Langlands duality for finite-dimensional representations of quantum affine algebras

We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this duality for the Kirillov-Reshetikhin modules and their irreducible tensor products. In the course of the proof we introduce and construct "interpolating (q,t)-characters" depending on two parameters which interpolate between the q-characters of a quantum affine algebra and its Langlands dual.Comment: 40 pages; several results and comments added. Accepted for publication in Letters in Mathematical Physic

On minimal affinizations of representations of quantum groups

In this paper we study minimal affinizations of representations of quantum groups (generalizations of Kirillov-Reshetikhin modules of quantum affine algebras introduced by Chari). We prove that all minimal affinizations in types A, B, G are special in the sense of monomials. Although this property is not satisfied in general, we also prove an analog property for a large class of minimal affinization in types C, D, F. As an application, the Frenkel-Mukhin algorithm works for these modules. For minimal affinizations of type A, B we prove the thin property (the l-weight spaces are of dimension 1) and a conjecture of Nakai-Nakanishi (already known for type A). The proof of the special property is extended uniformly for more general quantum affinizations of quantum Kac-Moody algebras.Comment: 38 pages; references and additional results added. Accepted for publication in Communications in Mathematical Physic

Extended T-systems

We use the theory of q-characters to establish a number of short exact sequences in the category of finite-dimensional representations of the quantum affine groups of types A and B. That allows us to introduce a set of 3-term recurrence relations which contains the celebrated T-system as a special case.Comment: 36 pages, latex; v2: version to appear in Selecta Mathematic

Dorey's Rule and the q-Characters of Simply-Laced Quantum Affine Algebras

Let Uq(ghat) be the quantum affine algebra associated to a simply-laced simple Lie algebra g. We examine the relationship between Dorey's rule, which is a geometrical statement about Coxeter orbits of g-weights, and the structure of q-characters of fundamental representations V_{i,a} of Uq(ghat). In particular, we prove, without recourse to the ADE classification, that the rule provides a necessary and sufficient condition for the monomial 1 to appear in the q-character of a three-fold tensor product V_{i,a} x V_{j,b} x V_{k,c}.Comment: 30 pages, latex; v2, to appear in Communications in Mathematical Physic

The ontology of temperature in nonequilibrium systems

The laws of thermodynamics provide a clear concept of the temperature for an equilibrium system in the continuum limit. Meanwhile, the equipartition theorem allows one to make a connection between the ensemble average of the kinetic energy and the uniform temperature. When a system or its environment is far from equilibrium, however, such an association does not necessarily apply. In small systems, the regression hypothesis may not even apply. Herein, we show that in small nonequilibrium systems, the regression hypothesis still holds though with a generalized definition of the temperature. The latter must now be defined for each such manifestation.Comment: J.Chem.Phys. (in press); 23 pages, 3 figures, 1 tabl

Eimeria tenella protein trafficking: differential regulation of secretion versus surface tethering during the life cycle

Eimeria spp. are intracellular parasites that have a major impact on poultry. Effective live vaccines are available and the development of reverse genetic technologies has raised the prospect of using Eimeria spp. as recombinant vectors to express additional immunoprotective antigens. To study the ability of Eimeria to secrete foreign antigens or display them on the surface of the sporozoite, transiently transfected populations of E. tenella expressing the fluorescent protein mCherry, linked to endogenous signal peptide (SP) and glycophosphatidylinositol-anchor (GPI) sequences, were examined. The SP from microneme protein EtMIC2 (SP2) allowed efficient trafficking of mCherry to cytoplasmic vesicles and following the C-terminal addition of a GPI-anchor (from surface antigen EtSAG1) mCherry was expressed on the sporozoite surface. In stable transgenic populations, mCherry fused to SP2 was secreted into the sporocyst cavity of the oocysts and after excystation, secretion was detected in culture supernatants but not into the parasitophorous vacuole after invasion. When the GPI was incorporated, mCherry was observed on the sporozites surface and in the supernatant of invading sporozoites. The proven secretion and surface exposure of mCherry suggests that antigen fusions with SP2 and GPI of EtSAG1 may be promising candidates to examine induction of protective immunity against heterologous pathogens

Ambiguity helps: classification with disagreements in crowdsourced annotations

Imagine we show an image to a person and ask her/him to decide whether the scene in the image is warm or not warm, and whether it is easy or not to spot a squirrel in the image. For exactly the same image, the answers to those questions are likely to differ from person to person. This is because the task is inherently ambiguous. Such an ambiguous, therefore challenging, task is pushing the boundary of computer vision in showing what can and can not be learned from visual data. Crowdsourcing has been invaluable for collecting annotations. This is particularly so for a task that goes beyond a clear-cut dichotomy as multiple human judgments per image are needed to reach a consensus. This paper makes conceptual and technical contributions. On the conceptual side, we define disagreements among annotators as privileged information about the data instance. On the technical side, we propose a framework to incorporate annotation disagreements into the classifiers. The proposed framework is simple, relatively fast, and outperforms classifiers that do not take into account the disagreements, especially if tested on high confidence annotations

Magnetic properties of GaMnAs single layers and GaInMnAs superlattices investigated at low temperature and high magnetic field

Magnetotransport properties of GaMnAs single layers and InGaMnAs/InGaAs superlattice structures were investigated at temperatures from 4 K to 300 K and magnetic fields up to 23 T to study the influence of carriers confinement through different structures. Both single layers and superlattice structures show paramagnetic-to-ferromagnetic phase transition. In GaMnAs/InGaAs superlattice beside the Curie temperature (Tc ~ 40 K), a new phase transition is observed close to 13 K.Comment: 8 pages, 5 figures, Proceedings of the XXXII International School on the Physics of Semiconducting Compounds, Jaszowiec 2003, Polan

Use of approximations of Hamilton-Jacobi-Bellman inequality for solving periodic optimization problems

We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem considered on the space of continuously differentiable functions. We approximate the latter with a maximin problem on a finite dimensional subspace of the space of continuously differentiable functions and show that a solution of this problem (existing under natural controllability conditions) can be used for construction of near optimal controls. We illustrate the construction with a numerical example.Comment: 29 pages, 2 figure