On Optimal Finite-length Binary Codes of Four Codewords for Binary Symmetric Channels

Finite-length binary codes of four codewords are studied for memoryless binary symmetric channels (BSCs) with the maximum likelihood decoding. For any block-length, best linear codes of four codewords have been explicitly characterized, but whether linear codes are better than nonlinear codes or not is unknown in general. In this paper, we show that for any block-length, there exists an optimal code of four codewords that is either linear or in a subset of nonlinear codes, called Class-I codes. Based on the analysis of Class-I codes, we derive sufficient conditions such that linear codes are optimal. For block-length less than or equal to 8, our analytical results show that linear codes are optimal. For block-length up to 300, numerical evaluations show that linear codes are optimal.Comment: accepted by ISITA 202

Regular solutions of the stationary Navier-Stokes equations on high dimensional Euclidean space

We study the existence of regular solutions of the incompressible stationary Navier-Stokes equations in $n$-dimensional Euclidean space with a given bounded external force of compact support. In dimensions $n\le 5$, the existence of such solutions was known. In this paper, we extend it to dimensions $n\le 15$.Comment: Exposition improved. To appear in Comm. Math. Phy

Multi-View Region Adaptive Multi-temporal DMM and RGB Action Recognition

Human action recognition remains an important yet challenging task. This work proposes a novel action recognition system. It uses a novel Multiple View Region Adaptive Multi-resolution in time Depth Motion Map (MV-RAMDMM) formulation combined with appearance information. Multiple stream 3D Convolutional Neural Networks (CNNs) are trained on the different views and time resolutions of the region adaptive Depth Motion Maps. Multiple views are synthesised to enhance the view invariance. The region adaptive weights, based on localised motion, accentuate and differentiate parts of actions possessing faster motion. Dedicated 3D CNN streams for multi-time resolution appearance information (RGB) are also included. These help to identify and differentiate between small object interactions. A pre-trained 3D-CNN is used here with fine-tuning for each stream along with multiple class Support Vector Machines (SVM)s. Average score fusion is used on the output. The developed approach is capable of recognising both human action and human-object interaction. Three public domain datasets including: MSR 3D Action,Northwestern UCLA multi-view actions and MSR 3D daily activity are used to evaluate the proposed solution. The experimental results demonstrate the robustness of this approach compared with state-of-the-art algorithms.Comment: 14 pages, 6 figures, 13 tables. Submitte

An inventory control model with interconnected logistic services for vendor inventory management

International audienceThis paper proposes an inventory control model taking advantage of interconnected logistic services in the Physical Internet for fast-moving consumer goods (FMCG) sector. Unlike current hierarchical inventory model where the source of each is pre-assigned, the goods are stored and distributed in an interconnected and open network of PI-hubs which enables storage capacity and transportation sharing among different companies around the network. As a result, theoretically, the suppliers can push their goods all around the network and the retailers can be served by any hub in the network. A non-linear global optimization inventory model to minimize the total logistic costs is proposed and a heuristic using simulated annealing is applied to solve the problem. Numerical experiments are taken to compare the performance of the proposed PI inventory model and classic inventory control model for different settings of a typical supply network. Results suggest that the PI inventory control model can always reduce the total logistic cost while reaching a comparable or improved end customer service level