1,235 research outputs found
Superstatistical generalisations of Wishart-Laguerre ensembles of random matrices
Using Beck and Cohen's superstatistics, we introduce in a systematic way a family of generalized WishartâLaguerre ensembles of random matrices with Dyson index ÎČ = 1, 2 and 4. The entries of the data matrix are Gaussian random variables whose variances η fluctuate from one sample to another according to a certain probability density f(η) and a single deformation parameter Îł. Three superstatistical classes for f(η) are usually considered: Ï2-, inverse Ï2- and log-normal distributions. While the first class, already considered by two of the authors, leads to a power-law decay of the spectral density, we here introduce and solve exactly a superposition of WishartâLaguerre ensembles with inverse Ï2-distribution. The corresponding macroscopic spectral density is given by a Îł-deformation of the semi-circle and MarÄenkoâPastur laws, on a non-compact support with exponential tails. After discussing in detail the validity of Wigner's surmise in the WishartâLaguerre class, we introduce a generalized Îł-dependent surmise with stretched-exponential tails, which well approximates the individual level spacing distribution in the bulk. The analytical results are in excellent agreement with numerical simulations. To illustrate our findings we compare the Ï2- and inverse Ï2-classes to empirical data from financial covariance matrices
DEVELOPMENT POLICIES IN SOUTHERN ITALY BETWEEN GOVERNMENT AND GOVERNANCE
The paper has analysed outputs generated by the development policies implemented in last decades in the South of Italy, starting from the Extraordinary Intervention (since 1950, until 1992) to the European cohesion policy (since 1996). The first one was a high-centralized development policy. Differently, the European cohesion policy is based on multilevel governance, and follows a bottom-up approach oriented to stimulate local stakeholdersâ participation. The analysis, exposed in previous paragraphs, has described these two different policy experiences, the related effects on local development and on convergence between North and South of Italy and among European regions. The paper has tried to answer to a fundamental question: what factors have negatively affected the implementation of these policies, generating unexpected effects
Spectra of Empirical Auto-Covariance Matrices
We compute spectra of sample auto-covariance matrices of second order
stationary stochastic processes. We look at a limit in which both the matrix
dimension and the sample size used to define empirical averages
diverge, with their ratio kept fixed. We find a remarkable scaling
relation which expresses the spectral density of sample
auto-covariance matrices for processes with dynamical correlations as a
continuous superposition of appropriately rescaled copies of the spectral
density for a sequence of uncorrelated random
variables. The rescaling factors are given by the Fourier transform
of the auto-covariance function of the stochastic process. We also obtain a
closed-form approximation for the scaling function
. This depends on the shape parameter , but
is otherwise universal: it is independent of the details of the underlying
random variables, provided only they have finite variance. Our results are
corroborated by numerical simulations using auto-regressive processes.Comment: 4 pages, 2 figure
Occlusion points identification algorithm
In this paper a very simple and efficient algorithm is proposed, to calculate the invisible regions of a
scene, or shadowed side of a body, when it is observed from a pre-set point. This is done by applying a
deterministic numerical procedure to the portion of scene in the field of view, after having been projected
in the observer reference frame. The great advantage of this approach is its generality and suitability for
a wide number of applications. They span from real time renderings, to the simulation of different types
of light sources, such as diffused or collimated, or simply to calculate the effective visible surface for a
camera mounted on board of an aircraft, in order to optimize its trajectory if remote sensing or aerial
mapping task should be carried out. Optimizing the trajectory, by minimizing at any time the occluded
surface, is also a powerful solution for a search and rescue mission, because a wider area in a shorter time
can be observed, particularly in situations where the time is a critical parameter, such as, during a forest
fire or in case of avalanches. For its simplicity of implementation, the algorithm is suitable for real time
applications, providing an extremely accurate solution in a fraction of a millisecond. In this paper, the
algorithm has been tested by calculating the occluded regions of a very complex mountainous scenario,
seen from a gimbal-camera mounted on board of a flying platform
"Spectrally gapped" random walks on networks: a Mean First Passage Time formula
We derive an approximate but explicit formula for the Mean First Passage Time of a random walker between a source and a target node of a directed and weighted network. The formula does not require any matrix inversion, and it takes as only input the transition probabilities into the target node. It is derived from the calculation of the average resolvent of a deformed ensemble of random sub-stochastic matrices
H
=
âš
H
â©
+
ÎŽ
H, with
âš
H
â©
rank-
1
and non-negative. The accuracy of the formula depends on the spectral gap of the reduced transition matrix, and it is tested numerically on several instances of (weighted) networks away from the high sparsity regime, with an excellent agreement
Jacobi Crossover Ensembles of Random Matrices and Statistics of Transmission Eigenvalues
We study the transition in conductance properties of chaotic mesoscopic
cavities as time-reversal symmetry is broken. We consider the Brownian motion
model for transmission eigenvalues for both types of transitions, viz.,
orthogonal-unitary and symplectic-unitary crossovers depending on the presence
or absence of spin-rotation symmetry of the electron. In both cases the
crossover is governed by a Brownian motion parameter {\tau}, which measures the
extent of time-reversal symmetry breaking. It is shown that the results
obtained correspond to the Jacobi crossover ensembles of random matrices. We
derive the level density and the correlation functions of higher orders for the
transmission eigenvalues. We also obtain the exact expressions for the average
conductance, average shot-noise power and variance of conductance, as functions
of {\tau}, for arbitrary number of modes (channels) in the two leads connected
to the cavity. Moreover, we give the asymptotic result for the variance of
shot-noise power for both the crossovers, the exact results being too long. In
the {\tau} \rightarrow 0 and {\tau} \rightarrow \infty limits the known results
for the orthogonal (or symplectic) and unitary ensembles are reproduced. In the
weak time-reversal symmetry breaking regime our results are shown to be in
agreement with the semiclassical predictions.Comment: 24 pages, 5 figure
Optimization of graphene-based materials outperforming host epoxy matrices
The degree of graphite exfoliation and edge-carboxylated layers can be controlled and balanced to design lightweight materials characterized by both low electrical percolation thresholds (EPT) and improved mechanical properties. So far, this challenging task has been undoubtedly very hard to achieve. The results presented in this paper highlight the effect of exfoliation degree and the role of edge-carboxylated graphite layers to give self-assembled structures embedded in the polymeric matrix. Graphene layers inside the matrix may serve as building blocks of complex systems that could outperform the host matrix. Improvements in electrical percolation and mechanical performance have been obtained by a synergic effect due to finely balancing the degree of exfoliation and the chemistry of graphene edges which favors the interfacial interaction between polymer and carbon layers. In particular, for epoxy-based resins including two partially exfoliated graphite samples, differing essentially in the content of carboxylated groups, the percolation threshold reduces from 3 wt% down to 0.3 wt%, as the carboxylated group content increases up to 10 wt%. Edge-carboxylated nanosheets also increase the nanofiller/epoxy matrix interaction, determining a relevant reinforcement in the elastic modulus
Number statistics for -ensembles of random matrices: applications to trapped fermions at zero temperature
Let be the probability that a
-ensemble of random matrices with confining potential
has eigenvalues inside an interval of the real
line. We introduce a general formalism, based on the Coulomb gas technique and
the resolvent method, to compute analytically for large . We show that this probability scales for large
as , where is the Dyson index of the
ensemble. The rate function , independent of ,
is computed in terms of single integrals that can be easily evaluated
numerically. The general formalism is then applied to the classical
-Gaussian (), -Wishart () and
-Cauchy () ensembles. Expanding the rate function
around its minimum, we find that generically the number variance exhibits a non-monotonic behavior as a function of the size
of the interval, with a maximum that can be precisely characterized. These
analytical results, corroborated by numerical simulations, provide the full
counting statistics of many systems where random matrix models apply. In
particular, we present results for the full counting statistics of zero
temperature one-dimensional spinless fermions in a harmonic trap.Comment: 34 pages, 19 figure
Le reti di impresa nella politica industriale. I contratti di rete e i contratti di sviluppo.
Le reti di impresa si sono affermate come un modello organizzativo e competitivo compiutamente alternativo sia al mercato sia alla gerarchia, superando una visione teorica che tendeva a confinarle come modello imperfetto o immaturo del capitalismo. I contributi raccolti nel volume, frutto di un lavoro di ricerca multidisciplinare, analizzano i presupposti teorici delle reti e si concentrano su due principali strumenti di politica industriale â i contratti di rete e i contratti di sviluppo â avvalendosi dei risultati emersi dai percorsi di attuazione di casi selezionati in quattro regioni italiane
Compact smallest eigenvalue expressions in Wishart-Laguerre ensembles with or without fixed-trace
The degree of entanglement of random pure states in bipartite quantum systems
can be estimated from the distribution of the extreme Schmidt eigenvalues. For
a bipartition of size M\geq N, these are distributed according to a
Wishart-Laguerre ensemble (WL) of random matrices of size N x M, with a
fixed-trace constraint. We first compute the distribution and moments of the
smallest eigenvalue in the fixed trace orthogonal WL ensemble for arbitrary
M\geq N. Our method is based on a Laplace inversion of the recursive results
for the corresponding orthogonal WL ensemble by Edelman. Explicit examples are
given for fixed N and M, generalizing and simplifying earlier results. In the
microscopic large-N limit with M-N fixed, the orthogonal and unitary WL
distributions exhibit universality after a suitable rescaling and are therefore
independent of the constraint. We prove that very recent results given in terms
of hypergeometric functions of matrix argument are equivalent to more explicit
expressions in terms of a Pfaffian or determinant of Bessel functions. While
the latter were mostly known from the random matrix literature on the QCD Dirac
operator spectrum, we also derive some new results in the orthogonal symmetry
class.Comment: 25 pag., 4 fig - minor changes, typos fixed. To appear in JSTA
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