Concurrency and Computation: Practice and Experience, 2017

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2010

Standard natural deduction rules for Int (intuitionistic predicate logic) in the style of Gentzen and Prawitz are presumed to be familiar. The theory of cut-elimination for sequent calculus rules is very clear; whether a derivation in a sequent calculus is cut-free or not is easily defined, according to the presence or absence of instances of the Cut rule. Normality of a (natural) deduction is less clear; there are many inequivalent definitions in the literature.

Grundlehren der mathematischen Wissenschaften, 2012

Derrida et al. and Schütz and Stinchcombe gave algebraic formulas for the correlation functions of the partially asymmetric simple exclusion process. Their derivations require familiarity with the formalism of quantum mechanics and a certain amount of physical intuition. Here we explain how to get this formulas starting from the generator of the process.

Journal of Mathematical Analysis and Applications, 1992

Using an n-species system of difference equations with very general density dependent growth functions, we prove that weak dominance and invariance gives the exclusion of all the (n-I)-dominated species in the system. This result is applied to very specific competition models. An example of coexistence in a competition model with no invariance is studied. A notion of strong dominance is developed in a general setting and shown to imply exclusion of the (n -l)dominated species. An example of a competition model illustrating that weak dominance plus invariance does not imply strong dominance is given. 0 1992

Mathematical Programming, 2007

We present a constructive proof for the well-known Ky Fan's coincidence theorem through a simplicial algorithm. In a finite number of steps the algorithm generates a simplex containing an approximate coincidence point. In the limit, when the mesh size converges to zero, the sequence of approximations converges to a coincidence point.

Electronic Notes in Theoretical Computer Science, 1999

IEEE Transactions on Information Theory

The aim of this paper is to show that spatial coupling can be viewed not only as a means to build better graphical models, but also as a tool to better understand uncoupled models. The starting point is the observation that some asymptotic properties of graphical models are easier to prove in the case of spatial coupling. In such cases, one can then use the so-called interpolation method to transfer known results for the spatially coupled case to the uncoupled one. Our main use of this framework is for LDPC codes, where we use interpolation to show that the average entropy of the codeword conditioned on the observation is asymptotically the same for spatially coupled as for uncoupled ensembles. We give three applications of this result for a large class of LDPC ensembles. The first one is a proof of the so-called Maxwell construction stating that the MAP threshold is equal to the Area threshold of the BP GEXIT curve. The second is a proof of the equality between the BP and MAP GEXIT curves above the MAP threshold. The third application is the intimately related fact that the replica symmetric formula for the conditional entropy in the infinite block length limit is exact.

Finite Elements in Analysis and Design, 1997

There exist two three-point integration rules for triangular elements. Both rules are precise up to the second order and used for evaluating the six-node triangles. While one of rules has its sampling stations inside the triangle, that of the other coincide with the edge nodes. Though the former is commonly employed, it will be seen in this short paper that latter is indeed more favourable in view of element accuracy.

The Color Exclusion Problem imposes inter alia that logic must look to conceptual arrangements in the world. This represents the collapse of what Wittgenstein held in his tractarian account of Logic (cf. 5.473 and 5.551). The kind of logical structure that we find inside elementary propositions in systems cannot be expressed in terms of truth-functionality, i.e., with logical products and sums. Moreover, since elementary propositions cannot be properly captured by the negation of a repeated item, the kind of exclusion within systems cannot be the contradiction. This means the necessary emergence of semantics in an alleged syntactical domain. We require then new tools to tackle non-neutral operators with restrictive scope and finer semantic exclusions. I introduce here, then, the notion of degrees of exclusion both internal and external (of second order) to a system. These degrees of exclusion may not be homogeneous, but must be infinite depending on the system of proposition that we are working with. Along the way, I advocate that we cannot reduce one system to another without distortions and that doing so is not necessary either.

2018

By elementary arguments of linear algebra and vector algebra we give here a proof of Pohlke’s fundamental theorem of oblique axonometry. We also give simple explicit formulae for the reference trihedrons (Pohlke matrices) and the corresponding directions of projection onto the drawing plane. Mathematics Subject Classification : Primary 51N10; Secondary 51N05.