Arbitrary Number Of States Research Articles

An extension of the Walsh-Hadamard transform to calculate and model epistasis in genetic landscapes of arbitrary shape and complexity.

Accurate models describing the relationship between genotype and phenotype are necessary in order to understand and predict how mutations to biological sequences affect the fitness and evolution of living organisms. The apparent abundance of epistasis (genetic interactions), both between and within genes, complicates this task and how to build mechanistic models that incorporate epistatic coefficients (genetic interaction terms) is an open question. The Walsh-Hadamard transform represents a rigorous computational framework for calculating and modeling epistatic interactions at the level of individual genotypic values (known as genetical, biological or physiological epistasis), and can therefore be used to address fundamental questions related to sequence-to-function encodings. However, one of its main limitations is that it can only accommodate two alleles (amino acid or nucleotide states) per sequence position. In this paper we provide an extension of the Walsh-Hadamard transform that allows the calculation and modeling of background-averaged epistasis (also known as ensemble epistasis) in genetic landscapes with an arbitrary number of states per position (20 for amino acids, 4 for nucleotides, etc.). We also provide a recursive formula for the inverse matrix and then derive formulae to directly extract any element of either matrix without having to rely on the computationally intensive task of constructing or inverting large matrices. Finally, we demonstrate the utility of our theory by using it to model epistasis within both simulated and empirical multiallelic fitness landscapes, revealing that both pairwise and higher-order genetic interactions are enriched between physically interacting positions.

Optimal State Estimation of a Generalized MAP Event Flow with an Arbitrary Number of States

Optimal State Estimation of a Generalized MAP Event Flow with an Arbitrary Number of States

Optimal pricing policies for tandem queues: Asymptotic optimality

We study the optimal pricing problem for a tandem queueing system with an arbitrary number of stations, finite buffers, and blocking. The problem is formulated using a Markov decision process model with the objective to maximize the long-run expected time-average revenue or gain of the service provider. Our interest lies in comparing the performances of static and dynamic pricing policies in maximizing the gain. We show that the optimal static pricing policies perform as well as the optimal dynamic pricing policies when the buffer size at station 1 becomes large and the arrival rate is either small or large. More importantly, we propose two specific static pricing policies for systems with small and large arrival rates, respectively, and show that each proposed policy produces a gain converging to the optimal gain with an approximately exponential rate as the buffer size before station 1 becomes large. We learn from numerical results that the proposed static policies perform as well as optimal dynamic policies even for a moderate-sized buffer at station 1. We also learn that there exist cases where optimal static pricing policies are, however, neither optimal nor near-optimal.

A PDE-based approach for the evaluation of probability of starvation in video streaming

Characterizing the dynamics of wireless channels is of crucial importance to the performance of application requiring quality of experience (QoE) guarantees like wireless-based time-sensitive video streaming applications. Therefore, in this study, we employ a novel approach to model the distribution of the total amount of data that can be transmitted over a wireless channel that is modeled by a multi-state Markov chain with an arbitrary number of states while permitting transitions to non-adjacent states. This is done by deriving a system of partial differential equations (PDEs) that characterizes the channel behavior. Then, the proposed system of PDEs is used to obtain the distribution of the total amount of data that can be transmitted through the wireless channel and evaluate the probability of starvation at the playback buffer in video streaming applications. The solution is presented analytically for a 2-state wireless channel with alternating good and bad intervals, and numerically for the general case of an n state channel. Moreover, the resulting distributions are verified for their accuracy by comparison with the results obtained using Monte-Carlo simulations. Finally, the cumulative distribution function (CDF) of the distribution is then used to evaluate the probability of starvation, based on which a rate control algorithm is proposed.

Оптимальная оценка состояний обобщенного асинхронного потока событий с произвольным числом состояний при непродлевающемся мертвом времени

Оптимальная оценка состояний обобщенного асинхронного потока событий с произвольным числом состояний при непродлевающемся мертвом времени

Model of Random Field with Piece-Constant Values and Sampling-Restoration Algorithm of Its Realizations.

We propose a description of the model of a random piecewise constant field formed by the sum of realizations of two Markov processes with an arbitrary number of states and defined along mutually perpendicular axes. The number of field quantization levels can be arbitrary. Realizations of a random field model of the desired shape are created by appropriate selection of parameters for formative realization of Markov processes. For the proposed field model, we investigated the sampling and restoration algorithm of any selected realizations. As a result, we determined the optimal sampling and recovery algorithms. The resulting sampling is fundamentally non-periodic. Recovery errors are calculated. Two examples are considered.

Оптимальная оценка состояний обобщённого асинхронного потока событий с произвольным числом состояний

Оптимальная оценка состояний обобщённого асинхронного потока событий с произвольным числом состояний

The Potts Model on a Bethe Lattice in an External Field

A solution for the Potts model with arbitrary number of states on a Bethe lattice in a nonzero external field has been obtained. A line of first-order phase transitions has been constructed in the temperature – external-field plane, terminating at the point of the second-order phase transition. The magnitude of the magnetization jump on the phase-transition lines has been found, as well as some of the critical exponents characterizing this phase transition.

Mean-field approximation for the potts model of a diluted magnet in the external field

The Potts model of a diluted magnet with an arbitrary number of states placed in the external field has been considered. Phase transitions of this model have been studied in the mean-field approximation, the dependence of the critical temperature on the external field and the density of magnetic atoms has been found, and the magnetic susceptibility has been calculated. An improved mean-field technique has been proposed, which provides more accurate account of the effects associated with nonmagnetic dilution. The influence of dilution on the first-order phase transition curve and the magnetization jump at the phase transition has been studied by this technique.

Dynamical rephasing of ensembles of qudits

Dynamical decoupling is an established tool for protecting the quantum state of a qubit from decoherence. This paper extends the simplest dynamical decoupling technique for qubits---the Carr-Purcell-Meiboom-Gill's two-pulse rephasing sequence---to qudits with an arbitrary number of states. The pulse sequences introduced here are particularly well suited for dynamical rephasing of the collective coherence of inhomogeneously broadened ensembles of atomic qudits.

Excitonic couplings between molecular crystal pairs by a multistate approximation.

In this paper, we present a diabatization scheme to compute the excitonic couplings between an arbitrary number of states in molecular pairs. The method is based on an algebraic procedure to find the diabatic states with a desired property as close as possible to that of some reference states. In common with other diabatization schemes, this method captures the physics of the important short-range contributions (exchange, overlap, and charge-transfer mediated terms) but it becomes particularly suitable in presence of more than two states of interest. The method is formulated to be usable with any level of electronic structure calculations and to diabatize different types of states by selecting different molecular properties. These features make the diabatization scheme presented here especially appropriate in the context of organic crystals, where several excitons localized on the same molecular pair may be found close in energy. In this paper, the method is validated on the tetracene crystal dimer, a well characterized case where the charge transfer (CT) states are closer in energy to the Frenkel excitons (FE). The test system was studied as a function of an external electric field (to explore the effect of changing the relative energy of the CT excited state) and as a function of different intermolecular distances (to probe the strength of the coupling between FE and CT states). Additionally, we illustrate how the approximation can be used to include the environment polarization effect.

General design of reversible sequential machines based on reversible logic elements

This paper proposes a scheme for decomposing reversible sequential machines (RSMs) into simple reversible logic elements (RLEs). This scheme is generalized from the previous constructions of reversible Turing machines (RTMs) using various RLEs (Lee et al. 2012), in which each RTM is composed by a uniform circuit of identical RSMs associated with two states. Each RSM's operation in the circuit, however, is subject to strict conditions that prevent direct extension of their constructions to more general RSMs. Our novel scheme to the contrary, imposes no condition on the operations of an RSM which may take any arbitrary number of states. Moreover, each RSM's construction can work asynchronously without a clock signal to synchronize all RLEs comprising the construction.

Heuristic approximation method for a random flow of events by an MC-flow with arbitrary number of states

This paper considers the approximation problem for an observable random flow of events using an MC-flow. A separation algorithm for stationarity segments is suggested. In addition, we propose an evaluation algorithm for the number of states and intensity of the approximating MC-flow by event occurrence instants in the observable flow.

Modelling Medium Access Control in IEEE 802.15.4 Nonbeacon-Enabled Networks with Probabilistic Timed Automata

This paper concerns the formal modelling of medium access control in nonbeacon-enabled IEEE 802.15.4 wireless personal area networks with probabilistic timed automata supported by the PRISM probabilistic model checker. In these networks, the devices contend for the medium by executing an unslotted carrier sense multiple access with collision avoidance algorithm. In the literature, a model of a network which consists of two stations sending data to two different destination stations is introduced. We have improved this model and, based on it, we propose two ways of modelling a network with an arbitrary number of sending stations, each having its own destination. We show that the same models are valid representations of a star-shaped network with an arbitrary number of stations which send data to the same destination station. We also propose how to model such a network if some of the sending stations are not within radio range of the others, i.e. if they are hidden. We present some results obtained for these models by probabilistic model checking using PRISM.

Modelling Medium Access Control in IEEE 802.15.4 Nonbeacon-Enabled Networks with Probabilistic Timed Automata

This paper concerns the formal modelling of medium access control in nonbeacon-enabled IEEE 802.15.4 wireless personal area networks with probabilistic timed automata supported by the PRISM probabilistic model checker. In these networks, the devices contend for the medium by executing an unslotted carrier sense multiple access with collision avoidance algorithm. In the literature, a model of a network which consists of two stations sending data to two different destination stations is introduced. We have improved this model and, based on it, we propose two ways of modelling a network with an arbitrary number of sending stations, each having its own destination. We show that the same models are valid representations of a star-shaped network with an arbitrary number of stations which send data to the same destination station. We also propose how to model such a network if some of the sending stations are not within radio range of the others, i.e. if they are hidden. We present some results obtained for these models by probabilistic model checking using PRISM.

Solving Limited Memory Influence Diagrams

We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions and limited information. The algorithm is empirically shown to outperform a state-of-the-art algorithm on randomly generated problems of up to 150 variables and 10^64 solutions. We show that these problems are NP-hard even if the underlying graph structure of the problem has low treewidth and the variables take on a bounded number of states, and that they admit no provably good approximation if variables can take on an arbitrary number of states.

Multi-dimensional laser spectroscopy of exciton polaritons with spatial light modulators

We describe an experimental system that allows one to easily access the dispersion curve of exciton-polaritons in a microcavity. Our approach is based on two spatial light modulators, one for changing the excitation angles (momenta), and the other for tuning the excitation wavelength. We show that with this setup, an arbitrary number of states can be excited accurately and that re-configuration of the excitation scheme can be done at high speed.

Extensions and Improvements to the Chordal Graph Approach to the Multistate Perfect Phylogeny Problem

The multistate perfect phylogeny problem is a classic problem in computational biology. When no perfect phylogeny exists, it is of interest to find a set of characters to remove in order to obtain a perfect phylogeny in the remaining data. This is known as the character removal problem. We show how to use chordal graphs and triangulations to solve the character removal problem for an arbitrary number of states, which was previously unsolved. We outline a preprocessing technique that speeds up the computation of the minimal separators of a graph. Minimal separators are used in our solution to the missing data character removal problem and to Gusfield's solution of the perfect phylogeny problem with missing data.

Improved bounds for performability evaluation algorithms using state generation

We present improved techniques for bounding the expectation of a performance measure over a very large state space generated by a system of independent components, each of which has an arbitrary number of states (called “modes”), when the values of the measure are known only on a subset of the global state space. Our results apply to any algorithm that evaluates performability by state generation, and consist of bounds in closed form or proofs that certain bounds cannot be improved. We give two example applications of our results, one to a large communications network and the other to a small database system.

Estimating parameters of the synchronous twofold-stochastic flow of events

Consideration was given to estimation of the parameters of the synchronous twofold-stochastic flow of events which makes up a mathematical model of the information flow of demands circulating in the queuing systems and networks. Two variants were studied. For the first variant, the problem of optimal estimation of the parameters of a synchronous flow of events with a finite arbitrary number of states was solved. The second variant differs in that the event flow operates in the environment where part of events is lost during the so-called dead time. Consideration was given to a synchronous flow with two states. The problem of estimating the length of the dead time in the conditions of continued dead time was solved. The results of numerical estimation based on the simulation model of the synchronous flow were presented for both variants.