A zero-crossing approach to uncover the mask by chaotic encryption with periodic modulation

We present a so-called zero-crossing identification method that can crack the security shell of the chaotic encryption method [Chaos, Solitons & Fractals 19 (2004) 919] with periodic modulation. By collecting a special set of truncated data from the zero-crossing incidents of the modulated signal, we can detect the modulating function from chaotic signal. Furthermore we extend the technique to extract modulating function from noise and discuss the potential applications of this method in engineering.     

Synchronization of chaotic solid-state Nd:YAG lasers: Application to secure communication

In this paper, the synchronization problem of coupled chaotic lasers in master–slave configuration is numerically studied. The approach used allows to give a simple design procedure for the slave laser. In particular, we consider a complex system composed by two chaotic Nd:YAG lasers coupled through the first state variable of the master laser. Synchronization of chaotic Nd:YAG lasers is achieved by injecting the chaotic signal from the master Nd:YAG laser into the slave Nd:YAG laser. The robustness of synchronization is discussed when a mismatch of parameters occurs, and the effects of the channel noise on recovered information are showed. A potential application of chaotic synchronization of Nd:YAG lasers to transmit encrypted digital information is also given.     

Queueing systems with hard delay constraints: a framework for real-time communication over unreliable wireless channels

We provide an account of recent work that formulates and addresses problems that arise when employing wireless networks to serve clients that generate real-time flows. From a queueing systems perspective, these problems can be described as single-server problems where there are several customer classes. Customers balk when their delay exceeds a threshold. There are a range of issues that are of interest. One of the first such issues is to determine what throughput rate vectors are feasible, and to determine the server’s schedule. Another is to maximize a utility function of the departure rates of the customer classes. Real-time flows have a delay bound for each of their packets. It is particularly challenging to provide delay guarantees for real-time flows in wireless networks since wireless transmissions are unreliable. We propose a model that jointly considers the delay bounds of packets, the unreliable wireless channels, and the throughput requirements of clients. We then determine the necessary and sufficient condition for feasibility of the client requirements. The analysis and condition are interesting since this problem gives rise to some new features concerning unavoidable idle times in a system. We further derive an efficient, nearly linear time algorithm for admission control, which precisely determines whether it is feasible to fulfill the requirements of all clients in the system. We also propose two on-line scheduling policies and prove that they can fulfill the requirements of all clients whenever that is feasible. We next turn to the scenario where the throughput requirements of clients are elastic, but with hard delay bounds. We formulate this as a utility maximization problem, where client utilities are based on their throughputs. We decompose this problem into two subproblems, and show that this decomposition can be naturally implemented as a bidding game among all clients and the access point, which plays the role of a centralized scheduler. In the bidding game, the strategy of each client is to carry out a simple selfish optimization. We show that the strategy of the access point can be implemented by a simple on-line scheduling policy. A surprising result is that the channel reliabilities need not be known a priori.     

Periodic real-time scheduling: from deadline-based model to latency-based model

This paper presents a connection between two real-time models: a deadline-based model and a latency-based model. The importance of the latency-based model is proved through a result showing that two deadlines, instead of a latency constraint, over-constrain the real-time applications. Moreover, we give a deadline-marking algorithm based on the relation between deadlines and latency constraints. This algorithm provides non-preemptive feasible schedules for systems with precedence constraints and deadlines, or more complex systems with deadlines and latencies. This is the first step toward non-preemptive schedulability for distributed architectures (without over-constraining the system) like, for example, the automotive applications using protocols such as Controller Area Network (CAN). These results were obtained while the first author was at INRIA Rocquencourt.     

Routes to chaos in continuous mechanical systems: Part 2. Modelling transitions from regular to chaotic dynamics

In second part of the paper both classical and novel scenarios of transition from regular to chaotic dynamics of dissipative continuous mechanical systems are studied. A detailed analysis allowed us to detect the already known classical scenarios of transition from periodic to chaotic dynamics, and in particular the Feigenbaum scenario. The Feigenbaum constant was computed for all continuous mechanical objects studied in the first part of the paper. In addition, we illustrate and discuss different and novel scenarios of transition of the analysed systems from regular to chaotic dynamics, and we show that the type of scenario depends essentially on excitation parameters.     

Strong bias of group generators: an obstacle to the “product replacement algorithm”

Let G be a finite group. Efficient generation of nearly uniformly distributed random elements in G, starting from a given set of generators of G, is a central problem in computational group theory. In this paper we demonstrate a weakness in the popular “product replacement algorithm,” widely used for this purpose. The main results are the following. Let be the set of generating k-tuples of elements of G. Consider the distribution of the first components of the k-tuples in induced by the uniform distribution over  . We show that there exist infinite sequences of groups G such that this distribution is very far from uniform in two different senses: (1) its variation distance from uniform is >1−ε; and (2) there exists a short word (of length (loglog|G|)^O(k)) which separates the two distributions with probability 1−ε. The class of groups we analyze is direct powers of alternating groups. The methods used include statistical analysis of permutation groups, the theory of random walks, the AKS sorting network, and a randomized simulation of monotone Boolean operations by group operations, inspired by Barrington's work on bounded-width branching programs. The problem is motivated by the product replacement algorithm which was introduced in [Comm. Algebra 23 (1995) 4931–4948] and is widely used. Our results show that for certain groups the probability distribution obtained by the product replacement algorithm has a bias which can be detected by a short straight line program.     

Hybrid port–Hamiltonian systems: From parameterized incidence matrices to hybrid automata

This paper shows how to formally design a hybrid automaton model for a wide class of dissipative physical systems with sources and switching topology. This method is based on a mathematical representation of the dynamic network graph and of its dual graph, using the hybrid incidence matrix, and on a constructive method for analyzing admissible and constrained configurations. The port–Hamiltonian representation associated with the set of hybrid system configurations, parameterized by the discrete state of the switches, is synthesized to be part of the hybrid automaton of the system. This is a further step towards a generic control synthesis for physical switching systems.     

Optimal number of bypasses: minimizing cost of calls to wireless phones under Calling Party Pays

In telecommunications, Calling Party Pays is a billing formula that prescribes that the person who makes the call pays its full cost. Under CPP land-line to wireless phone calls have a high cost for many organizations. They can reduce this cost at the expense of installing wireless bypasses to replace land-line to wireless traffic with wireless-to-wireless traffic, when the latter is cheaper than the former. Thus, for a given time-horizon, the cost of the project is a trade-off between traffic to-wireless and the number of bypasses. We present a method to determine the number of bypasses that minimizes the expected cost of the project. This method takes into account hourly varying traffic intensity. Our method takes advantage of parallels with inventory models for rental items. Examples illustrate the economic value of our approach.     

Application of a hybrid meshless technique for natural frequencies analysis in functionally graded thick hollow cylinder subjected to suddenly thermal loading

A hybrid meshless technique based on composition of meshless local Petrov–Galerkin method (for spatial variables) and Newmark finite difference method (for time domain) is developed for natural frequencies analysis of thick cylinder made of functionally graded materials (FGMs). The FG cylinder is assumed to be under suddenly thermal loading, axisymmetric and plane strain conditions. The dynamic behaviors and time history of displacements are obtained in time domain using Green–Naghdi (GN) theory of coupled thermo-elasticity (without energy dissipation). Using fast Fourier transform (FFT) technique, the displacements are transferred to frequency domain and all natural frequencies are illustrated for various grading patterns of FGMs. The variations of mechanical properties in FG thick hollow cylinder are considered to be in nonlinear volume fraction law through radial direction. The presented hybrid meshless technique furnishes a ground to analyze the effects of various grading patterns of FGMs on natural frequencies, which are obtained employing GN coupled thermo-elasticity governing equations. Also, the frequency history and natural frequencies are illustrated for various grading patterns at several points across thickness of cylinder.     

Application of a hybrid method to the nonlinear dynamic analysis of a flexible rotor supported by a spherical gas-lubricated bearing system

This paper employs a hybrid numerical method combining the differential transformation method and the finite difference method to study the nonlinear dynamic behavior of a flexible rotor supported by a spherical gas-lubricated bearing system. The analytical results reveal a complex dynamic behavior comprising periodic, sub-harmonic, and quasi-periodic responses of the rotor center and the journal center. Furthermore, the results reveal the changes which take place in the dynamic behavior of the bearing system as the rotor mass and bearing number are increased. The current analytical results are found to be in good agreement with those from other numerical methods. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of spherical gas film rotor–bearing systems.     

DESA: a new hybrid global optimization method and its application to analog integrated circuit sizing

This paper presents a new hybrid global optimization method referred to as DESA. The algorithm exploits random sampling and the metropolis criterion from simulated annealing to perform global search. The population of points and efficient search strategy of differential evolution are used to speed up the convergence. The algorithm is easy to implement and has only a few parameters. The theoretical global convergence is established for the hybrid method. Numerical experiments on 23 mathematical test functions have shown promising results. The method was also integrated into SPICE OPUS circuit simulator to evaluate its practical applicability in the area of analog integrated circuit sizing. Comparison was made with basic simulated annealing, differential evolution, and a multistart version of the constrained simplex method. The latter was already a part of SPICE OPUS and produced good results in past research.     

Modeling myopia: Application to non-renewable resource extraction

We develop a parsimonious model of myopia with an infinitesimal period of commitment as an extension to a standard dynamic optimization in a continuous-time environment. We clearly distinguish the processes of planning future controls and choosing the current control, which makes the model both analytically and numerically convenient. In its application to a simple non-renewable resource extraction problem, we show that whether the terminal time is free or fixed determines the appropriateness of the approximation to myopic agents by constant discounting. We also show that the expiry of extraction permits may be useful in the presence of myopia.     

Non–parametric probability density function estimation on a bounded support: Applications to shape classification and speech coding

In statistics, it is usually difficult to estimate the probability density function from N independent samples X₁,X₂, …?, X_N identically distributed. A lot of work has been done in the statistical literature on the problem of probability density estimation (e.g. Cencov, 1962; Devroye and Gyorfi, 1981; Hall, 1980 and 1982; Hominal, 1979; Izenman, 1991; Kronmal and Tarter, 1968; Parzen, 1962; Rosenblatt, 1956). In this paper, we consider random variables on bounded support. Orthogonal series estimators, studied in detail by Kronmal and Tarter (1968), by Hall (1982) and by Cencov (1962), show that there is a disadvantage related to the Gibbs phenomenon on the bias of these estimators. We suggest a new method for the non–parametric probability density function estimation based on the kernel method using an appropriately chosen regular change of variable. The new method can be used for several problems of signal processing applications (scalar or vector quantization, speech or image processing, pattern recognition, etc.). Applications to shape classification and speech coding are given.     

Generic properties of multifunctions: Application to differential inclusions

We prove that almost all in Baire sense Caratheodory multifunctions in finite dimensional space are Kamke continuous. Further the main properties of differential inclusions with Kamke and one sided Kamke right-hand sides are studied.As a corollary we prove that for almost all optimal control problems, the relaxation and relaxation stability properties hold.     

Reformulation by discretization: Application to economic lot sizing

In this paper we apply a discretization reformulation technique to the classical economic lot sizing problem. This reformulation yields the same LP bounds as the original model. We show, however, that by reducing adequately the coefficients of some variables, one obtains an enhanced reformulation whose LP relaxation solution is integer.     

Piecewise Smooth Spaces in Duality: Application to Blossoming

Given an (n+1)-dimensional space of piecewise smooth functions in which each basis has a non-vanishing Wronskian, and its dual space *, a canonical bilinear form is defined on × *, which provides a simple characterization of a contact of order rn. An intrinsic reproducing function is introduced, leading to Marsden-type identities. In the case of Chebyshev spaces connected with totally positive matrices, the bilinear form yields a general notion of blossom which can be extended to Chebyshev splines.     

Correction: An Application of Free Probability to Arithmetic Functions

In this paper, we study free probability on tensor product algebra \(\mathfrak {M} = M\,\otimes _{\mathbb {C}}\,{\mathcal {A}}\) of a \(W^{*}\)-algebra M and the algebra \({\mathcal {A}}\), consisting of all arithmetic functions equipped with the functional addition and the convolution. We study free-distributional data of certain elements of \(\mathfrak {M}\), and study freeness on \(\mathfrak {M}\), affected by fixed primes.