Human sensorimotor control is remarkably fast and accurate at the system level despite severe speed-accuracy trade-offs at the component level. The discrepancy between the contrasting speed-accuracy trade-offs at these two levels is a paradox. Meanwhile, speed accuracy trade-offs, heterogeneity, and layered architectures are ubiquitous in nerves, skeletons, and muscles, but they have only been studied in isolation using domain-specific models. In this article, we develop a mechanistic model for how component speed-accuracy trade-offs constrain sensorimotor control that is consistent with Fitts' law for reaching. The model suggests that diversity among components deconstrains the limitations of individual components in sensorimotor control. Such diversity-enabled sweet spots (DESSs) are ubiquitous in nature, explaining why large heterogeneities exist in the components of biological systems and how natural selection routinely evolves systems with fast and accurate responses using imperfect components.

Robust control is a core approach for controlling systems with performance guarantees that are robust to modeling error, and is widely used in real-world systems. However, current robust control approaches can only handle small system uncertainty, and thus require significant effort in system identification prior to controller design. We present an online approach that robustly controls a nonlinear system under large model uncertainty. Our approach is based on decomposing the problem into two sub-problems, “robust control design” (which assumes small model uncertainty) and “chasing consistent models”, which can be solved using existing tools from control theory and online learning, respectively. We provide a learning convergence analysis that yields a finite mistake bound on the number of times performance requirements are not met and can provide strong safety guarantees, by bounding the worst-case state deviation. To the best of our knowledge, this is the first approach for online robust control of nonlinear systems with such learning theoretic and safety guarantees. We also show how to instantiate this framework for general robotic systems, demonstrating the practicality of our approach.

WANs are often over-provisioned to accommodate worst-case operating conditions, with many links typically running at only around 30% capacity. In this paper, we show that in-network congestion management can play an important role in increasing network utilization. To mitigate the effects of in-network congestion caused by rapid variations in traffic demand, we propose using high-frequency traffic control (HFTraC) algorithms that exchange real-time flow rate and buffer occupancy information between routers to dynamically coordinate their link-service rates. We show that the design of such dynamic link-service rate policies can be cast as a distributed optimal control problem that allows us to systematically explore an enlarged design space of in-network congestion management algorithms. This also provides a means of quantitatively comparing different controller architectures: we show, perhaps surprisingly, that centralized control is not always better. We implement and evaluate HFTraC in the face of rapidly varying UDP and TCP flows and in combination with AQM algorithms. Using a custom experimental testbed, a Mininet emulator, and a production WAN, we show that HFTraC leads to up to 66% decreases in packet loss rates at high link utilizations as compared to FIFO policies.

The correlation method from brain imaging has been used to estimate functional connectivity in the human brain. However, brain regions might show very high correlation even when the two regions are not directly connected due to the strong interaction of the two regions with common input from a third region. One previously proposed solution to this problem is to use a sparse regularized inverse covariance matrix or precision matrix (SRPM) assuming that the connectivity structure is sparse. This method yields partial correlations to measure strong direct interactions between pairs of regions while simultaneously removing the influence of the rest of the regions, thus identifying regions that are conditionally independent. To test our methods, we first demonstrated conditions under which the SRPM method could indeed find the true physical connection between a pair of nodes for a spring-mass example and an RC circuit example. The recovery of the connectivity structure using the SRPM method can be explained by energy models using the Boltzmann distribution. We then demonstrated the application of the SRPM method for estimating brain connectivity during stage 2 sleep spindles from human electrocorticography (ECoG) recordings using an [Formula: see text] electrode array. The ECoG recordings that we analyzed were from a 32-year-old male patient with long-standing pharmaco-resistant left temporal lobe complex partial epilepsy. Sleep spindles were automatically detected using delay differential analysis and then analyzed with SRPM and the Louvain method for community detection. We found spatially localized brain networks within and between neighboring cortical areas during spindles, in contrast to the case when sleep spindles were not present.

It has been recently discovered that heavy-tailed completion times can result from protocol interaction even when file sizes are light-tailed. A key to this phenomenon is the use of a restart policy where if the file is interrupted before it is completed, it needs to restart from the beginning. In this paper, we show that fragmenting a file into pieces whose sizes are either bounded or independently chosen after each interruption guarantees light-tailed completion time as long as the file size is light-tailed; i.e., in this case, heavy-tailed completion time can only originate from heavy-tailed file sizes. If the file size is heavy-tailed, then the completion time is necessarily heavy-tailed. For this case, we show that when the file size distribution is regularly varying, then under independent or bounded fragmentation, the completion time tail distribution function is asymptotically bounded above by that of the original file size stretched by a constant factor. We then prove that if the distribution of times between interruptions has nondecreasing failure rate, the expected completion time is minimized by dividing the file into equal-sized fragments; this optimal fragment size is unique but depends on the file size. We also present a simple blind fragmentation policy where the fragment sizes are constant and independent of the file size and prove that it is asymptotically optimal. Both these policies are also shown to have desirable completion time tail behavior. Finally, we bound the error in expected completion time due to error in modeling of the failure process.

Many existing fluid-flow models of the Internet congestion control algorithms make simplifying assumptions on the effects of buffers on the data flows. In particular, they assume that the flow rate of a TCP flow at every link in its path is equal to the original source rate. However, a fluid flow in practice is modified by the queueing processes on its path, so that an intermediate link will generally not see the original source rate. In this paper, a more accurate model is derived for the behavior of the network under a congestion controller, which takes into account the effect of buffering on output flows. It is shown how this model can be deployed for some well-known service disciplines such as first-in-first-out and generalized weighted fair queueing. Based on the derived model, the dual and primal-dual algorithms are studied under the common pricing mechanisms, and it is shown that these algorithms can become unstable. Sufficient conditions are provided to guarantee the stability of the dual and primal-dual algorithms. Finally, a new pricing mechanism is proposed under which these congestion control algorithms are both stable.

Recent advances in network coding have shown great potential for efficient information multicasting in communication networks, in terms of both network throughput and network management. In this paper, the problem of flow control at end-systems for network-coding-based multicast flows is addressed. Optimization-based models are formulated for network resource allocation, based on which two sets of decentralized controllers at sources and links/nodes for congestion control are developed for wired networks with given coding subgraphs and without given coding subgraphs, respectively. With random network coding, both sets of controllers can be implemented in a distributed manner, and work at the transport layer to adjust source rates and at network layer to carry out network coding. The convergence of the proposed controllers to the desired equilibrium operating points is proved, and numerical examples are provided to complement the theoretical analysis. The extension to wireless networks is also briefly discussed.

Almost all existing fluid models of congestion control assume that the fluid flow at the output of a link is the same as the fluid flow at the input of the link. This means that all links in the path of a flow see the original source rate. In reality, a fluid flow is modified by the queueing processes on its path, so that an intermediate link will generally not see the original source rate. In this paper, we propose a simple model that explicitly takes into account of the effect of buffering on output flows. We study the dual and primal-dual algorithms that use implicit feedback and show that, while they are always asymptotically stable if feedback delay is ignored, they can be unstable in the new model.

We recently introduced passively controllable smart (PCS) antenna systems for efficient wireless transmission, with direct applications in wireless sensor networks. A PCS antenna system is accompanied by a tunable passive controller whose adjustment at every signal transmission generates a specific radiation pattern. To reduce co-channel interference and optimize the transmitted power, this antenna can be programmed to transmit data in a desired direction in such a way that no signal is transmitted (to the far field) at pre-specified undesired directions. The controller of a PCS antenna was assumed to be centralized in our previous work, which was an impediment to its implementation. In this work, we study the design of PCS antenna systems under decentralized controllers, which are both practically implementable and cost efficient. The PCS antenna proposed here is made of one active element and its programming needs solving second-order-cone optimizations. These properties differentiate a PCS antenna from the existing smart antennas, and make it possible to implement a PCS antenna on a small-sized, low-power silicon chip.

This paper is concerned with understanding the connection between the existing Internet congestion control algorithms and the optimal control theory. The available resource allocation controllers are mainly devised to derive the state of the system to a desired equilibrium point and, therefore, they are oblivious to the transient behavior of the closed-loop system. To take into account the real-time performance of the system, rather than merely its steady-state performance, the congestion control problem should be solved by maximizing a proper utility functional as opposed to a utility function. For this reason, this work aims to investigate what utility functionals the existing congestion control algorithms maximize. In particular, it is shown that there exist meaningful utility functionals whose maximization leads to the celebrated primal, dual and primal/dual algorithms. An implication of this result is that a real network problem may be solved by regarding it as an optimal control problem on which some practical constraints, such as a real-time link capacity constraint, are imposed.

It has been recently discovered that heavy-tailed file completion time can result from protocol interaction even when file sizes are light-tailed. A key to this phenomenon is the RESTART feature where if a file transfer is interrupted before it is completed, the transfer needs to restart from the beginning. In this paper, we show that independent or bounded fragmentation produces light-tailed file completion time as long as the file size is light-tailed, i.e., in this case, heavy-tailed file completion time can only originate from heavy-tailed file sizes. If the file size is heavy-tailed, then the file completion time is clearly heavy-tailed. For this case, we show that when the file size distribution is regularly varying, then under independent or bounded fragmentation, the completion time tail distribution function is asymptotically upper bounded by that of the original file size stretched by a constant factor. We then prove that if the failure distribution has non-decreasing failure rate, the expected completion time is minimized by dividing the file into equal sized fragments; this optimal fragment size is unique but depends on the file size. We also present a simple blind fragmentation policy where the fragment sizes are constant and independent of the file size and prove that it is asymptotically optimal. Finally, we bound the error in expected completion time due to error in modeling of the failure process.

Motivated partially by a control-theoretic viewpoint, we propose a game-theoretic model, calledrandom access game, for contention control. We characterize Nash equilibria of random access games, study their dynamics, and propose distributed algorithms (strategy evolutions) to achieve Nash equilibria. This provides a general analytical framework that is capable of modeling a large class of system-wide quality-of-service (QoS) models via the specification of per-node utility functions, in which system-wide fairness or service differentiation can be achieved in a distributed manner as long as each node executes a contention resolution algorithm that is designed to achieve the Nash equilibrium. We thus propose a novel medium access method derived from carrier sense multiple access/collision avoidance (CSMA/CA) according to distributed strategy update mechanism achieving the Nash equilibrium of random access game. We present a concrete medium access method that adapts to a continuous contention measure called conditional collision probability, stabilizes the network into a steady state that achieves optimal throughput with targeted fairness (or service differentiation), and can decouple contention control from handling failed transmissions. In addition to guiding medium access control design, the random access game model also provides an analytical framework to understand equilibrium and dynamic properties of different medium access protocols.

There exists a widely recognized need to better understand and manage complex “systems of systems,” ranging from biology, ecology, and medicine to network-centric technologies. This is motivating the search for universal laws of highly evolved systems and driving demand for new mathematics and methods that are consistent, integrative, and predictive. However, the theoretical frameworks available today are not merely fragmented but sometimes contradictory and incompatible. We argue that complexity arises in highly evolved biological and technological systems primarily to provide mechanisms to create robustness. However, this complexity itself can be a source of new fragility, leading to “robust yet fragile” tradeoffs in system design. We focus on the role of robustness and architecture in networked infrastructures, and we highlight recent advances in the theory of distributed control driven by network technologies. This view of complexity in highly organized technological and biological systems is fundamentally different from the dominant perspective in the mainstream sciences, which downplays function, constraints, and tradeoffs, and tends to minimize the role of organization and design.

In this era of complete genomes, our knowledge of neuroanatomical circuitry remains surprisingly sparse. Such knowledge is critical, however, for both basic and clinical research into brain function. Here we advocate for a concerted effort to fill this gap, through systematic, experimental mapping of neural circuits at a mesoscopic scale of resolution suitable for comprehensive, brainwide coverage, using injections of tracers or viral vectors. We detail the scientific and medical rationale and briefly review existing knowledge and experimental techniques. We define a set of desiderata, including brainwide coverage; validated and extensible experimental techniques suitable for standardization and automation; centralized, open-access data repository; compatibility with existing resources; and tractability with current informatics technology. We discuss a hypothetical but tractable plan for mouse, additional efforts for the macaque, and technique development for human. We estimate that the mouse connectivity project could be completed within five years with a comparatively modest budget.

Recent advances in network coding have shown great potential for efficient information multicasting in communication networks, in terms of both network throughput and network management. In this paper, we address the problem of rate control at end-systems for network coding based multicast flows. We develop two adaptive rate control algorithms for the networks with given coding subgraphs and without given coding subgraphs, respectively. With random network coding, both algorithms can be implemented in a distributed manner, and work at transport layer to adjust source rates and at network layer to carry out network coding. We prove that the proposed algorithms converge to the globally optimal solutions for intra-session network coding. Some related issues are discussed, and numerical examples are provided to complement our theoretical analysis.

Considerable attention is now being devoted to the study of "complexity science" with the intent of discovering and applying universal laws of highly interconnected and evolved systems. This paper considers several issues related to the use of these theories in the context of critical infrastructures, particularly the Internet. Specifically, we revisit the notion of "organized complexity" and suggest that it is fundamental to our ability to understand, operate, and design next-generation infrastructure networks. We comment on the role of engineering in defining an architecture to support networked infrastructures and highlight recent advances in the theory of distributed control driven by network technologies.

Network protocols in layered architectures have historically been obtained on anad hocbasis, and many of the recent cross-layer designs are also conducted through piecemeal approaches. Network protocol stacks may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems. This paper presents a survey of the recent efforts towards a systematic understanding of “layering” as “optimization decomposition,” where the overall communication network is modeled by a generalized network utility maximization problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. There can be many alternative decompositions, leading to a choice of different layering architectures. This paper surveys the current status of horizontal decomposition into distributed computation, and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and channel coding. Key messages and methods arising from many recent works are summarized, and open issues discussed. Through case studies, it is illustrated how “Layering as Optimization Decomposition” provides a common language to think about modularization in the face of complex, networked interactions, a unifying, top-down approach to design protocol stacks, and a mathematical theory of network architectures.

Abstract — This paper considers jointly optimal design of cross-layer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these con-straints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through congestion price. The global convergence property of this algorithm is proved. We next extend the dual algorithm to handle networks with time-varying channels and adaptive multi-rate devices. The stability of the resulting system is established, and its performance is characterized with respect to an ideal reference system which has the best feasible rate region at link layer. We then generalize the aforementioned results to a general model of queueing network served by a set of interdependent parallel servers with time-varying service capabilities, which models many design problems in communication networks. We show that for a general convex optimization problem where a subset of variables lie in a polytope and the rest in a convex set, the dual-based algorithm remains stable and optimal when the constraint set is modulated by an irreducible finite-state Markov chain. This paper thus presents a step toward a systematic way to carry out cross-layer design in the framework of “layering as optimization decomposition ” for time-varying channel models. I.

Network protocols in layered architectures have historically been obtained primarily on an ad-hoc basis. Recent research has shown that network protocols may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems in the form of Network Utility Maximization (NUM), providing insight into what they optimize and structures of the network protocol stack. This paper presents a short survey of the recent efforts towards a systematic understanding of 'layering' as 'optimization decomposition', where the overall communication network is modeled by a generalized NUM problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the sub-problems. Different decompositions lead to alternative layering architectures. We summarize several examples of horizontal decomposition into distributed computation and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and coding.

Modeling and analysis of complex biological networks presents a number of mathematical challenges. For the models to be useful from a biological standpoint, they must be systematically compared with data. Robustness is a key to biological understanding and proper feedback to guide experiments,including both the deterministic stability and performance properties of models in the presence of parametric uncertainties and their stochastic behavior in the presence of noise. In this paper, we present mathematical and algorithmic tools to address such questions for models that may be nonlinear, hybrid,and stochastic. These tools are rooted in solid mathematical theories, primarily from robust control and dynamical systems, but with important recent developments. They also have the potential for great practical relevance, which we explore through a series of biologically motivated examples.

Biological systems have evolved complex regulatory mechanisms, even in situations where much simpler designs seem to be sufficient for generating nominal functionality. Using module-based analysis coupled with rigorous mathematical comparisons, we propose that in analogy to control engineering architectures, the complexity of cellular systems and the presence of hierarchical modular structures can be attributed to the necessity of achieving robustness. We employ the Escherichia coli heat shock response system, a strongly conserved cellular mechanism, as an example to explore the design principles of such modular architectures. In the heat shock response system, the sigma-factor sigma32 is a central regulator that integrates multiple feedforward and feedback modules. Each of these modules provides a different type of robustness with its inherent tradeoffs in terms of transient response and efficiency. We demonstrate how the overall architecture of the system balances such tradeoffs. An extensive mathematical exploration nevertheless points to the existence of an array of alternative strategies for the existing heat shock response that could exhibit similar behavior. We therefore deduce that the evolutionary constraints facing the system might have steered its architecture toward one of many robustly functional solutions.

We present a model for the joint design of congestion control and media access control (MAC) for ad hoc wireless networks. Using contention graph and contention matrix, we formulate resource allocation in the network as a utility maximization problem with constraints that arise from contention for channel access. We present two algorithms that are not only distributed spatially, but more interestingly, they decompose vertically into two protocol layers where TCP and MAC jointly solve the system problem. The first is a primal algorithm where the MAC layer at the links generates congestion (contention) prices based on local aggregate source rates, and TCP sources adjust their rates based on the aggregate prices in their paths. The second is a dual subgradient algorithm where the MAC sub-algorithm is implemented through scheduling link-layer flows according to the congestion prices of the links. Global convergence properties of these algorithms are proved. This is a preliminary step towards a systematic approach to jointly design TCP congestion control algorithms and MAC algorithms, not only to improve performance, but more importantly, to make their interaction more transparent.

Layered architecture is one of the most fundamental and influential structures of network design. Can we integrate the various protocol layers into a single coherent theory by regarding them as carrying out an asynchronous distributed primal-dual computation over the network to implicitly solve a global optimization problem? Different layers iterate on different subsets of the decision variables using local information to achieve individual optimalities, but taken together, these local algorithms attempt to achieve a global objective. Such a theory will expose the interconnection between protocol layers and can be used to study rigorously the performance tradeoff in protocol layering as different ways to distribute a centralized computation. In this talk, we describe some preliminary work towards this goal and discuss some of the difficulties of this approach.

Building on a recent effort that combines a first-principles approach to modeling router-level connectivity with a more pragmatic use of statistics and graph theory, we show in this paper that for the Internet, an improved understanding of its physical infrastructure is possible by viewing the physical connectivity as an annotated graph that delivers raw connectivity and bandwidth to the upper layers in the TCP/IP protocol stack, subject to practical constraints (e.g., router technology) and economic considerations (e.g., link costs). More importantly, by relying on data from Abilene, a Tier-1 ISP, and the Rocketfuel project, we provide empirical evidence in support of the proposed approach and its consistency with networking reality. To illustrate its utility, we: 1) show that our approach provides insight into the origin of high variability in measured or inferred router-level maps; 2) demonstrate that it easily accommodates the incorporation of additional objectives of network design (e.g., robustness to router failure); and 3) discuss how it complements ongoing community efforts to reverse-engineer the Internet.

This paper is aimed at designing a congestion control system that scales gracefully with network capacity, providing high utilization, low queueing delay, dynamic stability, and fairness among users. The focus is on developing decentralized control laws at end-systems and routers at the level of fluid-flow models, that can provably satisfy such properties in arbitrary networks, and subsequently approximate these features through practical packet-level implementations. Two families of control laws are developed. The first "dual" control law is able to achieve the first three objectives for arbitrary networks and delays, but is forced to constrain the resource allocation policy. We subsequently develop a "primal-dual" law that overcomes this limitation and allows sources to match their steady-state preferences at a slower time-scale, provided a bound on round-trip-times is known. We develop two packet-level implementations of this protocol, using 1) ECN marking, and 2) queueing delay, as means of communicating the congestion measure from links to sources. We demonstrate using ns-2 simulations the stability of the protocol and its equilibrium features in terms of utilization, queueing and fairness, under a variety of scaling parameters.

TCP-AQM can be interpreted as distributed primal-dual algorithms to maximize aggregate utility over source rates. We show that an equilibrium of TCP/IP, if exists, maximizes aggregate utility over both source rates and routes, provided congestion prices are used as link costs. An equilibrium exists if and only if this utility maximization problem and its Lagrangian dual have no duality gap. In this case, TCP/IP incurs no penalty in not splitting traffic across multiple paths. Such an equilibrium, however, can be unstable. It can be stabilized by adding a static component to link cost, but at the expense of a reduced utility in equilibrium. If link capacities are optimally provisioned, however, pure static routing, which is necessarily stable, is sufficient to maximize utility. Moreover single-path routing again achieves the same utility as multipath routing at optimality.

A detailed understanding of the many facets of the Internet's topological structure is critical for evaluating the performance of networking protocols, for assessing the effectiveness of proposed techniques to protect the network from nefarious intrusions and attacks, or for developing improved designs for resource provisioning. Previous studies of topology have focused on interpreting measurements or on phenomenological descriptions and evaluation of graph-theoretic properties of topology generators. We propose a complementary approach of combining a more subtle use of statistics and graph theory with a first-principles theory of router-level topology that reflects practical constraints and tradeoffs. While there is an inevitable tradeoff between model complexity and fidelity, a challenge is to distill from the seemingly endless list of potentially relevant technological and economic issues the features that are most essential to a solid understanding of the intrinsic fundamentals of network topology. We claim that very simple models that incorporate hard technological constraints on router and link bandwidth and connectivity, together with abstract models of user demand and network performance, can successfully address this challenge and further resolve much of the confusion and controversy that has surrounded topology generation and evaluation.

Abstract Summary: MathSBML is a Mathematica package designed for manipulating Systems Biology Markup Language (SBML) models. It converts SBML models into Mathematica data structures and provides a platform for manipulating and evaluating these models. Once a model is read by MathSBML, it is fully compatible with standard Mathematica functions such as NDSolve (a differential-algebraic equations solver). MathSBML also provides an application programming interface for viewing, manipulating, running numerical simulations; exporting SBML models; and converting SBML models in to other formats, such as XPP, HTML and FORTRAN. By accessing the full breadth of Mathematica functionality, MathSBML is fully extensible to SBML models of any size or complexity. Availability: Open Source (LGPL) at http://www.sbml.org and http://www.sf.net/projects/sbml. Supplementary information: Extensive online documentation is available at http://www.sbml.org/mathsbml.html. Additional examples are provided at http://www.sbml.org/software/mathsbml/bioinformatics-application-note

This paper is aimed at designing a congestion control system that scales gracefully with network capacity, providing high utilization, low queueing delay, dynamic stability, and fairness among users. In earlier work we had developed fluid-level control laws that achieve the first three objectives for arbitrary networks and delays, but were forced to constrain the resource allocation policy. In this paper we extend the theory to include dynamics at TCP sources, preserving the earlier features at fast time-scales, but permitting sources to match their steady-state preferences, provided a bound on round-trip-times is known. We develop two packet-level implementations of this protocol, using (i) ECN marking, and (ii) queueing delay, as means of communicating the congestion measure from links to sources. We discuss parameter choices and demonstrate using ns-2 simulations the stability of the protocol and its equilibrium features in terms of utilization, queueing and fairness. We also demonstrate the scalability of these features to increases in capacity, delay, and load, in comparison with other deployed and proposed protocols.

TCP-AQM protocol can be interpreted as distributed primal-dual algorithms over the Internet to maximize aggregate utility. In this paper, we study whether TCP-AQM together with shortest-path routing can maximize utility with appropriate choice of link cost, on a slower timescale, over both source rates and routes. We show that this is generally impossible because the addition of route maximization makes the problem NP-hard. We exhibit an inevitable tradeoff between routing instability and utility maximization. For the special case of ring network, we prove rigorously that shortest-path routing based purely on congestion prices is unstable. Adding a sufficiently large static component to link cost, stabilizes it, but the maximum utility achievable by shortest-path routing decreases with the weight on the static component. We present simulation results to illustrate that these conclusions generalize to general network topology, and that routing instability can reduce utility to less than that achievable by the necessarily stable static routing.

MOTIVATION: Molecular biotechnology now makes it possible to build elaborate systems models, but the systems biology community needs information standards if models are to be shared, evaluated and developed cooperatively. RESULTS: We summarize the Systems Biology Markup Language (SBML) Level 1, a free, open, XML-based format for representing biochemical reaction networks. SBML is a software-independent language for describing models common to research in many areas of computational biology, including cell signaling pathways, metabolic pathways, gene regulation, and others. AVAILABILITY: The specification of SBML Level 1 is freely available from http://www.sbml.org/

We demonstrate that the dynamic behavior of queue and average window is determined predominantly by the stability of TCP/RED, not by AIMD probing nor noise traffic. We develop a general multi-link multi-source model for TCP/RED and derive a local stability condition in the case of a single link with heterogeneous sources. We validate our model with simulations and illustrate the stability region of TCP/RED. These results suggest that TCP/RED becomes unstable when delay increases, or more strikingly, when link capacity increases. The analysis illustrates the difficulty of setting RED parameters to stabilize TCP: they can be tuned to improve stability, but only at the cost of large queues even when they are dynamically adjusted. Finally, we present a simple distributed congestion control algorithm that maintains stability for arbitrary network delay, capacity, load and topology.

This paper considers Web layout design in the spirit of source coding for data compression and rate distortion theory, with the aim of minimizing the average size of files downloaded during Web browsing sessions. The novel aspect here is that the object of design is layout rather than codeword selection, and is subject to navigability constraints. This produces statistics for file transfers that are heavy tailed, completely unlike standard Shannon theory, and provides a natural and plausible explanation for the origin of observed power laws in Web traffic. We introduce a series of theoretical and simulation models for optimal Web layout design with varying levels of analytic tractability and realism with respect to modeling of structure, hyperlinks, and user behavior. All models produce power laws which are striking both for their consistency with each other and with observed data, and their robustness to modeling assumptions. These results suggest that heavy tails are a permanent and ubiquitous feature of Internet traffic, and not an artifice of current applications or user behavior. They also suggest new ways of thinking about protocol design that combines insights from information and control theory with traditional networking.