Floquet multipliers and the stability of periodic linear differential equations: a unified algorithm and its computer realization

Floquet multipliers (characteristic multipliers) play significant role in the stability of the periodic equations. Based on the iterative method, we provide a unified algorithm to compute the Floquet multipliers (characteristic multipliers) and determine the stability of the periodic linear differential equations on time scales unifying discrete, continuous, and hybrid dynamics. Our approach is based on calculating the value of A and B (see Theorem 3.1), which are the sum and product of all Floquet multipliers (characteristic multipliers) of the system, respectively. We obtain an explicit expression of A (see Theorem 4.1) by the method of variation and approximation theory and an explicit expression of B by Liouville's formula. Furthermore, a computer program is designed to realize our algorithm. Specifically, you can determine the stability of a second order periodic linear system, whether they are discrete, continuous or hybrid, as long as you enter the program codes associated with the parameters of the equation. In fact, few literatures have dealt with the algorithm to compute the Floquet multipliers, not mention to design the program for its computer realization. Our algorithm gives the explicit expressions of all Floquet multipliers and our computer program is based on the approximations of these explicit expressions. In particular, on an arbitrary discrete periodic time scale, we can do a finite number of calculations to get the explicit value of Floquet multipliers (see Theorem 4.2). Therefore, for any discrete periodic system, we can accurately determine the stability of the system even without computer! Finally, in Section 6, several examples are presented to illustrate the effectiveness of our algorithm

XSkill: Cross Embodiment Skill Discovery

Human demonstration videos are a widely available data source for robot learning and an intuitive user interface for expressing desired behavior. However, directly extracting reusable robot manipulation skills from unstructured human videos is challenging due to the big embodiment difference and unobserved action parameters. To bridge this embodiment gap, this paper introduces XSkill, an imitation learning framework that 1) discovers a cross-embodiment representation called skill prototypes purely from unlabeled human and robot manipulation videos, 2) transfers the skill representation to robot actions using conditional diffusion policy, and finally, 3) composes the learned skill to accomplish unseen tasks specified by a human prompt video. Our experiments in simulation and real-world environments show that the discovered skill prototypes facilitate both skill transfer and composition for unseen tasks, resulting in a more general and scalable imitation learning framework. The benchmark, code, and qualitative results are on https://xskill.cs.columbia.edu

ASPiRe:Adaptive Skill Priors for Reinforcement Learning

We introduce ASPiRe (Adaptive Skill Prior for RL), a new approach that leverages prior experience to accelerate reinforcement learning. Unlike existing methods that learn a single skill prior from a large and diverse dataset, our framework learns a library of different distinction skill priors (i.e., behavior priors) from a collection of specialized datasets, and learns how to combine them to solve a new task. This formulation allows the algorithm to acquire a set of specialized skill priors that are more reusable for downstream tasks; however, it also brings up additional challenges of how to effectively combine these unstructured sets of skill priors to form a new prior for new tasks. Specifically, it requires the agent not only to identify which skill prior(s) to use but also how to combine them (either sequentially or concurrently) to form a new prior. To achieve this goal, ASPiRe includes Adaptive Weight Module (AWM) that learns to infer an adaptive weight assignment between different skill priors and uses them to guide policy learning for downstream tasks via weighted Kullback-Leibler divergences. Our experiments demonstrate that ASPiRe can significantly accelerate the learning of new downstream tasks in the presence of multiple priors and show improvement on competitive baselines.Comment: 36th Conference on Neural Information Processing Systems (NeurIPS 2022

Efficient Core-selecting Incentive Mechanism for Data Sharing in Federated Learning

Federated learning is a distributed machine learning system that uses participants' data to train an improved global model. In federated learning, participants cooperatively train a global model, and they will receive the global model and payments. Rational participants try to maximize their individual utility, and they will not input their high-quality data truthfully unless they are provided with satisfactory payments based on their data quality. Furthermore, federated learning benefits from the cooperative contributions of participants. Accordingly, how to establish an incentive mechanism that both incentivizes inputting data truthfully and promotes stable cooperation has become an important issue to consider. In this paper, we introduce a data sharing game model for federated learning and employ game-theoretic approaches to design a core-selecting incentive mechanism by utilizing a popular concept in cooperative games, the core. In federated learning, the core can be empty, resulting in the core-selecting mechanism becoming infeasible. To address this, our core-selecting mechanism employs a relaxation method and simultaneously minimizes the benefits of inputting false data for all participants. However, this mechanism is computationally expensive because it requires aggregating exponential models for all possible coalitions, which is infeasible in federated learning. To address this, we propose an efficient core-selecting mechanism based on sampling approximation that only aggregates models on sampled coalitions to approximate the exact result. Extensive experiments verify that the efficient core-selecting mechanism can incentivize inputting high-quality data and stable cooperation, while it reduces computational overhead compared to the core-selecting mechanism

A Case for Leveraging 802.11p for Direct Phone-to-Phone Communications

WiFi cannot effectively handle the demands of device-to-device communication between phones, due to insufficient range and poor reliability. We make the case for using IEEE 802.11p DSRC instead, which has been adopted for vehicle-to-vehicle communications, providing lower latency and longer range. We demonstrate a prototype motivated by a novel fabrication process that deposits both III-V and CMOS devices on the same die. In our system prototype, the designed RF front-end is interfaced with a baseband processor on an FPGA, connected to Android phones. It consumes 0.02uJ/bit across 100m assuming free space. Application-level power control dramatically reduces power consumption by 47-56%.Singapore-MIT Alliance for Research and TechnologyAmerican Society for Engineering Education. National Defense Science and Engineering Graduate Fellowshi

Analysis of Patents Issued in China for Antihyperglycemic Therapies for Type 2 Diabetes Mellitus

Type 2 diabetes mellitus (T2DM) is prevalent, with a dramatic increase in recent years. Moreover, its microvascular and macrovascular complications cause significant societal issues. The demand for new and effective antidiabetic therapies grows with each passing day and motivates organizations and individuals to pay more attention to such products. In this article, we focused on oral antihyperglycemic drugs patented in China and introduced them according to their antihyperglycemic mechanisms. By searching the website of State Intellectual Property Office of the People’s Republic of China (http://www.sipo.gov.cn), 2,500 antihyperglycemic patents for T2DM were identified and analyzed. These consisted of 4 patents for derivatives of herbal extracts (0.2%), 162 patents for herbal extracts (6.5%), 61 compositions for traditional Chinese medicine (TCM) (2.4%), 2,263 patents for synthetic compounds (90.5%), and 10 (0.4%) patents of the combination of synthetic compounds and TCM. As the most common drugs for diabetes mellitus, synthetic compounds can also be classified into several categories according to their working mechanisms, such as insulin secretion promotor agents, insulin sensitizer agents, α-glucosidase inhibitors, and so forth. This article discussed the chemical structure, potential antihyperglycemic mechanism of these antihyperglycemic drugs in patents in China.Expert opinion: Insulin sensitivity and β-cell function could be improved by weight loss to prevent prediabetes into T2DM. However, 40–50% patients with impaired glucose tolerance (IGT) still progress to T2DM, even after successful long-term weight loss.Antihyperglycemic remedies provide a treatment option to improve insulin sensitivity and maintain β-cell function. Combination therapy is the best treatment for diabetes. Combination therapy can reduce the dosage of each single drug option, and avoid the side effects. Drugs with different mechanisms are complementary, and are better adapted to patients with changing conditions. Classical combination therapies include combinations such as sulfonylureas plus biguanides or glucosidase inhibitors, biguanide plus glucosidase inhibitors or insulin sensitizers, insulin treatment plus biguanides or glucosidase inhibitors. The general principle of combination therapy is that two drugs with different mechanisms are selected jointly, and the combination of three types of hypoglycemic drugs is not recommended. After reading a large amount of literature, we have rarely found a case of three oral hypoglycemic agents, which may mean that the combination of three oral hypoglycemic agents is unnecessary and has unpredictable risks. There is no objection to the idea of multi-drug therapy. But multiple drugs can only be used when it shows a significant benefit to the patients. Combined use of multiple antidiabetic drugs poses a risk to patients due to drug interactions and overtreatment

Guinea Pig Model for Evaluating the Potential Public Health Risk of Swine and Avian Influenza Viruses

BACKGROUND: The influenza viruses circulating in animals sporadically transmit to humans and pose pandemic threats. Animal models to evaluate the potential public health risk potential of these viruses are needed. METHODOLOGY/PRINCIPAL FINDINGS: We investigated the guinea pig as a mammalian model for the study of the replication and transmission characteristics of selected swine H1N1, H1N2, H3N2 and avian H9N2 influenza viruses, compared to those of pandemic (H1N1) 2009 and seasonal human H1N1, H3N2 influenza viruses. The swine and avian influenza viruses investigated were restricted to the respiratory system of guinea pigs and shed at high titers in nasal tracts without prior adaptation, similar to human strains. None of the swine and avian influenza viruses showed transmissibility among guinea pigs; in contrast, pandemic (H1N1) 2009 virus transmitted from infected guinea pigs to all animals and seasonal human influenza viruses could also horizontally transmit in guinea pigs. The analysis of the receptor distribution in the guinea pig respiratory tissues by lectin histochemistry indicated that both SAα2,3-Gal and SAα2,6-Gal receptors widely presented in the nasal tract and the trachea, while SAα2,3-Gal receptor was the main receptor in the lung. CONCLUSIONS/SIGNIFICANCE: We propose that the guinea pig could serve as a useful mammalian model to evaluate the potential public health threat of swine and avian influenza viruses