Forward-Backward and Tseng’s Type Penalty Schemes for Monotone Inclusion Problems

We deal with monotone inclusion problems of the form 0 ∈ A x + D x + N _C (x) in real Hilbert spaces, where A is a maximally monotone operator, D a cocoercive operator and C the nonempty set of zeros of another cocoercive operator. We propose a forward-backward penalty algorithm for solving this problem which extends the one proposed by Attouch et al. (SIAM J. Optim. 21(4): 1251-1274, 2011). The condition which guarantees the weak ergodic convergence of the sequence of iterates generated by the proposed scheme is formulated by means of the Fitzpatrick function associated to the maximally monotone operator that describes the set C. In the second part we introduce a forward-backward-forward algorithm for monotone inclusion problems having the same structure, but this time by replacing the cocoercivity hypotheses with Lipschitz continuity conditions. The latter penalty type algorithm opens the gate to handle monotone inclusion problems with more complicated structures, for instance, involving compositions of maximally monotone operators with linear continuous ones.     

Employing different loss functions for the classification of images via supervised learning

Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach is applied to an image classification task. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove that, whenever strong duality holds, the function to be learned can be expressed via the dual optimal solutions. Corresponding dual problems are then derived for different loss functions. The theoretical results are applied by numerically solving a classification task using high dimensional real-world data in order to obtain optimal classifiers. The results demonstrate the excellent performance of support vector classification for this particular problem.     

Rigidity around Poisson submanifolds

We prove a rigidity theorem in Poisson geometry around compact Poisson submanifolds, using the Nash–Moser fast convergence method. In the case of one-point submanifolds (fixed points), this implies a stronger version of Conn’s linearization theorem [2], also proving that Conn’s theorem is a manifestation of a rigidity phenomenon; similarly, in the case of arbitrary symplectic leaves, it gives a stronger version of the local normal form theorem [7]. We can also use the rigidity theorem to compute the Poisson moduli space of the sphere in the dual of a compact semisimple Lie algebra [17].     

Visual software analytics for the build optimization of large-scale software systems

Visual analytics is the science of analytical reasoning facilitated by interactive visual interfaces. In this paper, we present an adaptation of the visual analytics framework to the context of software understanding for maintenance. We discuss the similarities and differences of the general visual analytics context with the software maintenance context, and present in detail an instance of a visual software analytics application for the build optimization of large-scale code bases. Our application combines and adapts several data mining and information visualization techniques in answering several questions that help developers in assessing and reducing the build cost of such code bases by means of user-driven, interactive analysis techniques.     

Ab initio calculations of electronic interactions in inclusion complexes of calix- and thiacalix[n]arenes and block s cations

Ab initio calculations at the HF/6-31G(d) level of theory were performed on a series of thiacalix[4]arenes and calix[6]arenes in presence and in absence of monovalent (Li⁺, Na⁺ and Cs⁺) and divalent cations (Ca²⁺ and Ba²⁺) respectively, in order to evaluate their particular bonding properties as host systems towards electrically charged species. NBO, as well as NBO deletion calculations were undertaken to evaluate the energy difference in the circular hydrogen bonding at the lower rim once an ion was placed inside the cavity. Disruption of this H-bonded system is dependent on the position of the ion within the guest and not on its ionic ratio. The basis set superposition error and the NBO deletion energy between the host and guest species were calculated in order to assess the interaction energy between them.