Stability analysis of reaction-diffusion models on evolving domains: the effects of cross-diffusion

This article presents stability analytical results of a two component reaction-diffusion system with linear cross-diffusion posed on continuously evolving domains. First the model system is mapped from a continuously evolving domain to a reference stationary frame resulting in a system of partial differential equations with time-dependent coefficients. Second, by employing appropriately asymptotic theory, we derive and prove cross-diffusion-driven instability conditions for the model system for the case of slow, isotropic domain growth. Our analytical results reveal that unlike the restrictive diffusion-driven instability conditions on stationary domains, in the presence of cross-diffusion coupled with domain evolution, it is no longer necessary to enforce cross nor pure kinetic conditions. The restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Reaction-cross-diffusion models with equal diffusion coefficients in the principal components as well as those of the short-range inhibition, long-range activation and activator-activator form can generate patterns only in the presence of cross-diffusion coupled with domain evolution. To confirm our theoretical findings, detailed parameter spaces are exhibited for the special cases of isotropic exponential, linear and logistic growth profiles. In support of our theoretical predictions, we present evolving or moving finite element solutions exhibiting patterns generated by a short-range inhibition, long-range activation reaction-diffusion model with linear cross-diffusion in the presence of domain evolution

Compatibility between pricing rules and risk measures: The CCVaR

This paper has considered a risk measure ? and a (maybe incomplete and/or imperfect) arbitrage-free market with pricing rule p. They are said to be compatible if there are no reachable strategies y such that p (y) remains bounded and ?(y) is close to - 8. We show that the lack of compatibility leads to meaningless situations in financial or actuarial applications. The presence of compatibility is characterized by properties connecting the Stochastic Discount Factor of p and the sub-gradient of ? . Consequently, several examples pointing out that the lack of compatibility may occur in very important pricing models are yielded. For instance the CVaR and the DPT are not compatible with the Black and Scholes model or the CAPM. We prove that for a given incompatible couple (p,?) we can construct a minimal risk measure ?p compatible with p and such that ?p = ? . This result is particularized for the CVaR and the CAPM and the Black and Scholes model. Therefore we construct the Compatible Conditional Value at Risk (CCVaR). It seems that the CCVaR preserves the good properties of the CVaR and overcomes its shortcomings.Risk Measure, Pricing Rule, Compatibility, Compatible Conditional Value at Risk

Turbulent mixing layers in supersonic protostellar outflows, with application to DG Tauri

Turbulent entrainment processes may play an important role in the outflows from young stellar objects at all stages of their evolution. In particular, lateral entrainment of ambient material by high-velocity, well-collimated protostellar jets may be the cause of the multiple emission-line velocity components observed in the microjet-scale outflows driven by classical T Tauri stars. Intermediate-velocity outflow components may be emitted by a turbulent, shock- excited mixing layer along the boundaries of the jet. We present a formalism for describing such a mixing layer based on Reynolds decomposition of quantities measuring fundamental properties of the gas. In this model, the molecular wind from large disc radii provides a continual supply of material for entrainment. We calculate the total stress profile in the mixing layer, which allows us to estimate the dissipation of turbulent energy, and hence the luminosity of the layer. We utilize MAPPINGS IV shock models to determine the fraction of total emission that occurs in [Fe II] 1.644 {\mu}m line emission in order to facilitate comparison to previous observations of the young stellar object DG Tauri. Our model accurately estimates the luminosity and changes in mass outflow rate of the intermediate-velocity component of the DG Tau approaching outflow. Therefore, we propose that this component represents a turbulent mixing layer surrounding the well-collimated jet in this object. Finally, we compare and contrast our model to previous work in the field.Comment: 18 pages, 13 figures, accepted for publication in MNRA

Skip-Thought Vectors

We describe an approach for unsupervised learning of a generic, distributed sentence encoder. Using the continuity of text from books, we train an encoder-decoder model that tries to reconstruct the surrounding sentences of an encoded passage. Sentences that share semantic and syntactic properties are thus mapped to similar vector representations. We next introduce a simple vocabulary expansion method to encode words that were not seen as part of training, allowing us to expand our vocabulary to a million words. After training our model, we extract and evaluate our vectors with linear models on 8 tasks: semantic relatedness, paraphrase detection, image-sentence ranking, question-type classification and 4 benchmark sentiment and subjectivity datasets. The end result is an off-the-shelf encoder that can produce highly generic sentence representations that are robust and perform well in practice. We will make our encoder publicly available.Comment: 11 page

Breaking the News: First Impressions Matter on Online News

A growing number of people are changing the way they consume news, replacing the traditional physical newspapers and magazines by their virtual online versions or/and weblogs. The interactivity and immediacy present in online news are changing the way news are being produced and exposed by media corporations. News websites have to create effective strategies to catch people's attention and attract their clicks. In this paper we investigate possible strategies used by online news corporations in the design of their news headlines. We analyze the content of 69,907 headlines produced by four major global media corporations during a minimum of eight consecutive months in 2014. In order to discover strategies that could be used to attract clicks, we extracted features from the text of the news headlines related to the sentiment polarity of the headline. We discovered that the sentiment of the headline is strongly related to the popularity of the news and also with the dynamics of the posted comments on that particular news.Comment: The paper appears in ICWSM 201

Structural Changes in Data Communication in Wireless Sensor Networks

Wireless sensor networks are an important technology for making distributed autonomous measures in hostile or inaccessible environments. Among the challenges they pose, the way data travel among them is a relevant issue since their structure is quite dynamic. The operational topology of such devices can often be described by complex networks. In this work, we assess the variation of measures commonly employed in the complex networks literature applied to wireless sensor networks. Four data communication strategies were considered: geometric, random, small-world, and scale-free models, along with the shortest path length measure. The sensitivity of this measure was analyzed with respect to the following perturbations: insertion and removal of nodes in the geometric strategy; and insertion, removal and rewiring of links in the other models. The assessment was performed using the normalized Kullback-Leibler divergence and Hellinger distance quantifiers, both deriving from the Information Theory framework. The results reveal that the shortest path length is sensitive to perturbations.Comment: 12 pages, 4 figures, Central European Journal of Physic