The joint dynamics of a collection or network of interacting discrete-time automata can often be described by a single Markov chain. In general, however, analyzing such a chain is computationally intractable for even moderately sized networks because of the explosion in the size of the state space. Asavathiratham introduced the influence model (IM) as a framework for overcoming such limitations. The IM imposes constraints on the update behavior of a network of automata, allowing efficient analysis while still permitting interesting global behavior. However, some of the constraints of the IM are unnecessarily restrictive. The generalized IM (GIM) presented here relaxes some restrictions of the IM, thereby permitting more complex behavior without losing many of the attractive properties of the IM and actually enabling simpler proofs of several results. The GIM is explained and illustrated in relation to the IM from a variety of different perspectives, including geometric. Several examples of GIMs are presented.

A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input-output characteristic in a certain steady-state regime. Here, we systematically study the cycle's steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four different regimes, each with its specific input-output characteristics. These results are obtained using the total quasi-steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions. We invoke experimental data that suggest the possibility of signaling cycles operating in one of the new regimes. We then consider the cycle's dynamic behavior, which has so far been relatively neglected. We demonstrate that the intrinsic architecture of the cycles makes them act--in all four regimes--as tunable low-pass filters, filtering out high-frequency fluctuations or noise in signals and environmental cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical simulations show that our analytical results hold well even for noise of large amplitude. We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways.

This paper discusses fault tolerance in discrete-time dynamic systems, such as finite-state controllers or computer simulations, with focus on the use of coding techniques to efficiently provide fault tolerance to linear finite-state machines (LFSMs). Unlike traditional fault tolerance schemes, which rely heavily-particularly for dynamic systems operating over extended time horizons-on the assumption that the error-correcting mechanism is fault free, we are interested in the case when all components of the implementation are fault prone. The paper starts with a paradigmatic fault tolerance scheme that systematically adds redundancy into a discrete-time dynamic system in a way that achieves tolerance to transient faults in both the state transition and the error-correcting mechanisms. By combining this methodology with low-complexity error-correcting coding, we then obtain an efficient way of providing fault tolerance to k identical unreliable LFSMs that operate in parallel on distinct input sequences. The overall construction requires only a constant amount of redundant hardware per machine (but sufficiently large k) to achieve an arbitrarily small probability of overall failure for any prespecified (finite) time interval, leading in this way to a lower bound on the computational capacity of unreliable LFSMs.

We develop a sufficient condition for the least-squares measurement (LSM), or the square-root measurement, to minimize the probability of a detection error when distinguishing between a collection of mixed quantum states. Using this condition we derive the optimal measurement for state sets with a broad class of symmetries. We first consider geometrically uniform (GU) state sets with a possibly non-Abelian generating group, and show that if the generator satisfies a weighted norm constraint, then the LSM is optimal. In particular, for pure-state GU ensembles, the LSM is shown to be optimal. For arbitrary GU state sets we show that the optimal measurement operators are GU with generator that can be computed very efficiently in polynomial time, within any desired accuracy. We then consider compound GU (CGU) state sets which consist of subsets that are GU. When the generators satisfy a certain constraint, the LSM is again optimal. For arbitrary CGU state sets, the optimal measurement operators are shown to be CGU with generators that can be computed efficiently in polynomial time.

We consider the problem of designing an optimal quantum detector to minimize the probability of a detection error when distinguishing among a collection of quantum states, represented by a set of density operators. We show that the design of the optimal detector can be formulated as a semidefinite programming problem. Based on this formulation, we derive a set of necessary and sufficient conditions for an optimal quantum measurement. We then show that the optimal measurement can be found by solving a standard (convex) semidefinite program. By exploiting the many well-known algorithms for solving semidefinite programs, which are guaranteed to converge to the global optimum, the optimal measurement can be computed very efficiently in polynomial time within any desired accuracy. Using the semidefinite programming formulation, we also show that the rank of each optimal measurement operator is no larger than the rank of the corresponding density operator. In particular, if the quantum state ensemble is a pure-state ensemble consisting of (not necessarily independent) rank-one density operators, then we show that the optimal measurement is a pure-state measurement consisting of rank-one measurement operators.

This paper reviews some of the major approaches to modeling and simulation in power electronics, and provides references that can serve as a starting point for the extensive literature on the subject. The major focus of the paper is on averaged models of various kinds, but sampled-data models are also introduced. The importance of hierarchical modeling and simulation is emphasized.

A two-port impedance-network model of a single-degree-of-freedom remote manipulation system in which a human operator at the master port interacts with a task object at the slave port in a remote location is presented. The design of the network involves the selection of feedback gains for the servomechanisms that transmit motion and force information from one port of the two-port to the other in both directions. The proposed methodology allows this selection to be based on both stability requirements and specifications of desired port impedances, given models of the task and the human operator. The resulting design guidelines guarantee stability for any passive task object at the slave port and any passive human impedance at the master port.>

Given a wide-sense forwards Markovian model, namely a state-space system driven by a white-noise process that is uncorrelated with the random initial state of the system, several papers have shown how to obtain a corresponding {\sl backwards} Markovian model: a system driven backwards in time from a 'terminal' state by a white-noise process that is uncorrelated with this state, and such that the joint second-order statistics of the backwards-model state and output processes equal those of the corresponding forwards-model processes. A very direct derivation is presented that shows in effect how a simple rearrangement of the forwards