson number, Ri, and the flux Richardson number, Rf, exceed a `critical value' of about 0.20-0.25, the inertial subrange associated with the Richardson-Kolmogorov cascade dies out and vertical turbulent fluxes become small. Some small-scale turbulence survives even in this supercritical regime, but this is non-Kolmogorov turbulence, and it decays rapidly with further increasing stability. Similarity theory is based on the turbulent fluxes in the high-frequency part of the spectra that are associated with energy-containing/flux-carrying eddies. Spectral densities in this high-frequency band diminish as the Richardson-Kolmogorov energy cascade weakens; therefore, the applicability of local Monin-Obukhov similarity theory in stable conditions is limited by the inequalities Ri < Ri cr and Rf < Rf cr. However, it is found that Rf cr = 0.20-0.25 is a primary threshold for applicability. Applying this prerequisite shows that the data follow classical Monin-Obukhov local z-less predictions after the irrelevant cases (turbulence without the Richardson-Kolmogorov cascade) have been filtered out.
Optimized Local Infarct Restraint Improves Left Ventricular Function and Limits Remodeling
Koomalsingh, Kevin J.; Witschey, Walter R.T.; McGarvey, Jeremy R.; Shuto, Takashi; Kondo, Norihiro; Xu, Chun; Jackson, Benjamin M.; Gorman, Joseph H.; Gorman, Robert C.; Pilla, James J.
2013-01-01
Background Preventing expansion and dyskinetic movement of a myocardial infarction (MI) can limit left ventricular (LV) remodeling. Using a device designed to produce variable alteration of infarct stiffness and geometry, we sought to understand how these parameters affect LV function and remodeling early after MI. Methods Ten pigs had posterolateral infarctions. An unexpanded device was placed in 5 animals at the time of infarction, and 5 animals served as untreated controls. One week after MI animals underwent MRI to assess LV size and regional function. In the treatment group, after initial imaging, the device was expanded with 2ml, 4ml, 6ml, 8ml and 10ml of saline. The optimal degree of inflation was defined as that which maximized stroke volume (SV). The device was left optimally inflated in the treatment animals for three additional weeks. Results One week after MI, device inflation to ≥6ml significantly (p<0.05) decreased endsystolic volume (ESV) (0ml:59.9ml±3.8, 6ml:54.0ml≥±3.1, 8ml:50.5ml±4.8, 10ml:46.1ml±2.2) and increased ejection fraction (EF) (0ml:34.6%±1.6, 6ml:39.7%±0.9, 8ml:43.1%±2.7, 10ml:44.1%±0.9). SV significantly (p<0.05) improved for the 6ml and 8ml volumes (0ml: 31.2ml±2.6, 6ml: 35.7ml±2.0, 8ml: 37.5ml±1.9) but trended downward for 10ml (36.6ml±2.8). At four-weeks after MI, end-diastolic volume and ESV were unchanged from one-week values in the treatment group while the control group continued to dilate. SV (38.2±4.4ml vs. 34.0.1±4.8ml, p=0.08) and EF (36.0±2.6% vs. 27.6±1.4%, p=0.04) were also better in the treatment animals. Conclusions Optimized isolated infarct restraint can limit adverse LV remodeling after MI. The tested device affords the potential for a patient-specific therapy to preserve cardiac function after MI. PMID:23146279
Yan, Dongmei; Zhang, Yong; Zhu, Shuangli; Chen, Na; Li, Xiaolei; Wang, Dongyan; Ma, Xiaozhen; Zhu, Hui; Tong, Wenbin; Xu, Wenbo
2014-07-01
From August 2011 to February 2012, an outbreak caused by type 2 circulating vaccine-derived poliovirus (cVDPV) occurred in Aba County, Sichuan, China. During the outbreak, four type 2 VDPVs (≥0.6% nucleotide divergence in the VP1 region relative to the Sabin 2 strain) were isolated from 3 patients with acute flaccid paralysis (AFP) and one close contact. In addition, a type 2 pre-VDPV (0.3% to 0.5% divergence from Sabin 2) that was genetically related to these type 2 VDPVs was isolated from another AFP patient. These 4 patients were all unimmunized children 0.7 to 1.1 years old. Nucleotide sequencing revealed that the 4 VDPV isolates differed from Sabin 2 by 0.7% to 1.2% in nucleotides in the VP1 region and shared 5 nucleotide substitutions with the pre-VDPV. All 5 isolates were closely related, and all were S2/S3/S2/S3 recombinants sharing common recombination crossover sites. Although the two major determinants of attenuation and temperature sensitivity phenotype of Sabin 2 (A481 in the 5' untranslated region and Ile143 in the VP1 protein) had reverted in all 5 isolates, one VDPV (strain CHN16017) still retained the temperature sensitivity phenotype. Phylogenetic analysis of the third coding position of the complete P1 coding region suggested that the cVDPVs circulated locally for about 7 months following the initiating oral poliovirus vaccine (OPV) dose. Our findings reinforce the point that cVDPVs can emerge and spread in isolated communities with immunity gaps and highlight the emergence risks of type 2 cVDPVs accompanying the trivalent OPV used. To solve this issue, it is recommended that type 2 OPV be removed from the trivalent OPV or that inactivated polio vaccine (IPV) be used instead.
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.
Zalyubovskiy, Sergiy J; Bogdanova, Maria; Deinega, Alexei; Lozovik, Yurii; Pris, Andrew D; An, Kwang Hyup; Hall, W Paige; Potyrailo, Radislav A
2012-06-01
In this paper, the theoretical sensitivity limit of the localized surface plasmon resonance (LSPR) to the surrounding dielectric environment is discussed. The presented theoretical analysis of the LSPR phenomenon is based on perturbation theory. Derived results can be further simplified assuming quasistatic limit. The developed theory shows that LSPR has a detection capability limit independent of the particle shape or arrangement. For a given structure, sensitivity is directly proportional to the resonance wavelength and depends on the fraction of the electromagnetic energy confined within the sensing volume. This fraction is always less than unity; therefore, one should not expect to find an optimized nanofeature geometry with a dramatic increase in sensitivity at a given wavelength. All theoretical results are supported by finite-difference time-domain calculations for gold nanoparticles of different geometries (rings, split rings, paired rings, and ring sandwiches). Numerical sensitivity calculations based on the shift of the extinction peak are in good agreement with values estimated by perturbation theory. Numerical analysis shows that, for thin (≤10 nm) analyte layers, sensitivity of the LSPR is comparable with a traditional surface plasmon resonance sensor and LSPR has the potential to be significantly less sensitive to temperature fluctuations.
Du, Zheren; Chen, Lianwei; Kao, Tsung-Sheng; Wu, Mengxue; Hong, Minghui
2015-01-01
For practical application, optical limiting materials must exhibit a fast response and a low threshold in order to be used for the protection of the human eye and electro-optical sensors against intense light. Many nanomaterials have been found to exhibit optical limiting properties. Laser ablation offers the possibility of fabricating nanoparticles from a wide range of target materials. For practical use of these materials, their optical limiting performance, including optical limiting threshold and the ability to efficiently attenuate high intensity light, needs to be improved. In this paper, we fabricate nanoparticles of different metals by laser ablation in liquid. We study the optical nonlinear properties of the laser-generated nanoparticle dispersion. Silica microspheres are used to enhance the optical limiting performance of the nanoparticle dispersion. The change in the optical nonlinear properties of the laser-generated nanoparticle dispersion caused by silica microspheres is studied. It is found that the incident laser beam is locally focused by the microspheres, leading to an increased optical nonlinearity of the nanoparticle dispersion.
Kelkar, Manasi; Martin, Sophie G.
2015-01-01
Cells couple growth with division and regulate size in response to nutrient availability. In rod-shaped fission yeast, cell-size control occurs at mitotic commitment. An important regulator is the DYRK-family kinase Pom1, which forms gradients from cell poles and inhibits the mitotic activator Cdr2, itself localized at the medial cortex. Where and when Pom1 modulates Cdr2 activity is unclear as Pom1 medial cortical levels remain constant during cell elongation. Here we show that Pom1 re-localizes to cell sides upon environmental glucose limitation, where it strongly delays mitosis. This re-localization is caused by severe microtubule destabilization upon glucose starvation, with microtubules undergoing catastrophe and depositing the Pom1 gradient nucleator Tea4 at cell sides. Microtubule destabilization requires PKA/Pka1 activity, which negatively regulates the microtubule rescue factor CLASP/Cls1/Peg1, reducing CLASP's ability to stabilize microtubules. Thus, PKA signalling tunes CLASP's activity to promote Pom1 cell side localization and buffer cell size upon glucose starvation. PMID:26443240
Baik, Sunhee; Morgan, M Granger; Davis, Alexander L
2017-06-29
While they are rare, widespread blackouts of the bulk power system can result in large costs to individuals and society. If local distribution circuits remain intact, it is possible to use new technologies including smart meters, intelligent switches that can change the topology of distribution circuits, and distributed generation owned by customers and the power company, to provide limited local electric power service. Many utilities are already making investments that would make this possible. We use customers' measured willingness to pay to explore when the incremental investments needed to implement these capabilities would be justified. Under many circumstances, upgrades in advanced distribution systems could be justified for a customer charge of less than a dollar a month (plus the cost of electricity used during outages), and would be less expensive and safer than the proliferation of small portable backup generators. We also discuss issues of social equity, extreme events, and various sources of underlying uncertainty. © 2017 Society for Risk Analysis.
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.
Code of Federal Regulations, 2012 CFR
2012-04-01
... fuel used in intercity, local or school buses after July 31, 1984. 48.6427-6 Section 48.6427-6 Internal... intercity, local or school buses after July 31, 1984. (a) Limitation on amount of credit or refund—(1) In... except where fuel is used in a bus while such bus is being operated as a “qualified local bus” in...
Code of Federal Regulations, 2013 CFR
2013-04-01
... fuel used in intercity, local or school buses after July 31, 1984. 48.6427-6 Section 48.6427-6 Internal... intercity, local or school buses after July 31, 1984. (a) Limitation on amount of credit or refund—(1) In... except where fuel is used in a bus while such bus is being operated as a “qualified local bus” in...
Code of Federal Regulations, 2011 CFR
2011-04-01
... fuel used in intercity, local or school buses after July 31, 1984. 48.6427-6 Section 48.6427-6 Internal... intercity, local or school buses after July 31, 1984. (a) Limitation on amount of credit or refund—(1) In... except where fuel is used in a bus while such bus is being operated as a “qualified local bus” in...
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.
Verhille, Christine E; English, Karl K; Cocherell, Dennis E; Farrell, Anthony P; Fangue, Nann A
2016-01-01
Transformation of earth's ecosystems by anthropogenic climate change is predicted for the 21st century. In many regions, the associated increase in environmental temperatures and reduced precipitation will have direct effects on the physiological performance of terrestrial and aquatic ectotherms and have already threatened fish biodiversity and important fisheries. The threat of elevated environmental temperatures is particularly salient for members of the Oncorhynchus genus living in California, which is the southern limit of their range. Here, we report the first assessments of the aerobic capacity of a Californian population of wild Oncorhynchus mykiss Walbaum in relationship to water temperature. Our field measurements revealed that wild O. mykiss from the lower Tuolumne River, California maintained 95% of their peak aerobic scope across an impressive temperature range (17.8-24.6°C). The thermal range for peak performance corresponds to local high river temperatures, but represents an unusually high temperature tolerance compared with conspecifics and congeneric species from northern latitudes. This high thermal tolerance suggests that O. mykiss at the southern limit of their indigenous distribution may be locally adjusted relative to more northern populations. From fisheries management and conservation perspectives, these findings challenge the use of a single thermal criterion to regulate the habitat of the O. mykiss species along the entirety of its distribution range.
Verhille, Christine E.; English, Karl K.; Cocherell, Dennis E.; Farrell, Anthony P.; Fangue, Nann A.
2016-01-01
Transformation of earth's ecosystems by anthropogenic climate change is predicted for the 21st century. In many regions, the associated increase in environmental temperatures and reduced precipitation will have direct effects on the physiological performance of terrestrial and aquatic ectotherms and have already threatened fish biodiversity and important fisheries. The threat of elevated environmental temperatures is particularly salient for members of the Oncorhynchus genus living in California, which is the southern limit of their range. Here, we report the first assessments of the aerobic capacity of a Californian population of wild Oncorhynchus mykiss Walbaum in relationship to water temperature. Our field measurements revealed that wild O. mykiss from the lower Tuolumne River, California maintained 95% of their peak aerobic scope across an impressive temperature range (17.8–24.6°C). The thermal range for peak performance corresponds to local high river temperatures, but represents an unusually high temperature tolerance compared with conspecifics and congeneric species from northern latitudes. This high thermal tolerance suggests that O. mykiss at the southern limit of their indigenous distribution may be locally adjusted relative to more northern populations. From fisheries management and conservation perspectives, these findings challenge the use of a single thermal criterion to regulate the habitat of the O. mykiss species along the entirety of its distribution range. PMID:27957333
Initiation of Combustion of a Gel-Like Condensed Substance by a Local Source of Limited Power
NASA Astrophysics Data System (ADS)
Glushkov, D. O.; Kuznetsov, G. V.; Strizhak, P. A.
2017-01-01
A physical and a mathematical model of the gas-phase ignition of a gel-like condensed substance, containing a combustible (hydrazine) and an oxidizer (liquefied oxygen) in its composition, at a cryogenic initial temperature have been developed. A numerical investigation of the integral characteristics of the interrelated physicochemical processes occurring in the initiation of combustion of such a substance by a typical energy source of limited heat content (an individual small-size particle heated to a high temperature) has been perfumed. The dependence of the delay time of ignition of the indicated substance on the heat content of a local heat source was determined. The minimum values of the main parameters of hot particles (their temperature and sizes), at which the ignition conditions are fulfilled, were estimated. It is shown that the delay time of ignition of a gel-like condensed substance depends mainly on the initial temperature of an energy source. The characteristic features of the conditions and regimes of initiation of combustion of condensed substances found in different aggregate states (solid, liquid, gel-like) under conditions of their local heating by a heat source of limiting power were analyzed.
NASA Astrophysics Data System (ADS)
Sano, Nobuyuki
2015-12-01
The impurity-limited resistance and the effect of the phase interference among localized multiple impurities in the quasi-one dimensional (quasi-1D) nanowire structures are systematically investigated under the framework of the scattering theory. We derive theoretical expressions of the impurity-limited resistance in the nanowire under the linear response regime from the Landauer formula and from the Boltzmann transport equation (BTE) with the relaxation time approximation. We show that the formula from the BTE exactly coincides with that from the Landauer approach with the weak-scattering limit when the energy spectrum of the in-coming electrons from the reservoirs is narrow and, thus, point out a possibility that the distinction of the impurity-limited resistances derived from the Landauer formula and that of the BTE could be made clear. The derived formulas are applied to the quasi-1D nanowires doped with multiple localized impurities with short-range scattering potential and the validity of various approximations on the resistance are discussed. It is shown that impurity scattering becomes so strong under the nanowire structures that the weak-scattering limit breaks down in most cases. Thus, both phase interference and phase randomization simultaneously play a crucial role in determining the impurity-limited resistance even under the fully coherent framework. When the impurity separation along the wire axis direction is small, the constructive phase interference dominates and the resistance is much greater than the average resistance. As the separation becomes larger, however, it approaches the series resistance of the single-impurity resistance due to the phase randomization. Furthermore, under the uniform configuration of impurities, the space-average resistance of multiple impurities at room temperature is very close to the series resistance of the single-impurity resistance, and thus, each impurity could be regarded as an independent scattering center. The
Sano, Nobuyuki
2015-12-28
The impurity-limited resistance and the effect of the phase interference among localized multiple impurities in the quasi-one dimensional (quasi-1D) nanowire structures are systematically investigated under the framework of the scattering theory. We derive theoretical expressions of the impurity-limited resistance in the nanowire under the linear response regime from the Landauer formula and from the Boltzmann transport equation (BTE) with the relaxation time approximation. We show that the formula from the BTE exactly coincides with that from the Landauer approach with the weak-scattering limit when the energy spectrum of the in-coming electrons from the reservoirs is narrow and, thus, point out a possibility that the distinction of the impurity-limited resistances derived from the Landauer formula and that of the BTE could be made clear. The derived formulas are applied to the quasi-1D nanowires doped with multiple localized impurities with short-range scattering potential and the validity of various approximations on the resistance are discussed. It is shown that impurity scattering becomes so strong under the nanowire structures that the weak-scattering limit breaks down in most cases. Thus, both phase interference and phase randomization simultaneously play a crucial role in determining the impurity-limited resistance even under the fully coherent framework. When the impurity separation along the wire axis direction is small, the constructive phase interference dominates and the resistance is much greater than the average resistance. As the separation becomes larger, however, it approaches the series resistance of the single-impurity resistance due to the phase randomization. Furthermore, under the uniform configuration of impurities, the space-average resistance of multiple impurities at room temperature is very close to the series resistance of the single-impurity resistance, and thus, each impurity could be regarded as an independent scattering center. The
Beaton, E D; Stevenson, Bradley S; King-Sharp, Karen J; Stamps, Blake W; Nunn, Heather S; Stuart, Marilyne
2016-01-01
Microorganisms found in terrestrial subsurface environments make up a large proportion of the Earth's biomass. Biogeochemical cycles catalyzed by subsurface microbes have the potential to influence the speciation and transport of radionuclides managed in geological repositories. To gain insight on factors that constrain microbial processes within a formation with restricted groundwater flow we performed a meta-community analysis on groundwater collected from multiple discrete fractures underlying the Chalk River Laboratories site (located in Ontario, Canada). Bacterial taxa were numerically dominant in the groundwater. Although these were mainly uncultured, the closest cultivated representatives were from the phenotypically diverse Betaproteobacteria, Deltaproteobacteria, Bacteroidetes, Actinobacteria, Nitrospirae, and Firmicutes. Hundreds of taxa were identified but only a few were found in abundance (>1%) across all assemblages. The remainder of the taxa were low abundance. Within an ecological framework of selection, dispersal and drift, the local and regional diversity revealed fewer taxa within each assemblage relative to the meta-community, but the taxa that were present were more related than predicted by chance. The combination of dispersion at one phylogenetic depth and clustering at another phylogenetic depth suggest both niche (dispersion) and filtering (clustering) as drivers of local assembly. Distance decay of similarity reveals apparent biogeography of 1.5 km. Beta diversity revealed greater influence of selection at shallow sampling locations while the influences of dispersal limitation and randomness were greater at deeper sampling locations. Although selection has shaped each assemblage, the spatial scale of groundwater sampling favored detection of neutral processes over selective processes. Dispersal limitation between assemblages combined with local selection means the meta-community is subject to drift, and therefore, likely reflects the
Beaton, E. D.; Stevenson, Bradley S.; King-Sharp, Karen J.; Stamps, Blake W.; Nunn, Heather S.; Stuart, Marilyne
2016-01-01
Microorganisms found in terrestrial subsurface environments make up a large proportion of the Earth’s biomass. Biogeochemical cycles catalyzed by subsurface microbes have the potential to influence the speciation and transport of radionuclides managed in geological repositories. To gain insight on factors that constrain microbial processes within a formation with restricted groundwater flow we performed a meta-community analysis on groundwater collected from multiple discrete fractures underlying the Chalk River Laboratories site (located in Ontario, Canada). Bacterial taxa were numerically dominant in the groundwater. Although these were mainly uncultured, the closest cultivated representatives were from the phenotypically diverse Betaproteobacteria, Deltaproteobacteria, Bacteroidetes, Actinobacteria, Nitrospirae, and Firmicutes. Hundreds of taxa were identified but only a few were found in abundance (>1%) across all assemblages. The remainder of the taxa were low abundance. Within an ecological framework of selection, dispersal and drift, the local and regional diversity revealed fewer taxa within each assemblage relative to the meta-community, but the taxa that were present were more related than predicted by chance. The combination of dispersion at one phylogenetic depth and clustering at another phylogenetic depth suggest both niche (dispersion) and filtering (clustering) as drivers of local assembly. Distance decay of similarity reveals apparent biogeography of 1.5 km. Beta diversity revealed greater influence of selection at shallow sampling locations while the influences of dispersal limitation and randomness were greater at deeper sampling locations. Although selection has shaped each assemblage, the spatial scale of groundwater sampling favored detection of neutral processes over selective processes. Dispersal limitation between assemblages combined with local selection means the meta-community is subject to drift, and therefore, likely reflects 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)
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…
Liu, Han-Hsuan; Cline, Hollis T
2016-07-06
Fragile X mental retardation protein (FMRP) is thought to regulate neuronal plasticity by limiting dendritic protein synthesis, but direct demonstration of a requirement for FMRP control of local protein synthesis during behavioral plasticity is lacking. Here we tested whether FMRP knockdown in Xenopus optic tectum affects local protein synthesis in vivo and whether FMRP knockdown affects protein synthesis-dependent visual avoidance behavioral plasticity. We tagged newly synthesized proteins by incorporation of the noncanonical amino acid azidohomoalanine and visualized them with fluorescent noncanonical amino acid tagging (FUNCAT). Visual conditioning and FMRP knockdown produce similar increases in FUNCAT in tectal neuropil. Induction of visual conditioning-dependent behavioral plasticity occurs normally in FMRP knockdown animals, but plasticity degrades over 24 h. These results indicate that FMRP affects visual conditioning-induced local protein synthesis and is required to maintain the visual conditioning-induced behavioral plasticity. Fragile X syndrome (FXS) is the most common form of inherited intellectual disability. Exaggerated dendritic protein synthesis resulting from loss of fragile X mental retardation protein (FMRP) is thought to underlie cognitive deficits in FXS, but no direct evidence has demonstrated that FMRP-regulated dendritic protein synthesis affects behavioral plasticity in intact animals. Xenopus tadpoles exhibit a visual avoidance behavior that improves with visual conditioning in a protein synthesis-dependent manner. We showed that FMRP knockdown and visual conditioning dramatically increase protein synthesis in neuronal processes. Furthermore, induction of visual conditioning-dependent behavioral plasticity occurs normally after FMRP knockdown, but performance rapidly deteriorated in the absence of FMRP. These studies show that FMRP negatively regulates local protein synthesis and is required to maintain visual conditioning
Liu, Han-Hsuan
2016-01-01
Fragile X mental retardation protein (FMRP) is thought to regulate neuronal plasticity by limiting dendritic protein synthesis, but direct demonstration of a requirement for FMRP control of local protein synthesis during behavioral plasticity is lacking. Here we tested whether FMRP knockdown in Xenopus optic tectum affects local protein synthesis in vivo and whether FMRP knockdown affects protein synthesis-dependent visual avoidance behavioral plasticity. We tagged newly synthesized proteins by incorporation of the noncanonical amino acid azidohomoalanine and visualized them with fluorescent noncanonical amino acid tagging (FUNCAT). Visual conditioning and FMRP knockdown produce similar increases in FUNCAT in tectal neuropil. Induction of visual conditioning-dependent behavioral plasticity occurs normally in FMRP knockdown animals, but plasticity degrades over 24 h. These results indicate that FMRP affects visual conditioning-induced local protein synthesis and is required to maintain the visual conditioning-induced behavioral plasticity. SIGNIFICANCE STATEMENT Fragile X syndrome (FXS) is the most common form of inherited intellectual disability. Exaggerated dendritic protein synthesis resulting from loss of fragile X mental retardation protein (FMRP) is thought to underlie cognitive deficits in FXS, but no direct evidence has demonstrated that FMRP-regulated dendritic protein synthesis affects behavioral plasticity in intact animals. Xenopus tadpoles exhibit a visual avoidance behavior that improves with visual conditioning in a protein synthesis-dependent manner. We showed that FMRP knockdown and visual conditioning dramatically increase protein synthesis in neuronal processes. Furthermore, induction of visual conditioning-dependent behavioral plasticity occurs normally after FMRP knockdown, but performance rapidly deteriorated in the absence of FMRP. These studies show that FMRP negatively regulates local protein synthesis and is required to maintain visual
Deacon, Nicholas John; Cavender-Bares, Jeannine
2015-01-01
Background Quercus oleoides Cham. and Schlect., tropical live oak, is a species of conservation importance in its southern range limit of northwestern Costa Rica. It occurs in high-density stands across a fragmented landscape spanning a contrasting elevation and precipitation gradient. We examined genetic diversity and spatial genetic structure in this geographically isolated and genetically distinct population. We characterized population genetic diversity at 11 nuclear microsatellite loci in 260 individuals from 13 sites. We monitored flowering time at 10 sites, and characterized the local environment in order to compare observed spatial genetic structure to hypotheses of isolation-by-distance and isolation-by-environment. Finally, we quantified pollen dispersal distances and tested for local adaptation through a reciprocal transplant experiment in order to experimentally address these hypotheses. Results High genetic diversity is maintained in the population and the genetic variation is significantly structured among sampled sites. We identified 5 distinct genetic clusters and average pollen dispersal predominately occurred over short distances. Differences among sites in flowering phenology and environmental factors, however, were not strictly associated with genetic differentiation. Growth and survival of upland and lowland progeny in their native and foreign environments was expected to exhibit evidence of local adaptation due to the more extreme dry season in the lowlands. Seedlings planted in the lowland garden experienced much higher mortality than seedlings in the upland garden, but we did not identify evidence for local adaptation. Conclusion Overall, this study indicates that the Costa Rican Q. oleoides population has a rich population genetic history. Despite environmental heterogeneity and habitat fragmentation, isolation-by-distance and isolation-by-environment alone do not explain spatial genetic structure. These results add to studies of genetic
PET Cell Tracking Using 18F-FLT is Not Limited by Local Reuptake of Free Radiotracer
MacAskill, Mark G.; Tavares, Adriana S.; Wu, Junxi; Lucatelli, Christophe; Mountford, Joanne C.; Baker, Andrew H.; Newby, David E.; Hadoke, Patrick W. F.
2017-01-01
Assessing the retention of cell therapies following implantation is vital and often achieved by labelling cells with 2′-[18F]-fluoro-2′-deoxy-D-glucose (18F-FDG). However, this approach is limited by local retention of cell-effluxed radiotracer. Here, in a preclinical model of critical limb ischemia, we assessed a novel method of cell tracking using 3′-deoxy-3′-L-[18F]-fluorothymidine (18F-FLT); a clinically available radiotracer which we hypothesise will result in minimal local radiotracer reuptake and allow a more accurate estimation of cell retention. Human endothelial cells (HUVECs) were incubated with 18F-FDG or 18F-FLT and cell characteristics were evaluated. Dynamic positron emission tomography (PET) images were acquired post-injection of free 18F-FDG/18F-FLT or 18F-FDG/18F-FLT-labelled HUVECs, following the surgical induction of mouse hind-limb ischemia. In vitro, radiotracer incorporation and efflux was similar with no effect on cell viability, function or proliferation under optimised conditions (5 MBq/mL, 60 min). Injection of free radiotracer demonstrated a faster clearance of 18F-FLT from the injection site vs. 18F-FDG (p ≤ 0.001), indicating local cellular uptake. Using 18F-FLT-labelling, estimation of HUVEC retention within the engraftment site 4 hr post-administration was 24.5 ± 3.2%. PET cell tracking using 18F-FLT labelling is an improved approach vs. 18F-FDG as it is not susceptible to local host cell reuptake, resulting in a more accurate estimation of cell retention. PMID:28287126
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
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.
NASA Astrophysics Data System (ADS)
Scott, Dalton; Bradley, Robert; Bellenger, Jean-Philippe; Kathrin, Rousk; Michael, Gundale; DeLuca, Tom
2017-04-01
A major challenge facing biogeochemists is being able to predict how environmental changes alter the functioning of forest ecosystems. In particular, atmospheric N deposition (AND) from fossil fuel combustion is fertilizing forest ecosystems worldwide at an unprecedented rate. While much attention has been paid to regional and continental-scale AND patterns, very little is known about local scale patterns resulting from human activities. For example, busy roads have recently been identified as hotspots for AND, with steep gradients occurring within 100-400 m margins along busy roadsides. It was previously found that such gradients along boreal forest roadsides correlated negatively with changes in biological N fixation (BNF) by moss dwelling cyanobacteria. Here, we present data from a recent experiment designed to answer specific questions regarding this phenomenon, namely: (1) Can AND lead to shifts from N to P limitation of BNF in mosses? (2) Can AND shift the stoichiometry of P and Mo (i.e. nitrogenase enzyme cofactor) limiting BNF in mosses? (3) Do roadside BNF patterns occur because of a down regulation in nitrogenase enzyme activity, or as the result of changes in moss biomass? (4) Do roadside AND and BNF patterns correlate predictably with the relative N-to-P limitation of trees? Preliminary results confirm that roadside BNF gradients are site specific, with moisture and light availability as major environmental controls. P-limitations of BNF were observed along roadside gradients on some sites, as were changes in spruce needle N and P concentrations. Decreases in BNF due to high AND may partly be due to changes in moss biomass. Collectively, our project provides important insights that improve our knowledge of site-specific stoichiometric gradients due to AND, which can be used to improve the precision of biogeochemical models required to predict ecosystem responses to global changes.
Whitney's theorem in the L^p-metric, 0
NASA Astrophysics Data System (ADS)
Storozhenko, E. A.; Kryakin, Yu V.
1995-04-01
In the original proof of the theorem on local approximation of functions by algebraic polynomials, Whitney estimated the deviation of the function from an interpolating polynomial with equally spaced nodes by means of finite differences. In this article we show how Whitney's idea of choosing nodes depending on a parameter with subsequent averaging can be applied to functions in L^p. The methods indicated allow one to obtain an estimate for the speed of approximating functions given on au arc of the unit circle by trigonometric polynomials or splines.
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.
Salas-Montiel, Rafael; Berthel, Martin; Beltrán-Madrigal, Josslyn; Huant, Serge; Drezet, Aurélien; Blaize, Sylvain
2017-03-21
One of the most explored single quantum emitters for the development of nanoscale fluorescence lifetime imaging is the nitrogen-vacancy (NV) color center in diamond. Indeed, a NV center does not experience fluorescence bleaching and blinking at room temperature. Furthermore, its optical properties are preserved when embedded into nanodiamond hosts. This letter focuses on the modeling of the local density of states (LDOS) in a plasmonic nanofocusing structure with NV center acting as local illumination sources. Numerical calculations of the LDOS near such nanostructure were done with a classical electric dipole radiation placed inside a diamond sphere as well as near-field optical fluorescence lifetime imaging of the structure. We found that Purcell factors higher than 10 can be reached with diamond nanospheres of radius less than 5 nm and at a distance of less than 20 nm from the surface of the structure. Although the spatial resolution of the experiment is limited by the size of the nanodiamond, our work supports the analysis and interpretation of single NV color center in nanodiamond as a probe for scanning near-field optical microscopy.
NASA Astrophysics Data System (ADS)
Salas-Montiel, Rafael; Berthel, Martin; Beltran-Madrigal, Josslyn; Huant, Serge; Drezet, Aurélien; Blaize, Sylvain
2017-05-01
One of the most explored single quantum emitters for the development of nanoscale fluorescence lifetime imaging is the nitrogen-vacancy (NV) color center in diamond. An NV center does not experience fluorescence bleaching or blinking at room temperature. Furthermore, its optical properties are preserved when embedded into nanodiamond hosts. This paper focuses on the modeling of the local density of states (LDOS) in a plasmonic nanofocusing structure with an NV center acting as local illumination sources. Numerical calculations of the LDOS near such a nanostructure were done with a classical electric dipole radiation placed inside a diamond sphere as well as near-field optical fluorescence lifetime imaging of the structure. We found that Purcell factors higher than ten can be reached with diamond nanospheres of radius less than 5 nm and at a distance of less than 20 nm from the surface of the structure. Although the spatial resolution of the experiment is limited by the size of the nanodiamond, our work supports the analysis and interpretation of a single NV color center in a nanodiamond as a probe for scanning near-field optical microscopy.
Patsha, Avinash E-mail: dhara@igcar.gov.in; Dhara, Sandip; Tyagi, A. K.
2015-09-21
The localized effect of impurities in single GaN nanowires in the sub-diffraction limit is reported using the study of lattice vibrational modes in the evanescent field of Au nanoparticle assisted tip enhanced Raman spectroscopy (TERS). GaN nanowires with the O impurity and the Mg dopants were grown by the chemical vapor deposition technique in the catalyst assisted vapor-liquid-solid process. Symmetry allowed Raman modes of wurtzite GaN are observed for undoped and doped nanowires. Unusually very strong intensity of the non-zone center zone boundary mode is observed for the TERS studies of both the undoped and the Mg doped GaN single nanowires. Surface optical mode of A{sub 1} symmetry is also observed for both the undoped and the Mg doped GaN samples. A strong coupling of longitudinal optical (LO) phonons with free electrons, however, is reported only in the O rich single nanowires with the asymmetric A{sub 1}(LO) mode. Study of the local vibration mode shows the presence of Mg as dopant in the single GaN nanowires.
Coster, Stephanie S; Babbitt, Kimberly J; Cooper, Andrew; Kovach, Adrienne I
2015-02-01
Dispersal and gene flow within animal populations are influenced by the composition and configuration of the landscape. In this study, we evaluated hypotheses about the impact of natural and anthropogenic factors on genetic differentiation in two amphibian species, the spotted salamander (Ambystoma maculatum) and the wood frog (Lithobates sylvaticus) in a commercial forest in central Maine. We conducted this analysis at two scales: a local level, focused on factors measured at each breeding pond, and a landscape level, focused on factors measured between ponds. We investigated the effects of a number of environmental factors in six categories including Productivity, Physical, Land Composition, Land Configuration, Isolation and Location. Embryos were sampled from 56 spotted salamander breeding ponds and 39 wood frog breeding ponds. We used a hierarchical Bayesian approach in the program GESTE at each breeding pond and a random forest algorithm in conjunction with a network analysis between the ponds. We found overall high genetic connectivity across distances up to 17 km for both species and a limited effect of natural and anthropogenic factors on gene flow. We found the null models best explained patterns of genetic differentiation at a local level and found several factors at the landscape level that weakly influenced gene flow. This research indicates multiscale investigations that incorporate local and landscape factors are valuable for understanding patterns of gene flow. Our findings suggest that dispersal rates in this system are high enough to minimize genetic structuring and that current forestry practices do not significantly impede dispersal. © 2015 John Wiley & Sons Ltd.
Imbedding Locally Euclidean and Conformally Euclidean Metrics
NASA Astrophysics Data System (ADS)
Aleksandrov, V. A.
1992-02-01
The possibility of imbedding n-dimensional locally Euclidean metrics in the large in Rn is studied by means of the global inverse function theorem in the forms suggested by Hadamard, John, Levy and Plastock. The imbeddability of conformally Euclidean metrics is studied by means of a theorem of Zorich on the removability of an isolated singularity of a locally quasiconformal mapping.
Fortier, T M; Ashby, N; Bergquist, J C; Delaney, M J; Diddams, S A; Heavner, T P; Hollberg, L; Itano, W M; Jefferts, S R; Kim, K; Levi, F; Lorini, L; Oskay, W H; Parker, T E; Shirley, J; Stalnaker, J E
2007-02-16
We report tests of local position invariance and the variation of fundamental constants from measurements of the frequency ratio of the 282-nm 199Hg+ optical clock transition to the ground state hyperfine splitting in 133Cs. Analysis of the frequency ratio of the two clocks, extending over 6 yr at NIST, is used to place a limit on its fractional variation of <5.8x10(-6) per change in normalized solar gravitational potential. The same frequency ratio is also used to obtain 20-fold improvement over previous limits on the fractional variation of the fine structure constant of |alpha/alpha|<1.3x10(-16) yr-1, assuming invariance of other fundamental constants. Comparisons of our results with those previously reported for the absolute optical frequency measurements in H and 171Yb+ vs other 133Cs standards yield a coupled constraint of -1.5x10(-15)
Chua, Daniel T T; Sham, Jonathan S T; Kwong, Philip W K; Hung, Kwan-Ngai; Leung, Lucullus H T
2003-05-01
To evaluate the efficacy and complication of linear accelerator-based stereotactic radiosurgery (SRS) when used as salvage treatment for early-stage persistent and recurrent nasopharyngeal carcinoma (NPC) after primary radiotherapy (RT). Between March 1998 and June 2001, 18 patients (15 men and 3 women; median age 46 years, range 32-84) with locally persistent or recurrent NPC confined to the nasopharynx (rT1) or with limited extension to the nasal fossa or parapharyngeal space (rT2) were treated by SRS. Thirteen patients had rT1 disease and 5 had rT2 disease. Most patients had disease not amenable to surgery or brachytherapy. All patients had undergone previous radical RT. Persistent disease was defined as tumor relapse within 4 months of completion of primary RT, and recurrence as tumor relapse beyond 4 months. Seven patients were treated for persistent disease, eight for a first recurrence, and three for a second recurrence. SRS was performed using multiple noncoplanar arcs of photons delivered to the target volume, which was defined by axial CT at a 3 mm thickness, supplemented by MRI in selected patients (67%). The median target volume was 5.3 cm(3) (range 2.2-16.9). The median SRS dose was 12.5 Gy (range 11-14) delivered to the 80% isodose line. All patients underwent serial nasopharyngoscopy and imaging after SRS. The median follow-up was 26 months (range 11-48). After SRS, 16 (89%) of 18 patients had complete regression of tumor as assessed by nasopharyngoscopy and biopsy. Four patients with an initial complete response to SRS subsequently developed local relapse again, with one recurrence developing outside the target volume 8 months after SRS and three within the target volume at 6-26 months after SRS. Two patients with local disease controlled by SRS developed relapse in other sites (neck node and liver metastases). The actuarial 2-year local control rate after SRS was 72%. Patients treated for persistent disease had a better local control rate (100%; 7
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…
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
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…
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
Code of Federal Regulations, 2010 CFR
2010-04-01
... fuel used in intercity, local or school buses after July 31, 1984. 48.6427-6 Section 48.6427-6 Internal... intercity, local or school buses after July 31, 1984. (a) Limitation on amount of credit or refund—(1) In general. In the case of fuel sold or used after July 31, 1984, on which tax was imposed under section 4041...
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.
NASA Astrophysics Data System (ADS)
Spruzeniece, L.; Piazolo, S.
2015-04-01
This study focuses on physiochemical processes occurring in a brittle-ductile shear zone at both fluid-present and fluid-limited conditions. In the studied shear zone (Wyangala, SE Australia), a coarse-grained two feldspar-quartz-biotite granite is transformed into a medium grained orthogneiss at the shear zone margins and a fine-grained quartz-muscovite phyllonite in the central parts. The orthogneiss displays cataclasis of feldspar and crystal-plastic deformation of quartz. Quartz accommodates most of the deformation and is extensively recrystallized showing distinct crystallographic preferred orientation (CPO). Feldspar-to-muscovite, biotite-to-muscovite and albitization reactions occur locally at porphyroclasts' fracture surfaces and margins. However, the bulk rock composition shows very little change in respect to the wall rock composition. In contrast, in the shear zone centre quartz occurs as large, weakly deformed porphyroclasts, in sizes similar to that in the wall rock, suggesting that it has undergone little deformation. Feldspars and biotite are almost completely reacted to muscovite, which is arranged in a fine-grained interconnected matrix. Muscovite-rich layers contain significant amounts of fine-grained intermixed quartz with random CPO. These domains are interpreted to have accommodated most of the strain. Bulk rock chemistry data shows a significant increase in SiO2 and depletion in NaO content compared to the wall rock composition. We suggest that the high and low strain fabrics represent markedly different scenarios and cannot be interpreted as a simple sequential development with respect to strain. We suggest that the fabrics and mineralogical changes in the shear zone centre have formed due to fluid influx probably along an initially brittle fracture. Here, hydration reactions dramatically changed the rheological properties of the rock. In the newly produced muscovite-quartz layers creep cavitation associated with grain boundary sliding and
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.
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.
Jorgensen, Christopher F.; Powell, Larkin A.; Lusk, Jeffery J.; Bishop, Andrew A.; Fontaine, Joseph J.
2014-01-01
Landscapes in agricultural systems continue to undergo significant change, and the loss of biodiversity is an ever-increasing threat. Although habitat restoration is beneficial, management actions do not always result in the desired outcome. Managers must understand why management actions fail; yet, past studies have focused on assessing habitat attributes at a single spatial scale, and often fail to consider the importance of ecological mechanisms that act across spatial scales. We located survey sites across southern Nebraska, USA and conducted point counts to estimate Ring-necked Pheasant abundance, an economically important species to the region, while simultaneously quantifying landscape effects using a geographic information system. To identify suitable areas for allocating limited management resources, we assessed land cover relationships to our counts using a Bayesian binomial-Poisson hierarchical model to construct predictive Species Distribution Models of relative abundance. Our results indicated that landscape scale land cover variables severely constrained or, alternatively, facilitated the positive effects of local land management for Ring-necked Pheasants. PMID:24918779
Localization and interaction effects of epitaxial Bi2Se3 bulk states in two-dimensional limit
NASA Astrophysics Data System (ADS)
Dey, Rik; Roy, Anupam; Pramanik, Tanmoy; Guchhait, Samaresh; Sonde, Sushant; Rai, Amritesh; Register, Leonard F.; Banerjee, Sanjay K.
2016-10-01
Quantum interference effects and electron-electron interactions are found to play an important role in two-dimensional (2D) bulk transport of topological insulator (TI) thin films, which were previously considered as 2D electron gas (2DEG) and explained on basis of Hikami-Larkin-Nagaoka formula and Lee-Ramakrishnan theory. The distinct massive Dirac-type band structure of the TI bulk state gives rise to quantum corrections to conductivity due to interference and interaction effects, which are quite different from that of a 2DEG. We interpret the experimental findings employing Lu-Shen theory particularly derived for the TI system in the 2D limit. The surface and the bulk conductions are identified based on slopes of logarithmic temperature-dependent conductivities with magnetic fields. The perpendicular field magnetoresistance is analyzed considering suppression of weak antilocalization/localization of the surface/bulk electrons by the applied field. We propose corresponding theoretical models to explain the parallel and tilted field magnetoresistance. The effect of the band structure is found to be crucial for an accurate explanation of the magnetotransport results in the TI thin film.
Finite de Finetti theorem for conditional probability distributions describing physical theories
NASA Astrophysics Data System (ADS)
Christandl, Matthias; Toner, Ben
2009-04-01
We work in a general framework where the state of a physical system is defined by its behavior under measurement and the global state is constrained by no-signaling conditions. We show that the marginals of symmetric states in such theories can be approximated by convex combinations of independent and identical conditional probability distributions, generalizing the classical finite de Finetti theorem of Diaconis and Freedman. Our results apply to correlations obtained from quantum states even when there is no bound on the local dimension, so that known quantum de Finetti theorems cannot be used.
Fixed-point theorems for families of weakly non-expansive maps
NASA Astrophysics Data System (ADS)
Mai, Jie-Hua; Liu, Xin-He
2007-10-01
In this paper, we present some fixed-point theorems for families of weakly non-expansive maps under some relatively weaker and more general conditions. Our results generalize and improve several results due to Jungck [G. Jungck, Fixed points via a generalized local commutativity, Int. J. Math. Math. Sci. 25 (8) (2001) 497-507], Jachymski [J. Jachymski, A generalization of the theorem by Rhoades and Watson for contractive type mappings, Math. Japon. 38 (6) (1993) 1095-1102], Guo [C. Guo, An extension of fixed point theorem of Krasnoselski, Chinese J. Math. (P.O.C.) 21 (1) (1993) 13-20], Rhoades [B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977) 257-290], and others.
Kochen-Specker theorem as a precondition for secure quantum key distribution
Nagata, Koji
2005-07-15
We show that (1) the violation of the Ekert 1991 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 1992 (BBM92) inequality is, also, a sufficient condition for certification of the KS theorem. Therefore the success in each quantum key distribution protocol reveals the nonclassical feature of quantum theory, in the sense that the KS realism is violated. Further, it turned out that the Ekert inequality and the BBM inequality are depictured by distillable entanglement witness inequalities. Here, we connect the success in these two key distribution processes into the no-hidden-variables theorem and into witness on distillable entanglement. We also discuss the explicit difference between the KS realism and Bell's local realism in the Hilbert space formalism of quantum theory.
General proof of the Greenberger-Horne-Zeilinger theorem
Chen Zeqian
2004-09-01
It is proved that all states of three spin-(1/2) particles exhibiting an 'all versus nothing' contradiction between quantum mechanics and the local realism of Einstein, Podolsky, and Rosen are exactly the Greenberger-Horne-Zeilinger (GHZ) states and the states obtained from them by local unitary transformations. The proof is obtained by showing that there are at most four elements (except for a different sign) in a set of mutually commuting nonlocal spin observables in the three-qubit system and using the certain algebraic properties that Pauli's matrices satisfy. We show that only does such a set of four nonlocal spin observables present a Greenberger-Horne-Zeilinger-Mermin-like argument. This also reveals the equivalence between the GHZ theorem and maximal violation of the Bell inequality.
Bell's theorem and quantum mechanics
NASA Astrophysics Data System (ADS)
Rosen, Nathan
1994-02-01
Bell showed that assuming locality leads to a disagreement with quantum mechanics. Here the nature of the nonlocality that follows from quantum mechanics is investigated. Note by the Editor—Readers will recognize Professor Rosen, author of this paper, as one of the co-authors of the famous EPR paper, Albert Einstein, Boris Podolsky, and Nathan Rosen, ``Can Quantum-Mechanical Description of Physical Reality be considered Complete?'', Phys. Rev. 47, 770-780 (1935). Robert H. Romer, Editor
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.
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
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…
Manca, F; Rossi, G; Valle, M T; Lantero, S; Li Pira, G; Fenoglio, D; De Bruin, J; Costantini, M; Damiani, G; Balbi, B
1991-01-01
To detect possible differences in phenotype and fine specificity for mycobacterial antigens between CD4-positive T cells from peripheral blood (PB) and from inflammatory sites, we identified four patients presenting with a mycobacterial pleural exudate (PE) rich in PPD-specific lymphocytes and with a negative skin test to tuberculin purified protein derivative (PPD) and a negative proliferative response of PB lymphocytes to PPD at the same time. Several weeks after chemotherapy, these patients converted to PPD responsiveness in the periphery, and PPD-specific clones could be generated from PB at this stage. The phenotypic comparison of PE lymphocytes and concomitant PB lymphocytes obtained before treatment showed an increase of CD8 cells and a high frequency of HLA-DR-positive activated T cells in PE. The frequency of tetanus toxoid-specific and Candida albicans-specific proliferating T cells was lower than that of PPD-specific cells in PE but not in PB. PPD-specific clones were derived initially from PE and from PB once the patients had converted to PPD responsiveness. The two sets of clones from each patient were compared for proliferative response to mycobacterial antigen clusters of defined molecular weight ranges. A large number of PE-derived clones (36%) responded to a fraction of 27 to 35 kDa, whereas only one clone from PB responded to the same fraction. The purified antigen P32 (32 kDa), a soluble mycobacterial protein, stimulated PE-derived clones that were responsive to the 37- to 27-kDa fraction but did not stimulate PB-derived clones. The data demonstrate that PE- and PB-derived lymphocytes differ both in phenotype and in fine specificity, suggesting a limited clonal heterogeneity of T cells localizing at the inflammatory site in tuberculous patients without a PPD response in the periphery. Therefore T cells compartmentalized at inflammatory sites provide information that is different from that provided by T cells in the periphery. PMID:1898906
NASA Astrophysics Data System (ADS)
Dicecco, S.; Butcher, C.; Worswick, M.; Boettcher, E.; Chu, E.; Shi, C.
2016-11-01
The forming limit behaviour of AA6013-T6 aluminium alloy sheet was characterized under isothermal conditions at room temperature (RT) and 250°C using limiting dome height (LDH) tests. Full field strain measurements were acquired throughout testing using in situ stereoscopic digital image correlation (DIC) techniques. Limit strain data was generated from the resulting full field strain measurements using two localized necking criteria: ISO12004- 2:2008 and a time and position dependent criterion, termed the “Necking Zone” (NZ) approach in this paper, introduced by Martinez-Donaire et al. (2014). The limit strains resulting from the two localization detection schemes were compared. It was found that the ISO and NZ limit strains at RT are similar on the draw-side of the FLD, while the NZ approach yields a biaxial major limit strain 14.8% greater than the ISO generated major limit strain. At 250°C, the NZ generated major limit strains are 31-34% greater than the ISO generated major limit strains for near uniaxial, plane strain and biaxial loading conditions, respectively. The significant variance in limit strains between the two methodologies at 250°C highlights the need for a validation study regarding warm FLC determination.
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.
NASA Astrophysics Data System (ADS)
Rau, Uwe; Brendel, Rolf
1998-12-01
It is shown that a recently described general relationship between the local collection efficiency of solar cells and the dark carrier concentration (reciprocity theorem) directly follows from the principle of detailed balance. We derive the relationship for situations where transport of charge carriers occurs between discrete states as well as for the situation where electronic transport is described in terms of continuous functions. Combining both situations allows to extend the range of applicability of the reciprocity theorem to all types of solar cells, including, e.g., metal-insulator-semiconductor-type, electrochemical solar cells, as well as the inclusion of the impurity photovoltaic effect. We generalize the theorem further to situations where the occupation probability of electronic states is governed by Fermi-Dirac statistics instead of Boltzmann statistics as underlying preceding work. In such a situation the reciprocity theorem is restricted to small departures from equilibrium.
1986-02-01
literture - see e.g. [6 -81 so we will be rather sketchy. Suppose first that H 2 *Then n is determined as the solution of an ordinary differential equation ...finding periodic solutions of differential equations , Nonlinear Evolution Equations (M. G. Crandall, editor), Academic Press, New York, (1978), 225-251...in X.of the form: =-tw(r) !A() - n’’n (2.19) d nI(0,z) - z where )dn) =A (ri) ’’’()14~- *In (2.19), w is a locally Lipschitz continuous function
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…
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.
Large- N limit of the non-local 2D Yang Mills and generalized Yang Mills theories on a cylinder
NASA Astrophysics Data System (ADS)
Saaidi, K.; Khorrami, M.
2002-04-01
The large-group behavior of the non-local YM_2's and gYM_2's on a cylinder or a disk is investigated. It is shown that this behavior is similar to that of the corresponding local theory, but with the area of the cylinder replaced by an effective area depending on the dominant representation. The critical areas for non-local YM_2's on a cylinder with some special boundary conditions are also obtained.
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.
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
ERIC Educational Resources Information Center
Bokhari, M. A.; Yushau, B.
2006-01-01
At the start of a freshman calculus course, many students conceive the classical definition of limit as the most problematic part of calculus. They not only find it difficult to understand, but also consider it of no use while solving most of the limit problems and therefore, skip it. This paper reformulates the rigorous definition of limit, which…
Localized excitations from localized unitary operators
NASA Astrophysics Data System (ADS)
Sivaramakrishnan, Allic
2017-06-01
Localized unitary operators are basic probes of locality and causality in quantum systems: localized unitary operators create localized excitations in entangled states. Working with an explicit form, we explore properties of these operators in quantum mechanics and quantum field theory. We show that, unlike unitary operators, local non-unitary operators generically create non-local excitations. We present a local picture for quantum systems in which localized experimentalists can only act through localized Hamiltonian deformations, and therefore localized unitary operators. We demonstrate that localized unitary operators model certain quantum quenches exactly. We show how the Reeh-Schlieder theorem follows intuitively from basic properties of entanglement, non-unitary operators, and the local picture. We show that a recent quasi-particle picture for excited-state entanglement entropy in conformal field theories is not universal for all local operators. We prove a causality relation for entanglement entropy and connect our results to the AdS/CFT correspondence.
NASA Astrophysics Data System (ADS)
Hollen, S. M.; Fernandes, G. E.; Xu, J. M.; Valles, J. M.
2014-10-01
A Bose insulator composed of a low density of strongly localized Cooper pairs develops at the two-dimensional superconductor to insulator transition (SIT) in a number of thin film systems. Investigations of ultrathin amorphous PbBi films far from the SIT described here provide evidence that the Bose insulator gives way to a second insulating phase with decreasing film thickness. At a critical film thickness dc the magnetoresistance changes sign from positive, as expected for boson transport, to negative, as expected for fermion transport, signs of local Cooper-pair phase coherence effects on transport vanish, and the transport activation energy exhibits a kink. Below dc pairing fluctuation effects remain visible in the high-temperature transport while the activation energy continues to rise. These features show that Cooper pairing persists and suggest that the localized unpaired electron states involved in transport are interspersed among regions of strongly localized Cooper pairs in this strongly localized, low Cooper-pair density phase.
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.
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.
Gradient estimates for u=ΔF(u) on manifolds and some Liouville-type theorems
NASA Astrophysics Data System (ADS)
Xu, Xiangjin
In this paper, we first prove a localized Hamilton-type gradient estimate for the positive solutions of Porous Media type equations: u=ΔF(u), with F(u)>0, on a complete Riemannian manifold with Ricci curvature bounded from below. In the second part, we study Fast Diffusion Equation (FDE) and Porous Media Equation (PME): u=Δ(u), p>0, and obtain localized Hamilton-type gradient estimates for FDE and PME in a larger range of p than that for Aronson-Bénilan estimate, Harnack inequalities and Cauchy problems in the literature. Applying the localized gradient estimates for FDE and PME, we prove some Liouville-type theorems for positive global solutions of FDE and PME on noncompact complete manifolds with nonnegative Ricci curvature, generalizing Yau's celebrated Liouville theorem for positive harmonic functions.
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.
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.