960,266 research outputs found
Stochastic Mean-Field Limit: Non-Lipschitz Forces \& Swarming
We consider general stochastic systems of interacting particles with noise
which are relevant as models for the collective behavior of animals, and
rigorously prove that in the mean-field limit the system is close to the
solution of a kinetic PDE. Our aim is to include models widely studied in the
literature such as the Cucker-Smale model, adding noise to the behavior of
individuals. The difficulty, as compared to the classical case of globally
Lipschitz potentials, is that in several models the interaction potential
between particles is only locally Lipschitz, the local Lipschitz constant
growing to infinity with the size of the region considered. With this in mind,
we present an extension of the classical theory for globally Lipschitz
interactions, which works for only locally Lipschitz ones
The breakdown behavior of the maximum likelihood estimator in the logistic regression model.
In this note we discuss the breakdown behavior of the maximum likelihood (ML) estimator in the logistic regression model. We formally prove that the ML-estimator never explodes to infinity, but rather breaks down to zero when adding severe outliers to a data set. An example confirms this behavior. (C) 2002 Published by Elsevier Science B.V.breakdown point; logistic regression; maximum likelihood; robust estimation; generalized linear-models; robustness; existence; fits;
Shear-flexible finite-element models of laminated composite plates and shells
Several finite-element models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed finite-element models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different finite-element models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters
Coupled Minimal Models with and without Disorder
We analyse in this article the critical behavior of -state Potts
models coupled to -state Potts models () with and
without disorder. The technics we use are based on perturbed conformal
theories. Calculations have been performed at two loops. We already find some
interesting situations in the pure case for some peculiar values of and
with new tricritical points. When adding weak disorder, the results we obtain
tend to show that disorder makes the models decouple. Therefore, no relations
emerges, at a perturbation level, between for example the disordered -state Potts model and the two disordered -state Potts models
(), despite their central charges are similar according to recent
numerical investigations.Comment: 45 pages, Latex, 3 PS figure
Exotic Non-Supersymmetric Gauge Dynamics from Supersymmetric QCD
We extend Seiberg's qualitative picture of the behavior of supersymmetric QCD
to nonsupersymmetric models by adding soft supersymmetry breaking terms. In
this way, we recover the standard vacuum of QCD with flavors and
colors when . However, for , we find new exotic
states---new vacua with spontaneously broken baryon number for , and
a vacuum state with unbroken chiral symmetry for . These exotic
vacua contain massless composite fermions and, in some cases, dynamically
generated gauge bosons. In particular Seiberg's electric-magnetic duality seems
to persist also in the presence of (small) soft supersymmetry breaking. We
argue that certain, specially tailored, lattice simulations may be able to
detect the novel phenomena. Most of the exotic behavior does not survive the
decoupling limit of large SUSY breaking parameters.Comment: 36 pages, latex + 2 figures (uuencoded ps
Recursive Thick Modeling and the Choice of Monetary Policy in Mexico
By following the spirit in Favero and Milani (2005), we use recursive thick modeling to take into account model uncertainty for the choice of optimal monetary policy. We consider an open economy model and generate multiple models for only the aggregate demand and aggregate supply. Models are constructed by matching the rankings of aggregate demand and aggregate supply and adding other specifications for the rest of the variables. The main results show that recursive thick modeling with equal and different weights approximates the recent historical behavior of nominal interest rates in Mexico better than recursive thin modelingmodel uncertainty, optimal control, out-of-bag, thin modeling and thick modeling
Long ties accelerate noisy threshold-based contagions
Network structure can affect when and how widely new ideas, products, and
behaviors are adopted. In widely-used models of biological contagion,
interventions that randomly rewire edges (generally making them "longer")
accelerate spread. However, there are other models relevant to social
contagion, such as those motivated by myopic best-response in games with
strategic complements, in which an individual's behavior is described by a
threshold number of adopting neighbors above which adoption occurs (i.e.,
complex contagions). Recent work has argued that highly clustered, rather than
random, networks facilitate spread of these complex contagions. Here we show
that minor modifications to this model, which make it more realistic, reverse
this result: we allow very rare below-threshold adoption, i.e., rarely adoption
occurs when there is only one adopting neighbor. To model the trade-off between
long and short edges we consider networks that are the union of cycle-power-
graphs and random graphs on nodes. Allowing adoptions below threshold to
occur with order probability along some "short" cycle edges is
enough to ensure that random rewiring accelerates spread. Simulations
illustrate the robustness of these results to other commonly-posited models for
noisy best-response behavior. Hypothetical interventions that randomly rewire
existing edges or add random edges (versus adding "short", triad-closing edges)
in hundreds of empirical social networks reduce time to spread. This revised
conclusion suggests that those wanting to increase spread should induce
formation of long ties, rather than triad-closing ties. More generally, this
highlights the importance of noise in game-theoretic analyses of behavior
Decision Forest: A Nonparametric Approach to Modeling Irrational Choice
Customer behavior is often assumed to follow weak rationality, which implies
that adding a product to an assortment will not increase the choice probability
of another product in that assortment. However, an increasing amount of
research has revealed that customers are not necessarily rational when making
decisions. In this paper, we propose a new nonparametric choice model that
relaxes this assumption and can model a wider range of customer behavior, such
as decoy effects between products. In this model, each customer type is
associated with a binary decision tree, which represents a decision process for
making a purchase based on checking for the existence of specific products in
the assortment. Together with a probability distribution over customer types,
we show that the resulting model -- a decision forest -- is able to represent
any customer choice model, including models that are inconsistent with weak
rationality. We theoretically characterize the depth of the forest needed to
fit a data set of historical assortments and prove that with high probability,
a forest whose depth scales logarithmically in the number of assortments is
sufficient to fit most data sets. We also propose two practical algorithms --
one based on column generation and one based on random sampling -- for
estimating such models from data. Using synthetic data and real transaction
data exhibiting non-rational behavior, we show that the model outperforms both
rational and non-rational benchmark models in out-of-sample predictive ability.Comment: The paper is forthcoming in Management Science (accepted on July 25,
2021
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