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Since the discovery of the utility of the numbers, the human being tried to differentiate them. We decide between them according to whether they are even or odd. Or, according to the fact that they are prime or composite. A natural number n >1 is called a prime number if it has no positive divisors other than 1 and n. Therefore, other numbers that are not prime have other divisors. That is why we call them composite numbers because we can write them : n = p*q with {p,q} ≠ {1,n}. The problem has always been

The interdisciplinary character of urban morphology using the fundamental trio - form, scale and history - tries to characterize what we call the primitive morphological ontology. However, this ontology is less useful in other domains unless a formal langu ...

Inversion in Galois Fields is a famous primitive permutation for designing cryptographic algorithms e.g. for Rijndael because it has suitable differential and linear properties. Inputs and outputs are usually transformed by addition (e.g. XOR) to key bits. We call this construction the APA (Add-Permute-Add) scheme. In this paper we study its pseudorandomness in terms of k-wise independence. We show that the pairwise independence of the APA construction is related to the impossible differentials properties.

Consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform splines, and piecewise polynomials. Even though these signals are not bandlimited, we showthat they can be sampled uniformly at (or above) the rate of innovation using an appropriate kernel and then be perfectly reconstructed. Thus, we prove sampling theo

Algorithms for solving agreement problems can be classified in two categories: (1) those relying on failure detectors that we call \emph{FD-based}, and (2) those that rely on a Group Membership Service that we call

GMS-based''. The paper discusses the advantages and limitations of these two approaches, and proposes an extension to the GMS-approach that combines the advantages of both approaches, without their drawbacks. This extension leads us to distinguish between

time-triggered'' suspicions of proces

The failure of a single optical link or node in a Wavelength Division Multiplexing (WDM) network may cause the simultaneous failure of several optical channels. In some cases, this simultaneity may make it impossible for the higher level (SONET or IP) to restore service. This occurs when the higher level is not aware of the internal details of network design at the WDM level. We call this phenomenon ``failure propagation

Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are not interpolating. By opposition to traditional interpolation, we call their use generalized interpolation; they involve a prefiltering step when correctly applied. We explain why the approximation order inherent in any basis function is important to limit

Within object-oriented approaches, testing has almost been ignored in favor of analysis, design, and coding. However, object-orientedness does not solve the problem of testing by itself and may even induce new problems. Most work in testing has been done with "procedure-oriented" software in mind. Traditional methods, despite their efficiency, cannot be applied without adaptation to object-oriented systems. In an object-oriented system, the basic unit of testing is a class instead of a subprogram; testi

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Primality Testing

Event: A concept for morphological interdisciplinary constructions

On the Use of GF-Inversion as a Cryptographic Primitive

Sampling signals with finite rate of innovation

Time vs. Space in Fault-Tolerant Distributed Systems

Protection Interoperability for WDM Optical Networks

Interpolation Revisited

The Problematics of Testing Object-Oriented Software