Exact Analogue Research Articles

Logistic map with memory from economic model

A generalization of the economic model of logistic growth, which takes into account the effects of memory and crises, is suggested. Memory effect means that the economic factors and parameters at any given time depend not only on their values at that time, but also on their values at previous times. For the mathematical description of the memory effects, we use the theory of derivatives of non-integer order. Crises are considered as sharp splashes (bursts) of the price, which are mathematically described by the delta-functions. Using the equivalence of fractional differential equations and the Volterra integral equations, we obtain discrete maps with memory that are exact discrete analogs of fractional differential equations of economic processes. We derive logistic map with memory, its generalizations, and “economic” discrete maps with memory from the fractional differential equations, which describe the economic natural growth with competition, power-law memory and crises.

Exact Solution of T-Difference Radial Schrödinger Equation

In this paper, we get an exact discrete analog of the radial Schrodinger equation. We propose a difference equation that exactly corresponds to the standard radial Schrodinger equation. The suggested equation contains \({{{\mathcal {T}}}}\)-differences that are represented by infinite series. From a physical point of view, this discrete equation describes a lattice with long-range interactions of power-law type. From a mathematical point of view, it is a uniquely selected difference equation that exactly corresponds to continuous radial Schrodinger equation. Solution of the suggested difference radial Schrodinger equation is obtained.

Model-based Dynamic Control of Speculative Forays in Parallel Computation

In simulations running in parallel, the processors would have to synchronize with other processors to maintain correct global order of computations. This can be done either by blocking computation until correct order is guaranteed, or by speculatively proceeding with the best guess (based on local information) and later correcting errors if/as necessary. Since the gainful lengths of speculative forays depend on the dynamics of the application software and hardware at runtime, an online control system is necessary to dynamically choose and/or switch between the blocking and speculative strategies. In this paper, we formulate the reversible speculative computing in large-scale parallel computing as a dynamic linear feedback control (optimization) system model and evaluate its performance in terms of time and cost savings as compared to the traditional (forward) computing. We illustrate with an exact analogy in the form of vehicular travel under dynamic, delayed route information. The objective is to assist in making the optimal decision on what computational approach is to be chosen, by predicting the amount of time and cost savings (or losing) under different environments represented by different parameters and probability distribution functions. We consider the cases of Gaussian, exponential and log-normal distribution functions. The control system is intended for incorporating into speculative parallel applications such as optimistic parallel discrete event simulations to decide at runtime when and to what extent speculative execution can be performed gainfully.

Cyprideis torosa(Jones, 1850) in its type area and stratigraphical context: potential for mapping the freshwater/estuarine boundaries of the Thames–Medway river system in the MIS 9 and MIS 11 interglacials

This study explores the potential of the ostracod Cyprideis torosa (Jones, 1850) as a brackish-water indicator for mapping freshwater/estuarine boundaries in Pleistocene interglacials in SE England. Ostracod species records from MIS 9 (Purfleet) and MIS 11 (Hoxnian) interglacial sites are mapped onto established palaeogeographies of the Thames–Medway river system, revealing distribution patterns indicative of a salinity gradient from west (freshwater) to east (brackish estuarine) in both cases. Comparisons with the ostracod biofacies of the present-day Thames Estuary suggest there may be no exact modern analogue for the Thames/Medway palaeoenvironments of the MIS 9 and MIS 11 interglacials. A similar conclusion is drawn from discussion of noding in C. torosa , which is common in the interglacial assemblages but extremely rare in the modern estuary. The value of mapping C. torosa onto estuarine palaeogeography is limited by taphonomic considerations because post-mortem transport and mixing in a macrotidal estuary significantly influence the composition of ostracod assemblages. Nevertheless, its use in combination with other brackish-water taxa provides useful insights regarding the palaeosalinity regimes of the lower River Thames and River Medway during the MIS 9 and MIS 11 interglacials.

Subdivision exterior calculus for geometry processing

This paper introduces a new computational method to solve differential equations on subdivision surfaces. Our approach adapts the numerical framework of Discrete Exterior Calculus (DEC) from the polygonal to the subdivision setting by exploiting the refin-ability of subdivision basis functions. The resulting Subdivision Exterior Calculus (SEC) provides significant improvements in accuracy compared to existing polygonal techniques, while offering exact finite-dimensional analogs of continuum structural identities such as Stokes' theorem and Helmholtz-Hodge decomposition. We demonstrate the versatility and efficiency of SEC on common geometry processing tasks including parameterization, geodesic distance computation, and vector field design.

Exact Discrete Analogs of Canonical Commutation and Uncertainty Relations

An exact discretization of the canonical commutation and corresponding uncertainty relations are suggested. We prove that the canonical commutation relations of discrete quantum mechanics, which is based on standard finite difference, holds for constant wave functions only. In this paper, we use the recently proposed exact discretization of derivatives, which is based on differences that are represented by infinite series. This new mathematical tool allows us to build sensible discrete quantum mechanics based on the suggested differences and includes the correct canonical commutation and uncertainty relations.

Resonance Van Hove singularities in wave kinetics

Wave kinetic theory has been developed to describe the statistical dynamics of weakly nonlinear, dispersive waves. However, we show that systems which are generally dispersive can have resonant sets of wave modes with identical group velocities, leading to a local breakdown of dispersivity. This shows up as a geometric singularity of the resonant manifold and possibly as an infinite phase measure in the collision integral. Such singularities occur widely for classical wave systems, including acoustical waves, Rossby waves, helical waves in rotating fluids, light waves in nonlinear optics and also in quantum transport, e.g. kinetics of electron–hole excitations (matter waves) in graphene. These singularities are the exact analogue of the critical points found by Van Hove in 1953 for phonon dispersion relations in crystals. The importance of these singularities in wave kinetics depends on the dimension of phase space D=(N−2)d (d physical space dimension, N the number of waves in resonance) and the degree of degeneracy δ of the critical points. Following Van Hove, we show that non-degenerate singularities lead to finite phase measures for D>2 but produce divergences when D≤2 and possible breakdown of wave kinetics if the collision integral itself becomes too large (or even infinite). Similar divergences and possible breakdown can occur for degenerate singularities, when D−δ≤2, as we find for several physical examples, including electron–hole kinetics in graphene. When the standard kinetic equation breaks down, then one must develop a new singular wave kinetics. We discuss approaches from pioneering 1971 work of Newell & Aucoin on multi-scale perturbation theory for acoustic waves and field-theoretic methods based on exact Schwinger–Dyson integral equations for the wave dynamics.

Exact solutions and physical analogies for unidirectional flows

Unidirectional flow is the simplest phenomenon of fluid mechanics. Its mathematical description, the Dirichlet problem for Poisson's equation in two dimensions with constant forcing, arises in many physical contexts, such as the torsion of elastic beams, first solved by de Saint-Venant for complex shapes. Here, the literature is unified and extended by identifying seventeen physical analogies for unidirectional flow and describing their common mathematical structure. Besides classical analogies in fluid and solid mechanics, applications are discussed in stochastic processes (first passage in two dimensions), pattern formation (river growth by erosion), and electrokinetics (ion transport in nanochannels), which also involve Poisson's equation with non-constant forcing. Methods are given to construct approximate geometries that admit exact solutions, by adding harmonic functions to quadratic forms or by truncating eigenfunction expansions. Exact solutions for given geometries are also derived by conformal mapping. We prove that the remarkable geometrical interpretation of Poiseuille flow in an equilateral triangular pipe (the product of the distances from an interior point to the sides) is only shared by parallel plates and unbounded equilateral wedges (with the third side hidden behind the apex). We also prove Onsager reciprocity for linear electrokinetic phenomena in straight pores of arbitrary shape and surface charge, based on the mathematics of unidirectional flow.

Exterior field of slowly and rapidly rotating neutron stars: Rehabilitating spacetime metrics involving hyperextreme objects

The 4-parameter exact solution presumably describing the exterior gravitational field of a generic neutron star is presented in a concise explicit form defined by only three potentials. In the equatorial plane, the metric functions of the solution are found to be given by particularly simple expressions that make them very suitable for the use in concrete applications. Following Pappas and Apostolatos, we perform a comparison of the multipole structure of the solution with the multipole moments of the known physically realistic Berti-Stergioulas numerical models of neutron stars to argue that the hyperextreme sectors of the solution are not less (but possibly even more) important for the correct description of rapidly rotating neutron stars than the subextreme sector involving exclusively the black-hole constituents. We have also worked out in explicit form an exact analog of the well-known Hartle-Thorne approximate metric.

Spacetime dynamics of spinning particles: Exact electromagnetic analogies

We compare the rigorous equations describing the motion of spinning test particles in gravitational and electromagnetic fields, and show that if the Mathisson-Pirani spin condition holds then exact gravito-electromagnetic analogies emerge. These analogies provide a familiar formalism to treat gravitational problems, as well as a means for comparing the two interactions. Fundamental differences are manifest in the symmetries and time projections of the electromagnetic and gravitational tidal tensors. The physical consequences of the symmetries of the tidal tensors are explored comparing the following analogous setups: magnetic dipoles in the field of non-spinning/spinning charges, and gyroscopes in the Schwarzschild, Kerr, and Kerr-de Sitter spacetimes. The implications of the time projections of the tidal tensors are illustrated by the work done on the particle in various frames; in particular, a reciprocity is found to exist: in a frame comoving with the particle, the electromagnetic (but not the gravitational) field does work on it, causing a variation of its proper mass; conversely, for "static observers," a stationary gravitomagnetic (but not a magnetic) field does work on the particle, and the associated potential energy is seen to embody the Hawking-Wald spin-spin interaction energy. The issue of hidden momentum, and its counterintuitive dynamical implications, is also analyzed. Finally, a number of issues regarding the electromagnetic interaction and the physical meaning of Dixon's equations are clarified.

Molecular thermodynamics of quantum square-well fluids using a path-integral perturbation theory

ABSTRACTWe present a thermodynamic perturbation theory for fluids composed of N quantum particles of diameter α and mass m contained within a volume V at temperature T, interacting via a pair square-well potential (SW) with energy depth ε and range λ. Our approach is based on the exact analogy between the discretised path- integral formalism of quantum mechanics and the partition function of a classical system composed of necklace molecules, introducing a Zwanzig expansion method, using a quantum hard-spheres fluid (QHS) as reference system in order to calculate the perturbation terms for the Helmholtz free energy AQSW of the SW system. These terms are obtained with path-integral Monte Carlo simulations in the canonical ensemble, and analytical results are provided as functions of the inverse temperature β = 1/kT, density ρ* = Nσ3/V, SW range λ and de Broglie thermal wavelength , where h and k are the Planck's and Boltzmann's constants, respectively. Accurate results are obtained for thermodynamic states comprised in the region ρ* ≤ 0.7, 1.2 ≤ λ ≤ 1.8, and λ*B ⩽ 0.9. Quantum effects are more noticeable for shorter SW ranges, although the main thermodynamic effects are given by the QHS free energy.

Developing a Physiologically-Based Pharmacokinetic Model Knowledgebase in Support of Provisional Model Construction.

Developing physiologically-based pharmacokinetic (PBPK) models for chemicals can be resource-intensive, as neither chemical-specific parameters nor in vivo pharmacokinetic data are easily available for model construction. Previously developed, well-parameterized, and thoroughly-vetted models can be a great resource for the construction of models pertaining to new chemicals. A PBPK knowledgebase was compiled and developed from existing PBPK-related articles and used to develop new models. From 2,039 PBPK-related articles published between 1977 and 2013, 307 unique chemicals were identified for use as the basis of our knowledgebase. Keywords related to species, gender, developmental stages, and organs were analyzed from the articles within the PBPK knowledgebase. A correlation matrix of the 307 chemicals in the PBPK knowledgebase was calculated based on pharmacokinetic-relevant molecular descriptors. Chemicals in the PBPK knowledgebase were ranked based on their correlation toward ethylbenzene and gefitinib. Next, multiple chemicals were selected to represent exact matches, close analogues, or non-analogues of the target case study chemicals. Parameters, equations, or experimental data relevant to existing models for these chemicals and their analogues were used to construct new models, and model predictions were compared to observed values. This compiled knowledgebase provides a chemical structure-based approach for identifying PBPK models relevant to other chemical entities. Using suitable correlation metrics, we demonstrated that models of chemical analogues in the PBPK knowledgebase can guide the construction of PBPK models for other chemicals.

Concentric dual π aromaticity in bowl-like B30 cluster: an all-boron analogue of corannulene.

A chemical bonding model is presented for the bowl-like C5v B30 global-minimum cluster with a central pentagonal hole. The B30 cluster is composed of three concentric boron rings: first B5, second B10, and third B15. The first and second B rings constitute an inner double-chain ribbon and support a delocalized π sextet. The second and third rings form an outer double-chain ribbon, where 14π delocalized electrons are situated. The unique π systems lead to concentric dual π aromaticity for B30, a concept established from concerted computational data on the bases of canonical molecular orbital (CMO) analysis, adaptive natural density partitioning (AdNDP), nucleus-independent chemical shifts (NICS), and natural charge calculations. A proposal is put forward that the bowl-like B30 cluster is an exact all-boron analogue of corannulene (C20H10), a fragment of C60 fullerene. The bonding nature of corannulene is revisited and fully elucidated herein. A comparison of the bonding patterns in bowl-like C5v B30 cluster and two other structural isomers (Cs and C1) unravels the mechanism as to why the defective hole prefers to be positioned at the center.

Categorical abstract algebraic logic: skywatching in semilattice systems

Font and Moraschini established a bijective correspondence between congruences of semilattices with sectionally finite height and certain special subsets of their universes, called clouds. They provided a characterization of clouds and showed that the correspondence is given by the Leibniz operator of abstract algebraic logic. We extend the bijection to one between congruence systems on the semilattice systems of categorical abstract algebraic logic and what we call cloud families. In this context, the categorical analog of the Leibniz operator plays a similar role. In addition, we show that, even though the exact analogue of the Font–Moraschini condition fails in general, a more complex variant provides an analogous characterization of cloud families.

Exact discretization of Schrödinger equation

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations.

The Brauer category and invariant theory

A category of Brauer diagrams, analogous to Turaev's tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O (V) or the symplectic group Sp (V) over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that we obtain presentations for the endomorphism algebras of the module V^{\otimes r} , which are new in the classical symplectic case and in the orthogonal and symplectic quantum case, while in the orthogonal classical case, the proof we give here is more natural than in our earlier work. These presentations are obtained by appending to the standard presentation of the Brauer algebra of degree r one additional relation. This relation stipulates the vanishing of a single element of the Brauer algebra which is quasi-idempotent, and which we describe explicitly both in terms of diagrams and algebraically. In the symplectic case, if dim V=2n , the element is precisely the central idempotent in the Brauer subalgebra of degree n+1 , which corresponds to its trivial representation. Since this is the Brauer algebra of highest degree which is semisimple, our generator is an exact analogue for the Brauer algebra of the Jones idempotent of the Temperley-Lieb algebra. In the orthogonal case the additional relation is also a quasi-idempotent in the integral Brauer algebra. Both integral and quantum analogues of these results are given, the latter of which involve the BMW algebras.

Myers and Hawking Theorems: Geometry for the Limits of the Universe

It is known that the celebrated theorem by Hawking which assures the existence of a Big-Bang under physically motivated hypotheses, uses geometric ideas inspired in classical Myers theorem. Our aim here is to go a step further: first, a result which can be interpreted as the exact analogy in pure Riemannian geometry to Hawking theorem will be proven and, then, the isomorphic role of the hypotheses in both theorems will be analyzed. This will provide some interesting links between Riemannian and Lorentzian geometries, as well as an introduction to the latter.

Safety, efficacy, and immunogenicity of Flublok in the prevention of seasonal influenza in adults.

Flublok is the first recombinant hemagglutinin (HA) vaccine licensed by the US Food and Drugs Administration for the prevention of influenza in adults aged 18 and older. The HA proteins produced in insect cell culture using the baculovirus expression system technology are exact analogues of wild type circulating influenza virus HAs. The universal HA manufacturing process that has been successfully scaled to the 21,000L contributes to rapid delivery of a substantial number of doses. This review discusses the immunogenicity, efficacy and safety data from five pivotal clinical studies used to support licensure of trivalent Flublok for adults 18 years of age and older in the United States. The trial data demonstrate that the higher antigen content in Flublok results in improved immunogenicity. Data further suggest improved efficacy and a slightly lower local reactogenicity compared with standard inactivated influenza vaccine, despite the presence of more antigen (statistically significant). Flublok influenza vaccine can include HAs designed to mimic 'drift' in influenza viruses as the process of predicting antigenic drift advances and, at a minimum, could address late appearing influenza viruses. The implementation of the latter will require support from regulatory authorities.

Trajectory Guidance Using Periodic Relative Orbital Motion

Relative motion of one satellite about another in circular orbit, where the two objects have the same semimajor axis, is periodic in the linearized approximation. A set of orbital elements, the geometric relative orbital elements, which are an exact geometric analogy to the classical orbital elements, can be defined. The relative orbit is manifestly seen to be an ellipse or circle in apocentral coordinates, analogous to perifocal coordinates in inertial motion and different from the local-vertical local-horizontal Cartesian coordinates customarily used for analysis of relative motion problems. These provide a way to do relative motion trajectory design and guidance that stands in contrast to the use of Cartesian coordinates. Algorithms are presented for computing the delta- and timing for impulsive maneuvers to change a single element: two that change the plane and one that changes the size of the relative orbit. The change in size is a two-maneuver transfer and uses the solution of the three-point periodic boundary value problem, also solved and presented here. This solution permits the direct computation, with no iteration or searching, of the periodic relative orbit that connects two points. Optimization to minimize fuel use can be done with a one-dimensional search.

A FUNCTIONAL APPROACH TO d-ALGEBRAS

Abstract. In this paper we discuss a functional approach to obtain a lattice-likestructure in d -algebras, and obtain an exact analog of De Morgan law and someother properties. 1. Introduction Y. Imai and K. Is¶eki introduced two classes of abstract algebras: BCK -algebrasand BCI -algebras ([8, 9]). BCK -algebras have some connections with other areas:D. Mundici [13] proved that MV -algebras are categorically equivalent to boundedcommutative BCK -algebras, and J. Meng [11] proved that implicative commutativesemigroups are equivalent to a class of BCK -algebras. It is well known that boundedcommutative BCK -algebras, D -posets and MV -algebras are logically equivalenteach other (see [4, p. 420]). We refer useful textbooks for BCK=BCI -algebra to [4,6, 7, 12, 17]. J. Neggers and H. S. Kim ([14]) introduced the notion of d -algebraswhich is a useful generalization of BCK -algebras, and then investigated severalrelations between d -algebras and BCK -algebras as well as several other relationsbetween