Open spin chains with dynamic lattice supersymmetry

The quantum spin $1/2$ XXZ chain with anisotropy parameter $\Delta=-1/2$ possesses a dynamic supersymmetry on the lattice. This supersymmetry and a generalisation to higher spin are investigated in the case of open spin chains. A family of non-diagonal boundary interactions that are compatible with the lattice supersymmetry and depend on several parameters is constructed. The cohomology of the corresponding supercharges is explicitly computed as a function of the parameters and the length of the chain. For certain specific values of the parameters, this cohomology is shown to be non-trivial. This implies that the spin-chain ground states are supersymmetry singlets. Special scalar products involving an arbitrary number of these supersymmetry singlets for chains of different lengths are exactly computed. As a physical application, the logarithmic bipartite fidelity of the open quantum spin $1/2$ XXZ chain with $\Delta=-1/2$ and special diagonal boundary interactions is determined.Comment: 33 pages, 2 figure

On the limiting law of the length of the longest common and increasing subsequences in random words

Let $X=(X_i)_{i\ge 1}$ and $Y=(Y_i)_{i\ge 1}$ be two sequences of independent and identically distributed (iid) random variables taking their values, uniformly, in a common totally ordered finite alphabet. Let LCI$_n$ be the length of the longest common and (weakly) increasing subsequence of $X_1\cdots X_n$ and $Y_1\cdots Y_n$. As $n$ grows without bound, and when properly centered and normalized, LCI$_n$ is shown to converge, in distribution, towards a Brownian functional that we identify.Comment: Some corrections from the published version are provided, some typos are also correcte

A survey on signature-based Gr\"obner basis computations

This paper is a survey on the area of signature-based Gr\"obner basis algorithms that was initiated by Faug\`ere's F5 algorithm in 2002. We explain the general ideas behind the usage of signatures. We show how to classify the various known variants by 3 different orderings. For this we give translations between different notations and show that besides notations many approaches are just the same. Moreover, we give a general description of how the idea of signatures is quite natural when performing the reduction process using linear algebra. This survey shall help to outline this field of active research.Comment: 53 pages, 8 figures, 11 table

Between order and disorder: a 'weak law' on recent electoral behavior among urban voters?

A new viewpoint on electoral involvement is proposed from the study of the statistics of the proportions of abstentionists, blank and null, and votes according to list of choices, in a large number of national elections in different countries. Considering 11 countries without compulsory voting (Austria, Canada, Czech Republic, France, Germany, Italy, Mexico, Poland, Romania, Spain and Switzerland), a stylized fact emerges for the most populated cities when one computes the entropy associated to the three ratios, which we call the entropy of civic involvement of the electorate. The distribution of this entropy (over all elections and countries) appears to be sharply peaked near a common value. This almost common value is typically shared since the 1970's by electorates of the most populated municipalities, and this despite the wide disparities between voting systems and types of elections. Performing different statistical analyses, we notably show that this stylized fact reveals particular correlations between the blank/null votes and abstentionists ratios. We suggest that the existence of this hidden regularity, which we propose to coin as a `weak law on recent electoral behavior among urban voters', reveals an emerging collective behavioral norm characteristic of urban citizen voting behavior in modern democracies. Analyzing exceptions to the rule provide insights into the conditions under which this normative behavior can be expected to occur.Comment: Version 1: main text 19 pages, 13 figures, 2 tables; Supporting Information: 19 pages. Version 2: minor correction

Inference in non stationary asymmetric garch models

This paper considers the statistical inference of the class of asymmetric power-transformed GARCH(1,1) models in presence of possible explosiveness. We study the explosive behavior of volatility when the strict stationarity condition is not met. This allows us to establish the asymptotic normality of the quasi-maximum likelihood estimator (QMLE) of the parameter, including the power but without the intercept, when strict stationarity does not hold. Two important issues can be tested in this framework: asymmetry and stationarity. The tests exploit the existence of a universal estimator of the asymptotic covariance matrix of the QMLE. By establishing the local asymptotic normality (LAN) property in this nonstationary framework, we can also study optimality issues

ImpuR: A Collection of Diagnostic Tools Developed in R in the Context of Peak Impurity Detection in HPLC-DAD but Potentially Useful with Other Types of Time-Intensity Matrices

HPLC-DAD systems generate time intensity (absorbance) matrices called spectrochromatograms. Under good experimental conditions, spectro-chromatograms of elution peaks of pure analytes are bilinear products of a time peak and an absorbance spectrum. Co-eluting impurities create deviations from this pure bilinear structure. Unfortunately, other imperfections, such as scan averaging, large optical windows, imperfect lamp alignment, mobile phase fluctuations, etc. also create departures from the pure bilinear structure. This makes it hard to distinguish low concentration impurities from artifacts and hampers safe detection of contaminants. There are two main ways to deal with such artifacts: removal and simulation, and ImpuR provides R functions to do both and to integrate both approaches. More specifically, ImpuR provides a set of tools to explore time-intensity matrices with respect to their bilinear structure and departures from it. It includes exploratory graphs for bilinear matrices (bilinear residual graphs and singular value decompositions), spectral dissimilarity curves via window-evolving factor analysis with heteroscedasticity correction and the sine method, methods for removal of artifacts, and a comprehensive simulation tool to assess the impact of potential artifacts and to allow for the construction of guide curves for use with the sine method.

The Spectrum of the two dimensional Hubbard model at low filling

Using group theoretical and numerical methods we have calculated the exact energy spectrum of the two-dimensional Hubbard model on square lattices with four electrons for a wide range of the interaction strength. All known symmetries, i.e.\ the full space group symmetry, the SU(2) spin symmetry, and, in case of a bipartite lattice, the SU(2) pseudospin symmetry, have been taken explicitly into account. But, quite remarkably, a large amount of residual degeneracies remains giving strong evidence for the existence of a yet unknown symmetry. The level spacing distribution and the spectral rigidity are found to be in close to but not exact agreement with random matrix theory. In contrast, the level velocity correlation function presents an unexpected exponential decay qualitatively different from random matrix behavior.Comment: 4 pages, latex (revtex), 3 uuencoded postscript figure