Let 0 < a < b < ∞, and for each edge e of Zd let ωe = a or ωe = b, each with probability 1/2, independently. This induces a random metric distω on the vertices of Z d, called first passage percolation. We prove that for d > 1 the distance distω(0, v) from the origin to a vertex v, |v| > 2, has variance bounded by C |v|/ log |v|, where C = C(a, b, d) is a constant which may only depend on a, b a...

In this paper we consider the partial many-sorted first-order logic and its extension to the subsorted partial many-sorted first-order logic that underly the Casl specification formalism. First we present counterexamples showing that the generalization of the Craig Interpolation Property does not hold for these logics in general (i.e., with respect to arbitrary signature morphisms). Then we for...

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We propose and analyse a new countermeasure against Differential Power Analysis (DPA) for the AES encryption algorithm, based on permutation tables. As opposed to existing AES countermeasures, it does not use random masking. We prove that our new countermeasure is resistant against first-order DPA; we also show that it is quite efficient in practice.

Our goal is to show that the standard model-theoretic concept of types can be applied in the study of order-invariant properties, i.e., properties definable in a logic in the presence of an auxiliary order relation, but not actually dependent on that order relation. This is somewhat surprising since order-invariant properties are more of a combinatorial rather than a logical object. We provide ...

The Collatz problem is reformulated in three ways as a non-arithmetic problem in first-order logic.

The technique of minimizing information (infomin) has been commonly employed as a general method for both choosing and updating a subjective probability function. We argue that, in a wide class of cases, the use of infomin methods fails to cohere with our standard conception of rational degrees of belief. We introduce the notion of a deceptive updating method, and argue that non-deceptiveness i...

Credit scoring model development became a very important issue as the credit industry has many competitions and bad debt problems. Therefore, most credit scoring models have been widely studied in the areas of statistics to improve the accuracy of credit scoring models during the past few years. In order to solve the classification and decrease the Type I error of credit scoring model, this pap...