99 research outputs found
Learning curves for Soft Margin Classifiers
Typical learning curves for Soft Margin Classifiers (SMCs) learning both
realizable and unrealizable tasks are determined using the tools of Statistical
Mechanics. We derive the analytical behaviour of the learning curves in the
regimes of small and large training sets. The generalization errors present
different decay laws towards the asymptotic values as a function of the
training set size, depending on general geometrical characteristics of the rule
to be learned. Optimal generalization curves are deduced through a fine tuning
of the hyperparameter controlling the trade-off between the error and the
regularization terms in the cost function. Even if the task is realizable, the
optimal performance of the SMC is better than that of a hard margin Support
Vector Machine (SVM) learning the same rule, and is very close to that of the
Bayesian classifier.Comment: 26 pages, 10 figure
Of lice and math: using models to understand and control populations of head lice
In this paper we use detailed data about the biology of the head louse
(pediculus humanus capitis) to build a model of the evolution of head lice
colonies. Using theory and computer simulations, we show that the model can be
used to assess the impact of the various strategies usually applied to
eradicate head lice, both conscious (treatments) and unconscious (grooming). In
the case of treatments, we study the difference in performance that arises when
they are applied in systematic and non-systematic ways. Using some reasonable
simplifying assumptions (as random mixing of human groups and the same mobility
for all life stages of head lice other than eggs) we model the contagion of
pediculosis using only one additional parameter. It is shown that this
parameter can be tuned to obtain collective infestations whose variables are
compatible with what is given in the literature on real infestations. We
analyze two scenarios: one where group members begin treatment when a similar
number of lice are present in each head, and another where there is one
individual who starts treatment with a much larger threshold ('superspreader').
For both cases we assess the impact of several collective strategies of
treatment.Comment: manuscript of 23 pages and 13 figures, also a supporting file of 13
pages and 13 figure
Influence of network dynamics on the spread of sexually transmitted diseases
Network epidemiology often assumes that the relationships defining the social network of a population are static. The dynamics of relationships is only taken indirectly into account by assuming that the relevant information to study epidemic spread is encoded in the network obtained, by considering numbers of partners accumulated over periods of timeroughly proportional to the infectious period of the disease. On the other hand, models explicitly including social dynamics are often too schematic to provide a reasonable representation of a real population, or so detailed that no general conclusions can be drawn from them. Here, wepresent a model of social dynamics that is general enough so its parameters can be obtained by fitting data from surveys about sexual behaviour, but that can still be studied analytically, using mean-field techniques. This allows us to obtain some general results about epidemic spreading. We show that using accumulated network data to estimate the static epidemic threshold lead to a significant underestimation of that threshold. We also show that, for a dynamic network, the relative epidemic threshold is an increasing function of the infectious period of the disease, implying that the static value is a lower bound to the real threshold. A practical example is given of how to apply the model to the study of a real population.Fil: Risau Gusman, Sebastian Luis. Comisión Nacional de Energía Atómica. Gerencia del Área de Investigación y Aplicaciones No Nucleares. Gerencia de Física (Centro Atómico Bariloche); Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentin
Backbone structure of the Edwards-Anderson spin-glass model
We study the ground-state spatial heterogeneities of the Edwards-Anderson
spin-glass model with both bimodal and Gaussian bond distributions. We
characterize these heterogeneities by using a general definition of bond
rigidity, which allows us to classify the bonds of the system into two sets,
the backbone and its complement, with very different properties. This
generalizes to continuous distributions of bonds the well known definition of a
backbone for discrete bond distributions. By extensive numerical simulations we
find that the topological structure of the backbone for a given lattice
dimensionality is very similar for both discrete and continuous bond
distributions. We then analyze how these heterogeneities influence the
equilibrium properties at finite temperature and we discuss the possibility
that a suitable backbone picture can be relevant to describe spin-glass
phenomena.Comment: 12 pages, 10 figure
Backbone structure of the Edwards-Anderson spin-glass model
We study the ground-state spatial heterogeneities of the Edwards-Anderson spin-glass model with both bimodal and Gaussian bond distributions. We characterize these heterogeneities by using a general definition of bond rigidity, which allows us to classify the bonds of the system into two sets, the backbone and its complement, with very different properties. This generalizes to continuous distributions of bonds the well-known definition of a backbone for discrete bond distributions. By extensive numerical simulations we find that the topologicalstructure of the backbone for a given lattice dimensionality is very similar for both discrete and continuous bond distributions. We then analyze how these heterogeneities influence the equilibrium properties at finite temperature and we discuss the possibility that a suitable backbone picture can be relevant to describe spin-glass phenomena.Fil: Romá, Federico José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico - CONICET - San Luis. Instituto de Física Aplicada; Argetnina;Fil: Risau-Gusman, S.. Comisión Nacional de Energía Atomica. Gerencia del Área de Investigaciones y Aplicaciones No Nucleares. Gerencia de Física (cab). División Física Estadistica; Argentina
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