On the generalized Hyers-Ulam stability of multi-quadratic mappings

A mapping f:Vⁿ?W, where V is a commutative group, W is a linear space, and n≥2 is an integer, is called multi-quadratic if it is quadratic in each variable. In this paper, we prove the generalized Hyers-Ulam stability of multi-quadratic mappings in Banach spaces and complete non-Archimedean spaces.     

Maximum throughput of multiple access channels in adversarial environments

We consider deterministic distributed broadcasting on multiple access channels in the framework of adversarial queuing. Packets are injected dynamically by an adversary that is constrained by the injection rate and the number of packets that may be injected simultaneously; the latter we call burstiness. A protocol is stable when the number of packets in queues at the stations stays bounded. The maximum injection rate that a protocol can handle in a stable manner is called the throughput of the protocol. We consider adversaries of injection rate 1, that is, of one packet per round, to address the question if the maximum throughput 1 can be achieved, and if so then with what quality of service. We develop a protocol that achieves throughput 1 for any number of stations against leaky-bucket adversaries. The protocol has O(n²+\textburstiness){\mathcal{O}(n^2+\text{burstiness})} packets queued simultaneously at any time, where n is the number of stations; this upper bound is proved to be best possible. A protocol is called fair when each packet is eventually broadcast. We show that no protocol can be both stable and fair for a system of at least two stations against leaky-bucket adversaries. We study in detail small systems of exactly two and three stations against window adversaries to exhibit differences in quality of broadcast among classes of protocols. A protocol is said to have fair latency if the waiting time of packets is O(\textburstiness){\mathcal{O}(\text{burstiness})}. For two stations, we show that fair latency can be achieved by a full sensing protocol, while there is no stable acknowledgment based protocol. For three stations, we show that fair latency can be achieved by a general protocol, while no full sensing protocol can be stable. Finally, we show that protocols that either are fair or do not have the queue sizes affect the order of transmissions cannot be stable in systems of at least four stations against window adversaries.     

Immune-based algorithms for dynamic optimization

The main problem with biologically inspired algorithms (like evolutionary algorithms or particle swarm optimization) when applied to dynamic optimization is to force their readiness for continuous search for new optima occurring in changing locations. Immune-based algorithm, being an instance of an algorithm that adapt by innovation seem to be a perfect candidate for continuous exploration of a search space. In this paper we describe various implementations of the immune principles and we compare these instantiations on complex environments.     

Speeding up global optimization with the help of intelligent supervisors

It is shown in the paper that Developmental Genetic Programming is an efficient tool for evolutionary development of intelligent supervisors that solve an extension of Resource-Constrained Project Scheduling Problem. The extension assumes that resources are only partially available. It also assumes that renewable resources affect the project cost. The cost should be as low as possible and a deadline of the project must be met. This is apparent with regard to software houses and building enterprises. Computational experiments showed that supervisors find solutions of the problem much faster than other genetic approaches. A specific property of the supervisor is that it has various strategies of allocating the resources to the tasks. The supervisor uses the strategies in order to develop a procedure for producing the best schedule for the whole project. The analysis of the evolutionary process was performed and experimental results were compared with the optimal ones obtained by means of the exhaustive search method.     

Erotetic Search Scenarios and Three-Valued Logic

Our aim is to model the behaviour of a cognitive agent trying to solve a complex problem by dividing it into sub-problems, but failing to solve some of these sub-problems. We use the powerful framework of erotetic search scenarios (ESS) combined with Kleene’s strong three-valued logic. ESS, defined on the grounds of Inferential Erotetic Logic, has appeared to be a useful logical tool for modelling cognitive goal-directed processes. Using the logical tools of ESS and the three-valued logic, we will show how an agent could solve the initial problem despite the fact that the sub-problems remain unsolved. Thus our model not only indicates missing information but also specifies the contexts in which the problem-solving process may end in success despite the lack of information. We will also show that this model of problem solving may find use in an analysis of natural language dialogues.     

Vocal-based emotion recognition using random forests and decision tree

This paper proposes a new vocal-based emotion recognition method using random forests, where pairs of the features on the whole speech signal, namely, pitch, intensity, the first four formants, the first four formants bandwidths, mean autocorrelation, mean noise-to-harmonics ratio and standard deviation, are used in order to recognize the emotional state of a speaker. The proposed technique adopts random forests to represent the speech signals, along with the decision-trees approach, in order to classify them into different categories. The emotions are broadly categorised into the six groups, which are happiness, fear, sadness, neutral, surprise, and disgust. The Surrey Audio-Visual Expressed Emotion database is used. According to the experimental results using leave-one-out cross-validation, by means of combining the most significant prosodic features, the proposed method has an average recognition rate of \(66.28\%\), and at the highest level, the recognition rate of \(78\%\) has been obtained, which belongs to the happiness voice signals. The proposed method has \(13.78\%\) higher average recognition rate and \(28.1\%\) higher best recognition rate compared to the linear discriminant analysis as well as \(6.58\%\) higher average recognition rate than the deep neural networks results, both of which have been implemented on the same database.     

Quantum steering borders in three-qubit systems

We discuss a family of states describing three-qubit systems in a context of quantum steering phenomena. We show that symmetric steering cannot appear between two qubits—only asymmetric steering can appear in such systems. The main aim of this paper is to discuss the possible relations between the entanglement measures and steering parameter for two-mode mixed state corresponding to the qubit–qubit subsystem. We have derived the conditions determining boundary values of the negativity parametrized by concurrence. We show that two-qubit mixed state cannot be steerable when the negativity of such state is smaller than, or equal to, its boundary value. Finally, we have found ranges of the values of the mixedness measure, parametrized by concurrence and negativity for steerable and unsteerable two-qubit mixed states.     

Constrained motion planning of nonholonomic systems

This paper addresses the constrained motion planning problem for nonholonomic systems represented by driftless control systems with output. The problem consists in defining a control function driving the system output to a desirable point at a given time instant, whereas state and control variables remain over the control horizon within prescribed bounds. The state and control constraints are handled by extending the control system with a pair of state equations driven by the violation of constraints, and adding regularizing perturbations. For the regularized system a Jacobian motion planning algorithm is designed, called imbalanced. Solutions of example constrained motion planning problems for the rolling ball illustrate the theoretical concepts.     

Modified versions of the Bayesian Information Criterion for sparse Generalized Linear Models

The classical model selection criteria, such as the Bayesian Information Criterion (BIC) or Akaike information criterion (AIC), have a strong tendency to overestimate the number of regressors when the search is performed over a large number of potential explanatory variables. To handle the problem of the overestimation, several modifications of the BIC have been proposed. These versions rely on supplementing the original BIC with some prior distributions on the class of possible models. Three such modifications are presented and compared in the context of sparse Generalized Linear Models (GLMs). The related choices of priors are discussed and the conditions for the asymptotic equivalence of these criteria are provided. The performance of the modified versions of the BIC is illustrated with an extensive simulation study and a real data analysis. Also, simplified versions of the modified BIC, based on least squares regression, are investigated.     

Matrix approach to deadlock-free dispatching in multi-class finite buffer flowlines

For finite-buffer manufacturing systems, the major stability issue is "deadlock," rather than "bounded-buffer-length stability." The paper introduces the concept of "system deadlock," defined rigorously in Petri net terms, and system operation with uninterrupted part-flow is characterized in terms of the absence of this condition. For a large class of finite-buffer multiclass re-entrant flowline systems, an analysis of "circular waits" yields necessary and sufficient conditions for the occurrence of "system deadlock." This allows the formulation of a maximally permissive one-step-look-ahead deadlock-avoidance control policy for dispatching jobs, while maximizing the percent utilization of resources. The result is a generalized kanban dispatching strategy, which is more general than the standard multiclass last buffer first serve (LBFS) dispatching strategies for finite buffer flowlines that typically under-utilize the resources. The problem of computational complexity associated with Petri net (PN) applications is overcome by using certain sub-matrices of the PN incidence matrix. Computationally efficient matrix techniques are given for implementing the deadlock-free dispatching policy.