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

As a field, synthetic biology strives to engineer increasingly complex artificial systems in living cells. Active feedback in closed loop systems offers a dynamic and adaptive way to ensure constant relative activity independent of intrinsic and extrinsic noise. In this work, we use synthetic protein scaffolds as a modular and tunable mechanism for concentration tracking through negative feedback. Input to the circuit initiates scaffold production, leading to colocalization of a two-component system and resulting in the production of an inhibitory antiscaffold protein. Using a combination of modeling and experimental work, we show that the biomolecular concentration tracker circuit achieves dynamic protein concentration tracking in Escherichia coli and that steady state outputs can be tuned.

https://pubs.acs.org/doi/pdf/10.1021/sb500024b

Design and implementation of a biomolecular concentration tracker.

Trajectory Generation for a Towed Cable System Using Differential Flatness

: The initial phase of this activity, supported by this grant, is now complete. A panel meeting was held in June 2000 and the input from that meeting is being used by a writing committee to generate the panel report. An initial draft of the report was distributed to the controls community in January 2001. It is anticipated that the final version of the report, to be published by SIAM, will be available in July 2001.

Panel on Future Directions in Control, Dynamics, and Systems

Feedback loops are ubiquitous features of biological networks and can produce significant phenotypic heterogeneity, including a bimodal distribution of gene expression across an isogenic cell population. In this work, a combination of experiments and computational modeling was used to explore the roles of multiple feedback loops in the bimodal, switch-like response of the Saccharomyces cerevisiae galactose regulatory network. Here, we show that bistability underlies the observed bimodality, as opposed to stochastic effects, and that two unique positive feedback loops established by Gal1p and Gal3p, which both regulate network activity by molecular sequestration of Gal80p, induce this bimodality. Indeed, systematically scanning through different single and multiple feedback loop knockouts, we demonstrate that there is always a concentration regime that preserves the system’s bimodality, except for the double deletion of GAL1 and the GAL3 feedback loop, which exhibits a graded response for all conditions tested. The constitutive production rates of Gal1p and Gal3p operate as bifurcation parameters because variations in these rates can also abolish the system’s bimodal response. Our model indicates that this second loss of bistability ensues from the inactivation of the remaining feedback loop by the overexpressed regulatory component. More broadly, we show that the sequestration binding affinity is a critical parameter that can tune the range of conditions for bistability in a circuit with positive feedback established by molecular sequestration. In this system, two positive feedback loops can significantly enhance the region of bistability and the dynamic response time.

https://www.pnas.org/content/pnas/109/48/E3324.full.pdf

Richard M. Murray

Papers

Design and implementation of a biomolecular concentration tracker.

Trajectory Generation for a Towed Cable System Using Differential Flatness

Panel on Future Directions in Control, Dynamics, and Systems

Synergistic dual positive feedback loops established by molecular sequestration generate robust bimodal response

Modelling efficient pisciform swimming for control