Two-Sided Wasserstein Procrustes Analysis

Learning correspondence between sets of objects is a key component in many machine learning tasks.Recently, optimal Transport (OT) has been successfully applied to such correspondence problems and it is appealing as a fully unsupervised approach. However, OT requires pairwise instances be directly comparable in a common metric space. This limits its applicability when feature spaces are of different dimensions or not directly comparable. In addition, OT only focuses on pairwise correspondence without sensing global transformations. To address these challenges, we propose a new method to jointly learn the optimal coupling between twosets, and the optimal transformations (e.g. rotation, projection and scaling) of each set based on a two-sided Wassertein Procrustes analysis (TWP). Since the joint problem is a non-convex optimization problem, we present a reformulation that renders the problem component-wise convex. We then propose a novel algorithm to solve the problem harnessing a Gauss–Seidel method. We further present competitive results of TWP on various applicationscompared with state-of-the-art methods.

Entropy-Regularized Optimal Transport on Multivariate Normal and q-normal Distributions

The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions from other distances or divergences. Although computing the Wasserstein distance is costly, entropy-regularized optimal transport was proposed to computationally efficiently approximate the Wasserstein distance. The purpose of this study is to understand the theoretical aspect of entropy-regularized optimal transport. In this paper, we focus on entropy-regularized optimal transport on multivariate normal distributions and q-normal distributions. We obtain the explicit form of the entropy-regularized optimal transport cost on multivariate normal and q-normal distributions; this provides a perspective to understand the effect of entropy regularization, which was previously known only experimentally. Furthermore, we obtain the entropy-regularized Kantorovich estimator for the probability measure that satisfies certain conditions. We also demonstrate how the Wasserstein distance, optimal coupling, geometric structure, and statistical efficiency are affected by entropy regularization in some experiments. In particular, our results about the explicit form of the optimal coupling of the Tsallis entropy-regularized optimal transport on multivariate q-normal distributions and the entropy-regularized Kantorovich estimator are novel and will become the first step towards the understanding of a more general setting.

Synchronization of Delayed Quantum Dot Light Emitting Diodes

Chaos synchronization of two quantum dot light emitting diodes (QDLEDs) theoretically is studied, which is delay coupled via a closed or open –loop and mutual coupling system. Whereas the synchronized- chaotic systems, the dynamics of there are identical to uncoupled DLED under optical feedback effect. Complete synchronization was obtained under certain conditions for the coupling parameters. We evaluated the range of the QDLED’s chaos with extrinsic optical feedback in methods of the chaos synchronization residue diagram and discussion as well of the coherence for the optimal coupling strength range. With proper conditions of the coupling parameters and the evaluation methods, the synchronization was satisfactorily obtained between the transmitter and receiver

Multiscale communication in cortico-cortical networks

Signaling events in brain networks unfold over multiple topological scales. Areas may exchange information over local circuits, primarily encompassing direct neighbours and areas with similar functions. Alternatively, areas may exchange information over global circuits, encompassing more distant neighbours with increasingly dissimilar functions. In the present report, we study communication in cortico-cortical networks by characterizing a region’s structural embedding over a continuous range of topological scales. We find that the centrality of a brain region varies across scales and that connection diversity determines scale preference, with less diverse unimodal regions showing preference for local communication and more diverse multimodal regions showing preferences for global communication. These preferences manifest as scale-specific structure-function relationships, with unimodal areas showing optimal coupling at local scales and multimodal regions showing optimal coupling at global scales. Altogether, the present findings reveal how functional hierarchies emerge from hidden but highly structured multiscale connection patterns.

Evaluation of quantum dot light-emitting diodes synchronization under optically feedback

Chaos synchronization of two quantum dot light-emitting diodes (QDLEDs) theoretically is studied, which are via a closed or open-loop and mutual coupling system. Whereas the synchronized-chaotic systems, the dynamics of there are identical to uncoupled dot light-emitting diodes (DLEDs) under optical feedback effect. Complete synchronization was obtained under certain conditions for the coupling parameters. We evaluated the range of the QDLED’s chaos with extrinsic optical feedback in methods of the chaos synchronization residue diagram and discussion as well as the coherence for the optimal coupling strength range. With proper conditions of the coupling parameters and the evaluation methods, the synchronization was satisfactorily obtained between the transmitter and receiver.