Modeling and Optimal Control of a Class of Warfare Hybrid Dynamic Systems Based on Lanchester (

For the particularity of warfare hybrid dynamic process, a class of warfare hybrid dynamic systems is established based on Lanchester equation in a (n,1) battle, where a heterogeneous force of n different troop types faces a homogeneous force. This model can be characterized by the interaction of continuous-time models (governed by Lanchester equation), and discrete event systems (described by variable tactics). Furthermore, an expository discussion is presented on an optimal variable tactics control problem for warfare hybrid dynamic system. The optimal control strategies are designed based on dynamic programming and differential game theory. As an example of the consequences of this optimal control problem, we take the (2, 1) case and solve the optimal strategies in a (2, 1) case. Simulation results show the feasibility of warfare hybrid system model and the effectiveness of the optimal control strategies designed

Differential Game for a Class of Warfare Dynamic Systems with Reinforcement Based on Lanchester Equation

This paper concerns the optimal reinforcement game problem between two opposing forces in military conflicts. With some moderate assumptions, we employ Lanchester equation and differential game theory to develop a corresponding optimization game model. After that, we establish the optimum condition for the differential game problem and give an algorithm to obtain the optimal reinforcement strategies. Furthermore, we also discuss the convergence of the algorithm. Finally, a numerical example illustrates the effectiveness of the presented optimal schemes. Our proposed results provide a theoretical guide for both making warfare command decision and assessing military actions

Perception of social interaction compresses subjective duration in an oxytocin-dependent manner

Communication through body gestures permeates our daily life. Efficient perception of the message therein reflects one's social cognitive competency. Here we report that such competency is manifested temporally as shortened subjective duration of social interactions: motion sequences showing agents acting communicatively are perceived to be significantly shorter in duration as compared with those acting noncommunicatively. The strength of this effect is negatively correlated with one's autistic-like tendency. Critically, intranasal oxytocin administration restores the temporal compression effect in socially less proficient individuals, whereas the administration of atosiban, a competitive antagonist of oxytocin, diminishes the effect in socially proficient individuals. These findings indicate that perceived time, rather than being a faithful representation of physical time, is highly idiosyncratic and ingrained with one's personality trait. Moreover, they suggest that oxytocin is involved in mediating time perception of social interaction, further supporting the role of oxytocin in human social cognition

Finite-time stochastic input-to-state stability and observer-based controller design for singular nonlinear systems

This paper investigated observer-based controller for a class of singular nonlinear systems with state and exogenous disturbance-dependent noise. A new sufficient condition for finite-time stochastic input-to-state stability (FTSISS) of stochastic nonlinear systems is developed. Based on the sufficient condition, a sufficient condition on impulse-free and FTSISS for corresponding closed-loop error systems is provided. A linear matrix inequality condition, which can calculate the gains of the observer and state-feedback controller, is developed. Finally, two simulation examples are employed to demonstrate the effectiveness of the proposed approaches

Predicting Transportation Carbon Emission with Urban Big Data

Transportation carbon emission is a significant contributor to the increase of greenhouse gases, which directly threatens the change of climate and human health. Under the pressure of the environment, it is very important to master the information of transportation carbon emission in real time. In the traditional way, we get the information of the transportation carbon emission by calculating the combustion of fossil fuel in the transportation sector. However, it is very difficult to obtain the real-time and accurate fossil fuel combustion in the transportation field. In this paper, we predict the real-time and fine-grained transportation carbon emission information in the whole city, based on the spatio-temporal datasets we observed in the city, that is taxi GPS data, transportation carbon emission data, road networks, points of interests (POIs), and meteorological data. We propose a three-layer perceptron neural network (3-layerPNN) to learn the characteristics of collected data and infer the transportation carbon emission. We evaluate our method with extensive experiments based on five real data sources obtained in Zhuhai, China. The results show that our method has advantages over the well-known three machine learning methods (Gaussian Naive Bayes, Linear Regression, and Logistic Regression) and two deep learning methods (Stacked Denoising Autoencoder and Deep Belief Networks)

Visual duration aftereffect is position invariant

Adaptation to relatively long or short sensory events leads to a negative aftereffect, such that the durations of the subsequent events within a certain range appear to be contracted or expanded. The distortion in perceived duration is presumed to arise from the adaptation of duration detectors. Here, we focus on the positional sensitivity of those visual duration detectors by exploring whether the duration aftereffect may be constrained by the visual location of stimuli. We adopted two different paradigms, one that tests for transfer across visual hemifields, and the other that tests for simultaneous selectivity between visual hemifields. By employing these experimental designs, we show that the duration aftereffect strongly transfers across visual hemifields and is not contingent on them. The lack of position specificity suggests that duration detectors in the visual system may operate at a relatively later stage of sensory processing

Observer-Based Robust Tracking Control for a Class of Switched Nonlinear Cascade Systems

This paper is devoted to robust output feedback tracking control design for a class of switched nonlinear cascade systems. The main goal is to ensure the global input-to-state stable (ISS) property of the tracking error nonlinear dynamics with respect to the unknown structural system uncertainties and external disturbances. First, a nonlinear observer is constructed through state transformation to reconstruct the unavailable states, where only one parameter should be determined. Then, by virtue of the nonlinear sliding mode control (SMC), a discontinuous nonlinear output feedback controller is designed using a backstepping like design procedure to ensure the ISS property. Finally, an example is provided to show the effectiveness of the proposed approach

New Interpretations of Normalization Methods in Deep Learning

In recent years, a variety of normalization methods have been proposed to help train neural networks, such as batch normalization (BN), layer normalization (LN), weight normalization (WN), group normalization (GN), etc. However, mathematical tools to analyze all these normalization methods are lacking. In this paper, we first propose a lemma to define some necessary tools. Then, we use these tools to make a deep analysis on popular normalization methods and obtain the following conclusions: 1) Most of the normalization methods can be interpreted in a unified framework, namely normalizing pre-activations or weights onto a sphere; 2) Since most of the existing normalization methods are scaling invariant, we can conduct optimization on a sphere with scaling symmetry removed, which can help stabilize the training of network; 3) We prove that training with these normalization methods can make the norm of weights increase, which could cause adversarial vulnerability as it amplifies the attack. Finally, a series of experiments are conducted to verify these claims.Comment: Accepted by AAAI 202

The Explicit Identities for Spectral Norms of Circulant-Type Matrices Involving Binomial Coefficients and Harmonic Numbers

The explicit formulae of spectral norms for circulant-type matrices are investigated; the matrices are circulant matrix, skew-circulant matrix, and g-circulant matrix, respectively. The entries are products of binomial coefficients with harmonic numbers. Explicit identities for these spectral norms are obtained. Employing these approaches, some numerical tests are listed to verify the results