Negative specific heat in a quasi-2D vortex system

Negative specific heat is a dramatic phenomenon where processes decrease in temperature when adding energy. It has been observed in gravo-thermal collapse of globular clusters. We now report finding this phenomenon in bundles of nearly parallel, periodic, single-sign generalized vortex filaments in the electron magnetohydrodynamic (EMH) model for the unbounded plane under strong magnetic confinement. We derive the specific heat using a steepest descent method and a mean field property. Our derivations show that as temperature increases, the overall size of the system increases exponentially and the energy drops. The implication of negative specific heat is a runaway reaction, resulting in a collapsing inner core surrounded by an expanding halo of filaments. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An optimization approach to multiple sequence alignment

The problem of multiple sequence alignment is recast as an optimization problem using Markov decision theory. One seeks to minimize the expected or average cost of alignment subject to data-derived constraints. In this setting, the problem is equivalent to a linear program which can be solved efficiently using modern interior-point methods. We present numerical results from an implementation of the algorithm for protein sequence alignment     

Mass-Selection in Alignment Models with Non-Deterministic Effects

In this paper we consider a kinetic model for alignment of cells or filaments with probabilistic turning. For this equation existence of solutions is known, see [6 Kang , K. , Perthame , B. , Stevens , A. , Velazquez , J. J. L. ( 2009 ). An integro- differential equation model for alignment and orientational aggregation . J. Diff Equations 246 : 1387 – 1421 . [Google Scholar]]. To understand its qualitative behavior, especially with respect to the selection of orientations and mass distributions for long times, the model is approximated by a diffusion equation in the limit of small deviations of the interactions between the cell bundles. For this new equation existence of steady states is shown. In contrast to the kinetic equation discussed in [6 Kang , K. , Perthame , B. , Stevens , A. , Velazquez , J. J. L. ( 2009 ). An integro- differential equation model for alignment and orientational aggregation . J. Diff Equations 246 : 1387 – 1421 . [Google Scholar]] with deterministic turning, where local stability of two opposite orientations was shown but no selection of mass could be observed, for the new approximating problem with probabilistic turning additionally mass selection takes place. In the limit of small diffusion, steady states can only be constructed, if the aligning masses are either equal or the total mass is concentrated in one direction. By numerical simulations we tested stability of these steady states and for situations with 4 symmetrically placed smooth distributions of alignment. Convergence of the numerical code was proved. The simulations suggest, that only the 2- and the 1-peak steady states can be stable, whereas the 4 peak steady state is always unstable. We conjecture that the noise in the system is responsible for this final selection of masses. There exist other steady states with an arbitrary number of aligned bundles of cells or filaments, but we suspect that, as numerically shown for the 4 peak case, these multi-peak states are all unstable.     

On the simulation of textile reinforced concrete using a multi scale approach

Textile reinforced concrete (TRC) is a composite of textile structures made of multi-filament yarns (rovings) within a cementitious matrix. Experimental investigations of textile reinforced concrete specimen show very complex failure mechanisms on different length scales. Therefore mechanical models on the micro, meso and macro scale are introduced. The paper presents a hierarchical material model of TRC on three scales. While on the micro scale the individual filaments of the fiber bundles are distinguished to determine an effective roving behavior, models on the meso scale are used to predict the macroscopic response of the composite material. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

One-dimensional free boundary problem for actin-based propulsion of Listeria

Some bacteria move inside cells by recruiting the actin filaments of the host cells. The filaments are polymerized at the back surface of the bacteria, and they move away, forming a “comet” tail behind the bacterium, which consists of gel network. We develop a one-dimensional mathematical model of the gel based on partial differential equations which involve the number of filaments, the density and velocity of the gel, and the pressure. The two end-points of the gel form two free boundaries. The resulting free boundary problem is rather non-standard. We prove local existence and uniqueness.     

Parallel connections over symmetric spaces

Let M be a simply connected Riemannian symmetric space, with at most one flat direction. We show that every Riemannian (or unitary) vector bundle with parallel curvature over M is an associated vector bundle of a canonical principal bundle, with the connection inherited from the principal bundle. The problem of finding Riemannian (or unitary) vector bundles with parallel curvature then reduces to finding representations of the structure group of the canonical principal bundle.     

Holomorphic vector bundles on non-algebraic surfacesFibrés vectoriels holomorphes sur les surfaces non algébriques

The existence problem for holomorphic structures on vector bundles over non-algebraic surfaces is, in general, still open. We solve this problem in the case of rank 2 vector bundles over K3 surfaces and in the case of vector bundles of arbitrary rank over all known surfaces of class VII. Our methods, which are based on Donaldson theory and deformation theory, can be used to solve the existence problem of holomorphic vector bundles on further classes of non-algebraic surfaces. To cite this article: A. Teleman, M. Toma, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 383–388.     

Weighted area-minimizing submanifolds with soap-film-like singularities assembled from special Lagrangian pieces

A suffcient condition for a set of calibrated submanifolds to be area-minimizing with multiplicities,also call weighted area-minimizing under diffeomorphisms (WAMD) is stated.We construct some WAMD submanifolds by assembling pieces of special Lagrangian (SL) normal bundles including the one of three surfaces meeting at an angle of 120° along soap-film-like singularities.We also mention a symmetry property of SL submanifolds and Bjrling type problem for SL normal bundles.     

Reflections about pseudo-dual prices in combinatorial auctions

Combinatorial auctions permitting bids on bundles of items have been developed to remedy the exposure problem associated with single-item auctions. Given winning bundle prices, a set of item prices is called market clearing or equilibrium if all the winning (losing) bids are greater (less) than or equal to the total price of the bundle items. However, the prices for individual items are not readily computed once the winner determination problem is solved. This is due to the duality gap of integer programming caused by the indivisibility of the items. In this paper, we reflect on the calculation of approximate or pseudo-dual item prices. In particular, we present a novel scheme based on the aggregation of winning bids. Our analysis is illustrated by means of numerical examples.     

Cohomology groups of deformations of line bundles on complex tori

The cohomology groups of line bundles over complex tori (or abelian varieties) are classically studied invariants of these spaces. In this article, we compute the cohomology groups of line bundles over various holomorphic, non-commutative deformations of complex tori. Our analysis interpolates between two extreme cases. The first case is a calculation of the space of (cohomological) theta functions for line bundles over constant, commutative deformations. The second case is a calculation of the cohomologies of non-commutative deformations of degree-zero line bundles.     

The Fshape Framework for the Variability Analysis of Functional Shapes

This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis. Functional shapes can be described as signal functions supported on varying geometrical supports. Analyzing variability of fshapes’ ensembles requires the modeling and quantification of joint variations in geometry and signal, which have been treated separately in previous approaches. Instead, building on the ideas of shape spaces for purely geometrical objects, we propose the extended concept of fshape bundles and define Riemannian metrics for fshape metamorphoses to model geometric-functional transformations within these bundles. We also generalize previous works on data attachment terms based on the notion of varifolds and demonstrate the utility of these distances. Based on these, we propose variational formulations of the atlas estimation problem on populations of fshapes and prove existence of solutions for the different models. The second part of the article examines thoroughly the numerical implementation of the tangential simplified metamorphosis model by detailing discrete expressions for the metrics and gradients and proposing an optimization scheme for the atlas estimation problem. We present a few results of the methodology on a synthetic dataset as well as on a population of retinal membranes with thickness maps.     

On the Weilian prolongations of natural bundles

We characterize Weilian prolongations of natural bundles from the viewpoint of certain recent general results. First we describe the iteration F(EM) of two natural bundles E and F. Then we discuss the Weilian prolongation of an arbitrary associated bundle. These two auxiliary results enables us to solve our original problem.     

Equilibrium statistical theory for nearly parallel vortex filaments

The first mathematically rigorous equilibrium statistical theory for three‐dimensional vortex filaments is developed here in the context of the simplified asymptotic equations for nearly parallel vortex filaments, which have been derived recently by Klein, Majda, and Damodaran. These simplified equations arise from a systematic asymptotic expansion of the Navier‐Stokes equation and involve the motion of families of curves, representing the vortex filaments, under linearized self‐induction and mutual potential vortex interaction. We consider here the equilibrium statistical mechanics of arbitrarily large numbers of nearly parallel filaments with equal circulations. First, the equilibrium Gibbs ensemble is written down exactly through function space integrals; then a suitably scaled mean field statistical theory is developed in the limit of infinitely many interacting filaments. The mean field equations involve a novel Hartree‐like problem with a two‐body logarithmic interaction potential and an inverse temperature given by the normalized length of the filaments. We analyze the mean field problem and show various equivalent variational formulations of it. The mean field statistical theory for nearly parallel vortex filaments is compared and contrasted with the well‐known mean field statistical theory for two‐dimensional point vortices. The main ideas are first introduced through heuristic reasoning and then are confirmed by a mathematically rigorous analysis. A potential application of this statistical theory to rapidly rotating convection in geophysical flows is also discussed briefly. © 2000 John Wiley & Sons, Inc.     

A genetic algorithm solution for one-dimensional bundled stock cutting

This paper discusses a one-dimensional cutting stock problem in which lumber is cut in bundles. The nature of this problem is such that the traditional approaches of linear programming with an integer round-up procedure or sequential heuristics are not effective. A good solution to this problem must consider trim loss, stock usage and ending inventory levels. A genetic search algorithm is proposed and results compared to optimal solutions for an integer programming formulation of the problem.     

Affine Gelfand-Dickey brackets and holomorphic vector bundles

We define the (second) Adler-Gelfand-Dickey Poisson structure on differential operators over an elliptic curve and classify symplectic leaves of this structure. This problem leads to the problem of classification of coadjoint orbits for double loop algebras, conjugacy classes in loop groups, and holomorphic vector bundles over the elliptic curve. We show that symplectic leaves have a finite but (unlike the traditional case of operators on the circle) arbitrarily large codimension, and compute it explicitly.     

Singular cosphere bundle reduction

This paper studies singular contact reduction for cosphere bundles at the zero value of the momentum map. A stratification of the singular quotient, finer than the contact one and better adapted to the bundle structure of the problem, is obtained. The strata of this new stratification are a collection of cosphere bundles and coisotropic or Legendrian submanifolds of their corresponding contact components.

     

The mathematical model and optimistic algorithm of two protein structures alignment

Protein structure alignment is one of the most important computational problems in molecular biology. From the viewpoint of computational complexity, a pairwise structure alignment is a NP-hard problem. In this paper, based on the discrepancy of two proteins, we define the structure alignment as a mixed integer-programming (MIP) problem with the simpler form and prove the existence of optimal solution. The optimal alignment is achieved by incorporating improved complete information set method used to modify the score matrix into iterative double dynamic programming algorithm. Convergence of algorithm is proved. A number of benchmark examples are tested. The results show that our model and approach are general and improve computational efficiency as well as quality of the structure alignment.     

模丛上的嵌入子丛

利用模丛之间的嵌入关系,构造出了自由丛 的嵌入子丛和任一模丛的嵌入子自由丛. 得到一般模丛都能够成为一个自由丛 的嵌入子丛; 同时任一模丛也能够有一自由丛(或投射丛)是它的嵌入子丛; 还给出了投射丛转化为自由丛的条件.     

On some properties of the control problem under a program disturbance in a formalization based on the minimax risk (regret) criterion

A control problem under uncertainty for a system described by an ordinary differential equation with a terminal performance index is considered. The control and disturbance are subject to geometric constraints. The problem is formalized in classes of nonanticipating control strategies and program disturbances with the use of constructive ideal motions and the Savage minimax risk (regret) criterion. The properties of the used motion bundles are described and a number of relations characterizing the optimal risk function, which is an element of the formalization, are presented.     

Time-optimal braking and triaxial alignment of a rigid body

We consider the problem of time-optimal braking and triaxial alignment of a spinning rigid body with an arbitrary geometry of masses. The problem is solved by a numerical-analytical approach based on simultaneous use of Rodrigues-Hamilton parameter and Euler angles. Results of analysis of particular problems are reported.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 66, pp. 89–95, 1988.