725 research outputs found
Generalized Mixability via Entropic Duality
Mixability is a property of a loss which characterizes when
constant regret is possible in the game of prediction with expert
advice. We show that a key property of mixability generalizes, and
the and operations present in the usual theory are not as
special as one might have thought.
In doing so we introduce a
more general notion of -mixability where is a general
entropy (\ie, any convex function on probabilities). We show how a property
shared by the convex dual of any such entropy yields a natural
algorithm (the minimizer of a regret bound) which, analogous to the
classical Aggregating Algorithm, is guaranteed a constant regret
when used with -mixable losses.
We characterize which have non-trivial -mixable losses and
relate -mixability and its associated Aggregating
Algorithm to potential-based methods, a Blackwell-like
condition, mirror descent, and risk measures from finance.
We also define a notion of ``dominance'' between different
entropies in terms of bounds they guarantee and
conjecture that classical mixability gives optimal bounds, for which we
provide some supporting empirical evidence
The Stress Transmission Universality Classes of Periodic Granular Arrays
The transmission of stress is analysed for static periodic arrays of rigid
grains, with perfect and zero friction. For minimal coordination number (which
is sensitive to friction, sphericity and dimensionality), the stress
distribution is soluble without reference to the corresponding displacement
fields. In non-degenerate cases, the constitutive equations are found to be
simple linear in the stress components. The corresponding coefficients depend
crucially upon geometrical disorder of the grain contacts.Comment: 7 pages, 1 figur
An inclusion result for dagger closure in certain section rings of abelian varieties
We prove an inclusion result for graded dagger closure for primary ideals in
symmetric section rings of abelian varieties over an algebraically closed field
of arbitrary characteristic.Comment: 11 pages, v2: updated one reference, fixed 2 typos; final versio
Even-odd correlations in capacitance fluctuations of quantum dots
We investigate effects of short range interactions on the addition spectra of
quantum dots using a disordered Hubbard model. A correlation function \cS(q) is
defined on the inverse compressibility versus filling data, and computed
numerically for small lattices. Two regimes of interaction strength are
identified: the even/odd fluctuations regime typical of Fermi liquid ground
states, and a regime of structureless \cS(q) at strong interactions. We
propose to understand the latter regime in terms of magnetically correlated
localized spins.Comment: 3 pages, Revtex, Without figure
Density functional theory of spin-polarized disordered quantum dots
Using density functional theory, we investigate fluctuations of the ground
state energy of spin-polarized, disordered quantum dots in the metallic regime.
To compare to experiment, we evaluate the distribution of addition energies and
find a convolution of the Wigner-Dyson distribution, expected for noniteracting
electrons, with a narrower Gaussian distribution due to interactions. The tird
moment of the total distribution is independent of interactions, and so is
predicted to decrease by a factor of 0.405 upon application of a magnetic field
which transforms from the Gaussian orthogonal to the Gaussian unitary ensemble.Comment: 13 pages, 2 figure
The Solution Space of the Unitary Matrix Model String Equation and the Sato Grassmannian
The space of all solutions to the string equation of the symmetric unitary
one-matrix model is determined. It is shown that the string equation is
equivalent to simple conditions on points and in the big cell \Gr
of the Sato Grassmannian . This is a consequence of a well-defined
continuum limit in which the string equation has the simple form \lb \cp
,\cq_- \rb =\hbox{\rm 1}, with \cp and \cq_- matrices of
differential operators. These conditions on and yield a simple
system of first order differential equations whose analysis determines the
space of all solutions to the string equation. This geometric formulation leads
directly to the Virasoro constraints \L_n\,(n\geq 0), where \L_n annihilate
the two modified-KdV \t-functions whose product gives the partition function
of the Unitary Matrix Model.Comment: 21 page
Spectrum of non-Hermitian heavy tailed random matrices
Let (X_{jk})_{j,k>=1} be i.i.d. complex random variables such that |X_{jk}|
is in the domain of attraction of an alpha-stable law, with 0< alpha <2. Our
main result is a heavy tailed counterpart of Girko's circular law. Namely,
under some additional smoothness assumptions on the law of X_{jk}, we prove
that there exists a deterministic sequence a_n ~ n^{1/alpha} and a probability
measure mu_alpha on C depending only on alpha such that with probability one,
the empirical distribution of the eigenvalues of the rescaled matrix a_n^{-1}
(X_{jk})_{1<=j,k<=n} converges weakly to mu_alpha as n tends to infinity. Our
approach combines Aldous & Steele's objective method with Girko's Hermitization
using logarithmic potentials. The underlying limiting object is defined on a
bipartized version of Aldous' Poisson Weighted Infinite Tree. Recursive
relations on the tree provide some properties of mu_alpha. In contrast with the
Hermitian case, we find that mu_alpha is not heavy tailed.Comment: Expanded version of a paper published in Communications in
Mathematical Physics 307, 513-560 (2011
Spatial representation of temporal information through spike timing dependent plasticity
We suggest a mechanism based on spike time dependent plasticity (STDP) of
synapses to store, retrieve and predict temporal sequences. The mechanism is
demonstrated in a model system of simplified integrate-and-fire type neurons
densely connected by STDP synapses. All synapses are modified according to the
so-called normal STDP rule observed in various real biological synapses. After
conditioning through repeated input of a limited number of of temporal
sequences the system is able to complete the temporal sequence upon receiving
the input of a fraction of them. This is an example of effective unsupervised
learning in an biologically realistic system. We investigate the dependence of
learning success on entrainment time, system size and presence of noise.
Possible applications include learning of motor sequences, recognition and
prediction of temporal sensory information in the visual as well as the
auditory system and late processing in the olfactory system of insects.Comment: 13 pages, 14 figures, completely revised and augmented versio
Shrinking a large dataset to identify variables associated with increased risk of Plasmodium falciparum infection in Western Kenya
Large datasets are often not amenable to analysis using traditional single-step approaches. Here, our general objective was to apply imputation techniques, principal component analysis (PCA), elastic net and generalized linear models to a large dataset in a systematic approach to extract the most meaningful predictors for a health outcome. We extracted predictors for Plasmodium falciparum infection, from a large covariate dataset while facing limited numbers of observations, using data from the People, Animals, and their Zoonoses (PAZ) project to demonstrate these techniques: data collected from 415 homesteads in western Kenya, contained over 1500 variables that describe the health, environment, and social factors of the humans, livestock, and the homesteads in which they reside. The wide, sparse dataset was simplified to 42 predictors of P. falciparum malaria infection and wealth rankings were produced for all homesteads. The 42 predictors make biological sense and are supported by previous studies. This systematic data-mining approach we used would make many large datasets more manageable and informative for decision-making processes and health policy prioritization
Global Search for New Physics with 2.0/fb at CDF
Data collected in Run II of the Fermilab Tevatron are searched for
indications of new electroweak-scale physics. Rather than focusing on
particular new physics scenarios, CDF data are analyzed for discrepancies with
the standard model prediction. A model-independent approach (Vista) considers
gross features of the data, and is sensitive to new large cross-section
physics. Further sensitivity to new physics is provided by two additional
algorithms: a Bump Hunter searches invariant mass distributions for "bumps"
that could indicate resonant production of new particles; and the Sleuth
procedure scans for data excesses at large summed transverse momentum. This
combined global search for new physics in 2.0/fb of ppbar collisions at
sqrt(s)=1.96 TeV reveals no indication of physics beyond the standard model.Comment: 8 pages, 7 figures. Final version which appeared in Physical Review D
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