Small eigenvalues of the low temperature linear relaxation Boltzmann equation with a confining potential

We study the linear relaxation Boltzmann equation, a simple semiclassical kinetic model. We provide a resolvent estimate for an associated non-selfadjoint operator as well as an estimate on the return to equilibrium. This is done using a scaling argument and non-semiclassical hypocoercive estimate.Comment: 17 page

Long runs under a conditional limit distribution

This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a function of its summands as their number tends to infinity. In the large deviation range of the conditioning event it extends the Gibbs conditional principle in the sense that it provides a description of the distribution of the random walk on long subsequences. An approximation of the density of the runs is also obtained when the conditioning event states that the end value of the random walk belongs to a thin or a thick set with a nonempty interior. The approximations hold either in probability under the conditional distribution of the random walk, or in total variation norm between measures. An application of the approximation scheme to the evaluation of rare event probabilities through importance sampling is provided. When the conditioning event is in the range of the central limit theorem, it provides a tool for statistical inference in the sense that it produces an effective way to implement the Rao-Blackwell theorem for the improvement of estimators; it also leads to conditional inference procedures in models with nuisance parameters. An algorithm for the simulation of such long runs is presented, together with an algorithm determining the maximal length for which the approximation is valid up to a prescribed accuracy.Comment: Published in at http://dx.doi.org/10.1214/13-AAP975 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: text overlap with arXiv:1010.361

Long runs under point conditioning. The real case

This paper presents a sharp approximation of the density of long runs of a random walk conditioned on its end value or by an average of a functions of its summands as their number tends to infinity. The conditioning event is of moderate or large deviation type. The result extends the Gibbs conditional principle in the sense that it provides a description of the distribution of the random walk on long subsequences. An algorithm for the simulation of such long runs is presented, together with an algorithm determining their maximal length for which the approximation is valid up to a prescribed accuracy

The Network-Firm as a Single Real Entity: Beyond the Aggregate of Distinct Legal Entities

This paper intends to depart from a critique of the nexus of contracts theory of the firm endowed with its moral personification to propose some theoretical foundations of the firm as a real entity. Some old legal views of the corporation are mobilized to complete the conceptual vacuity of economic theories. This provides crucial insights for modern complex organizations such as the network-firm. The integrating and unifying role of intra-network power relationships is then emphasized and some law and economics of the network-firm are ultimately proposed to clarify the argument that the network-firm − as the firm stricto sensu − is a singular real entity composed from distinct legal entities.Law and economics, contract theory of the firm, network-firm, legal fiction, real entity

Controlling for Unobserved Confounds in Classification Using Correlational Constraints

As statistical classifiers become integrated into real-world applications, it is important to consider not only their accuracy but also their robustness to changes in the data distribution. In this paper, we consider the case where there is an unobserved confounding variable $z$ that influences both the features $\mathbf{x}$ and the class variable $y$. When the influence of $z$ changes from training to testing data, we find that the classifier accuracy can degrade rapidly. In our approach, we assume that we can predict the value of $z$ at training time with some error. The prediction for $z$ is then fed to Pearl's back-door adjustment to build our model. Because of the attenuation bias caused by measurement error in $z$, standard approaches to controlling for $z$ are ineffective. In response, we propose a method to properly control for the influence of $z$ by first estimating its relationship with the class variable $y$, then updating predictions for $z$ to match that estimated relationship. By adjusting the influence of $z$, we show that we can build a model that exceeds competing baselines on accuracy as well as on robustness over a range of confounding relationships.Comment: 9 page

Modules and Logic Programming

We study conditions for a concurrent construction of proof-nets in the framework developed by Andreoli in recent papers. We define specific correctness criteria for that purpose. We first study closed modules (i.e. validity of the execution of a logic program), then extend the criterion to open modules (i.e. validity during the execution) distinguishing criteria for acyclicity and connectability in order to allow incremental verification

Towards zero variance estimators for rare event probabilities

Improving Importance Sampling estimators for rare event probabilities requires sharp approximations of conditional densities. This is achieved for events E_{n}:=(f(X_{1})+...+f(X_{n}))\inA_{n} where the summands are i.i.d. and E_{n} is a large or moderate deviation event. The approximation of the conditional density of the real r.v's X_{i} 's, for 1\leqi\leqk_{n} with repect to E_{n} on long runs, when k_{n}/n\to1, is handled. The maximal value of k compatible with a given accuracy is discussed; algorithms and simulated results are presented