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

RNA regulators are emerging as powerful tools to engineer synthetic genetic networks or rewire existing ones. A potential strength of RNA networks is that they may be able to propagate signals on timescales that are set by the fast degradation rates of RNAs. However, a current bottleneck to verifying this potential is the slow design-build-test cycle of evaluating these networks in vivo. Here we adapt an Escherichia coli-based cell- free transcription-translation (TX-TL) system for rapidly prototyping RNA networks. We used this system to measure the response time of an RNA transcription cascade to be approximately five minutes per step of the cascade. We also show that this response time can be adjusted with temperature and regulator threshold response tuning. Finally we use TX-TL to prototype a new RNA network, an RNA single input module, and show that this network temporally stages the expression of two genes in vivo. Now published as: ACS Synthetic Biology doi:10.1021/sb400206c

https://www.biorxiv.org/content/biorxiv/early/2014/03/17/003335.full.pdf

Rapidly characterizing the fast dynamics of RNA genetic circuitry with cell-free transcription-translation (TX-TL) systems

We describe how noise propagates through a network by calculating the variance of the outputs. Using stochastic calculus and dynamical systems theory, we study the network topologies that accentuate or alleviate the effect of random variance in the network for both directed and undirected graphs. Given a linear tree network, the variance in the output is a convex function of the poles of the individual nodes. Cycles create correlations which in turn increase the variance in the output. Feedforward and feedback have a limited effect on noise propagation when the respective cycles is sufficiently long. Crosstalk between the elements of different pathways helps reduce the output noise, but makes the network slower. Next, we study the differences between disturbances in the inputs and disturbances in the network parameters, and how they propagate to the outputs. Finally, we show how noise correlations can affect the steady state of the system in chemical reaction networks with reactions of two or more reactants, each of which may be affected by independent or correlated noise sources.

Noise Propagation in Biological and Chemical Reaction Networks

This thesis addresses the problem of estimating the state in multi-agent decision and control systems. In particular, a novel approach to state estimation is developed that uses partial order theory in order to overcome some of the severe computational complexity issues arising in multi-agent systems. Within this approach, state estimation algorithms are developed that enjoy provable convergence properties and are scalable with the number of agents. 
The dynamic evolution of the systems under study are characterized by the interplay of continuous and discrete variables. Continuous variables usually represent physical quantities such as position, velocity, voltage, and current, while the discrete variables usually represent quantities internal to the decision protocol that are used for coordination, communication, and control. Within the proposed state estimation approach, the estimation of continuous and discrete variables is developed in the same mathematical framework as a joint continuous-discrete space is considered for the estimator. This way, the dichotomy between the continuous and discrete world is overcome for the purpose of state estimation. 
Application examples are considered, which include the state estimation in competitive multi-robot systems and in multi-agent discrete event systems, and the monitoring of distributed environments.

/pdf/state-estimation-in-multi-agent-decision-and-control-systems-4lqhehhxnl.pdf

State estimation in multi-agent decision and control systems

Proper Orthogonal Decomposition of 2D Compressible DNS of the Flow over a Rectangular Cavity

Engineering microbial consortia is an important new frontier for synthetic biology given its efficiency in performing complex tasks and endurance to environmental uncertainty. Most synthetic circuits regulate populational behaviors via cell-to-cell interactions, which are affected by spatially heterogeneous environments. Therefore, it is important to understand the limits on controlling system dynamics and provide a control strategy for engineering consortia under spatial structures. Here, we build a network model for a fractional population control circuit in two-strain consortia, and characterize the cell-to-cell interaction network by topological properties, such as symmetry, locality and connectivity. Using linear network control theory, we relate the network topology to system output's tracking performance. We analytically and numerically demonstrate that the minimum network control cost for good tracking depends on locality difference between two cell population's spatial distributions and how strongly the controller node contributes to interaction strength. To realize a robust consortia, we can manipulate the environment to form a strongly connected network. Our results ground the expected cell population dynamics in its spatially organized interaction network, and inspire directions in cooperative control in microbial consortia.

/pdf/role-of-interaction-network-topology-in-controlling-4dk4olkzpg.pdf

Richard M. Murray

Papers

Rapidly characterizing the fast dynamics of RNA genetic circuitry with cell-free transcription-translation (TX-TL) systems

Noise Propagation in Biological and Chemical Reaction Networks

State estimation in multi-agent decision and control systems

Proper Orthogonal Decomposition of 2D Compressible DNS of the Flow over a Rectangular Cavity

Role of interaction network topology in controlling microbial population in consortia