There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.

/pdf/consensus-problems-in-networks-of-agents-with-switching-25c3hqvtd8.pdf

Consensus problems in networks of agents with switching topology and time-delays

In this paper, analysis of dynamical systems interconnected over networks is considered. A framework for the analysis of the stability of interconnection is given. Previous results that studies the single-input/single-output case for a constant interconnection matrix are generalised to the multi-input/multi-output case where arbitrary dynamic interconnection is allowed. The analysis shows existence of a separation principle that is very useful in the sense of the simplicity for stability analysis. Stability can be checked graphically using a Nyquist-like criterion. The problem with time-delays and interconnection variation and robustness appear to be natural special cases.

Simple condition for stability of systems interconnected over networks

Motivated by exploration of communication-constrained underground environments using robot teams, we study the problem of planning for intermittent connectivity in multi-agent systems. We propose a novel concept of information-consistency to handle situations where the plan is not initially known by all agents, and suggest an integer linear program for synthesizing information-consistent plans that also achieve auxiliary goals. Furthermore, inspired by network flow problems we propose a novel way to pose connectivity constraints that scales much better than previous methods. In the second part of the paper we apply these results in an exploration setting, and propose a clustering method that separates a large exploration problem into smaller problems that can be solved independently. We demonstrate how the resulting exploration algorithm is able to coordinate a team of ten agents to explore a large environment.

/pdf/intermittent-connectivity-for-exploration-in-communication-4ts3myw1cn.pdf

Intermittent Connectivity for Exploration in Communication-Constrained Multi-Agent Systems

In this paper we consider estimation of dynam- ical systems over wireless communication channels. We show that the communication protocols suitable for non real-time applications like data networks may not be entirely applicable for estimation and control of a rapidly changing dynamical system. We then develop new design paradigms for these applications to show how noisy packets should be handled in the receiver. We prove that, in the presence of a cross- layer feedback, keeping all the packets will both maximize the stability range and minimize the estimation error variance. In the absence of such a feedback, we show that keeping all the packets still maximizes the stability range, independent of the shape of the communication noise profile. In order to optimize the performance, in the absence of a cross-layer feedback, we prove that packet drop should be designed to balance information loss and communication noise.

/pdf/receiver-design-principles-for-estimation-over-fading-3pcc39x292.pdf

Receiver Design Principles for Estimation over Fading Channels

The mammalian gut contains trillions of microbes that interact with host cells and monitor changes in the environment. Opportunistic pathogens exploit environmental conditions to stimulate their growth and virulence, leading to a resurgence of chronic disorders such as inflammatory bowel disease (IBD). Current therapies are effective in less than 30% of patients due to the lack of adherence to prescription schedules and overall, off-target effects. Smart microbial therapeutics can be engineered to colonize the gut, providing in situ surveillance and conditional disease modulation. However, many current engineered microbes can only respond to single gut environmental factors, limiting their effectiveness. In this work, we implement the previously characterized split activator AND logic gate in the probiotic E. coli strain Nissle 1917. Our system can respond to two input signals: the inflammatory biomarker tetrathionate and a second input signal, IPTG. We report 4-6 fold induction with minimal leak when both signals are present. We model the dynamics of the AND gate using chemical reaction networks, and by tuning parameters in silico, we identified perturbations that affect our circuit9s selectivity. We anticipate that our results will prove useful for designing living therapeutics for spatial targeting and signal processing in complex environments.

/pdf/engineering-logical-inflammation-sensing-circuit-for-gut-1weilngg7e.pdf

Engineering Logical Inflammation Sensing Circuit for Gut Modulation

. We present a framework for merging unit tests for autonomous systems. Typically, it is intractable to test an autonomous system for every scenario in its operating environment. The question of whether it is possible to design a single test for multiple requirements of the system motivates this work. First, we formally define three attributes of a test: a test specification that characterizes behaviors observed in a test execution, a test environment, and a test policy. Using the merge operator from contract-based design theory, we provide a formalism to construct a merged test specification from two unit test specifications. Temporal constraints on the merged test specification guarantee that non-trivial satisfaction of both unit test specifications is necessary for a successful merged test execution. We assume that the test environment remains the same across the unit tests and the merged test. Given a test specification and a test environment, we synthesize a test policy filter using a receding horizon approach, and use the test policy filter to guide a search procedure (e.g. Monte-Carlo Tree Search) to find a test policy that is guaranteed to satisfy the test specification. This search procedure finds a test policy that maximizes a pre-defined robustness metric for the test while the filter guarantees a test policy for satisfying the test specification. We prove that our algorithm is sound. Furthermore, the receding horizon approach to synthesizing the filter ensures that our algorithm is scalable. Finally, we show that merging unit tests is impactful for designing efficient test campaigns to achieve similar levels of coverage in fewer test executions. We illustrate our framework on two self-driving examples in a discrete-state setting.

Richard M. Murray

Papers

Simple condition for stability of systems interconnected over networks

Intermittent Connectivity for Exploration in Communication-Constrained Multi-Agent Systems

Receiver Design Principles for Estimation over Fading Channels

Engineering Logical Inflammation Sensing Circuit for Gut Modulation

Towards Better Test Coverage: Merging Unit Tests for Autonomous Systems