Show newer

Improvement of system identification of stochastic systems via Koopman generator and locally weighted expectation arxiv.org/abs/2406.15357

Improvement of system identification of stochastic systems via Koopman generator and locally weighted expectation

Estimation of equations from data is of interest in physics. One of the famous methods is the sparse identification of nonlinear dynamics (SINDy), which utilizes sparse estimation techniques to estimate equations from data. Recently, a method based on the Koopman operator has been developed; the generator extended dynamic mode decomposition (gEDMD) estimates a time evolution generator of dynamical and stochastic systems. However, a naive application of the gEDMD algorithm could not work well for stochastic differential equations because of the noise effects in the data. Hence, the estimation based on conditional expectation values is practical, in which we approximate the first and second derivatives on each coordinate. A naive approach is the usage of locally weighted expectations. We show that the naive locally weighted expectation is not enough because of the nonlinear behavior of the underlying system. As for the improvement, we apply the clustering method in two ways; one is to reduce the effective number of data, and the other is to capture local information more accurately. We demonstrate the improvement of the proposed method for the double-well potential system with state-dependent noise.

arxiv.org

Method for finding solution to "quasidifferentiable" differential inclusion arxiv.org/abs/2406.15384

Method for finding solution to "quasidifferentiable" differential inclusion

The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the sum of the maximum and the minimum of the finite number of continuously differentiable (in phase coordinates) functions. It is required to find a trajectory that would satisfy differential inclusion with the boundary conditions prescribed and simultaneously lie on the surface given. We give substantial examples of problems where such differential inclusions may occur: models of discontinuous systems, linear control systems where the control function or/and disturbance of the right-hand side is/are known to be subject to some nonsmooth (in phase vector) constraints, some real mechanical models and differential inclusions per se with special geometrical structure of the right-hand side. The initial problem is reduced to a variational one. It is proved that the resulting functional to be minimized is quasidifferentiable. The necessary minimum conditions in terms of quasidifferential are formulated. The steepest (or the quasidifferential) descent method in a classical form is then applied to find stationary points of the functional obtained. Herewith, the functional is constructed in such a way that one can verify whether the stationary point constructed is indeed a global minimum point of the problem. The ``weak'' convergence of the method proposed is proved for some particular cases. The method constructed is illustrated by numerical examples.

arxiv.org

A counterexample to conjecture "Catch 22" with 3 players, and 5 outcomes: 2 terminal and 3 cyclic arxiv.org/abs/2406.14587

A counterexample to conjecture "Catch 22" with 3 players, and 5 outcomes: 2 terminal and 3 cyclic

We construct a finite deterministic graphical (DG) game without Nash equilibria in pure stationary strategies. This game has 3 players $I=\{1,2,3\}$ and 5 outcomes: 2 terminal $a_1$ and $a_2$ and 3 cyclic. Furthermore, for 2 players a terminal outcome is the best: $a_1$ for player 3 and $a_2$ for player 1. Hence, the rank vector $r$ is at most $(1,2,1)$. Here $r_i$ is the number of terminal outcomes that are worse than some cyclic outcome for the player $i \in I$. This is a counterexample to conjecture ``Catch 22" from the paper ``On Nash-solvability of finite $n$-person DG games, Catch 22" (2021) arXiv:2111.06278, according to which, at least 2 entries of $r$ are at least 2 for any NE-free game. However, Catch 22 remains still open for the games with a unique cyclic outcome, not to mention a weaker (and more important) conjecture claiming that an $n$-person finite DG game has a Nash equilibrium (in pure stationary strategies) when $r = (0^n)$, that is, all $n$ entries of $r$ are 0; in other words, when the following condition holds: $\qquad\bullet$ ($C_0$) any terminal outcome is better than every cyclic one for each player. A game is play-once if each player controls a unique position. It is known that any play-once game satisfying ($C_0$) has a Nash equilibrium. We give a new and very short proof of this statement. Yet, not only conjunction but already disjunction of the above two conditions may be sufficient for Nash-solvability. This is still open.

arxiv.org

Age of Information Versions: a Semantic View of Markov Source Monitoring arxiv.org/abs/2406.14594 .SY .IT .NI .SY

Age of Information Versions: a Semantic View of Markov Source Monitoring

We consider the problem of real-time remote monitoring of a two-state Markov process, where a sensor observes the state of the source and makes a decision on whether to transmit the status updates over an unreliable channel or not. We introduce a modified randomized stationary sampling and transmission policy where the decision to perform sampling occurs probabilistically depending on the current state of the source and whether the system was in a sync state during the previous time slot or not. We then propose two new performance metrics, coined the Version Innovation Age (VIA) and the Age of Incorrect Version (AoIV) and analyze their performance under the modified randomized stationary and other state-of-the-art sampling and transmission policies. Specifically, we derive closed-form expressions for the distribution and the average of VIA, AoIV, and Age of Incorrect Information (AoII) under these policies. Furthermore, we formulate and solve three constrained optimization problems. The first optimization problem aims to minimize the average VIA subject to constraints on the time-averaged sampling cost and time-averaged reconstruction error. In the second and third problems, the objective is to minimize the average AoIV and AoII, respectively, while considering a constraint on the time-averaged sampling cost. Finally, we compare the performance of various sampling and transmission policies and identify the conditions under which each policy outperforms the others in optimizing the proposed metrics.

arxiv.org

A macroscopic pedestrian model with variable maximal density arxiv.org/abs/2406.14649

A macroscopic pedestrian model with variable maximal density

In this paper we propose a novel macroscopic (fluid dynamics) model for describing pedestrian flow in low and high density regimes. The model is characterized by the fact that the maximal density reachable by the crowd - usually a fixed model parameter - is instead a state variable. To do that, the model couples a conservation law, devised as usual for tracking the evolution of the crowd density, with a Burgers-like PDE with a nonlocal term describing the evolution of the maximal density. The variable maximal density is used here to describe the effects of the psychological/physical pushing forces which are observed in crowds during competitive or emergency situations. Specific attention is also dedicated to the fundamental diagram, i.e., the function which expresses the relationship between crowd density and flux. Although the model needs a well defined fundamental diagram as known input parameter, it is not evident a priori which relationship between density and flux will be actually observed, due to the time-varying maximal density. An a posteriori analysis shows that the observed fundamental diagram has an elongated "tail" in the congested region, thus resulting similar to the concave/concave fundamental diagram with a "double hump" observed in real crowds.

arxiv.org
Show older
Qoto Mastodon

QOTO: Question Others to Teach Ourselves
An inclusive, Academic Freedom, instance
All cultures welcome.
Hate speech and harassment strictly forbidden.