A note on the connection between nonextensive entropy and hh-derivative

In order to study as a whole the major part of entropy measures, we introduce a two-parameter non-extensive entropic form with respect to the \textit{h}-derivative which generalizes the conventional Newton-Leibniz calculus. This new entropy, $S_{h,h'}$, is proved to describe the non-extensive systems and recover several types of the well-known non-extensive entropic expressions, such as the Tsallis entropy, the Abe entropy, the Shafee entropy, the Kaniadakis entropy and even the classical Boltzmann\,--\,Gibbs one. As a generalized entropy, its corresponding properties are also analyzed.Comment: 6 pages, 1 figur

Natural products by synthetic biology and microbial engineering

Natural products are made from simple building blocks, the structural diversity found in natural products is the result of Nature’s intrinsic use of combinatorial biosynthesis, and recent progress in microbial genomics and synthetic biology has sparked the emergence of a suite of contemporary approaches to natural products by microbial engineering and fermentation. Current strategies are mainly based on the collective knowledge of genetics, microbiology, evolution, enzymology, and structural biology that governs the natural product biosynthetic machinery. While successful, they are limited by what information is gleaned from the above disciplines and how that information can be applied to construct the designer pathways. Nature has used evolution over billions of years to become an expert in combinatorial biosynthesis and microbial engineering, and we have only begun to tap into this knowledge. Selected examples from our current researches will be presented to highlight the opportunities in accessing natural products and expanding natural product structural diversity by exploring the vast combinatorial biosynthesis repertoire found in Nature

An ILP Solver for Multi-label MRFs with Connectivity Constraints

Integer Linear Programming (ILP) formulations of Markov random fields (MRFs) models with global connectivity priors were investigated previously in computer vision, e.g., \cite{globalinter,globalconn}. In these works, only Linear Programing (LP) relaxations \cite{globalinter,globalconn} or simplified versions \cite{graphcutbase} of the problem were solved. This paper investigates the ILP of multi-label MRF with exact connectivity priors via a branch-and-cut method, which provably finds globally optimal solutions. The method enforces connectivity priors iteratively by a cutting plane method, and provides feasible solutions with a guarantee on sub-optimality even if we terminate it earlier. The proposed ILP can be applied as a post-processing method on top of any existing multi-label segmentation approach. As it provides globally optimal solution, it can be used off-line to generate ground-truth labeling, which serves as quality check for any fast on-line algorithm. Furthermore, it can be used to generate ground-truth proposals for weakly supervised segmentation. We demonstrate the power and usefulness of our model by several experiments on the BSDS500 and PASCAL image dataset, as well as on medical images with trained probability maps.Comment: 19 page

Deep Learning Features at Scale for Visual Place Recognition

The success of deep learning techniques in the computer vision domain has triggered a range of initial investigations into their utility for visual place recognition, all using generic features from networks that were trained for other types of recognition tasks. In this paper, we train, at large scale, two CNN architectures for the specific place recognition task and employ a multi-scale feature encoding method to generate condition- and viewpoint-invariant features. To enable this training to occur, we have developed a massive Specific PlacEs Dataset (SPED) with hundreds of examples of place appearance change at thousands of different places, as opposed to the semantic place type datasets currently available. This new dataset enables us to set up a training regime that interprets place recognition as a classification problem. We comprehensively evaluate our trained networks on several challenging benchmark place recognition datasets and demonstrate that they achieve an average 10% increase in performance over other place recognition algorithms and pre-trained CNNs. By analyzing the network responses and their differences from pre-trained networks, we provide insights into what a network learns when training for place recognition, and what these results signify for future research in this area.Comment: 8 pages, 10 figures. Accepted by International Conference on Robotics and Automation (ICRA) 2017. This is the submitted version. The final published version may be slightly differen