The looping probability of random heteropolymers helps to understand the scaling properties of biopolymers

Random heteropolymers are a minimal description of biopolymers and can provide a theoretical framework to the investigate the formation of loops in biophysical experiments. A two--state model provides a consistent and robust way to study the scaling properties of loop formation in polymers of the size of typical biological systems. Combining it with self--adjusting simulated--tempering simulations, we can calculate numerically the looping properties of several realizations of the random interactions within the chain. Differently from homopolymers, random heteropolymers display at different temperatures a continuous set of scaling exponents. The necessity of using self--averaging quantities makes finite--size effects dominant at low temperatures even for long polymers, shadowing the length--independent character of looping probability expected in analogy with homopolymeric globules. This could provide a simple explanation for the small scaling exponents found in experiments, for example in chromosome folding

On defining partition entropy by inequalities

Partition entropy is the numerical metric of uncertainty within a partition of a finite set, while conditional entropy measures the degree of difficulty in predicting a decision partition when a condition partition is provided. Since two direct methods exist for defining conditional entropy based on its partition entropy, the inequality postulates of monotonicity, which conditional entropy satisfies, are actually additional constraints on its entropy. Thus, in this paper partition entropy is defined as a function of probability distribution, satisfying all the inequalities of not only partition entropy itself but also its conditional counterpart. These inequality postulates formalize the intuitive understandings of uncertainty contained in partitions of finite sets.We study the relationships between these inequalities, and reduce the redundancies among them. According to two different definitions of conditional entropy from its partition entropy, the convenient and unified checking conditions for any partition entropy are presented, respectively. These properties generalize and illuminate the common nature of all partition entropies

Probing Dark Energy with the Kunlun Dark Universe Survey Telescope

Dark energy is an important science driver of many upcoming large-scale surveys. With small, stable seeing and low thermal infrared background, Dome A, Antarctica, offers a unique opportunity for shedding light on fundamental questions about the universe. We show that a deep, high-resolution imaging survey of 10,000 square degrees in \emph{ugrizyJH} bands can provide competitive constraints on dark energy equation of state parameters using type Ia supernovae, baryon acoustic oscillations, and weak lensing techniques. Such a survey may be partially achieved with a coordinated effort of the Kunlun Dark Universe Survey Telescope (KDUST) in \emph{yJH} bands over 5000--10,000 deg$^2$ and the Large Synoptic Survey Telescope in \emph{ugrizy} bands over the same area. Moreover, the joint survey can take advantage of the high-resolution imaging at Dome A to further tighten the constraints on dark energy and to measure dark matter properties with strong lensing as well as galaxy--galaxy weak lensing.Comment: 9 pages, 6 figure

Formalization of the fundamental group in untyped set theory using auto2

We present a new framework for formalizing mathematics in untyped set theory using auto2. Using this framework, we formalize in Isabelle/FOL the entire chain of development from the axioms of set theory to the definition of the fundamental group for an arbitrary topological space. The auto2 prover is used as the sole automation tool, and enables succinct proof scripts throughout the project.Comment: 17 pages, accepted for ITP 201

Linear Optimal Noncausal Control of Wave Energy Converters

This paper addresses the fundamental theoretical development of a linear optimal noncausal control for wave energy converters (WECs) in a closed analytic form. It is well known that the WEC control is a noncausal control problem, i.e., the future wave information contributes to the present control action. This paper provides a reliable, efficient, and simple linear optimal controller with guaranteed stability for the WEC control problem. The proposed WEC linear optimal control consists of a causal linear state feedback part and an anticausal linear feedforward part to incorporate the influence of future incoming waves. The stability of the closed-loop WEC control system with the proposed linear optimal controller is proven. The contribution of the noncausal term using wave prediction information to the optimal control and the energy output is analyzed quantitatively. The proposed linear controller can be more preferred when constraint satisfaction becomes a less important issue for mild sea states and some well-designed WECs with an ample operation range. The proposed optimal control strategy can be extended for a generic class of energy maximization problems. Numerical simulations are presented to justify the efficacy of the proposed WEC optimal contro

Reverse Engineering Psychologically Valid Facial Expressions of Emotion into Social Robots

Social robots are now part of human society, destined for schools, hospitals, and homes to perform a variety of tasks. To engage their human users, social robots must be equipped with the essential social skill of facial expression communication. Yet, even state-of-the-art social robots are limited in this ability because they often rely on a restricted set of facial expressions derived from theory with well-known limitations such as lacking naturalistic dynamics. With no agreed methodology to objectively engineer a broader variance of more psychologically impactful facial expressions into the social robots' repertoire, human-robot interactions remain restricted. Here, we address this generic challenge with new methodologies that can reverse-engineer dynamic facial expressions into a social robot head. Our data-driven, user-centered approach, which combines human perception with psychophysical methods, produced highly recognizable and human-like dynamic facial expressions of the six classic emotions that generally outperformed state-of-art social robot facial expressions. Our data demonstrates the feasibility of our method applied to social robotics and highlights the benefits of using a data-driven approach that puts human users as central to deriving facial expressions for social robots. We also discuss future work to reverse-engineer a wider range of socially relevant facial expressions including conversational messages (e.g., interest, confusion) and personality traits (e.g., trustworthiness, attractiveness). Together, our results highlight the key role that psychology must continue to play in the design of social robots