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 we consider state estimation carried over a sensor network. A fusion center forms a local multi-hop tree of sensors and gateways and fuses the data into a state estimate. It is shown that the optimal estimator over a sensor tree is given by a Kalman filter of certain structure. The number of hops that the sensors use to communicate data with the fusion center is optimized such that either the overall transmission energy is minimized or the network lifetime is maximized. In both cases the fusion center provides a specified level of estimation accuracy. Some heuristic algorithms are proposed which lead to suboptimal solutions in the energy minimization problem, while an algorithm that leads to the global optimal solution is proposed in the lifetime maximization problem. In both cases, the algorithms are shown to have low computational complexity. Examples are provided to demonstrate the theory and algorithms.

/pdf/optimal-sensor-hop-selection-sensor-energy-minimization-and-48qdp6qlnz.pdf

Optimal sensor hop selection: Sensor energy minimization and network lifetime maximization with guaranteed system performance

Rotating stall is one type of aerodynamic instability limiting the performance of aeroengines. A set of magnetic bearings supporting the compressor rotor is a potential actuator for active control of rotating stall. Based on a first-principles model we show that using this type of actuation, the first harmonic mode of rotating stall is linearly controllable, but the zeroth and the second harmonic modes are linearly uncontrollable. For systems with a stable zeroth (surge) mode, we give an explicit procedure for designing feedback laws such that the Hopf bifurcation of the second mode stall inception is supercritical. We also investigate the effects of magnitude saturation on the size of the region of attraction. We demonstrate the theoretical results by numerical simulations of a model for a transonic compressor at the NASA Glenn Research Center.

https://ieeexplore.ieee.org/iel5/6503/17370/00807752.pdf

Nonlinear control design for rotating stall with magnetic bearing actuators

Abstract Advances in synthetic biology, bioengineering, and computation allow us to rapidly and reliably program cells with increasingly complex and useful functions. However, because the functions we engineer cells to perform are typically burdensome to cell growth, they can be rapidly lost due to the processes of mutation and natural selection. Here, we show that a strategy of terminal differentiation improves the evolutionary stability of burdensome functions in a general manner by realizing a reproductive and metabolic division of labor. To implement this strategy, we develop a genetic differentiation circuit in Escherichia coli using unidirectional integrase-recombination. With terminal differentiation, differentiated cells uniquely express burdensome functions driven by the orthogonal T7 RNA polymerase, but their capacity to proliferate is limited to prevent the propagation of advantageous loss-of-function mutations that inevitably occur. We demonstrate computationally and experimentally that terminal differentiation increases duration and yield of high-burden expression and that its evolutionary stability can be improved with strategic redundancy. Further, we show this strategy can even be applied to toxic functions. Overall, this study provides an effective, generalizable approach for protecting burdensome engineered functions from evolutionary degradation. 

/pdf/integrase-mediated-differentiation-circuits-improve-2pjoldfn.pdf

Integrase-mediated differentiation circuits improve evolutionary stability of burdensome and toxic functions in E. coli

Trajectory generation for mechanical systems with application to robotic locomotion

Ensuring safety through set invariance has proven a useful method in a variety of applications in robotics and control. However, finding analytical expressions for maximal invariant sets, so as to maximize the operational freedom of the system without compromising safety, is notoriously difficult for high-dimensional systems with input constraints. Here we present a generic method for characterizing invariant sets of nth-order integrator systems, based on analyzing roots of univariate polynomials. Additionally, we obtain analytical expressions for the orders n ≤ 4. Using differential flatness we subsequently leverage the results for the n = 4 case to the problem of obstacle avoidance for quadrotor UAVs. The resulting controller has a light computational footprint that showcases the power of finding analytical expressions for control-invariant sets.

/pdf/invariant-sets-for-integrators-and-quadrotor-obstacle-2bktmk9q24.pdf

Richard M. Murray

Papers

Optimal sensor hop selection: Sensor energy minimization and network lifetime maximization with guaranteed system performance

Nonlinear control design for rotating stall with magnetic bearing actuators

Integrase-mediated differentiation circuits improve evolutionary stability of burdensome and toxic functions in E. coli

Trajectory generation for mechanical systems with application to robotic locomotion

Invariant Sets for Integrators and Quadrotor Obstacle Avoidance