Artificial Neural Networks (ANNs)-based techniques have dominated state-of-the-art results in most problems related to computer vision, audio recognition, and natural language processing in the past few years, resulting in strong industrial adoption from all leading technology companies worldwide. One of the major obstacles that have historically delayed large-scale adoption of ANNs is the huge computational and power costs associated with training and testing (deploying) them. In the mean-time, Neuromorphic Computing platforms have recently achieved remarkable performance running the bio-realistic Spiking Neural Networks at high throughput and very low power consumption making them a natural alternative to ANNs. Here, we propose using the Random Neural Network, a spiking neural network with both theoretical and practical appealing properties, as a general purpose classifier that can match the classification power of ANNs on a number of tasks while enjoying all the features of being a spiking neural network. This is demonstrated on a number of real-world classification datasets.

The random neural network (RNN) is a mathematical model for an “integrate and fire” spiking network that closely resembles the stochastic behavior of neurons in mammalian brains. Since its proposal in 1989, there have been numerous investigations into the RNN's applications and learning algorithms. Deep learning (DL) has achieved great success in machine learning. Recently, the properties of the RNN for DL have been investigated, in order to combine their power. Recent results demonstrate that the gap between RNNs and DL can be bridged and the DL tools based on the RNN are faster and can potentially be used with less energy expenditure than existing methods.

A pair of bouncing geometric Brownian motions (GBMs) is studied. The bouncing GBMs behave like GBMs except that, when they meet, they bounce off away from each other. The object of interest is the position process, which is defined as the position of the latest meeting point at each time. We study the distributions of the time and position of their meeting points, and show that the suitably scaled logarithmic position process converges weakly to a standard Brownian motion as the bounce size δ→0. We also establish the convergence of the bouncing GBMs to mutually reflected GBMs as δ→0. Finally, applying our model to limit order books, we derive a simple and effective prediction formula for trading prices.

Abstract The general problem under investigation is to understand how the complexity of a system which has been adapted to its random environment affects the level of randomness of its output (which is a function of its random input). In this paper, we consider a specific instance of this problem in which a deterministic finite-state decision system operates in a random environment that is modeled by a binary Markov chain. The system interacts with it by trying to match states of inactivity (represented by 0). Matching means that the system selects the (t + 1)th bit from the Markov chain whenever it predicts at time t that the environment will take a 0 value. The actual value at time t + 1 may be 0 or 1 thus the selected sequence of bits (which forms the system's output) may have both binary values. To try to predict well, the system's decision function is inferred based on a sample of the random environment.We are interested in assessing how non-random the output sequence may be. To do that, we apply the adapted system on a second random sample of the environment and derive an upper bound on the deviation between the average number of 1 bit in the output sequence and the probability of a 1. The bound shows that the complexity of the system has a direct effect on this deviation and hence on how non-random the output sequence may be. The bound takes the form of $O(\sqrt {(2^k/n} ))$ where 2k is the complexity of the system and n is the length of the second sample.

Abstract Suppose there arenplayers, with playerihaving valuevi> 0, and suppose that a game betweeniandjis won byiwith probabilityvi/(vi+vj). In the winner plays random knockout tournament, we suppose that the players are lined up in a random order; the first two play, and in each subsequent game the winner of the last game plays the next in line. Whoever wins the game involving the last player in line, is the tournament winner. We give bounds on players’ tournament win probabilities and make some conjectures. We also discuss how simulation can be efficiently employed to estimate the win probabilities.

An expression of the extropy of a mixed system's lifetime was given firstly. Based on this expression, two mixed systems with same signature but with different components were compared. It was shown that the extropy of lifetime of a mixed system equals to that of its dual system if the lifetimes of the components have symmetric probability density function. Moreover, some bounds of the extropy of lifetimes of mixed systems were obtained and the concept of Jensen–extropy (JE) divergence of mixed systems was proposed. The JE divergence is non-negative and it can be used as an alternative information criteria for comparing mixed systems with homogeneous components. To illustrate the applications of JE divergence, some examples are addressed at the end of this paper.

The main aim of this paper is to present two new results concerning the characterization of likelihood ratio and reversed hazard rate orders between largest order statistics from two sets of independent heterogeneous and homogeneous exponentiated generalized gamma distributed random variables. These characterization results complete and strengthen some previous ones in the literature.

We exploit a novel bounding argument to obtain sharp bounds for survival functions belonging to the Increasing initially then Decreasing Mean Residual Life (IDMRL) class introduced by Guess, Hollander and Proschan (1986) [8]. The bounds obtained are in terms of the mean, change point and pinnacle of the mean residual life function. The bounds for the monotonic ageing classes Decreasing Mean Residual Life (DMRL) and Increasing Mean Residual Life (IMRL) are obtained as special cases. Discussions on the bounds as well as two concrete illustrative examples are included.

The relation between extropy and variational distance is studied in this paper. We determine the distribution which attains the minimum or maximum extropy among these distributions within a given variation distance from any given probability distribution, obtain the tightest upper bound on the difference of extropies of any two probability distributions subject to the variational distance constraint, and establish an analytic formula for the confidence interval of an extropy. Such a study parallels to that of Ho and Yeung [3] concerning entropy. However, the proofs of the main results in this paper are different from those in Ho and Yeung [3]. In fact, our arguments can simplify several proofs in Ho and Yeung [3].

Investigation of the G-network with multiple classes of positive and negative customers has been carried out in the article. The purpose of the investigation is to analyze such a network at a transient regime, finding expected revenues in the network systems depending on time. A negative customer arriving to the system and destroys a positive customer of its class. Streams of positive and negative customers arriving to each of the network systems are independent. Services of positive customers of all types occur in accordance with a random selection of them for service. For the expected revenues, a system of Kolmogorov's difference-differential equations has been derived. A method for their finding is proposed. It is based on the use of a modified method of successive approximations, combined with the method of series. A model example illustrating the finding of time-dependent expected revenues of network systems has been calculated, which shows that the expected revenues of network systems can be either increasing or decreasing time functions. The obtained results can be applied in forecasting losses in information and telecommunication systems and networks from the penetration of computer viruses into it and conducting computer attacks.