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

A New Golden Age of Natural Products Drug Discovery

The 2015 Nobel Prize in Physiology or Medicine has been awarded to William C. Campbell, Satoshi Omura, and Youyou Tu for the discovery of avermectins and artemisinin, respectively, therapies that revolutionized the treatment of devastating parasite diseases. With the recent technological advances, a New Golden Age of natural products drug discovery is dawning

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

Deforming black holes with even multipolar differential rotation boundary

Motivated by the novel asymptotically global AdS$_4$ solutions with deforming horizon in [JHEP {\bf 1802}, 060 (2018)], we analyze the boundary metric with even multipolar differential rotation and numerically construct a family of deforming solutions with quadrupolar differential rotation boundary, including two classes of solutions: solitons and black holes. In contrast to solutions with dipolar differential rotation boundary, we find that even though the norm of Killing vector $\partial_t$ becomes spacelike for certain regions of polar angle $\theta$ when $\varepsilon>2$, solitons and black holes with quadrupolar differential rotation still exist and do not develop hair due to superradiance. Moreover, at the same temperature, the horizonal deformation of quadrupolar rotation is smaller than that of dipolar rotation. Furthermore, we also study the entropy and quasinormal modes of the solutions, which have the analogous properties to that of dipolar rotation.Comment: 18 pages, 21 figure