Impulse differential game with fixed time and one-dimensional aim

2017 ◽  
Author(s):  
Viktor Ukhobotov ◽  
Igor' Izmest'ev
Keyword(s):  
Differential Game ◽  
Fixed Time ◽  
One Dimensional

scholarly journals Action minimization and macroscopic interface motion under forced displacement

2018 ◽  
Vol 24 (2) ◽  
pp. 765-792 ◽  
Author(s):  
Panagiota Birmpa ◽  
Dimitrios Tsagkarogiannis
Keyword(s):  
Stochastic Process ◽  
Evolution Equation ◽  
Fixed Time ◽  
Companion Paper ◽  
The Other ◽  
Final Position ◽  
Dimensional Model ◽  
Interface Motion ◽  
One Dimensional ◽  
Non Local

We study an one dimensional model where an interface is the stationary solution of a mesoscopic non local evolution equation which has been derived by a microscopic stochastic spin system. Deviations from this evolution equation can be quantified by obtaining the large deviations cost functional from the underlying stochastic process. For such a functional, derived in a companion paper, we investigate the optimal way for a macroscopic interface to move from an initial to a final position distant by R within fixed time T. We find that for small values of R∕T the interface moves with a constant speed, while for larger values there appear nucleations of the other phase ahead of the front.

scholarly journals Forecasting characteristic earthquakes in a minimalist model

2003 ◽  
Vol 10 (6) ◽  
pp. 565-571 ◽  
Author(s):  
M. Vázquez-Prada ◽  
Á. González ◽  
J. B. Gómez ◽  
A. F. Pacheco
Keyword(s):  
Loss Function ◽  
Three Dimensional ◽  
Fixed Time ◽  
One Dimensional ◽  
Independent Evaluation ◽  
Characteristic Earthquakes ◽  
Seismic Cycles ◽  
The Impact ◽  
Numerical Explorations

Abstract. Using error diagrams, we quantify the forecasting of characteristic-earthquake occurrence in a recently introduced minimalist model. Initially we connect the earthquake alarm at a fixed time after the ocurrence of a characteristic event. The evaluation of this strategy leads to a one-dimensional numerical exploration of the loss function. This first strategy is then refined by considering a classification of the seismic cycles of the model according to the presence, or not, of some factors related to the seismicity observed in the cycle. These factors, statistically speaking, enlarge or shorten the length of the cycles. The independent evaluation of the impact of these factors in the forecast process leads to two-dimensional numerical explorations. Finally, and as a third gradual step in the process of refinement, we combine these factors leading to a three-dimensional exploration. The final improvement in the loss function is about 8.5%.

An algorithm of pretrained fuzzy actor–critic learning applying in fixed-time space differential game

2021 ◽  
pp. 095441002199243
Author(s):  
Xiao Wang ◽  
Peng Shi ◽  
Howard Schwartz ◽  
Yushan Zhao
Keyword(s):  
Differential Game ◽  
Fuzzy Inference ◽  
Learning Algorithm ◽  
Optimal Strategies ◽  
Fixed Time ◽  
Inference System ◽  
The Real ◽  
Real Environment ◽  
Time Space ◽  
Evasion Game

Solving space differential game in an unknown environment remains a challenging problem. This article proposes a pretrained fuzzy actor–critic learning algorithm for dealing with the space pursuit-evasion game in fixed time. It is supposed that the research objects are two agents including one pursuer and one evader in space. A virtual environment, which is defined as the known part of the real environment, is utilized for deriving optimal strategies of the pursuer and the evader, respectively. Through employing the fuzzy inference system, a pretrained process, which is based on the genetic algorithm, is designed to obtain the initial consequent set of the pursuer and the evader. Besides, an actor–critic framework is applied to finely learn the suitable consequent set of the pursuer and evader in the real environment. Numerical experimental results validate the effectiveness of the proposed algorithms on improving the ability of the agents to adapt to the real environment.

scholarly journals Reflected forward-backward SDEs and obstacle problems with boundary conditions

2001 ◽  
Vol 14 (2) ◽  
pp. 113-138 ◽  
Author(s):  
Jin Ma ◽  
Jakša Cvitanić
Keyword(s):  
Boundary Conditions ◽  
Neumann Boundary Condition ◽  
Obstacle Problem ◽  
Neumann Boundary ◽  
Fixed Time ◽  
Obstacle Problems ◽  
Convex Region ◽  
One Dimensional ◽  
Backward Equation ◽  
Backward Sdes

In this paper we study a class of forward-backward stochastic differential equations with reflecting boundary conditions (FBSDER for short). More precisely, we consider the case in which the forward component of the FBSDER is restricted to a fixed, convex region, and the backward component will stay, at each fixed time, in a convex region that may depend on time and is possibly random. The solvability of such FBSDER is studied in a fairly general way. We also prove that if the coefficients are all deterministic and the backward equation is one-dimensional, then the adapted solution of such FBSDER will give the viscosity solution of a quasilinear variational inequality (obstacle problem) with a Neumann boundary condition. As an application, we study how the solvability of FBSDERs is related to the solvability of an American game option.

A Stochastic Differential Game with Safe and Risky Choices

1988 ◽  
Vol 2 (1) ◽  
pp. 31-39
Author(s):  
J. M. McNamara
Keyword(s):  
Differential Equation ◽  
Diffusion Coefficient ◽  
Stochastic Differential Equation ◽  
Differential Game ◽  
The State ◽  
Stochastic Differential Game ◽  
Final Time ◽  
One Dimensional ◽  
Zero Sum ◽  
Drift Coefficient

This paper considers a two-person zero-sum stochastic differential game. The dynamics of the game are given by a one-dimensional stochastic differential equation whose diffusion coefficient may be controlled by the players. The drift coefficient is held constant and cannot be controlled. Player l's objective is to maximize the probability that the state at final time, T, is positive, while Player 2's objective is to maximize the probability that the state is negative.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Electron-Mirror Microscopic Aspects of Ferroelectric Domains of BaTiO3 And Ca2Sr (C2H5CO2)6

1970 ◽  
Vol 28 ◽  
pp. 478-479
Author(s):  
Teruo Someya ◽  
Jinzo Kobayashi
Keyword(s):  
Surface Layer ◽  
Electric Fields ◽  
Quantitative Study ◽  
Recent Progress ◽  
Ferroelectric Domain ◽  
Resolving Power ◽  
Surface Pattern ◽  
Crystal Surfaces ◽  
One Dimensional ◽  
Ferroelectric Domains

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

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