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On the Expressibility of Stochastic Switching Circuits
"... Abstract — Stochastic switching circuits are relay circuits that consist of stochastic switches (that we call pswitches). We study the expressive power of these circuits; in particular, we address the following basic question: given an arbitrary integer q, and a pswitch set { 1 2 q−1, ,...,}, can we ..."
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Cited by 7 (6 self)
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Abstract — Stochastic switching circuits are relay circuits that consist of stochastic switches (that we call pswitches). We study the expressive power of these circuits; in particular, we address the following basic question: given an arbitrary integer q, and a pswitch set { 1 2 q−1, ,...,}, can we realize any rational q q q probability with denominator q n (for arbitrary n) by a simple seriesparallel stochastic switching circuit? In this paper, we generalized previous results and prove that when q is a multiple of 2 or 3 the answer is positive. We also show that when q is a prime number the answer is negative. In addition, we propose a greedy algorithm to realize desired reachable probabilities, and thousands of experiments show that this algorithm can achieve almost optimal size. Finally, we prove that any desired probability can be approximated well by a linear size circuit. I.
A synthesis flow for digital signal processing with biomolecular reactions
 in IEEE International Conference on ComputerAided Design, 2010
"... Abstract—We present a methodology for implementing digital signal processing (DSP) operations such as filtering with biomolecular reactions. From a DSP specification, we demonstrate how to synthesize biomolecular reactions that produce timevarying output quantities of molecules as a function of t ..."
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Cited by 4 (4 self)
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Abstract—We present a methodology for implementing digital signal processing (DSP) operations such as filtering with biomolecular reactions. From a DSP specification, we demonstrate how to synthesize biomolecular reactions that produce timevarying output quantities of molecules as a function of timevarying input quantities. Unlike all previous schemes for biomolecular computation, ours produces designs that are dependent only on coarse rate categories for the reactions (“fast” and “slow”). Given such categories, the computation is exact and independent of the specific reaction rates. We implement DSP operations through a selftimed “handshaking ” protocol that transfers quantities between molecular types based on the absence of other types. We illustrate our methodology with the design of a simple movingaverage filter as well as a more complex biquad filter. We validate our designs through transient stochastic simulations of the chemical kinetics. Although conceptual for the time being, the proposed methodology has potential applications in domains of synthetic biology such as biochemical sensing and drug delivery. We are exploring DNAbased computation via strand displacement as a possible experimental chassis. I.
The Synthesis and Analysis of Stochastic Switching Circuits
, 2011
"... Stochastic switching circuits are relay circuits that consist of stochastic switches called pswitches. The study of stochastic switching circuits has widespread applications in many fields of computer science, neuroscience, and biochemistry. In this paper, we discuss several properties of stochastic ..."
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Stochastic switching circuits are relay circuits that consist of stochastic switches called pswitches. The study of stochastic switching circuits has widespread applications in many fields of computer science, neuroscience, and biochemistry. In this paper, we discuss several properties of stochastic switching circuits, including robustness, expressibility, and probability approximation. First, we study the effect caused by introducing an error of size ϵ to each pswitch in a stochastic circuit. We analyze two constructions–simple seriesparallel and general seriesparallel circuits–and prove that simple seriesparallel circuits are robust to small error perturbations, while general seriesparallel circuits are not. Specifically, the total error introduced by perturbations of size less than ϵ is bounded by a constant multiple of ϵ in a simple seriesparallel circuit, independent of the size of the circuit. Next, we study the expressibility of stochastic switching circuits: Given an integer q and a pswitch set S = { 1 2,}, can we synthesize any q q rational probability with denominator qn (for arbitrary n) with a simple seriesparallel stochastic switching circuit? We generalize previous results and prove that when q is a multiple of 2 or 3, the answer is yes. We also show that when q is a prime number larger than 3, the answer is no. Probability approximation is studied for a general case of an arbitrary q−1
Correcting Errors Due to Species Correlations in the Marginal Probability Density Evolution Algorithm
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STOCHASTIC TRANSIENT ANALYSIS OF BIOCHEMICAL SYSTEMS AND ITS APPLICATION TO THE DESIGN OF BIOCHEMICAL LOGIC GATES
, 2008
"... In order to better characterize the behavior of biochemical systems, it is sometimes helpful and necessary to introduce timedependent input signals. If the state of a biochemical system with such signals is assumed to evolve deterministically and continuously, then it can be readily analyzed by so ..."
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In order to better characterize the behavior of biochemical systems, it is sometimes helpful and necessary to introduce timedependent input signals. If the state of a biochemical system with such signals is assumed to evolve deterministically and continuously, then it can be readily analyzed by solving ordinary differential equations. However, if it assumed to evolve discretely and stochastically, then existing simulation methods cannot be applied. In this paper, we incorporate conditions for transient analysis into stochastic simulation and we develop the corresponding simulation algorithm. Applying our method to examples, we demonstrate that it can yield new insights into the dynamics of biochemical systems; specifically, it can be used to verify the design of biochemical logic gates. 1.