On Computation of Groebner Bases for Linear Difference Systems

In this paper we present an algorithm for computing Groebner bases of linear ideals in a difference polynomial ring over a ground difference field. The input difference polynomials generating the ideal are also assumed to be linear. The algorithm is an adaptation to difference ideals of our polynomial algorithm based on Janet-like reductions.Comment: 5 pages, presented at ACAT-200

Non-commutative spaces in physics and mathematics

The present review aims both to offer some motivations and mathematical prerequisites for a study of NCG from the viewpoint of a theoretical physicist and to show a few applications to matrix theory and results obtained. Lectures given by the author at the TMR School on contemporary string theory and brane physics, 26 Jan--2 Feb 2000, Torino.Comment: 27 pages + figures (in .eps format), first part appeared as hep-th/9802129. submitted to Class. Quant. Gra

Reducing the size and number of linear programs in a dynamic Gr\"obner basis algorithm

The dynamic algorithm to compute a Gr\"obner basis is nearly twenty years old, yet it seems to have arrived stillborn; aside from two initial publications, there have been no published followups. One reason for this may be that, at first glance, the added overhead seems to outweigh the benefit; the algorithm must solve many linear programs with many linear constraints. This paper describes two methods of reducing the cost substantially, answering the problem effectively.Comment: 11 figures, of which half are algorithms; submitted to journal for refereeing, December 201

Imposex in gastropods from Venezuela

Se denomina imposex a la aparición de caracteres sexuales secundarios en hembras de neogasterópodos producidos por laexposición a tributil-estaño (TBT). No existen hasta la fecha reportes de este fenómeno en el Caribe sur, donde habitanpoblaciones de gasterópodos marinos que son comestibles y explotados comercialmente. Con el fin de determinar si elfenómeno de imposex afecta a poblaciones de gasterópodos, realizamos muestreos en diferentes zonas en Isla Margarita y lazona continental de Venezuela con distintos niveles de actividad náutica. Las especies afectadas fueron Chicoreus brevifrons,Chicoreus (Phylonotus) margaritensis y Leucozonia nasa; sin embargo, no se encontraron hembras con la vagina obstruida. Seencontró imposex en una laguna costera con alta densidad de botes pintados con anti-incrustantes, mientras que en costasabiertas y con bajo tránsito marino el fenómeno no fue observado. Una encuesta realizada con dueños de embarcaciones revelóque el TBT no se utiliza desde dos a tres años previos al presente estudio, pero ha sido reemplazado con otras pinturas anti-incrustantes. Este es el primer reporte de imposex en Venezuela, pero se necesitan otros estudios utilizando los bioindicadoresidentificados en este trabajo para determinar la dispersión de la contaminación por TBT y sus implicancias biológicas en zonascon tránsito marino.The imposex phenomenon is a superimposition of male characters on gastropod females due to exposure to tributyltin (TBT). There have been no previous reports of this phenomenon in the southern Caribbean, which is inhabited by some edible and commercially exploited gastropod populations. To determine whether imposex is affecting some of these local gastropod populations, surveys were conducted at several sites with different levels of boating activity around Margarita Island and on the continental coast of Venezuela. The species affected were Chicoreus brevifrons, Chicoreus (Phylonotus) margaritensis and Leucozonia nasa; however, no females with obstructed vagina were observed. Imposex was observed in a coastal lagoon and on the coast at sites characterized by medium to high boat concentrations, but was not detected in open waters with low marine traffic. A survey of local boat operators indicated that the use of TBT had stopped 2–3 years prior to this study and had been replaced by regular application of other antifouling paints. This is the first report of imposex in Venezuela, but further studies incorporating the bioindicators identified here are needed in order to determine the full extent of TBT contamination and the biological implications in zones with marine traffic.Fil: Miloslavich, P.. Universidad Simon Bolivar.; VenezuelaFil: Penchaszadeh, Pablo Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: Bigatti, Gregorio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Nacional Patagónico; Argentin

Commutator Anomaly in Noncommutative Quantum Mechanics

In this letter, firstly, the Schr$\ddot{o}$dinger equation on noncommutative phase space is given by using a generalized Bopp's shift. Then the anomaly term of commutator of arbitrary physical observable operators on noncommutative phase space is obtained. Finally, the basic uncertainty relations for space-space and space-momentum as well as momentum-momentum operators in noncommutative quantum mechanics (NCQM), and uncertainty relation for arbitrary physical observable operators in NCQM are discussed.Comment: 7 page

Hamiltonian Formulation of Open WZW Strings

Using a Hamiltonian approach, we construct the classical and quantum theory of open WZW strings on a strip. (These are the strings which end on WZW branes.) The development involves non-abelian generalized Dirichlet images in an essential way. At the classical level, we find a new non-commutative geometry in which the equal-time coordinate brackets are non-zero at the world-sheet boundary, and the result is an intrinsically non-abelian effect which vanishes in the abelian limit. Using the classical theory as a guide to the quantum theory, we also find the operator algebra and the analogue of the Knizhnik-Zamolodchikov equations for the the conformal field theory of open WZW strings.Comment: 34 pages. Added an equation in Appendix C; some typos corrected. Footnote b changed. Version to appear on IJMP

Twist Deformation of Rotationally Invariant Quantum Mechanics

Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering the Hamiltonian have to be reinterpreted as primitive elements of a dynamical Lie algebra which could be either finite (for the harmonic oscillator) or infinite (in the general case). The deformed brackets of the deformed angular momenta close the so(3) algebra. On the other hand, undeformed rotationally invariant operators can become, under deformation, anomalous (the anomaly vanishes when the deformation parameter goes to zero). The deformed operators, Taylor-expanded in the deformation parameter, can be selected to minimize the anomaly. We present the deformations (and their anomalies) of undeformed rotationally-invariant operators corresponding to the harmonic oscillator (quadratic potential), the anharmonic oscillator (quartic potential) and the Coulomb potential.Comment: 20 page

Markov bases and subbases for bounded contingency tables

In this paper we study the computation of Markov bases for contingency tables whose cell entries have an upper bound. In general a Markov basis for unbounded contingency table under a certain model differs from a Markov basis for bounded tables. Rapallo, (2007) applied Lawrence lifting to compute a Markov basis for contingency tables whose cell entries are bounded. However, in the process, one has to compute the universal Gr\"obner basis of the ideal associated with the design matrix for a model which is, in general, larger than any reduced Gr\"obner basis. Thus, this is also infeasible in small- and medium-sized problems. In this paper we focus on bounded two-way contingency tables under independence model and show that if these bounds on cells are positive, i.e., they are not structural zeros, the set of basic moves of all $2 \times 2$ minors connects all tables with given margins. We end this paper with an open problem that if we know the given margins are positive, we want to find the necessary and sufficient condition on the set of structural zeros so that the set of basic moves of all $2 \times 2$ minors connects all incomplete contingency tables with given margins.Comment: 22 pages. It will appear in the Annals of the Institution of Statistical Mathematic

Noncommutative effective theory of vortices in a complex scalar field

We derive a noncommutative theory description for vortex configurations in a complex field in 2+1 dimensions. We interpret the Magnus force in terms of the noncommutativity, and obtain some results for the quantum dynamics of the system of vortices in that context

Holographic Principle bounds on Primordial Black Hole abundances

The generalized Second Law of thermodynamics and the Holographic Principle are combined to obtain the maximum mass of black holes formed inside a static spherical box of size $R$ filled with radiation at initial temperature $T_{i}$. The final temperature after the formation of black holes is evaluated, and we show that a critical threshold exists for the radiation to be fully consumed by the process. We next argue that if some form of Holographic Principle holds, upper bounds to the mass density of PBHs formed in the early universe may be obtained. The limits are worked out for inflationary and non-inflationary cosmological models. This method is independent of the known limits based on the background fluxes (from cosmic rays, radiation and other forms of energy) and applies to potentially important epochs of PBH formation, resulting in quite strong constraints to $\Omega_{pbh}$.Comment: Latex file, 2 .ps figures. To appear in Classical and Quantum Gravit