Sequential decision making with partially ordered preferences

This paper presents new insights and novel algorithms for strategy selection in sequential decision making with partially ordered preferences; that is, where some strategies may be incomparable with respect to expected utility. We assume that incomparability amongst strategies is caused by indeterminacy/imprecision in probability values. We investigate six criteria for consequentialist strategy selection: Gamma-Maximin, Gamma-Maximax, Gamma-Maximix, Interval Dominance, Maximality and E-admissibility. We focus on the popular decision tree and influence diagram representations. Algorithms resort to linear/multilinear programming; we describe implementation and experiments. (C) 2010 Elsevier B.V. All rights reserved.

Fixed point theorems in partially ordered spaces and aplications

[ES]Recientemente, en la Teoría del punto fijo, han aparecido muchos resultados que obtienen condiciones suficientes para la existencia de un punto fijo si trabajamos con aplicaciones en un conjunto dotado de un orden parcial. Generalmente, estos resultados combinan dos teoremas del punto fijo fundamentales: el Teorema de la contracción de Banach y el Teorema de Knaster-Tarski.

Partially ordered classes of finite automata /

Vita.

Revealed preference and indifferent selection

It is shown that preferences can be constructed from observed choice behavior in a way that is robust to indifferent selection (i.e., the agent is indifferent between two alternatives but, nevertheless, is only observed selecting one of them). More precisely, a suggestion by Savage (1954) to reveal indifferent selection by considering small monetary perturbations of alternatives is formalized and generalized to a purely topological framework: references over an arbitrary topological space can be uniquely derived from observed behavior under the assumptions that they are continuous and nonsatiated and that a strictly preferred alternative is always chosen, and indifferent selection is then characterized by discontinuity in choice behavior. Two particular cases are then analyzed: monotonic preferences over a partially ordered set, and preferences representable by a continuous pseudo-utility function.

Contractive-like mapping principles in ordered metric spaces and application to ordinary differential equations

[EN] The purpose of this paper is to present a fixed point theorem for generalized contractions in partially ordered complete metric spaces. We also present an application to first-order ordinary differential equations.

Stability of nonlinear difference inclusions

The stability of difference inclusions x(k+1) is an element of F(x(k)) is studied, where F(x) = {F(x, gimel) : is an element of Lambda} and the selections F(., gimel) : E -->E assume values in a Banach space E, partially ordered by a cone K. It is assumed that the operators F(.,gimel) are heterotone or pseudoconcave. The main results concern asymptotically stable absorbing sets, and include the case of a single equilibrium point. The results are applied to a number of practical problems.

Automorphisms of partial endomorphism semigroups

Publicationes Mathematicae Debrecen

Conservation Laws in Cellular Automata

Conservation laws in physics are numerical invariants of the dynamics of a system. In cellular automata (CA), a similar concept has already been defined and studied. To each local pattern of cell states a real value is associated, interpreted as the “energy” (or “mass”, or . . . ) of that pattern.The overall “energy” of a configuration is simply the sum of the energy of the local patterns appearing on different positions in the configuration. We have a conservation law for that energy, if the total energy of each configuration remains constant during the evolution of the CA. For a given conservation law, it is desirable to find microscopic explanations for the dynamics of the conserved energy in terms of flows of energy from one region toward another. Often, it happens that the energy values are from non-negative integers, and are interpreted as the number of “particles” distributed on a configuration. In such cases, it is conjectured that one can always provide a microscopic explanation for the conservation laws by prescribing rules for the local movement of the particles. The onedimensional case has already been solved by Fuk´s and Pivato. We extend this to two-dimensional cellular automata with radius-0,5 neighborhood on the square lattice. We then consider conservation laws in which the energy values are chosen from a commutative group or semigroup. In this case, the class of all conservation laws for a CA form a partially ordered hierarchy. We study the structure of this hierarchy and prove some basic facts about it. Although the local properties of this hierarchy (at least in the group-valued case) are tractable, its global properties turn out to be algorithmically inaccessible. In particular, we prove that it is undecidable whether this hierarchy is trivial (i.e., if the CA has any non-trivial conservation law at all) or unbounded. We point out some interconnections between the structure of this hierarchy and the dynamical properties of the CA. We show that positively expansive CA do not have non-trivial conservation laws. We also investigate a curious relationship between conservation laws and invariant Gibbs measures in reversible and surjective CA. Gibbs measures are known to coincide with the equilibrium states of a lattice system defined in terms of a Hamiltonian. For reversible cellular automata, each conserved quantity may play the role of a Hamiltonian, and provides a Gibbs measure (or a set of Gibbs measures, in case of phase multiplicity) that is invariant. Conversely, every invariant Gibbs measure provides a conservation law for the CA. For surjective CA, the former statement also follows (in a slightly different form) from the variational characterization of the Gibbs measures. For one-dimensional surjective CA, we show that each invariant Gibbs measure provides a conservation law. We also prove that surjective CA almost surely preserve the average information content per cell with respect to any probability measure.

Extracting Ramachandran torsional angle distributions from 2D NMR data using Tikhonov regularization /

Solid state nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for studying structural and dynamical properties of disordered and partially ordered materials, such as glasses, polymers, liquid crystals, and biological materials. In particular, twodimensional( 2D) NMR methods such as ^^C-^^C correlation spectroscopy under the magicangle- spinning (MAS) conditions have been used to measure structural constraints on the secondary structure of proteins and polypeptides. Amyloid fibrils implicated in a broad class of diseases such as Alzheimer's are known to contain a particular repeating structural motif, called a /5-sheet. However, the details of such structures are poorly understood, primarily because the structural constraints extracted from the 2D NMR data in the form of the so-called Ramachandran (backbone torsion) angle distributions, g{^,'4)), are strongly model-dependent. Inverse theory methods are used to extract Ramachandran angle distributions from a set of 2D MAS and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) data. This is a vastly underdetermined problem, and the stability of the inverse mapping is problematic. Tikhonov regularization is a well-known method of improving the stability of the inverse; in this work it is extended to use a new regularization functional based on the Laplacian rather than on the norm of the function itself. In this way, one makes use of the inherently two-dimensional nature of the underlying Ramachandran maps. In addition, a modification of the existing numerical procedure is performed, as appropriate for an underdetermined inverse problem. Stability of the algorithm with respect to the signal-to-noise (S/N) ratio is examined using a simulated data set. The results show excellent convergence to the true angle distribution function g{(j),ii) for the S/N ratio above 100.

Non-emptiness of the alpha-core

We prove non-emptiness of the alpha-core for balanced games with non-ordered preferences, extending and generalizing in several aspects the results of Scarf (1971), Border (1984), Florenzano (1989), Yannelis (1991) and Kajii (1992). In particular we answer an open question in Kajii (1992) regarding the applicability of the non-emptiness results to models with infinite dimensional strategy spaces. We provide two models with Knightian and voting preferences for which the results of Scarf (1971) and Kajii (1992) cannot be applied while our non-emptiness result applies.

Sheaves, local homeomorphisms and local sets as Hilbert locale modules

We give a thorough account of the various equivalent notions for \sheaf" on a locale, namely the separated and complete presheaves, the local home- omorphisms, and the local sets, and to provide a new approach based on quantale modules whereby we see that sheaves can be identi¯ed with certain Hilbert modules in the sense of Paseka. This formulation provides us with an interesting category that has immediate meaningful relations to those of sheaves, local homeomorphisms and local sets. The concept of B-set (local set over the locale B) present in [3] is seen as a simetric idempotent matrix with entries on B, and a map of B-sets as de¯ned in [8] is shown to be also a matrix satisfying some conditions. This gives us useful tools that permit the algebraic manipulation of B-sets. The main result is to show that the existing notions of \sheaf" on a locale B are also equivalent to a new concept what we call a Hilbert module with an Hilbert base. These modules are the projective modules since they are the image of a free module by a idempotent automorphism On the ¯rst chapter, we recall some well known results about partially ordered sets and lattices. On chapter two we introduce the category of Sup-lattices, and the cate- gory of locales, Loc. We describe the adjunction between this category and the category Top of topological spaces whose restriction to spacial locales give us a duality between this category and the category of sober spaces. We ¯nish this chapter with the de¯nitions of module over a quantale and Hilbert Module. Chapter three concerns with various equivalent notions namely: sheaves of sets, local homeomorphisms and local sets (projection matrices with entries on a locale). We ¯nish giving a direct algebraic proof that each local set is isomorphic to a complete local set, whose rows correspond to the singletons. On chapter four we de¯ne B-locale, study open maps and local homeo- morphims. The main new result is on the ¯fth chapter where we de¯ne the Hilbert modules and Hilbert modules with an Hilbert and show this latter concept is equivalent to the previous notions of sheaf over a locale.

Intermolecular interactions and characterization of the novel factor Xa exosite involved in macromolecular recognition and inhibition: Crystal structure of human Gla-domainless factor Xa complexed with the anticoagulant protein NAPc2 from the hematophagous nematode Ancylostoma caninum

NAPc2, an anticoagulant protein from the hematophagous nematode Ancylostoma caninum evaluated in phase-II/IIa clinical trials, inhibits the extrinsic blood coagulation pathway by a two step mechanism, initially interacting with the hitherto uncharacterized factor Xa exosite involved in macromolecular recognition and subsequently inhibiting factor VIIa (K-i = 8.4 pM) of the factor VIIa/tissue factor complex. NAPc2 is highly flexible, becoming partially ordered and undergoing significant structural changes in the C terminus upon binding to the factor Xa exosite. In the crystal structure of the ternary factor Xa/NAPc2/selectide complex, the binding interface consists of an intermolecular antiparallel beta-sheet formed by the segment of the polypeptide chain consisting of residues 74-80 of NAPc2 with the residues 86-93 of factor Xa that is additional maintained by contacts between the short helical segment (residues 67-73) and a turn (residues 26-29) of NAPc2 with the short C-terminal helix of factor Xa (residues 233-243). This exosite is physiologically highly relevant for the recognition and inhibition of factor X/Xa by macromolecular substrates and provides a structural motif for the development of a new class of inhibitors for the treatment of deep vein thrombosis and angioplasty. (c) 2006 Elsevier Ltd. All rights reserved.

Association and Structure of Thermosensitive Comblike Block Copolymers in Aqueous Solutions

The structures and association properties of thermosensitive block copolymers of poly(methoxyoligo( ethylene glycol) norbornenyl esters) in D2O were investigated by small angle neutron scattering (SANS). Each block is a comblike polymer with a polynorbornene (PNB) backbone and oligo ethylene glycol (OEG) side chains (one side chain per NB repeat unit). The chemical formula of the block copolymer is (OEG3NB) 79- (OEG6.6NB) 67, where subscripts represent the degree of polymerization (DP) of OEG and NB in each block. The polymer concentration was fixed at 2.0 wt % and the structural changes were investigated over a temperature range between 25 and 68°C. It was found that at room temperature polymers associate to form micelles with a spherical core formed by the block (OEG3NB) 79 and corona formed by the block (OEG6.6NB) 67 and that the shape of the polymer in the corona could be described by the form factor of rigid cylinders. At elevated temperatures, the aggregation number increased and the micelles became more compact. At temperatures around the cloud point temperature (CPT) T ) 60 °C a correlation peak started to appear and became pronounced at 68 °C due to the formation of a partially ordered structure with a correlation length ∼349 Å.

Kleiner's theorem for unitary representations of posets

A subspace representation of a poset S = {s(1), ..., S-t} is given by a system (V; V-1, ..., V-t) consisting of a vector space V and its sub-spaces V-i such that V-i subset of V-j if s(i) (sic) S-j. For each real-valued vector chi = (chi(1), ..., chi(t)) with positive components, we define a unitary chi-representation of S as a system (U: U-1, ..., U-t) that consists of a unitary space U and its subspaces U-i such that U-i subset of U-j if S-i (sic) S-j and satisfies chi 1 P-1 + ... + chi P-t(t) = 1, in which P-i is the orthogonal projection onto U-i. We prove that S has a finite number of unitarily nonequivalent indecomposable chi-representations for each weight chi if and only if S has a finite number of nonequivalent indecomposable subspace representations; that is, if and only if S contains any of Kleiner's critical posets. (c) 2012 Elsevier Inc. All rights reserved.