29,274 research outputs found
Open spin chains with dynamic lattice supersymmetry
The quantum spin XXZ chain with anisotropy parameter
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
XXZ chain with 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 and be two sequences of independent
and identically distributed (iid) random variables taking their values,
uniformly, in a common totally ordered finite alphabet. Let LCI be the
length of the longest common and (weakly) increasing subsequence of and . As grows without bound, and when properly
centered and normalized, LCI 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
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