A simplified approach to a three-part Wiener-Hopf problem arising in diffraction theory

A direct and simple approach, utilizing Watson's lemma, is presented for obtaining an approximate solution of a three-part Wiener-Hopf problem associated with the problem of diffraction of a plane wave by a soft strip.

Quantum-Ohmic Resistance Fluctuation In Disordered Conductors - An Invariant Imbedding Approach

It is now well known that in extreme quantum limit, dominated by the elastic impurity scattering and the concomitant quantum interference, the zero-temperature d.c. resistance of a strictly one-dimensional disordered system is non-additive and non-self-averaging. While these statistical fluctuations may persist in the case of a physically thin wire, they are implicitly and questionably ignored in higher dimensions. In this work, we have re-examined this question. Following an invariant imbedding formulation, we first derive a stochastic differential equation for the complex amplitude reflection coefficient and hence obtain a Fokker-Planck equation for the full probability distribution of resistance for a one-dimensional continuum with a Gaussian white-noise random potential. We then employ the Migdal-Kadanoff type bond moving procedure and derive the d-dimensional generalization of the above probability distribution, or rather the associated cumulant function –‘the free energy’. For d=3, our analysis shows that the dispersion dominates the mobilitly edge phenomena in that (i) a one-parameter B-function depending on the mean conductance only does not exist, (ii) an approximate treatment gives a diffusion-correction involving the second cumulant. It is, however, not clear whether the fluctuations can render the transition at the mobility edge ‘first-order’. We also report some analytical results for the case of the one dimensional system in the presence of a finite electric fiekl. We find a cross-over from the exponential to the power-low length dependence of resistance as the field increases from zero. Also, the distribution of resistance saturates asymptotically to a poissonian form. Most of our analytical results are supported by the recent numerical simulation work reported by some authors.

Unsupervised Domain Adaptation by Domain Invariant Projection

Domain-invariant representations are key to addressing the domain shift problem where the training and test exam- ples follow different distributions. Existing techniques that have attempted to match the distributions of the source and target domains typically compare these distributions in the original feature space. This space, however, may not be di- rectly suitable for such a comparison, since some of the fea- tures may have been distorted by the domain shift, or may be domain specific. In this paper, we introduce a Domain Invariant Projection approach: An unsupervised domain adaptation method that overcomes this issue by extracting the information that is invariant across the source and tar- get domains. More specifically, we learn a projection of the data to a low-dimensional latent space where the distance between the empirical distributions of the source and target examples is minimized. We demonstrate the effectiveness of our approach on the task of visual object recognition and show that it outperforms state-of-the-art methods on a stan- dard domain adaptation benchmark dataset

Repeatable Condition-Invariant Visual Odometry for Sequence-Based Place Recognition

This paper describes a vision-only system for place recognition in environments that are tra- versed at different times of day, when chang- ing conditions drastically affect visual appear- ance, and at different speeds, where places aren’t visited at a consistent linear rate. The ma- jor contribution is the removal of wheel-based odometry from the previously presented algo- rithm (SMART), allowing the technique to op- erate on any camera-based device; in our case a mobile phone. While we show that the di- rect application of visual odometry to our night- time datasets does not achieve a level of perfor- mance typically needed, the VO requirements of SMART are orthogonal to typical usage: firstly only the magnitude of the velocity is required, and secondly the calculated velocity signal only needs to be repeatable in any one part of the environment over day and night cycles, but not necessarily globally consistent. Our results show that the smoothing effect of motion constraints is highly beneficial for achieving a locally consis- tent, lighting-independent velocity estimate. We also show that the advantage of our patch-based technique used previously for frame recogni- tion, surprisingly, does not transfer to VO, where SIFT demonstrates equally good performance. Nevertheless, we present the SMART system us- ing only vision, which performs sequence-base place recognition in extreme low-light condi- tions where standard 6-DOF VO fails and that improves place recognition performance over odometry-less benchmarks, approaching that of wheel odometry.

Locality and order-invariant logics

Malli on logiikassa käytetty abstraktio monille matemaattisille objekteille. Esimerkiksi verkot, ryhmät ja metriset avaruudet ovat malleja. Äärellisten mallien teoria on logiikan osa-alue, jossa tarkastellaan logiikkojen, formaalien kielten, ilmaisuvoimaa malleissa, joiden alkioiden lukumäärä on äärellinen. Rajoittuminen äärellisiin malleihin mahdollistaa tulosten soveltamisen teoreettisessa tietojenkäsittelytieteessä, jonka näkökulmasta logiikan kaavoja voidaan ajatella ohjelmina ja äärellisiä malleja niiden syötteinä. Lokaalisuus tarkoittaa logiikan kyvyttömyyttä erottaa toisistaan malleja, joiden paikalliset piirteet vastaavat toisiaan. Väitöskirjassa tarkastellaan useita lokaalisuuden muotoja ja niiden säilymistä logiikkoja yhdistellessä. Kehitettyjä työkaluja apuna käyttäen osoitetaan, että Gaifman- ja Hanf-lokaalisuudeksi kutsuttujen varianttien välissä on lokaalisuuskäsitteiden hierarkia, jonka eri tasot voidaan erottaa toisistaan kasvavaa dimensiota olevissa hiloissa. Toisaalta osoitetaan, että lokaalisuuskäsitteet eivät eroa toisistaan, kun rajoitutaan tarkastelemaan äärellisiä puita. Järjestysinvariantit logiikat ovat kieliä, joissa on käytössä sisäänrakennettu järjestysrelaatio, mutta sitä on käytettävä siten, etteivät kaavojen ilmaisemat asiat riipu valitusta järjestyksestä. Määritelmää voi motivoida tietojenkäsittelyn näkökulmasta: vaikka ohjelman syötteen tietojen järjestyksellä ei olisi odotetun tuloksen kannalta merkitystä, on syöte tietokoneen muistissa aina jossakin järjestyksessä, jota ohjelma voi laskennassaan hyödyntää. Väitöskirjassa tutkitaan minkälaisia lokaalisuuden muotoja järjestysinvariantit ensimmäisen kertaluvun predikaattilogiikan laajennukset yksipaikkaisilla kvanttoreilla voivat toteuttaa. Tuloksia sovelletaan tarkastelemalla, milloin sisäänrakennettu järjestys lisää logiikan ilmaisuvoimaa äärellisissä puissa.

Invariant magneto-electric and piezomagnetic coefficients

Invariant magneto-electric coefficients and invariant piezomagnetic coefficients are obtained for all the magnetic crystal classes.

The curvature invariant for a class of homogeneous operators

For an operator T in the class B-n(), introduced by Cowen and Douglas, the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle E-T determine the unitary equivalence class of the operator T. In a subsequent paper, the authors ask if the simultaneous unitary equivalence class of the curvature and these covariant derivatives are necessary to determine the unitary equivalence class of the operator T is an element of B-n(). Here we show that some of the covariant derivatives are necessary. Our examples consist of homogeneous operators in B-n(). For homogeneous operators, the simultaneous unitary equivalence class of the curvature and all its covariant derivatives at any point w in the unit disc are determined from the simultaneous unitary equivalence class at 0. This shows that it is enough to calculate all the invariants and compare them at just one point, say 0. These calculations are then carried out in number of examples. One of our main results is that the curvature along with its covariant derivative of order (0, 1) at 0 determines the equivalence class of generic homogeneous Hermitian holomorphic vector bundles over the unit disc.

Structural Studies on the Second Mycobacterium smegmatis Dps: Invariant and Variable Features of Structure, Assembly and Function

A second DNA binding protein from stationary-phase cells of Mycobacterium smegmatis (MsDps2) has been identified from the bacterial genome. It was cloned, expressed and characterised and its crystal structure was determined. The core dodecameric structure of MsDps2 is the same as that of the Dps from the organism described earlier (MsDps1). However, MsDps2 possesses a long N-terminal tail instead of the C-terminal tail in MsDps1. This tail appears to be involved in DNA binding. It is also intimately involved in stabilizing the dodecamer. Partly on account of this factor, MsDps2 assembles straightway into the dodecamer, while MsDps1 does so on incubation after going through an intermediate trimeric stage. The ferroxidation centre is similar in the two proteins, while the pores leading to it exhibit some difference. The mode of sequestration of DNA in the crystalline array of molecules, as evidenced by the crystal structures, appears to be different in MsDps1 and MsDps2, highlighting the variability in the mode of Dps–DNA complexation. A sequence search led to the identification of 300 Dps molecules in bacteria with known genome sequences. Fifty bacteria contain two or more types of Dps molecules each, while 195 contain only one type. Some bacteria, notably some pathogenic ones, do not contain Dps. A sequence signature for Dps could also be derived from the analysis.

Gauge-invariant reformulation of an anomalous gauge theory

An anomalous gauge theory can be reformulated in a gauge invariant way without any change in its physical content. This is demonstrated here for the exactly soluble chiral Schwinger model. Our gauge invariant version is very different from the Faddeev-Shatashvili proposal [L.D. Faddeev and S.L. Shatashvili, Theor. Math. Phys. 60 (1984) 206] and involves no additional gauge-group-valued fields. The status of the "gauge" A0=0 sometimes used in anomalous theories is also discussed and justified in our reformulation.

Invariant-preserving Petri net reduction and conditions for invariant-existence

The use of invariants is an important tool for analysis of distributed and concurrent systems modeled by Petri nets. For a large practical system, the computation of desired invariants by the existing techniques is a time-consuming task. This paper proposes a theoretical foundation for simplified computation of desired invariants. We provide invariant-preserving Petri net reduction rules followed by the conditions for the existence of invariants in various well-structured nets. If an invariant exists, it can be found directly from the net structure using the formulas derived, or by applying the existing techniques on the reduced net.

A generalised cole-hopf transformation for nonlinear parabolic and hyperbolic equations

The Cole-Hopf transformation has been generalized to generate a large class of nonlinear parabolic and hyperbolic equations which are exactly linearizable. These include model equations of exchange processes and turbulence. The methods to solve the corresponding linear equations have also been indicated.La transformation de Cole et de Hopf a été généralisée en vue d'engendrer une classe d'équations nonlinéaires paraboliques et hyperboliques qui peuvent être rendues linéaires de façon exacte. Elles comprennent des équations modèles de procédés d'échange et de turbulence. Les méthodes pour résoudre les équations linéaires correspondantes ont également été indiquées.

Invariant norm quantifying nonlinear content of Hamiltonian systems

Given a Hamiltonian system, one can represent it using a symplectic map. This symplectic map is specified by a set of homogeneous polynomials which are uniquely determined by the Hamiltonian. In this paper, we construct an invariant norm in the space of homogeneous polynomials of a given degree. This norm is a function of parameters characterizing the original Hamiltonian system. Such a norm has several potential applications. (C) 2010 Elsevier Inc. All rights reserved.