Singularities of Affine Schubert Varieties

This paper studies the singularities of affine Schubert varieties in the affine Grassmannian (of type $\mathrm{A}^{(1)}_\ell$). For two classes of affine Schubert varieties, we determine the singular loci; and for one class, we also determine explicitly the tangent spaces at singular points. For a general affine Schubert variety, we give partial results on the singular locus.Comment: 13 figure

Bounded-rank tensors are defined in bounded degree

Matrices of rank at most k are defined by the vanishing of polynomials of degree k + 1 in their entries (namely, their (k + 1)-times-(k + 1)-subdeterminants), regardless of the size of the matrix. We prove a qualitative analogue of this statement for tensors of arbitrary dimension, where matrices correspond to two-dimensional tensors. More specifically, we prove that for each k there exists an upper bound d = d(k) such that tensors of border rank at most k are defined by the vanishing of polynomials of degree at most d, regardless of the dimension of the tensor and regardless of its sizes in each dimension. Our proof involves passing to an infinite-dimensional limit of tensor powers of a vector space, whose elements we dub infinite-dimensional tensors, and exploiting the symmetries of this limit in crucial way.Comment: Corrected the formulation of Corollary 1.4---thanks to Sonja Petrovic

Climate and air hygiene investigations for urban planning

Összefoglalás - A tanulmány az alkalmazott városklimatológia bizonyos aspektusaival foglalkozik, majd a tudományág feladatainak, céljainak leírása után különböző vizsgálati módszereket mutat be. A továbbiakban a hőmérsékleti és levegő higéniás értékek mobil mérésére összpontosít és a levegő higéniás helyzetek szintetikus klímafunkciós térképeksegítségével történő bemutatását és kiértékelését tárgyalja. Summary - This paper deals with certain aspects of applied urban climatology. Following a description of the objectives of this branch of science, various investigation methods are presented. The paper concentrates on the use of mobile measurements of temperature and air hygiene values and concludes with a discussion of the possibilities of presenting and evaluating air hygiene situations using synthetic climate function maps

Simulating bacterial transcription and translation in a stochastic pi-calculus

International audienceStochastic simulation of genetic networks based on models in the stochastic pi-calculus is a promising recent approach. This paper contributes an extensible model of the central mechanisms of gene ex- pression i.e. transcription and translation, at the prototypical instance of bacteria. We reach extensibility through object-oriented abstractions, that are expressible in a stochastic π-calculus with pattern guarded inputs. We illustrate our generic model by simulating the effect of translational bursting in bacterial gene expression

Theoretical basis of the community effect in development

Peer reviewedPublisher PD