Equivalent contractive conditions in symmetric spaces

In this paper, we introduce 22 contractive conditions in symmetric spaces. We prove that all these contractive conditions are equivalent. Then we use these conditions to get some common fixed point theorems for noncompatible maps.     

Mean message waiting times in symmetric multi-queue systems with cyclic service

A new performance analysis is provided for a cyclic service system consisting of statistically identical stations where at most one message is served for any station in a cycle. We assume that the time is slotted and that the number of message arrivals at each station in any slot is independent and generally distributed. The switch-over time and message service time (integral multiples of the slot size) are also generally distributed. For this system (called limited service system) we find the mean message waiting time explicitly. In the case of Poisson arrivals we show that our mean message waiting time is greater than that for the gated service system which is greater than that for the exhaustive service system. We also summarize the corresponding results for the three types of services in continuous-time systems.     

On initial conditions in iterative learning control

Initial conditions, or initial resetting conditions, play a fundamental role in all kinds of iterative learning control methods. In this note, we study five different initial conditions, disclose the inherent relationship between each initial condition and corresponding learning convergence (or boundedness) property. The iterative learning control method under consideration is based on Lyapunov theory, which is suitable for plants with time-varying parametric uncertainties and local Lipschitz nonlinearities.     

Square roots of $${3\times 3}$$ matrices

We find square roots of a complex-valued matrix \(A_{3 \times 3}\) using equation \(B^{2}=A\). The proposed method is faster than Higham’s method and provides up to 8 square roots with less relative residual and error.     

Tuning Parameter Selection Based on Blocked $$3\times 2$$3×2 Cross-Validation for High-Dimensional Linear Regression Model

Neural Processing Letters - In high-dimensional linear regression, selecting an appropriate tuning parameter is essential for the penalized linear models. From the perspective of the expected...     

Choosing Between Two Classification Learning Algorithms Based on Calibrated Balanced $$5\times 2$$ Cross-Validated F-Test

Ion-channel variability has critical effect on the spike initiation and propagation in nervous system. Noise can play a constructive role leading to increased reliability or regularity of neuronal firing and spike propagation in the nervous system. In this paper we show that memristors can be considered as an electronic analogous of the Hodgkin–Huxley ion channels not only in terms of threshold switching effect but also in terms of stochastic behavior. In other words, memristor can also implement stochastic version of Hodgkin–Huxley equation. Switching effect in memristive devices is thermodynamically driven, which is stochastic in nature. We show that if the intrinsic stochastic behavior of memristor is taken into account, memristor based neuristor can also implement stochastic version of Hodgkin–Huxley axon model in generation of action potential. Ion channel variability in neurons can be modeled by intrinsic stochastic behavior of memristor. We incorporate noise in the memristor model by adding white Gaussian noise to the deterministic part of dynamical state evolution function of the memristor. We study the reliability of spike timing for spike train generated by memristor based neuristor in which the noise included memristor model is used. Also, the reliability of spike propagation along thin axons is discussed. A series connection of neuristors can be used as an axon in which neuristor acts as a node of Ranvier on an axon. Probabilistic nature of spike propagation on thin axons can be modeled using neuristor in which the variability nature of memristor is included.     

Necessary conditions for constant solutions of coupled Riccati equations in Nash games

The asymptotic behaviour of solutions as t → ∞ for coupled matrix Riccati equations occurring in open-loop linear-quadratic Nash games is studied in this paper. A general formula representing all possible solutions is given. Necessary conditions for constant real solutions are derived and an estimate for the rate of convergence is obtained. Two examples illustrate these results.     

Sufficient conditions of capture in differential games of m-person pursuit of one evader

Cybernetics and Systems Analysis -     

Necessary and sufficient conditions for optimality in constrained general sum stochastic games

In this paper we first derive a necessary and sufficient condition for a stationary strategy to be the Nash equilibrium of discounted constrained stochastic game under certain assumptions. In this process we also develop a nonlinear (non-convex) optimization problem for a discounted constrained stochastic game. We use the linear best response functions of every player and complementary slackness theorem for linear programs to derive both the optimization problem and the equivalent condition. We then extend this result to average reward constrained stochastic games. Finally, we present a heuristic algorithm motivated by our necessary and sufficient conditions for a discounted cost constrained stochastic game. We numerically observe the convergence of this algorithm to Nash equilibrium.     

具有不稳定初始状态的连续时间系统辨识

针对传统辨识方法不适用于具有不稳定初始状态的连续时间系统的问题,提出一种全新的状态估计辨识法.首先,用状态空间模型中状态变量的初始值表征系统初始状态,并将状态变量的初始值看作待辨识参数的一部分.然后,用粒子群优化算法获得所有参数的最优估计.该方法在测试开始前不需要任何过程数据,对测试信号无任何要求,可直接用于闭环辨识.仿真实验证明该算法是有效的.     

How initial conditions affect generalization performance in large networks.

Generalization is one of the most important problems in neural-network research. It is influenced by several factors in the network design, such as network size, weight decay factor, and others. We show here that the initial weight distribution (for gradient decent training algorithms) is one other factor that influences generalization. The initial conditions guide the training algorithm to search particular places of the weight space. For instance small initial weights tend to result in low complexity networks, and therefore can effectively act as a regularization factor. We propose a novel network complexity measure, which is helpful in shedding insight into the phenomenon, as well as in studying other aspects of generalization.     

Finite cooperative games with a parametric concept of equilibrium under uncertainty conditions

The parametric concept of equilibrium (the optimality principle) in a finite cooperative game of several players in a normal form is introduced. This concept is defined by the partitioning of the players into coalitions. In this situation, two extreme cases of this partitioning correspond to the lexicographically optimal situation and the Nash equilibrium situation, respectively. The analysis of the stability of a generalized optimal situation under the perturbations of the coefficients of the linear payoff functions in the l ₁-metric is performed. The limiting level of such perturbations, conserving the optimality of the situation is found.     

Influence of head-up displays’ characteristics on user experience in video games

Head-up displays (HUD) are important parts of visual interfaces of virtual environments such as video games. However, few studies have investigated their role in player–video game interactions. Two experiments were designed to investigate the influence of HUDs on player experience according to player expertise and game genre. Experiment 1 used eye-tracking and interviews to understand how and to what extent players use and experience HUDs in two types of commercial games: first-person shooter and real-time strategy games. Results showed that displaying a permanent HUD within the visual interface may improve the understanding of this environment by players. They also revealed that two HUD characteristics, namely composition and spatial organization, have particular influence on player experience. These critical characteristics were manipulated in experiment 2 to study more precisely the influence of HUD design choices on player experience. Results showed that manipulation of design of these HUD characteristics influences player experience in different ways according to player expertise and game genre. For games with HUDs that are perceived as very useful, the higher player expertise is, the more player experience is influenced. Recommendations for video game design based on these results are proposed.     

Influence of initial and boundary conditions for ozone modeling in very complex terrains: A case study in the northeastern Iberian Peninsula

Initial (IC) and boundary conditions (BC) are required in order to solve the set of stiff differential equations included in air quality models. In this work, the influences of IC–BC are analyzed in the northeastern Iberian Peninsula (NEIP) by applying MM5–EMICAT2000–CMAQ. A multiscale-nested configuration has been used to generate the IC–BC. The wider domain (D1) covers an area of 1392 × 1104 km² centered in the Iberian Peninsula. Domain 2 (D2) covers an area of 272 × 272 km² in the NEIP (D2) with high spatial and temporal resolution. The information related to BC has been supplied to D2 through one-way nesting. Different scenarios were considered (base case, increments of +50% in ozone (O₃) IC, +50% in O₃ BC, +50% in O₃ precursors IC, +50% in O₃ precursors BC and clean BC). The impacts of the IC on a site decrease with simulation time. Focusing on the conditions within the PBL, a 48-h spin-up time is sufficient to reduce the impact factor of IC to 10% or less for O₃ since the influence of pervasive local emissions. The influences of BC are more important for areas near domain boundaries, especially in areas where the contribution of O₃ precursors is due to a short-medium range transport.     

Drift conditions for estimating the first hitting times of evolutionary algorithms

For the global optimization problems with continuous variables, evolutionary algorithms (EAs) are often used to find the approximate solutions. The number of generations for an EA to find the approximate solutions, called the first hitting time, is an important index to measure the performance of the EA. However, calculating the first hitting time is still difficult in theory. This paper proposes some new drift conditions that are used to estimate the upper bound of the first hitting times of EAs for finding the approximate solutions. Two case studies are given to show how to apply these conditions to estimate the first hitting times.     

Distributed sediment yield modelling: Importance of initial sediment conditions

The importance of initial sediment conditions on model calibration and validation is analysed. A sediment model was calibrated and validated under three different initial sediment conditions: (0) no sediment availability, (1) calibration of the initial sediment condition and (2) using a warm-up simulation. The model results were assessed in terms of the graphic of fine sediment transport, or sedigraphs, and the visual fit of the hysteresis on the sediment rating.All strategies provided adequate results. However, the loop rating curve analysis demonstrated that the choice of initial sediment conditions affected the simulation results. Without any initial sediment condition, the model results were typically inferior to the simulation results with calibration or warm-up. The calibration of initial conditions proved to be the most reliable technique to generate clockwise hysteresis loops, but failed in reproducing other loop types. Overall, the warm-up simulations showed encouraging results, providing satisfactory fine sedigraph simulation results.