Second order mean field games with degenerate diffusion and local coupling

We analyze a (possibly degenerate) second order mean field games system of partial differential equations. The distinguishing features of the model considered are (1) that it is not uniformly parabolic, including the first order case as a possibility, and (2) the coupling is a local operator on the density. As a result we look for weak, not smooth, solutions. Our main result is the existence and uniqueness of suitably defined weak solutions, which are characterized as minimizers of two optimal control problems. We also show that such solutions are stable with respect to the data, so that in particular the degenerate case can be approximated by a uniformly parabolic (viscous) perturbation

Simultaneous occurrence of sliding and crossing limit cycles in piecewise linear planar vector fields

In the present study we consider planar piecewise linear vector fields with two zones separated by the straight line $x=0$. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector fields. First, we provide a canonical form for these systems assuming that each linear system has center, a real one for $y<0$ and a virtual one for $y>0$, and such that the real center is a global center. Then, working with a first order piecewise linear perturbation we obtain piecewise linear differential systems with three crossing limit cycles. Second, we see that a sliding cycle can be detected after a second order piecewise linear perturbation. Finally, imposing the existence of a sliding limit cycle we prove that only one adittional crossing limit cycle can appear. Furthermore, we also characterize the stability of the higher amplitude limit cycle and of the infinity. The main techniques used in our proofs are the Melnikov method, the Extended Chebyshev systems with positive accuracy, and the Bendixson transformation.Comment: 24 pages, 7 figure

Classifying Crises-Information Relevancy with Semantics

Social media platforms have become key portals for sharing and consuming information during crisis situations. However, humanitarian organisations and affected communities often struggle to sieve through the large volumes of data that are typically shared on such platforms during crises to determine which posts are truly relevant to the crisis, and which are not. Previous work on automatically classifying crisis information was mostly focused on using statistical features. However, such approaches tend to be inappropriate when processing data on a type of crisis that the model was not trained on, such as processing information about a train crash, whereas the classifier was trained on floods, earthquakes, and typhoons. In such cases, the model will need to be retrained, which is costly and time-consuming. In this paper, we explore the impact of semantics in classifying Twitter posts across same, and different, types of crises. We experiment with 26 crisis events, using a hybrid system that combines statistical features with various semantic features extracted from external knowledge bases. We show that adding semantic features has no noticeable benefit over statistical features when classifying same-type crises, whereas it enhances the classifier performance by up to 7.2% when classifying information about a new type of crisis

Cross-Lingual Classification of Crisis Data

Many citizens nowadays flock to social media during crises to share or acquire the latest information about the event. Due to the sheer volume of data typically circulated during such events, it is necessary to be able to efficiently filter out irrelevant posts, thus focusing attention on the posts that are truly relevant to the crisis. Current methods for classifying the relevance of posts to a crisis or set of crises typically struggle to deal with posts in different languages, and it is not viable during rapidly evolving crisis situations to train new models for each language. In this paper we test statistical and semantic classification approaches on cross-lingual datasets from 30 crisis events, consisting of posts written mainly in English, Spanish, and Italian. We experiment with scenarios where the model is trained on one language and tested on another, and where the data is translated to a single language. We show that the addition of semantic features extracted from external knowledge bases improve accuracy over a purely statistical model

Central and storage carbon metabolism of the brown alga Ectocarpus siliculosus: insights into the origin and evolution of storage carbohydrates in Eukaryotes

International audienceBrown algae exhibit a unique carbon (C) storage metabolism. The photoassimilate d‐fructose 6‐phosphate is not used to produce sucrose but is converted into d‐mannitol. These seaweeds also store C as β‐1,3‐glucan (laminarin), thus markedly departing from most living organisms, which use α‐1,4‐glucans (glycogen or starch).Using a combination of bioinformatic and phylogenetic approaches, we identified the candidate genes for the enzymes involved in C storage in the genome of the brown alga Ectocarpus siliculosus and traced their evolutionary origins.Ectocarpus possesses a complete set of enzymes for synthesis of mannitol, laminarin and trehalose. By contrast, the pathways for sucrose, starch and glycogen are completely absent.The synthesis of β‐1,3‐glucans appears to be a very ancient eukaryotic pathway. Brown algae inherited the trehalose pathway from the red algal progenitor of phaeoplasts, while the mannitol pathway was acquired by lateral gene transfer from Actinobacteria. The starch metabolism of the red algal endosymbiont was entirely lost in the ancestor of Stramenopiles. In light of these novel findings we question the validity of the ‘Chromalveolate hypothesis’

TFM-Explorer: mining cis-regulatory regions in genomes

DNA-binding transcription factors (TFs) play a central role in transcription regulation, and computational approaches that help in elucidating complex mechanisms governing this basic biological process are of great use. In this perspective, we present the TFM-Explorer web server that is a toolbox to identify putative TF binding sites within a set of upstream regulatory sequences of genes sharing some regulatory mechanisms. TFM-Explorer finds local regions showing overrepresentation of binding sites. Accepted organisms are human, mouse, rat, chicken and drosophila. The server employs a number of features to help users to analyze their data: visualization of selected binding sites on genomic sequences, and selection of cis-regulatory modules. TFM-Explorer is available at http://bioinfo.lifl.fr/TFM

Symmetric periodic orbits for the collinear charged 3-body problem

Agraïments: The first author is partially supported by a CAPES grant number 88881.030454/2013-01 from the program CSF-PVE. The second author is supported by grant#2012/10 26 7000 803, Goiás Research Foundation (FAPEG), PRO-CAD/CAPES grant 88881.0 68462/2014-01 and by CNPq-Brazil.In this paper we study the existence of periodic symmetric orbits of the 3-body problem when each body possess mass and an electric charge. The main technique applied in this study is the continuation method of Poincar\'e

Combustion instability research Summary report, 1970

Combustion instability in liquid rocket engine

Summary of combustion instability research at Princeton University, 1969

Control and causes of combustion instability in rocket engine

A decomposition theorem for BV functions

The Jordan decomposition states that a function f: R \u2192 R is of bounded variation if and only if it can be written as the dierence of two monotone increasing functions. In this paper we generalize this property to real valued BV functions of many variables, extending naturally the concept of monotone function. Our result is an extension of a result obtained by Alberti, Bianchini and Crippa. A counterexample is given which prevents further extensions