The proportion of failures of the Hasse norm principle

For any number field we calculate the exact proportion of rational numbers which are everywhere locally a norm but not globally a norm from the number field.

Invariant theory and reversible-equivariant vector fields

In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants. (C) 2008 Elsevier B.V, All rights reserved.

A Parallel Hardware Architecture for Scale and Rotation Invariant Feature Detection

This paper proposes a parallel hardware architecture for image feature detection based on the Scale Invariant Feature Transform algorithm and applied to the Simultaneous Localization And Mapping problem. The work also proposes specific hardware optimizations considered fundamental to embed such a robotic control system on-a-chip. The proposed architecture is completely stand-alone; it reads the input data directly from a CMOS image sensor and provides the results via a field-programmable gate array coupled to an embedded processor. The results may either be used directly in an on-chip application or accessed through an Ethernet connection. The system is able to detect features up to 30 frames per second (320 x 240 pixels) and has accuracy similar to a PC-based implementation. The achieved system performance is at least one order of magnitude better than a PC-based solution, a result achieved by investigating the impact of several hardware-orientated optimizations oil performance, area and accuracy.

QCD sum rule calculation for the charmonium-like structures in the J/psi phi and J/psi omega invariant mass spectra

Using the QCD sum rules we test if the charmonium-like structure Y(4274), observed in the J/psi phi invariant mass spectrum, can be described with a D(s)(D) over bar (s0)(2317)+ h.c. molecular current with J(PC) = 0(-+). We consider the contributions of condensates up to dimension ten and we work at leading order in alpha(s). We keep terms which are linear in the strange quark mass m(s). The mass obtained for such state is mD(s)D(s0) = (4.78 +/- 0.54) GeV. We also consider a molecular 0(-+) D (D) over bar (0)(2400)+ h.c. current and we obtain m(DD0) = (4.55 +/- 0.49) GeV. Our study shows that the newly observed Y(4274) in the J/psi phi invariant mass spectrum can be, considering the uncertainties, described using a molecular charmonium current. (C) 2011 Elsevier B.V. All rights reserved.

A new scale-invariant ratio and finite-size scaling for the stochastic susceptible-infected-recovered model

The critical behavior of the stochastic susceptible-infected-recovered model on a square lattice is obtained by numerical simulations and finite-size scaling. The order parameter as well as the distribution in the number of recovered individuals is determined as a function of the infection rate for several values of the system size. The analysis around criticality is obtained by exploring the close relationship between the present model and standard percolation theory. The quantity UP, equal to the ratio U between the second moment and the squared first moment of the size distribution multiplied by the order parameter P, is shown to have, for a square system, a universal value 1.0167(1) that is the same for site and bond percolation, confirming further that the SIR model is also in the percolation class.

A conformal invariant growth model

We present a one-parameter extension of the raise and peel one-dimensional growth model. The model is defined in the configuration space of Dyck (RSOS) paths. Tiles from a rarefied gas hit the interface and change its shape. The adsorption rates are local but the desorption rates are non-local; they depend not only on the cluster hit by the tile but also on the total number of peaks (local maxima) belonging to all the clusters of the configuration. The domain of the parameter is determined by the condition that the rates are non-negative. In the finite-size scaling limit, the model is conformal invariant in the whole open domain. The parameter appears in the sound velocity only. At the boundary of the domain, the stationary state is an adsorbing state and conformal invariance is lost. The model allows us to check the universality of non-local observables in the raise and peel model. An example is given.

Illumination-invariant face recognition from a single image across extreme pose using a dual dimension AAM ensemble in the thermal infrared spectrum

Over the course of the last decade, infrared (IR) and particularly thermal IR imaging based face recognition has emerged as a promising complement to conventional, visible spectrum based approaches which continue to struggle when applied in practice. While inherently insensitive to visible spectrum illumination changes, IR data introduces specific challenges of its own, most notably sensitivity to factors which affect facial heat emission patterns, e.g. emotional state, ambient temperature, and alcohol intake. In addition, facial expression and pose changes are more difficult to correct in IR images because they are less rich in high frequency detail which is an important cue for fitting any deformable model. In this paper we describe a novel method which addresses these major challenges. Specifically, when comparing two thermal IR images of faces, we mutually normalize their poses and facial expressions by using an active appearance model (AAM) to generate synthetic images of the two faces with a neutral facial expression and in the same view (the average of the two input views). This is achieved by piecewise affine warping which follows AAM fitting. A major contribution of our work is the use of an AAM ensemble in which each AAM is specialized to a particular range of poses and a particular region of the thermal IR face space. Combined with the contributions from our previous work which addressed the problem of reliable AAM fitting in the thermal IR spectrum, and the development of a person-specific representation robust to transient changes in the pattern of facial temperature emissions, the proposed ensemble framework accurately matches faces across the full range of yaw from frontal to profile, even in the presence of scale variation (e.g. due to the varying distance of a subject from the camera). The effectiveness of the proposed approach is demonstrated on the largest public database of thermal IR images of faces and a newly acquired data set of thermal IR motion videos. Our approach achieved perfect recognition performance on both data sets, significantly outperforming the current state of the art methods even when they are trained with multiple images spanning a range of head views.

An illumination invariant face recognition system for access control using video

Illumination and pose invariance are the most challenging aspects of face recognition. In this paper we describe a fully automatic face recognition system that uses video information to achieve illumination and pose robustness. In the proposed method, highly nonlinear manifolds of face motion are approximated using three Gaussian pose clusters. Pose robustness is achieved by comparing the corresponding pose clusters and probabilistically combining the results to derive a measure of similarity between two manifolds. Illumination is normalized on a per-pose basis. Region-based gamma intensity correction is used to correct for coarse illumination changes, while further refinement is achieved by combining a learnt linear manifold of illumination variation with constraints on face pattern distribution, derived from video. Comparative experimental evaluation is presented and the proposed method is shown to greatly outperform state-of-the-art algorithms. Consistent recognition rates of 94-100% are achieved across dramatic changes in illumination.