Exponential sensitivity of noise-driven switching in genetic networks

Cells are known to utilize biochemical noise to probabilistically switch between distinct gene expression states. We demonstrate that such noise-driven switching is dominated by tails of probability distributions and is therefore exponentially sensitive to changes in physiological parameters such as transcription and translation rates. However, provided mRNA lifetimes are short, switching can still be accurately simulated using protein-only models of gene expression. Exponential sensitivity limits the robustness of noise-driven switching, suggesting cells may use other mechanisms in order to switch reliably.

A Lower-Bound Result on the Power of a Genetic Algorithm

This paper presents a lower-bound result on the computational power of a genetic algorithm in the context of combinatorial optimization. We describe a new genetic algorithm, the merged genetic algorithm, and prove that for the class of monotonic functions, the algorithm finds the optimal solution, and does so with an exponential convergence rate. The analysis pertains to the ideal behavior of the algorithm where the main task reduces to showing convergence of probability distributions over the search space of combinatorial structures to the optimal one. We take exponential convergence to be indicative of efficient solvability for the sample-bounded algorithm, although a sampling theory is needed to better relate the limit behavior to actual behavior. The paper concludes with a discussion of some immediate problems that lie ahead.

On the Emergence of Highly Variable Distributions in the Autonomous System Topology

Recent studies have noted that vertex degree in the autonomous system (AS) graph exhibits a highly variable distribution [15, 22]. The most prominent explanatory model for this phenomenon is the Barabási-Albert (B-A) model [5, 2]. A central feature of the B-A model is preferential connectivity—meaning that the likelihood a new node in a growing graph will connect to an existing node is proportional to the existing node’s degree. In this paper we ask whether a more general explanation than the B-A model, and absent the assumption of preferential connectivity, is consistent with empirical data. We are motivated by two observations: first, AS degree and AS size are highly correlated [11]; and second, highly variable AS size can arise simply through exponential growth. We construct a model incorporating exponential growth in the size of the Internet, and in the number of ASes. We then show via analysis that such a model yields a size distribution exhibiting a power-law tail. In such a model, if an AS’s link formation is roughly proportional to its size, then AS degree will also show high variability. We instantiate such a model with empirically derived estimates of growth rates and show that the resulting degree distribution is in good agreement with that of real AS graphs.

Resource Management for Responsive Web Computing

The exploding demand for services like the World Wide Web reflects the potential that is presented by globally distributed information systems. The number of WWW servers world-wide has doubled every 3 to 5 months since 1993, outstripping even the growth of the Internet. At each of these self-managed sites, the Common Gateway Interface (CGI) and Hypertext Transfer Protocol (HTTP) already constitute a rudimentary basis for contributing local resources to remote collaborations. However, the Web has serious deficiencies that make it unsuited for use as a true medium for metacomputing --- the process of bringing hardware, software, and expertise from many geographically dispersed sources to bear on large scale problems. These deficiencies are, paradoxically, the direct result of the very simple design principles that enabled its exponential growth. There are many symptoms of the problems exhibited by the Web: disk and network resources are consumed extravagantly; information search and discovery are difficult; protocols are aimed at data movement rather than task migration, and ignore the potential for distributing computation. However, all of these can be seen as aspects of a single problem: as a distributed system for metacomputing, the Web offers unpredictable performance and unreliable results. The goal of our project is to use the Web as a medium (within either the global Internet or an enterprise intranet) for metacomputing in a reliable way with performance guarantees. We attack this problem one four levels: (1) Resource Management Services: Globally distributed computing allows novel approaches to the old problems of performance guarantees and reliability. Our first set of ideas involve setting up a family of real-time resource management models organized by the Web Computing Framework with a standard Resource Management Interface (RMI), a Resource Registry, a Task Registry, and resource management protocols to allow resource needs and availability information be collected and disseminated so that a family of algorithms with varying computational precision and accuracy of representations can be chosen to meet realtime and reliability constraints. (2) Middleware Services: Complementary to techniques for allocating and scheduling available resources to serve application needs under realtime and reliability constraints, the second set of ideas aim at reduce communication latency, traffic congestion, server work load, etc. We develop customizable middleware services to exploit application characteristics in traffic analysis to drive new server/browser design strategies (e.g., exploit self-similarity of Web traffic), derive document access patterns via multiserver cooperation, and use them in speculative prefetching, document caching, and aggressive replication to reduce server load and bandwidth requirements. (3) Communication Infrastructure: Finally, to achieve any guarantee of quality of service or performance, one must get at the network layer that can provide the basic guarantees of bandwidth, latency, and reliability. Therefore, the third area is a set of new techniques in network service and protocol designs. (4) Object-Oriented Web Computing Framework A useful resource management system must deal with job priority, fault-tolerance, quality of service, complex resources such as ATM channels, probabilistic models, etc., and models must be tailored to represent the best tradeoff for a particular setting. This requires a family of models, organized within an object-oriented framework, because no one-size-fits-all approach is appropriate. This presents a software engineering challenge requiring integration of solutions at all levels: algorithms, models, protocols, and profiling and monitoring tools. The framework captures the abstract class interfaces of the collection of cooperating components, but allows the concretization of each component to be driven by the requirements of a specific approach and environment.

Deciding Isomorphisms of Simple Types in Polynomial Time

The isomorphisms holding in all models of the simply typed lambda calculus with surjective and terminal objects are well studied - these models are exactly the Cartesian closed categories. Isomorphism of two simple types in such a model is decidable by reduction to a normal form and comparison under a finite number of permutations (Bruce, Di Cosmo, and Longo 1992). Unfortunately, these normal forms may be exponentially larger than the original types so this construction decides isomorphism in exponential time. We show how using space-sharing/hash-consing techniques and memoization can be used to decide isomorphism in practical polynomial time (low degree, small hidden constant). Other researchers have investigated simple type isomorphism in relation to, among other potential applications, type-based retrieval of software modules from libraries and automatic generation of bridge code for multi-language systems. Our result makes such potential applications practically feasible.

What Are Polymorphically-Typed Ambients?

Abstract: The Ambient Calculus was developed by Cardelli and Gordon as a formal framework to study issues of mobility and migrant code. We consider an Ambient Calculus where ambients transport and exchange programs rather that just inert data. We propose different senses in which such a calculus can be said to be polymorphically typed, and design accordingly a polymorphic type system for it. Our type system assigns types to embedded programs and what we call behaviors to processes; a denotational semantics of behaviors is then proposed, here called trace semantics, underlying much of the remaining analysis. We state and prove a Subject Reduction property for our polymorphically typed calculus. Based on techniques borrowed from finite automata theory, type-checking of fully type-annotated processes is shown to be decidable; the time complexity of our decision procedure is exponential (this is a worst-case in theory, arguably not encountered in practice). Our polymorphically-typed calculus is a conservative extension of the typed Ambient Calculus originally proposed by Cardelli and Gordon.