Discrete Moments Of Time Research Articles

ANALYTICAL DESCRIPTION OF THE CONDITIONS OF NON-INTERSECTION OF GEOMETRIC OBJECTS IN THE PROBLEMS OF MODELING THE MOVEMENT OF PEOPLE FLOW

Optimal placement problems are part of the theory of operations research and computational geometry. This class relates to geometric design problems and has a wide range of applications.Despite the presence of various models and methods for solving problems of geometric design, they, as before, are relevant in those areas whose formalization is insufficient for the application of existing models and methods related to the need to take into account the characteristics of a particular subject area.One of the problems today is the organization of controlled evacuation of people from buildings of the necessary time, which calculated on the basis of their space-planning decisions. At present, there are no models of individual-stream movement of people that are adequate to the real flow. The interest in the model is motivated both by the need to pay attention to the movement of people with limited mobile capabilities in a mixed stream in a fairly wide range of public buildings of various classes of functional fire hazard, and by the impossibility of constructing adequate mathematical models, which based on an analytical description of relationships between people (for example, non-intersections), which have different dimensions, age, functionality, etc. It should be noted that the task of modeling the movement of people in each particular discrete time moment is a configuration of the placement of objects according to given constraints, the main of which are the conditions for their non-intersection.Therefore, an urgent problem for solving placement problems is the further development of the mathematical apparatus for describing the conditions for the non-intersection of objects of arbitrary spatial shapes, taking into account their continuous translations and rotations.In the work, quasi-phi functions are modified for the analytical description of non-intersection conditions for a rectangle and an ellipse, for an object composed of a rectangle and an ellipse, with a rectangle, for an object composed of a rectangle and an ellipse, with an ellipse. The use of a quasi-phi function allowed us to formalize the relations of objects (touch, non-intersection, intersection) for a wider class of spatial forms.The mathematical apparatus for the interaction of geometric objects is the basis of methods for modeling placement according to given constraints, modeling the movement of a stream of people.

On the Theory of Position Pursuit Differential Games

The paper is devoted to the study of a position pursuit problem described by first-order linear differential equations. Sufficient conditions of the possibility of pursuit termination for such controllable systems are obtained. For finding control values of the pursuer at each time point, values of the phase vector at discrete moments of time are used.

Вероятностный анализ требований к угломерной системе обнаружения смещения эллиптической орбиты

The article addresses the requirements for a goniometric system intended to detect displacements of the space body orbit, which measures angles at discrete moments of time with a random error. Two statistical hypotheses about the zero and specified nonzero displacement values are considered. The likelihood ratio statistics is obtained, and the information distance for it is determined, which characterizes the discrimination confidence level, and which depends on the measurement device accuracy s and discreteness Dt, and also on the orbit parameters. By specifying the orbits and discrimination confidence level, the accuracy s and discreteness Dt are determined through information discrepancy. The information discrepancy is calculated on a family of orbits unfavorable for the observer, the plane of which touches the orbit of the moving observer, and the touching point is the intersection point of the corresponding trajectories. To refine the information distance, a simple flat approximate motion-measurement model is substantiated, in which the true motion of the observer (outside the space body orbit plane) is replaced, without changing its speed, by motion in the space body orbit plane over the earth's sphere circumference. The justification is corroborated by calculating the errors. The obtained simple model is used for estimating the potential possibility of detecting the specified displacement. Tables and graphs for practically determining the discreteness and accuracy of the system are given. The appendix contains all formulas necessary for carrying out similar calculations. Examples show that from angular measurements it is possible to obtain quite reliable detection for the range of orbit parameters that are of practical interest.

CYCLIC PROCESSES CONTROL IN DISCRETE SPACE-TIME TASKS

In many industries there are technological processes that are cyclical in nature. In the control of such processes, the high-efficiency method has been demonstrated by the method of control with iterative learning (ILC). The article introduces a new modification of the method of control with iterative learning (ILC) in a situation where the task of the system is given by a set of values of initial variables at certain points at certain discrete moments of time. Such a statement of the problem calls for the construction of the trajectory of the system through specified points. In this article, we propose a method that ensures that the system passes through given points at a given time without constructing the trajectory of a task. This method involves the formation of control signals using the ILC-algorithm. This allows you to simplify calculations and improve the quality of the system. This method is considered for both continuous and discrete systems. The proposed algorithm of control with iterative learning provides tracking of given output variables with sufficient accuracy at high convergence of the algorithm. Simultaneously, this algorithm is simple and does not require the preliminary construction of the trajectory of the system.

Determining the source data to form a control algorithm for hydrogen generators

Constructing an algorithm to control the technical condition of hydrogen generators employs using their amplitude-frequency and phase-frequency characteristics as the source data. Applying the classic method for defining such characteristics predetermines several drawbacks. One of the significant disadvantages is the long time required to form an array of source data. To shorten this time, determining the frequency characteristics of a hydrogen generator is carried out based on the results of measuring its transition function over discrete moments of time. During these time moments, the transition function is approximated by the Heaviside functions. Such an approach reduces the time for determining the frequency characteristics of a hydrogen generator by 1–2 orders. Applying the Kotelnikov–Nyquist–Shannon theorem for determining these discrete time moments is due to uncertainty about the maximum frequency of the test-signal spectrum. To avoid this uncertainty, discrete time moments for measuring the transitional function of a hydrogen generator are chosen under condition for the permissible error of its approximation. The error of approximation is determined based on the result from solving a test-problem that uses model characteristics as a standard for the frequency characteristics. It has been shown that at a sampling interval of (0.25¸2.5) ms the magnitude of such an error does not exceed 1.7 %. Inertial properties of the device that forms a test-impact have been taken into consideration. It has been shown that it is appropriate to apply such a procedure if the equivalent time constant of such a device exceeds the magnitudes of time constants for a hydrogen generator. The inertial properties are taken into consideration by introducing an additional multiplier, which contains the equivalent time constant of the device, to the analytical expressions for the frequency characteristics of a hydrogen generator

Conservative Relativistic Algebrodynamics Induced on an Implicitly Defined World Line

In the framework of the Stueckelberg-Wheeler-Feynman concept of a ``one-electron Universe'' we consider a worldline implicitly defined by a system of algebraic (precisely, polynomial) equations. Collection of pointlike ``particles'' of two kinds on the worldline (or its complex extension) is defined by the real (complex conjugate) roots of the polynomial system and detected then by an external inertial observer through the light cone connections. Then the observed collective dynamics of the particles' ensemble is, generally, subject to a number of Lorentz invariant conservation laws. Remarkably, this poperty follows from the Vieta's formulas for the roots of the generating polynomial system. At some discrete moments of the observer's proper time, mergings and subsequent transmutations of a pair of particles-roots take place simulating thus the processes of annihilation/creation of a particle/antiparticle pair

COMPUTATIONAL AND EXPERIMENTAL STUDY OF GRANULATION IN FLUIDIZED BED REACTOR

The objective of the study is to build a simple but informative model to describe the kinetics of layering granulation in a batch fluidized bed reactor. A cell model based on the theory of Markov chains to describe this kinetics is proposed. Several parallel chains of perfectly mixed cell according to the number of size fractions, which are under observation, were introduced. The vectors of particles volume content in the cells describe the state of the process. Evolution of the state is conditioned by particles transition from the cells of one chain to another due to their size enlargement during granulation and by particles migration along the chains due to their interaction with fluidizing gas upstream flow. The process is observed in a discrete moments of time. It is supposed that the volume of binding solution coming into a cell of a chain during one time step interacts only with the particles that can enlarge their size to transit to the cell of the next larger size fraction. The migration of the particles of a size fraction along its chain is controlled by the matrix of transition probabilities, which is different for each size fraction and depends on the total particles concentration. The model allows qualitative estimating of influence of the process parameters on the granulation kinetics. In order to validate the model, the experimental study of ammonium sulphate granulation in the lab scale fluidized bed reactor was carried out. The comparison of theoretical and experimental results was done for the example of particle size enlargement at different flow rate of the binding solution feed. A good correlation between theoretical and experimental data was found for both the mean particle size growth and the fraction size distribution at different moments of time.

Quarks of Consciousness and the Representation of the Rose: Philosophy of Science Meets the Vaiśeṣika-Vaibhāṣika-Vijñaptimātra Dialectic in Vasubandhu’s Viṃśikā

The representation of a rose varies considerably across philosophical, religious, and scientific schools of thought. While many would suggest that a rose exists objectively, as a physical object in geometric space reducible to fundamental particles such as atoms or quarks, others propose that a rose is an emergent whole that exists meaningfully when experienced subjectively for its sweet fragrance and red hue, its soft petals and thorny stem. Some might even maintain that a rose is “consciousness-only,” having no existence apart from conscious perception. Thus, we find a spectrum of realist to idealist perspectives. Even in Dharma studies, with a common basis in Indian thought, the Vaiśeṣikas, Vaibhāṣikas, and the vijnaptimātra doctrine of the Yogācārin-Vijnānavādins entertain diverging perspectives. On one hand, the Vaiśeṣikas, a school of Vedic philosophy, propounded a theory of reality in the form of indivisible, eternal atoms, a metaphysical approach counter to the doctrine of not-self (anātman) in Buddhism. The Vaibhāṣikas, a school of early Buddhist atomism, on the other hand, denied the existence of a true self or eternal soul (ātman) as substratum for reality but maintained their own theory of atomism. For the Vaibhāṣikas, the flow of consciousness may be segmented into discrete moments, yet unlike many of their Buddhist contemporaries from other schools, they asserted that all cognizable phenomena are truly existent insofar as they consist of physically irreducible atoms. Among their objectors were the Yogācārin-Vijnānavādins who proposed the theory of consciousness-only (vijnaptimātra), rejecting the independent existence of indivisible atoms and discrete moments of time. This paper introduces the dialectic that formed between these schools through Vasubandhu’s fourth century C.E. text Twenty Verses on Consciousness-Only (Viṃśikāvijnaptimātratāsiddhi). While the gulf between the realist and idealist positions may seem, at times, irreconcilable, we integrate findings from the field of physics, particularly quantum mechanics (and several philosophical interpretations thereof) within the realm of modern science as a possible bridge between these otherwise seemingly disparate systems of Dharma.

Synchronization of Discretely Coupled Harmonic Oscillators Using Sampled Position States Only

This technical note studies the synchronization of discretely coupled harmonic oscillators by using an impulsive control strategy. In the absence of velocity measurements, a distributed protocol for the coupled harmonic oscillators is proposed under the assumption that each oscillator can only obtain the information of its position relative to its neighbors at a series of discrete time moments. Necessary and sufficient conditions are established for the synchronization of the networked system with and without an active leader over an undirected communication topology. The desirable sampling period is analytically found to be dependent on the network topology and position gain. A simple iterative method is developed to calculate the range in which the sampling period falls. Finally, numerical simulations are performed to show the effectiveness of the proposed protocols.

Temporal Network Optimization Subject to Connectivity Constraints

In this work we consider temporal networks, i.e. networks defined by a labelinglambda assigning to each edge of an underlying graphG a set of discrete time-labels. The labels of an edge, which are natural numbers, indicate the discrete time moments at which the edge is available. We focus on path problems of temporal networks. In particular, we consider time-respecting paths, i.e. paths whose edges are assigned by lambda a strictly increasing sequence of labels. We begin by giving two efficient algorithms for computing shortest time-respecting paths on a temporal network. We then prove that there is a natural analogue of Menger’s theorem holding for arbitrary temporal networks. Finally, we propose two cost minimization parameters for temporal network design. One is the temporality of G, in which the goal is to minimize the maximum number of labels of an edge, and the other is the temporal cost of G, in which the goal is to minimize the total number of labels used. Optimization of these parameters is performed subject to some connectivity constraint. We prove several lower and upper bounds for the temporality and the temporal cost of some very basic graph families such as rings, directed acyclic graphs, and trees.

Consensus of multi-agent systems via hybrid impulsive protocols with time-delay

This paper studies consensus problems of multi-agent systems. A novel hybrid consensus protocol with dynamically changing interaction topologies is designed to take the time-delay into account in both the continuous-time communication among agents and the instant information exchange at discrete-time moments. By using a new Halanay-type inequality and an auxiliary function, sufficient conditions are established to guarantee that the proposed consensus protocols lead to average-consensus. Our consensus criteria show that the networked multi-agent system with time-delay can achieve average-consensus with appropriate network topologies, suitably designed impulsive instants, and admissible time delays. Numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

On cellular automata, traffic and dynamical systems in graphs

Qualitative studies of discrete dynamical systems behavior on networks are relevant in many fields such as system biology, transportation, information traffic, material sciences and so on. We consider cellular automata on one-dimensional and two-dimensional toroidal supporters. At every discrete time moment, each cell of a cellular automaton is in one of two states 0 and 1. We introduce concept of the cellular automaton mass at fixed time. The cellular automaton mass is the quantity of cells such that these cells are in the state 1. The mass conservation law takes place if the mass of cellular automaton is the same at every time. Concepts of explosion and annihilation have been introduced. Explosion takes place if the mass of cellular automaton increases at each iteration until all cells are in the state 1. Annihilation takes place if the mass of cellular automaton decreases at each iteration until all cells are in the state 0. We consider classes of cellular automata such that the state of cell at the next time depends on the state at current time and states of neighboring cells belonging to fixed set. We have found sets of cellular automata such that the mass conservation law, explosion or annihilation takes place for these automata.

Graph-analytical interpretation and modeling of phase portraits of cellular structures during their phase transformations

The article shows the possibility of representing the state of the cellular structures in the form of “phase portraits” of states in discrete moments of time. The generated structures are presented in the form of dynamic systems. Models of states of dynamical systems, is developed, based on the analysis and processing of laser speckle and other structures. The simulation algorithm of the phase portraits given in the paper allows to create information systems casts at given discrete points in time, and to control the process of formation of properties of structures. The transition of the studied systems from their initial states to the final presents a recursive algorithm with deferred calculation of the parameters of designed objects. The initial parameters of the studied systems are reported in the form of a graphic-analytical statistics and are defined further as texture geometric shapes of cellular structures.

Multinomial analysis of behavior: statistical methods

Behavioral ecologists frequently use observational methods, such as instantaneous scan sampling, to record the behavior of animals at discrete moments in time. We develop and apply multilevel, multinomial logistic regression models for analyzing such data. These statistical methods correspond to the multinomial character of the response variable while also accounting for the repeated observations of individuals that characterize behavioral datasets. Correlated random effects potentially reveal individual-level trade-offs across behaviors, allowing for models that reveal the extent to which individuals who regularly engage in one behavior also exhibit relatively more or less of another behavior. Using an example dataset, we demonstrate the estimation of these models using Hamiltonian Monte Carlo algorithms, as implemented in the RStan package in the R statistical environment. The supplemental files include a coding script and data that demonstrate auxiliary functions to prepare the data, estimate the models, summarize the posterior samples, and generate figures that display model predictions. We discuss possible extensions to our approach, including models with random slopes to allow individual-level behavioral strategies to vary over time and the need for models that account for temporal autocorrelation. These models can potentially be applied to a broad class of statistical analyses by behavioral ecologists, focusing on other polytomous response variables, such as behavior, habitat choice, or emotional states.

Collective behavior of large-scale neural networks with GPU acceleration.

In this paper, the collective behaviors of a small-world neuronal network motivated by the anatomy of a mammalian cortex based on both Izhikevich model and Rulkov model are studied. The Izhikevich model can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. Rulkov model is in the form of difference equations that generate a sequence of membrane potential samples in discrete moments of time to improve computational efficiency. These two models are suitable for the construction of large scale neural networks. By varying some key parameters, such as the connection probability and the number of nearest neighbor of each node, the coupled neurons will exhibit types of temporal and spatial characteristics. It is demonstrated that the implementation of GPU can achieve more and more acceleration than CPU with the increasing of neuron number and iterations. These two small-world network models and GPU acceleration give us a new opportunity to reproduce the real biological network containing a large number of neurons.

Hydraulic fracture crack propagation in an elastic medium with varying fracture toughness

Hydraulic fracture crack propagation in an isotropic elastic medium with varying fracture toughness is considered. The crack is subjected to the pressure of fluid injected at a point on the crack surface. The fluid is viscous Newtonian and incompressible, the medium is impermeable. The analysis of crack growth is based on the three-parameter model of pressure distribution on the crack surface. The model allows one to satisfy the condition at the point of fluid injection, the balance equation of the volume of injected fluid and the crack volume, and fracture criterion at the crack edge. The analysis of evolution of the crack boundary is based on an original method of fast numerical solution of crack problems. In this method, Gaussian approximating functions are used for discretization of the problem, and fast Fourier transform technique is applied for solution of the discretized equation. The method allows constructing the crack boundary at discrete time moments for media with varying fracture toughness and time dependent positive injection rate. Examples of hydraulic fracture crack propagation in the medium that consists of two half-spaces with different fracture toughnesses and a layer of the material with another fracture toughness in a homogeneous elastic medium are considered. Evolution of the crack boundaries in the process of fluid injection, time dependence of pressure distributions and crack openings are presented in graphic forms.

On an adaptive method of regulator parameters adjustment at discrete time points

We offer an adaptive method of regulator parameters correction at discrete points of time. The method is based on the following idea: we choose the parameters of the parametric regulator at discrete moments of time minimizing the quality criterion. The criterion describes Euclidean distance between the system trajectory and the equilibrium point. In order to solve the minimization problem, we linearise the solution of the system in the neighbourhood of the current parameter value via the sensitivity function. The sensitivity function depends on the system solution. We calculate this function plugging the current system solution into the right part of the differential matrix sensitivity equation. We obtain the method and its modifications by minimizing the quadratic part of the quality criterion at the current time. Further we apply the developed algorithm to the problem of stabilization of two-mass oscillations. For this purpose we find the parametric representation of the proper regulator. In computational experiment we use the case of one parameter regulator and the constant time step. The results of the computational experiment are given in the last section of the paper.

Automated image analysis to characterize the melt densification stage of polymer sintering processes

Knowledge of melt densification during sintering is generally acquired by visualization methods, recording bubble formation and dissolution with time. Only manual visualization methods have been reported for polymer studies, which restrict the availability of data to a few discrete moments in time for the overall process. An automated vision system is presented in this paper to provide an improved level of analysis on densification, validated against a manual method. The machine vision technique was applied in the analysis of sintering for various polyethylenes of differing melt flow index and particle size. The automated technique was found to be very accurate and capable of collecting bubble size distributions on a timescale of seconds, which is an improvement in data collection. The method was prone to underestimate bubble numbers (∼20% error), especially those less than 100 μm in size, till the bed temperature rose significantly above the melting temperature of the polymer.

Stochastic Actor-Oriented Models for Network Dynamics

This article discusses the stochastic actor-oriented model for analyzing panel data of networks. The model is defined as a continuous-time Markov chain, observed at two or more discrete time moments. It can be regarded as a generalized linear model with a large amount of missing data. Several estimation methods are discussed. After presenting the model for evolution of networks, attention is given to coevolution models. These use the same approach of a continuous-time Markov chain observed at a small number of time points, but now with an extended state space. The state space can be, for example, the combination of a network and nodal variables, or a combination of several networks. This leads to models for the dynamics of multivariate networks. The article emphasizes the approach to modeling and algorithmic issues for estimation; some attention is given to comparison with other models.

Estimation of the energy spectrums of reflections in pulse doppler weather radars. Part 3. Statistical analysis of the reconstruction techniques of continuous spectrums of the reflections from meteorological objects

This is the third paper in a series of papers dedicated to the peculiarities of estimation of the continuous energy spectrums of random processes of different nature, which are determined by their samples at discrete moments of time. In the article we justify the methodology and present the quantitative results of analytical and experimental investigation and comparison of statistical characteristics of classical and “parametric” methods of energy spectrums reconstruction for interperiod fluctuations of different nature reflections (including the ones from meteorological objects) in pulse radars. The methodology is followed by quantitative results which correspond to and obtained for a real-world “adaptive” case. Under the latter, a priori unknown echoes’ covariance matrix is replaced with different-kind estimates formed from finite-size training samples. Based on the results obtained, we substantiate the spectral estimation algorithms reasonable for utilization in different-purpose radars, in particular in pulse Doppler weather ones. Discussion of efficient ways for their practical implementation on a unified basis of adaptive lattice filters concludes the paper.