In this note we prove that an extended-real-valued lower semi-continuous convex function Φ defined on a reflexive Banach space X achieves its supremum on every nonempty bounded and closed convex set of its effective domain Dom Φ, if and only if the restriction of Φ to Dom Φ is sequentially continuous with respect to the weak topology on the underlying space X .

The goal of this paper is the automatic identification of characters in TV and feature film material. In contrast to standard approaches to this task, which rely on the weak supervision afforded by transcripts and subtitles, we propose a new method requiring only a cast list. This list is used to obtain images of actors from freely available sources on the web, providing a form of partial super...

A branch-and-cut algorithm for solving linear problems with continuous separable piecewise linear cost functions was developed in 2005 by Keha et. al. This algorithm is based on valid inequalities for an SOS2 based formulation of the problem. In this paper we study the extension of the algorithm to the case where the cost function is only lower semicontinuous. We extend the SOS2 based formulati...

We show that convex lower semicontinuous functionals deened on functions of bounded variation are characterized by their minima, and we prove a derivation formula which allows an integral representation of such functionals. Applications to relaxation and homogenization are given.

Twitter has become an important data source for detecting events, especially tracking detailed information for events of a specific domain. Previous studies on targeteddomain Twitter information extraction have used supervised learning techniques to identify domain-related tweets, however, the need for extensive manual labeling makes these supervised systems extremely expensive to build and mai...

The notion of a maximal monotone operator is crucial in optimization as it captures both the subdifferential operator of a convex, lower semicontinuous, and proper function and any (not necessarily symmetric) continuous linear positive operator. It was recently discovered that most fundamental results on maximal monotone operators allow simpler proofs utilizing Fitzpatrick functions. In this pa...

Recent studies have demonstrated that specificity is an important characterization of texts potentially beneficial for a range of applications such as multi-document news summarization and analysis of science journalism. The feasibility of automatically predicting sentence specificity from a rich set of features has also been confirmed in prior work. In this paper we present a practical system ...

It has been demonstrated that there is a geometrical order in text structures. Fractal geometry, as a modern mathematical approach and a new geometrical standpoint on natural objects including both processes and structures, is here employed for textual analysis. For this first study, the works of William Shakespeare were chosen as the most important items in Western literature. By counting the ...

Balanced Viscosity solutions to rate-independent systems arise as limits of regularized rate-independent flows by adding a superlinear vanishing-viscosity dissipation. We address the main issue of proving the existence of such limits for infinite-dimensional systems and of characterizing them by a couple of variational properties that combine a local stability condition and a balanced energy-di...

In this paper, we consider the interpretability of the foundational Laplacian-based semi-supervised learning approaches on graphs. We introduce a novel flow-based learning framework that subsumes the foundational approaches and additionally provides a detailed, transparent, and easily understood expression of the learning process in terms of graph flows. As a result, one can visualize and inter...