438 research outputs found
A priori -estimates for degenerate complex Monge-Amp\`ere equations
We study families of complex Monge-Amp\`ere equations, focusing on the case
where the cohomology classes degenerate to a non big class.
We establish uniform a priori -estimates for the normalized
solutions, generalizing the recent work of S. Kolodziej and G. Tian. This has
interesting consequences in the study of the K\"ahler-Ricci flow.Comment: 6 page
Dichotomize and Generalize: PAC-Bayesian Binary Activated Deep Neural Networks
We present a comprehensive study of multilayer neural networks with binary activation, relying on the PAC-Bayesian theory. Our contributions are twofold: (i) we develop an end-to-end framework to train a binary activated deep neural network, overcoming the fact that binary activation function is non-differentiable; (ii) we provide nonvacuous PAC-Bayesian generalization bounds for binary activated deep neural networks. Noteworthy, our results are obtained by minimizing the expected loss of an architecture-dependent aggregation of binary activated deep neural networks. The performance of our approach is assessed on a thorough numerical experiment protocol on real-life datasets
Green Currents for Meromorphic Maps of Compact K\"ahler Manifolds
We consider the dynamics of meromorphic maps of compact K\"ahler manifolds.
In this work, our goal is to locate the non-nef locus of invariant classes and
provide necessary and sufficient conditions for existence of Green currents in
codimension one.Comment: Statement of Theorem 1.5 is slightly improved. Proposition 5.2 and
Theorem 5.3 are adde
Analysis of Hepatitis C Viral Dynamics Using Latin Hypercube Sampling
We consider a mathematical model comprising of four coupled ordinary
differential equations (ODEs) for studying the hepatitis C (HCV) viral
dynamics. The model embodies the efficacies of a combination therapy of
interferon and ribavirin. A condition for the stability of the uninfected and
the infected steady states is presented. A large number of sample points for
the model parameters (which were physiologically feasible) were generated using
Latin hypercube sampling. Analysis of our simulated values indicated
approximately 24% cases as having an uninfected steady state. Statistical tests
like the chi-square-test and the Spearman's test were also done on the sample
values. The results of these tests indicate a distinctly differently
distribution of certain parameter values and not in case of others, vis-a-vis,
the stability of the uninfected and the infected steady states
Learning Stochastic Majority Votes by Minimizing a PAC-Bayes Generalization Bound
We investigate a stochastic counterpart of majority votes over finite ensembles of classifiers, and study its generalization properties. While our approach holds for arbitrary distributions, we instantiate it with Dirichlet distributions: this allows for a closed-form and differentiable expression for the expected risk, which then turns the generalization bound into a tractable training objective.The resulting stochastic majority vote learning algorithm achieves state-of-the-art accuracy and benefits from (non-vacuous) tight generalization bounds, in a series of numerical experiments when compared to competing algorithms which also minimize PAC-Bayes objectives -- both with uninformed (data-independent) and informed (data-dependent) priors
Increase of precuneus metabolism correlates with reduction of PTSD symptoms after EMDR therapy in military veterans: an 18F-FDG PET study during virtual reality exposure to war
International audienc
Univalent Foundations and the UniMath Library
We give a concise presentation of the Univalent Foundations of mathematics outlining the main ideas, followed by a discussion of the UniMath library of formalized mathematics implementing the ideas of the Univalent Foundations (section 1), and the challenges one faces in attempting to design a large-scale library of formalized mathematics (section 2). This leads us to a general discussion about the links between architecture and mathematics where a meeting of minds is revealed between architects and mathematicians (section 3). On the way our odyssey from the foundations to the "horizon" of mathematics will lead us to meet the mathematicians David Hilbert and Nicolas Bourbaki as well as the architect Christopher Alexander
Attributing and Referencing (Research) Software: Best Practices and Outlook from Inria
Software is a fundamental pillar of modern scientiic research, not only in computer science, but actually across all elds and disciplines. However, there is a lack of adequate means to cite and reference software, for many reasons. An obvious rst reason is software authorship, which can range from a single developer to a whole team, and can even vary in time. The panorama is even more complex than that, because many roles can be involved in software development: software architect, coder, debugger, tester, team manager, and so on. Arguably, the researchers who have invented the key algorithms underlying the software can also claim a part of the authorship. And there are many other reasons that make this issue complex. We provide in this paper a contribution to the ongoing eeorts to develop proper guidelines and recommendations for software citation, building upon the internal experience of Inria, the French research institute for digital sciences. As a central contribution, we make three key recommendations. (1) We propose a richer taxonomy for software contributions with a qualitative scale. (2) We claim that it is essential to put the human at the heart of the evaluation. And (3) we propose to distinguish citation from reference
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