289 research outputs found
Cooperation in one machine scheduling
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172966.pdf (publisher's version ) (Open Access
On the top eigenvalue of heavy-tailed random matrices
We study the statistics of the largest eigenvalue lambda_max of N x N random
matrices with unit variance, but power-law distributed entries, P(M_{ij})~
|M_{ij}|^{-1-mu}. When mu > 4, lambda_max converges to 2 with Tracy-Widom
fluctuations of order N^{-2/3}. When mu < 4, lambda_max is of order
N^{2/mu-1/2} and is governed by Fr\'echet statistics. The marginal case mu=4
provides a new class of limiting distribution that we compute explicitely. We
extend these results to sample covariance matrices, and show that extreme
events may cause the largest eigenvalue to significantly exceed the
Marcenko-Pastur edge. Connections with Directed Polymers are briefly discussed.Comment: 4 pages, 2 figure
Allocation in Practice
How do we allocate scarcere sources? How do we fairly allocate costs? These
are two pressing challenges facing society today. I discuss two recent projects
at NICTA concerning resource and cost allocation. In the first, we have been
working with FoodBank Local, a social startup working in collaboration with
food bank charities around the world to optimise the logistics of collecting
and distributing donated food. Before we can distribute this food, we must
decide how to allocate it to different charities and food kitchens. This gives
rise to a fair division problem with several new dimensions, rarely considered
in the literature. In the second, we have been looking at cost allocation
within the distribution network of a large multinational company. This also has
several new dimensions rarely considered in the literature.Comment: To appear in Proc. of 37th edition of the German Conference on
Artificial Intelligence (KI 2014), Springer LNC
Quenched complexity of the p-spin spherical spin-glass with external magnetic field
We consider the p-spin spherical spin-glass model in the presence of an
external magnetic field as a general example of a mean-field system where a one
step replica symmetry breaking (1-RSB) occurs. In this context we compute the
complexity of the Thouless-Anderson-Palmer states, performing a quenched
computation. We find what is the general connection between this method and the
standard static 1-RSB one, formulating a clear mapping between the parameters
used in the two different calculations. We also perform a dynamical analysis of
the model, by which we confirm the validity of our results.Comment: RevTeX, 11 pages, including 2 EPS figure
Financial correlations at ultra-high frequency: theoretical models and empirical estimation
A detailed analysis of correlation between stock returns at high frequency is
compared with simple models of random walks. We focus in particular on the
dependence of correlations on time scales - the so-called Epps effect. This
provides a characterization of stochastic models of stock price returns which
is appropriate at very high frequency.Comment: 22 pages, 8 figures, 1 table, version to appear in EPJ
Regularizing Portfolio Optimization
The optimization of large portfolios displays an inherent instability to
estimation error. This poses a fundamental problem, because solutions that are
not stable under sample fluctuations may look optimal for a given sample, but
are, in effect, very far from optimal with respect to the average risk. In this
paper, we approach the problem from the point of view of statistical learning
theory. The occurrence of the instability is intimately related to over-fitting
which can be avoided using known regularization methods. We show how
regularized portfolio optimization with the expected shortfall as a risk
measure is related to support vector regression. The budget constraint dictates
a modification. We present the resulting optimization problem and discuss the
solution. The L2 norm of the weight vector is used as a regularizer, which
corresponds to a diversification "pressure". This means that diversification,
besides counteracting downward fluctuations in some assets by upward
fluctuations in others, is also crucial because it improves the stability of
the solution. The approach we provide here allows for the simultaneous
treatment of optimization and diversification in one framework that enables the
investor to trade-off between the two, depending on the size of the available
data set
Mean-Field Equations for Spin Models with Orthogonal Interaction Matrices
We study the metastable states in Ising spin models with orthogonal
interaction matrices. We focus on three realizations of this model, the random
case and two non-random cases, i.e.\ the fully-frustrated model on an infinite
dimensional hypercube and the so-called sine-model. We use the mean-field (or
{\sc tap}) equations which we derive by resuming the high-temperature expansion
of the Gibbs free energy. In some special non-random cases, we can find the
absolute minimum of the free energy. For the random case we compute the average
number of solutions to the {\sc tap} equations. We find that the
configurational entropy (or complexity) is extensive in the range
T_{\mbox{\tiny RSB}}. Finally we present an apparently
unrelated replica calculation which reproduces the analytical expression for
the total number of {\sc tap} solutions.Comment: 22+3 pages, section 5 slightly modified, 1 Ref added, LaTeX and
uuencoded figures now independent of each other (easier to print). Postscript
available http://chimera.roma1.infn.it/index_papers_complex.htm
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