95,257 research outputs found

    Critical behaviours of contact near phase transitions

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    A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. It appears in universal relations among thermodynamic quantities, such as large momentum tails, energy, and dynamic structure factors, through the renowned Tan relations. However, a conceptual question remains open as to whether or not contact can signify phase transitions that are insensitive to short-range physics. Here we show that, near a continuous classical or quantum phase transition, contact exhibits a variety of critical behaviors, including scaling laws and critical exponents that are uniquely determined by the universality class of the phase transition and a constant contact per particle. We also use a prototypical exactly solvable model to demonstrate these critical behaviors in one-dimensional strongly interacting fermions. Our work establishes an intrinsic connection between the universality of dilute many-body systems and universal critical phenomena near a phase transition.Comment: Final version published in Nat. Commun. 5:5140 doi: 10.1038/ncomms6140 (2014

    Analyticity of the Susceptibility Function for Unimodal Markovian Maps of the Interval

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    In a previous note [Ru] the susceptibility function was analyzed for some examples of maps of the interval. The purpose of the present note is to give a concise treatment of the general unimodal Markovian case (assuming ff real analytic). We hope that it will similarly be possible to analyze maps satisfying the Collet-Eckmann condition. Eventually, as explained in [Ru], application of a theorem of Whitney [Wh] should prove differentiability of the map fρff\mapsto\rho_f restricted to a suitable set.Comment: 8 page

    Bounded perturbation resilience of projected scaled gradient methods

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    We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected Newton method, the projected Landweber-type methods and the generalized Expectation-Maximization (EM)-type methods. We prove the convergence of the PSG methods in the presence of bounded perturbations. This resilience to bounded perturbations is relevant to the ability to apply the recently developed superiorization methodology to PSG methods, in particular to the EM algorithm.Comment: Computational Optimization and Applications, accepted for publicatio

    Diving Deep into Sentiment: Understanding Fine-tuned CNNs for Visual Sentiment Prediction

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    Visual media are powerful means of expressing emotions and sentiments. The constant generation of new content in social networks highlights the need of automated visual sentiment analysis tools. While Convolutional Neural Networks (CNNs) have established a new state-of-the-art in several vision problems, their application to the task of sentiment analysis is mostly unexplored and there are few studies regarding how to design CNNs for this purpose. In this work, we study the suitability of fine-tuning a CNN for visual sentiment prediction as well as explore performance boosting techniques within this deep learning setting. Finally, we provide a deep-dive analysis into a benchmark, state-of-the-art network architecture to gain insight about how to design patterns for CNNs on the task of visual sentiment prediction.Comment: Preprint of the paper accepted at the 1st Workshop on Affect and Sentiment in Multimedia (ASM), in ACM MultiMedia 2015. Brisbane, Australi
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