Asymptotic Behavior of Solutions for the Cauchy Problem of a Dissipative Boussinesq-Type Equation

We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time weighted spaces are established by the contraction mapping principle

Feature-Based Classification of Bidirectional Transformation Approaches

International audienceBidirectional model transformation is a key technology in model-driven engineering (MDE), when two models that can change over time have to be kept constantly consistent with each other. While several model transformation tools include at least a partial support to bidirectionality, it is not clear how these bidirectional capabilities relate to each other and to similar classical problems in computer science, from the view update problem in databases to bidirectional graph transformations. This paper tries to clarify and visualize the space of design choices for bidirectional transformations from an MDE point of view, in the form of a feature model. The selected list of existing approaches are characterized by mapping them to the feature model. Then, the feature model is used to highlight some unexplored research lines in bidirectional transformations

Entropy production in systems with unidirectional transitions

The entropy production is one of the most essential features for systems operating out of equilibrium. The formulation for discrete-state systems goes back to the celebrated Schnakenberg's work and hitherto can be carried out when for each transition between two states also the reverse one is allowed. Nevertheless, several physical systems may exhibit a mixture of both unidirectional and bidirectional transitions, and how to properly define the entropy production in this case is still an open question. Here, we present a solution to such a challenging problem. The average entropy production can be consistently defined, employing a mapping that preserves the average fluxes, and its physical interpretation is provided. We describe a class of stochastic systems composed of unidirectional links forming cycles and detailed-balanced bidirectional links, showing that they behave in a pseudo-deterministic fashion. This approach is applied to a system with time-dependent stochastic resetting. Our framework is consistent with thermodynamics and leads to some intriguing observations on the relation between the arrow of time and the average entropy production for resetting events.Comment: (Accepted for publication in Physical Review Research

Bidirectional mapping coupled GAN for generalized zero-shot learning

Bidirectional mapping-based generalized zero-shot learning (GZSL) methods rely on the quality of synthesized features to recognize seen and unseen data. Therefore, learning a joint distribution of seen-unseen classes and preserving the distinction between seen-unseen classes is crucial for GZSL methods. However, existing methods only learn the underlying distribution of seen data, although unseen class semantics are available in the GZSL problem setting. Most methods neglect retaining seen-unseen classes distinction and use the learned distribution to recognize seen and unseen data. Consequently, they do not perform well. In this work, we utilize the available unseen class semantics alongside seen class semantics and learn joint distribution through a strong visual-semantic coupling. We propose a bidirectional mapping coupled generative adversarial network (BMCoGAN) by extending the concept of the coupled generative adversarial network into a bidirectional mapping model. We further integrate a Wasserstein generative adversarial optimization to supervise the joint distribution learning. We design a loss optimization for retaining distinctive information of seen-unseen classes in the synthesized features and reducing bias towards seen classes, which pushes synthesized seen features towards real seen features and pulls synthesized unseen features away from real seen features. We evaluate BMCoGAN on benchmark datasets and demonstrate its superior performance against contemporary methods. © 1992-2012 IEEE

Matching Lenses: Alignment and View Update

Bidirectional programming languages have been proposed as a practical approach to the view update problem. Programs in these languages, often called lenses, can be read in two ways— from left to right as functions mapping sources to views, and from right to left as functions mapping updated views back to updated sources. Lenses address the view update problem by making it possible to define a view and its associated update policy together. One issue that has not received sufficient attention in the design of bidirectional languages is alignment. In general, to correctly propagate an update to a view, a lens needs to match up the pieces of the edited view with corresponding pieces of the underlying source. Unfortunately, existing bidirectional languages are extremely limited in their treatment of alignment—they only support simple strategies that do not suffice for many examples of practical interest. In this paper, we propose a novel framework of matching lenses that extends basic lenses with new mechanisms for calculating and using alignments. We enrich the types of lenses with “chunks” that identify the locations of data that should be re-aligned after updates, and we formulate refined behavioral laws that capture essential constraints on the handling of chunks. To demonstrate the utility of our approach, we develop a core language of matching lenses for string data, and we extend it with primitives for describing a number of useful alignment heuristics