Faithfulness Of Representations Research Articles

On the faithfulness of molecular mechanics representations of proteins towards quantum-mechanical energy surfaces.

Force fields based on molecular mechanics (MM) are the main computational tool to study the relationship between protein structure and function at the molecular level. To validate the quality of such force fields, high-level quantum-mechanical (QM) data are employed to test their capability to reproduce the features of all major conformational substates of a series of blocked amino acids. The phase-space overlap between MM and QM is quantified in terms of the average structural reorganization energies over all energy minima. Here, the structural reorganization energy is the MM potential-energy difference between the structure of the respective QM energy minimum and the structure of the closest MM energy minimum. Thus, it serves as a measure for the relative probability of visiting the QM minimum during an MM simulation. We evaluate variants of the AMBER, CHARMM, GROMOS and OPLS biomolecular force fields. In addition, the two blocked amino acids alanine and serine are used to demonstrate the dependence of the measured agreement on the QM method, the phase, and the conformational preferences. Blocked serine serves as an example to discuss possible improvements of the force fields, such as including polarization with Drude particles, or using tailored force fields. The results show that none of the evaluated force fields satisfactorily reproduces all energy minima. By decomposing the average structural reorganization energies in terms of individual energy terms, we can further assess the individual weaknesses of the parametrization strategies of each force field. The dominant problem for most force fields appears to be the van der Waals parameters, followed to a lesser degree by dihedral and bonded terms. Our results show that performing a simple QM energy optimization from an MM-optimized structure can be a first test of the validity of a force field for a particular target molecule.

Nuclearity of semigroup [formula omitted]-algebras and the connection to amenability

We study C∗-algebras associated with subsemigroups of groups. For a large class of such semigroups including positive cones in quasi-lattice ordered groups and left Ore semigroups, we describe the corresponding semigroup C∗-algebras as C∗-algebras of inverse semigroups, groupoid C∗-algebras and full corners in associated group crossed products. These descriptions allow us to characterize nuclearity of semigroup C∗-algebras in terms of faithfulness of left regular representations and amenability of group actions. Moreover, we also determine when boundary quotients of semigroup C∗-algebras are UCT Kirchberg algebras. This leads to a unified approach to Cuntz algebras and ring C∗-algebras.

State-Dependent Representation of Amplitude-Modulated Noise Stimuli in Rat Auditory Cortex

Cortical responses can vary greatly between repeated presentations of an identical stimulus. Here we report that both trial-to-trial variability and faithfulness of auditory cortical stimulus representations depend critically on brain state. A frozen amplitude-modulated white noise stimulus was repeatedly presented while recording neuronal populations and local field potentials (LFPs) in auditory cortex of urethane-anesthetized rats. An information-theoretic measure was used to predict neuronal spiking activity from either the stimulus envelope or simultaneously recorded LFP. Evoked LFPs and spiking more faithfully followed high-frequency temporal modulations when the cortex was in a desynchronized state. In the synchronized state, neural activity was poorly predictable from the stimulus envelope, but the spiking of individual neurons could still be predicted from the ongoing LFP. Our results suggest that although auditory cortical activity remains coordinated as a population in the synchronized state, the ability of continuous auditory stimuli to control this activity is greatly diminished.

Some asymptotics of Topological quantum field theory via skein theory

For each oriented surface Σ of genus g, we study a limit of quantum representations of the mapping class group arising in topological quantum field theory (TQFT) derived from the Kauffman bracket. We determine that these representations converge in the Fell topology to the representation of the mapping class group on H(Σ), the space of regular functions on the SL(2,C)-representation variety with its Hermitian structure coming from the symplectic structure of the SU(2)-representation variety. As a corollary, we give a new proof of the asymptotic faithfulness of quantum representations

C*-Algebras of Irreversible Dynamical Systems

AbstractWe show that certain C*-algebras which have been studied by, among others, Arzumanian, Vershik, Deaconu, and Renault, in connection with a measure-preserving transformation of a measure space or a covering map of a compact space, are special cases of the endomorphism crossed product construction recently introduced by the first named author. As a consequence these algebras are given presentations in terms of generators and relations. These results come as a consequence of a general theorem on faithfulness of representations which are covariant with respect to certain circle actions. For the case of topologically free covering maps we prove a stronger result on faithfulness of representations which needs no covariance. We also give a necessary and sufficient condition for simplicity.

On the residual nilpotence of pure Artin groups

In this very short note we show that the residual nilpotence of pure Artin groups of spherical type is easily deduced from the faithfulness of the Krammer-Digne representations.

Two-sided ideals in [formula omitted]-deformed Heisenberg algebras

In this article, the structure of two-sided ideals in the q -deformed Heisenberg algebras defined by the q -deformed Heisenberg canonical commutation relation AB - qBA = I is investigated. We show that these algebras are simple if and only if q = 1 . For q ≠ 1 , 0 we present an infinite descending chain of non-trivial two-sided ideals, thus deducing by explicit construction that the q -deformed Heisenberg algebras are not just non-simple but also non-artinian for q ≠ 1 , 0 . We establish a connection between the quotients of the q -deformed Heisenberg algebras by these ideals and the quotients of the quantum plane. We also present a number of reordering formulae in q -deformed Heisenberg algebras, investigate properties of deformed commutator mappings, show their fundamental importance for investigation of ideals in q -deformed Heisenberg algebras, and demonstrate how to apply these results to the investigation of faithfulness of representations of q -deformed Heisenberg algebras.

The faithfulness of the monodromy representations associated with certain families of algebraic curves

We consider the faithfulness of the monodromy representation associated with the universal family of n-pointed algebraic curves of genus g (2−2 g− n<0). We shall show that the restriction ρ g, n of the representation to the geometric fundamental group is faithful for g=0,1. We shall also show that if ρ g, n is faithful, then so is ρ g, n+1 .

ON THE GENERAL THEORY OF RELATIONALMORPHISMS

Many diverse problems of compatibility of structures can be unified by generalizing tjie concept of a homomorphism. The paper introduces generalized proteromorphisms and amphimorphisms, forward and backward compatibility of relations, as well as other new useful concepts. These generalizations find application in solving relational equalions, investigation of compatibility of systems and data structures, in examining faithfulness of representations of knowledge structures in knowledge-based systems, in semiotics and elsewhere.