Set Of Discrete Parameters Research Articles

On Stretching, Bending, Shearing, and Twisting of Actin Filaments I: Variational Models.

Mechanochemical simulations of actomyosin networks are traditionally based on one-dimensional models of actin filaments having zero width. Here, and in the follow up paper (arXiv, DOI 10.48550/arXiv.2203.01284), approaches are presented for more efficient modeling that incorporates stretching, shearing, and twisting of actin filaments. Our modeling of a semiflexible filament with a small but finite width is based on the Cosserat theory of elastic rods, which allows for six degrees of freedom at every point on the filament's backbone. In the variational models presented in this paper, a small and discrete set of parameters is used to describe a smooth filament shape having all degrees of freedom allowed in the Cosserat theory. Two main approaches are introduced: one where polynomial spline functions describe the filament's configuration, and one in which geodesic curves in the space of the configurational degrees of freedom are used. We find that in the latter representation the strain energy function can be calculated without resorting to a small-angle expansion, so it can describe arbitrarily large filament deformations without systematic error. These approaches are validated by a dynamical model of a Cosserat filament, which can be further extended by using multiresolution methods to allow more detailed monomer-based resolution in certain parts of the actin filament, as introduced in the follow up paper. The presented framework is illustrated by showing how torsional compliance in a finite-width filament can induce broken chiral symmetry in the structure of a cross-linked bundle.

Thomae formula for abelian covers of ℂℙ¹

Abelian covers of C P 1 \mathbb {CP}^{1} , with fixed Galois group A A , are classified, as a first step, by a discrete set of parameters. Any such cover X X , of genus g ≥ 1 g\geq 1 , say, carries a finite set of A A -invariant divisors of degree g − 1 g-1 on X X that produce nonzero theta constants on X X . We show how to define a quotient involving a power of the theta constant on X X that is associated with such a divisor Δ \Delta , some polynomial in the branching values, and a fixed determinant on X X that does not depend on Δ \Delta , such that the quotient is constant on the moduli space of A A -covers with the given discrete parameters. This generalizes the classical formula of Thomae, as well as all of its known extensions by various authors.

Fluorescence Technologies for Evaluating Male Gamete (Dys)Function

For many years, andrologists have sought ways of assessing sperm fertility, especially of new sires entering the breeding chain. As knowledge of the complex processes that enable sperm to fertilize eggs has increased, it has become clearer that quantitative estimation of the fertilizing potential of a sire or an ejaculate is actually unlikely ever to be fully realized. Here, we propose that a better approach is to identify substandard males and semen samples. During the past decades, the use of fluorescence technologies in biomedical science has burgeoned, with the development of very powerful instrumentation such as confocal microscopy and flow cytometers of ever-increasing capabilities together with a vast range of fluorochromes and fluorochrome conjugates. This technology has been applied to andrology but thus far in only a relatively simple way. In this review, we offer strategies for assessing a large range of sperm functions thought to be related to fertilizing ability over a temporal window rather than at a single time point. From such an assessment profile, sperm samples that over-respond or do not respond sufficiently could be identified, termed dysfunctional and rejected. We outline the rationales behind such tests, present information on new potentially useful fluorochromes and current flow cytometer models that would be suitable for the multicolour multifunctional tests we propose, and we offer suggestions as to how andrologists might design such multicolour tests for themselves.

Discrete Models of Electromagnetic Wave Scatterers in a Frequency Range

We investigate the spatial and frequency characteristics of electromagnetic fields scattered by some object. Frequency functions that allow the expression of all elements of the object scatter matrix are introduced. The sampling theorems that are proved for the introduced functions make it possible to characterize the scatterer by a set of discrete parameters. The application of the proved theorems provides for the creation of a versatile scatterer discrete model that determines the dependence of scattered fields both on spatial coordinates and frequency. A random scatterer is considered and the conditions under which the discrete parameters are statistically independent normalized random variables are stated. The article presents the results of a random scatterer modeling.

Toward Optimal Choices of Control Space Representation for Geophysical Data Assimilation

In geophysical data assimilation, observations shed light on a control parameter space through a model, a statistical prior, and an optimal combination of these sources of information. This control space can be a set of discrete parameters, or, more often in geophysics, part of the state space, which is distributed in space and time. When the control space is continuous, it must be discretized for numerical modeling. This discretization, in this paper called a representation of this distributed parameter space, is always fixed a priori. In this paper, the representation of the control space is considered a degree of freedom on its own. The goal of the paper is to demonstrate that one could optimize it to perform data assimilation in optimal conditions. The optimal representation is then chosen over a large dictionary of adaptive grid representations involving several space and time scales. First, to motivate the importance of the representation choice, this paper discusses the impact of a change of representation on the posterior analysis of data assimilation and its connection to the reduction of uncertainty. It is stressed that in some circumstances (atmospheric chemistry, in particular) the choice of a proper representation of the control space is essential to set the data assimilation statistical framework properly. A possible mathematical framework is then proposed for multiscale data assimilation. To keep the developments simple, a measure of the reduction of uncertainty is chosen as a very simple optimality criterion. Using this criterion, a cost function is built to select the optimal representation. It is a function of the control space representation itself. A regularization of this cost function, based on a statistical mechanical analogy, guarantees the existence of a solution. This allows numerical optimization to be performed on the representation of control space. The formalism is then applied to the inverse modeling of an accidental release of an atmospheric contaminant at European scale, using real data.

Simulated Annealing with Adaptive Neighborhood Applied to the Placement over Containers with Fixed Dimensions

This work deals with the problem of minimizing the waste of space that occurs on a rotational placement of a set of irregular bi-dimensional items inside a bi-dimensional container. This problem is approached with an heuristic based on Simulated Annealing (SA) with adaptive neighborhood. Traditional “external penalization” techniques are avoided through the application of the no–fit polygon, that determinates the collision-free area for each polygon before its placement. The SA controls continuous and discrete parameters. The rotation applied and the translation of the polygon are continuous parameters, and the sequence of placement is represented as a set of discrete parameters. For each non–placed item, a limited depth binary search is performed to find a scale factor that when applied to the item, would allow it to be fitted in the container.

Movable $(n_{4})$ Configurations

An $(n_{k})$ configuration is a collection of points and straight lines, usually in the Euclidean plane, so that each point lies on $k$ lines and each line passes through $k$ points; such a configuration will be called symmetric if it possesses non-trivial geometric symmetry. Although examples of symmetric $(n_{3})$ configurations with continuous parameters are known, to this point, all known connected infinite families of $(n_{4})$ configurations with non-trivial geometric symmetry had the property that each set of discrete parameters describing the configuration corresponded to a single $(n_{4})$ configuration. This paper presents several new classes of highly symmetric $(n_{4})$ configurations which have at least one continuous parameter; that is, the configurations are movable.

Phantom cosmology as a simple model with dynamical complexity

We study the Friedman-Robertson-Walker model with phantom fields modeled in terms of scalar fields. We apply the Ziglin theory of integrability and find that the flat model is nonintegrable. Then we cannot expect to determine simple analytical solutions of the Einstein equations. We demonstrate that there is only a discrete set of parameters where this model is integrable. For comparison we describe the phantoms fields in terms of the barotropic equation of state. It is shown that in contrast to the phantoms modeled as scalar fields, the dynamics is always integrable and phase portraits are contracted. In this case we find the duality relation.

Maxwell's equations in periodic chiral structures

AbstractConsider a time–harmonic electromagnetic plane wave incident on a biperiodic structure in ℝ3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and heterogeneous. In general, wave propagation in the chiral medium is governed by Maxwell's equations together with the Drude– Born–Fedorov (constitutive) equations. In this paper, the diffraction problem is formulated in a bounded domain by introducing a pair of transparent boundary conditions. It is then shown that for all but possibly a discrete set of parameters, there is a unique quasi–periodic weak solution to the diffraction problem. Our proof is based on the Hodge decomposition, a compact imbedding result, and the Lax–Milgram Lemma. In addition, an energy conservation for the weak solution is also shown.

Continuous action reinforcement learning automata and their application to adaptive digital filter design

In the design of adaptive IIR filters, the multi-modal nature of the error surfaces can limit the use of gradient-based and other iterative search methods. Stochastic learning automata have previously been shown to have global optimisation properties making them suitable for the optimisation of filter coefficients. Continuous action reinforcement learning automata are presented as an extension to the standard automata which operate over discrete parameter sets. Global convergence is claimed, and demonstrations are carried out via a number of computer simulations.

Asymptotic behaviour of Gaussian processes with integral representation

The aim of this work is the study of limit points of Gaussian processes with continuous paths defined by an integral representation. Precisely, we control the asymptotic behaviour of a( t) X t , where a is a function which vanishes at infinity and X is a Gaussian process. At first, we study real-valued processes indexed by a discrete set of parameters: we give a simple expression of the upper limit at infinity. We provide examples for which our assumptions hold but where the covariance decreases too slowly in order to use results of the existing literature. Next, we specialize our study to stationary processes with a spectral density and compute the set of limit values of a( t) X t , where X t is an n-dimensional Gaussian process. Finally, we establish results for the Ornstein–Uhlenbeck diffusion.

A Queueing Model for the Design and Analysis of a MiningStockyard

In this paper we model the operation of a mining stockyard by an \erk queue. We describe the stockpile configuration of the stockyard by a set of discrete parameters, taking values in the set of positive integers, which define the queueing system. Our goal is to optimise both the throughput and a penalised throughput of this queueing system, by selecting the optimal number and size of the stockpiles within the stockyard. This is accomplished by the development of several tools, including a local search algorithm that exploits the specific nature and constraints of the system.

Analysis of the diffraction from periodic chiral structures

Consider a time-harmonic electromagnetic plane wave incident on a biperiodic structure in R 3. The periodic structure separates two homogeneous regions. The medium inside the structure is chiral and heterogeneous. In general, wave propagation in the chiral medium is governed by Maxwell's equations together with the Drude-Born-Fedorov (constitutive) equations. In this Note, it is shown that for all but possibly a discrete set of parameters, there is a unique quasiperiodic weak solution to the diffraction problem. Our proof is based on a Hodge decomposition, a compact imbedding result, as well as the Lax-Milgram Lemma.

Optimal simultaneous detection and estimation under a false alarm constraint

This paper addresses the problem of finite sample simultaneous detection and estimation which arises when estimation of signal parameters is desired but signal presence is uncertain. In general, a joint detection and estimation algorithm cannot simultaneously achieve optimal detection and optimal estimation performance. We develop a multihypothesis testing framework for studying the tradeoffs between detection and parameter estimation (classification) for a finite discrete parameter set. Our multihypothesis testing problem is based on the worst case detection and worst case classification error probabilities of the class of joint detection and classification algorithms which are subject to a false alarm constraint. This framework leads to the evaluation of greatest lower bounds on the worst case decision error probabilities and a construction of decision rules which achieve these lower bounds. For illustration, we apply these methods to signal detection, order selection, and signal classification for a multicomponent signal in noise model. For two or fewer signals, an SNR of 3 dB and signal space dimension of N=10 numerical results are obtained which establish the existence of fundamental tradeoffs between three performance criteria: probability of signal detection, probability of correct order selection, and probability of correct classification. Furthermore, based on numerical performance comparisons between our optimal decision rule and other suboptimal penalty function methods, we observe that Rissanen's (1978) order selection penalty method is nearly min-max optimal in some nonasymptotic regimes. >

Parallel sample path generation for discrete event systems and the traffic smoothing problem

We review two approaches, the Standard Clock (SC) technique and Augmented System Analysis (ASA), that have been proposed for generating sample paths of Discrete Event Systems (DES) in parallel. These are placed in the unifying framework of the fundamentalsample path constructability problem: for a finite discrete parameter set Θ = {θ1, ..., θm}given a sample path under θ1 the problem is to simultaneously construct sample paths under all remaining parameter values. Using the ASA approach we then consider the problem of smoothing arbitrary, generally bursty, and possibly nonstationary traffic processes which are encountered in many applications, especially in the area of flow control for integrated-service, high-speed networks. We derive some basic structural properties of a smoothing scheme known as the Leaky Bucket (LB) mechanism through which it is seen that the variability of a traffic process can be monotonically decreased by decreasing an integer-valued parameter of this scheme. Finally, we show that a sample path under any value of this parameter is constructable with respect to an observed sample path under any other value. Therefore, by controlling this parameter on line, we show how simple iterative optimization schemes can be used to achieve typical design objectives such as keeping both the mean packet delay due to smoothing and the variability of the traffic process low.

"Rapid Learning" Techniques for Discrete Event Systems: Some Recent Results and Applications to Traffic Smoothing

We present a unified framework based on the fundamental sample path constructabilitY problem for Discrete Event Systems (DES): for a finite discrete parameter set Θ = {θ1,…., θm}. given a sample path under θ1, the problem is to simultaneously construct sample paths under all remaining parameter values. We review and compare two approaches for the solution of this problem. the Standard Clock (SC) approach and Augmented System Analysls (ASA). Next, we present a new area of potential use of the ASA approach: smoothing arbitrary, highly bursty, and possibly nonstationary traffic processes which are encountered in many applications (e.g., high-speed networks). We show how ASA can be used to (a) derive some basic structural properties of a simple smoothing scheme known as the "Leaky Bucket" mechanism under very general conditions. and (b) control a parameter of the scheme on line.

An optimal design method for magnetic resonance imaging gradient waveforms

A method of using nonlinear constrained optimization to design gradient waveforms for magnetic resonance imaging is described. Formulation and solution of the waveform optimization problem are described and example waveforms are presented for a variety of design objectives and constraint sets. Most design objectives can be expressed as linear or quadratic functions of the discrete parameter set, and most constraint functions are linear. Thus, linear and quadratic programming techniques can be utilized to solve the optimization problem. Among the objectives considered are: minimize RMS current; minimize waveform slewing; minimize waveform moments to reduce motion induced dephasing; minimize echo time (TE) for given imaging and motion refocusing conditions; maximize the gradient amplitude during RF application and sampling and the area of the phase encoding waveform to maximize resolution; and minimize or maximize the gradient b factor or diffusion sensitivity. This optimal design procedure produces physically realizable waveforms which optimally achieve specific imaging and motion artifact reduction goals, and it is likely to reduce waveform design time by making it more scientifically (rather than heuristically) based.

Continual-discrete modelling of a multicomponent laminar body by using a system of two-dimensional continua

A method is considered for constructing continual-discrete models of multicomponent layered bodies by using a system consisting of an arbitrary number of two-dimensional continua with finite intervals between them. Consistency relationships are presented for the fundamental kinematic, deformation, and dynamic parameters which enable rheological relationships to be obtained for the body as a whole taking the properties and nature of the interaction of the individual components into account. An example of the modelling of a thin laminar elastic body is examined. Methods for modelling a biological membrane are discussed. Physical objects exist for which a direct description is impossible by methods of the mechanics of three-dimensional continuous media, or is insufficiently effective because the physical properties of the object are discrete in one of the directions, i.e., the requirements for the continuity hypothesis /1/ are not satisfied in this direction. The object here posssesses fairly continuous properties in the other two directions and allows of a continual description. Among tho discrete objects in the transverse direction is the shell of a live cell, a biological membrane, say, consisting of several layers of macromolecules where the individual layers include molecules of different species. Moreover, a broad class of laminar and stratified bodies exists, whose properties in the transverse direction can possibly be described by a discrete set of parameters. In a number of papers (/2–7/, for example) the concept has been introduced of a two-dimensional continuum (a material surface possessing mass) that is characterized by appropriate kinematic, dynamic, and energy parameters. The ideal of modelling multicomponent laminar bodies by using systems of two-dimensional continua /8/ is natural ∗ ∗ See also: Pribyleva, T.A. Investigations in Biomechanics. Model of a multisheet continuum: kinematics and mass balance. Report 2555, Moscow Univ. Mechanics.Inst., 1981. . Certain elements of this approach are elucidated in /9, 10/.

The mixed discrete‐continuous inverse problem: Application to the simultaneous determination of earthquake hypocenters and velocity structure

Some inverse problems are characterized by a model consisting of a piecewise continuous function and a set of discrete parameters. For linear problems of this general type, which we call mixed, we show that when the number of data d is greater than the number of parameters p, it is always possible to construct a set of a least d ‐ p equations that are independent of the values of the discrete part of the model. These equations, which we call the annulled data set, can be used to estimate the continuous part of the model. The discrete part of the model can be estimated from a second set of p equations that relate the discrete and continuous parts of the model. The linearization of the nonlinear travel time functional that enter in the hypocenter location problem leads to a mixed inverse problem. The splitting procedure is natural to this problem if the hypocenters are estimated initially by conventional nonlinear least squares by using travel times calculated from some initial estimate of the velocity model. The annulled data are a set of linear combinations of the residuals that are unbiased by that initial location, and as a result, they can be used directly to estimate a perturbation to the velocity model by a Backus‐Gilbert procedure. This makes an iterative algorithm possible that consists of a conventional hypocenter location followed by estimating a perturbation of the velocity model from the annulled data set. The uniqueness of the final velocity model is assessed via the linear resolution analysis of Backus and Gilbert (1968, 1970). We also construct a set of Frechet derivatives that relate perturbations of each hypocenter component to perturbations of the velocity model. These kernels are used to assess the possible error of the hypocenters due to inadequate knowledge of the velocity structure by an application of the generalized prediction approach of Backus (1970a). Good results are obtained when the procedure is applied to a simple synthetic data set.

Performance of a Square Law Pseudonoise Ranging Time-of-Arrival Estimator

The performance of a square law time-of-arrival (TOA) estimator that has been proposed for use in ASTRO-DABS, part of a possible satellite-based fourth generation air traffic control system is considered. The transmitted message consists of a pulse amplitude modulated (PAM) ranging sequence that, due to transmitter characteristics, is corrupted by an unknown frequency offset. The optimum TOA estimator, for the case of no frequency uncertainty, is first presented, together with a lower bound on the variance of the estimate generated. This is followed by the consideration of a suboptimum TOA estimator for which a high signal-to-noise ratio (SNR) performance analysis is carried out; here, the effects of frequency uncertainty are included. Next, the zero-crossing properties of the derivative of the (suboptimum) estimation statistic are presented and the results used to derive an upper bound to the TOA estimate variance that is valid for all SNR values. This latter result is significant because it displays the system threshold effect and complements performance lower bounds that may be derived via other methods. In addition, the method presented here may be applied to other optimum and suboptimum systems where a discrete set of parameters is to be estimated.