The spectral shift function and spectral flow

This paper extends Krein's spectral shift function theory to the setting of semifinite spectral triples. We define the spectral shift function under these hypotheses via Birman-Solomyak spectral averaging formula and show that it computes spectral flow.Comment: 47 page

Development of holistic vs. featural processing in face recognition

According to a classic view developed by Carey and Diamond (1977), young children process faces in a piecemeal fashion before adult-like holistic processing starts to emerge at the age of around 10 years. This is known as the encoding switch hypothesis . Since then,a growing body of studies have challenged the theory. This article will provide a critical appraisal of this literature, followed by an analysis of some more recent developments. We will conclude, quite contrary to the classical view, that holistic processing is not only present in early child development, but could even precede the development of part-based processing

Automatic grid construction for few-body quantum mechanical calculations

An algorithm for generating optimal nonuniform grids for solving the two-body Schr\"odinger equation is developed and implemented. The shape of the grid is optimized to accurately reproduce the low-energy part of the spectrum of the Schr\"odinger operator. Grids constructed this way are applicable to more complex few-body systems where the number of grid points is a critical limitation to numerical accuracy. The utility of the grid generation for improving few-body calculations is illustrated through an application to bound states of He trimers

The Birman-Schwinger principle in von Neumann algebras of finite type

We introduce a relative index for a pair of dissipative operators in a von Neumann algebra of finite type and prove an analog of the Birman-Schwinger principle in this setting. As an application of this result, revisiting the Birman-Krein formula in the abstract scattering theory, we represent the de la Harpe-Skandalis determinant of the characteristic function of dissipative operators in the algebra in terms of the relative index

Extracting individual contributions from their mixture: a blind source separation approach, with examples from space and laboratory plasmas

Multipoint or multichannel observations in plasmas can frequently be modelled as an instantaneous mixture of contributions (waves, emissions, ...) of different origins. Recovering the individual sources from their mixture then becomes one of the key objectives. However, unless the underlying mixing processes are well known, these situations lead to heavily underdetermined problems. Blind source separation aims at disentangling such mixtures with the least possible prior information on the sources and their mixing processes. Several powerful approaches have recently been developed, which can often provide new or deeper insight into the underlying physics. This tutorial paper briefly discusses some possible applications of blind source separation to the field of plasma physics, in which this concept is still barely known. Two examples are given. The first one shows how concurrent processes in the dynamical response of the electron temperature in a tokamak can be separated. The second example deals with solar spectral imaging in the Extreme UV and shows how empirical temperature maps can be built.Comment: expanded version of an article to appear in Contributions to Plasma Physics (2010

Evaluation of the Algorithms and Parameterizations for Ground Thawing and Freezing Simulation in Permafrost Regions

Ground thawing and freezing depths (GTFDs) strongly influence the hydrology and energy balances of permafrost regions. Current methods to simulate GTFD differ in algorithm type, soil parameterization, representation of latent heat, and unfrozen water content. In this study, five algorithms (one semiempirical, two analytical, and two numerical), three soil thermal conductivity parameterizations, and three unfrozen water parameterizations were evaluated against detailed field measurements at four field sites in Canada’s discontinuous permafrost region. Key findings include: (1) de Vries’ parameterization is recommended to determine the thermal conductivity in permafrost soils; (2) the three unfrozen water parameterization methods exhibited little difference in terms of GTFD simulations, yet the segmented linear function is the simplest to be implemented; (3) the semiempirical algorithm reasonably simulates thawing at permafrost sites and freezing at seasonal frost sites with site-specific calibration. However, large interannual and intersite variations in calibration coefficients limit its applicability for dynamic analysis; (4) when driven by surface forcing, analytical algorithms performed marginally better than the semiempirical algorithm. The inclusion of bottom forcing improved analytical algorithm performance, yet their results were still poor compared with those achieved by numerical algorithms; (5) when supplied with the optimal inputs, soil parameterizations, and model configurations, the numerical algorithm with latent heat treated as an apparent heat capacity achieved the best GTFD simulations among all algorithms at all sites. Replacing the observed bottom temperature with a zero heat flux boundary condition did not significantly reduce simulation accuracy, while assuming a saturated profile caused large errors at several sites

Characterisation of a pucBA deletion mutant from Rhodopseudomonas palustris lacking all but the pucBAd genes

Rhodopseudomonas palustris is a species of purple photosynthetic bacteria that has a multigene family of puc genes that encode the alpha and beta apoproteins, which form the LH2 complexes. A genetic dissection strategy has been adopted in order to try and understand which spectroscopic form of LH2 these different genes produce. This paper presents a characterisation of one of the deletion mutants generated in this program, the pucBAd only mutant. This mutant produces an unusual spectroscopic form of LH2 that only has a single large NIR absorption band at 800 nm. Spectroscopic and pigment analyses on this complex suggest that it has basically a similar overall structure as that of the wild-type HL LH2 complex. The mutant has the unique phenotype where the mutant LH2 complex is only produced when cells are grown at LL. At HL the mutant only produces the LH1-RC core complex

Exact solution of a 2D interacting fermion model

We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a square lattice with local hopping and density-density interactions if, close to half filling, the system develops a partial energy gap. The necessary regularization of the QFT model is based on this proposed relation to lattice fermions. We use bosonization methods to diagonalize the Hamiltonian and to compute all correlation functions. We also discuss how, after appropriate multiplicative renormalizations, all short- and long distance cutoffs can be removed. In particular, we prove that the renormalized two-point functions have algebraic decay with non-trivial exponents depending on the interaction strengths, which is a hallmark of Luttinger-liquid behavior.Comment: 59 pages, 3 figures, v2: further references added; additional subsections elaborating mathematical details; additional appendix with details on the relation to lattice fermion