Universal finite memory machines for coding binary sequences

Artifacts and noise as well as outlier beats from physiological causes can lead to inaccurate estimates of heart rate and heart rate variability. Especially with the increased popularity of wearables, there is an increased need to be able to identify when motion artifacts and poor sensor contact lead to incorrect detection of heartbeats. In this paper, we propose a sequential probability assignment procedure to detect outlier heartbeats. The procedure uses a time-varying point process model that estimates a two-parameter exponential family distribution per time index. By allowing both parameters of the distribution to vary with time, this model has more flexibility than many previous models and is able to capture changes in both the mean and variance of the intervals. We formulate a maximum likelihood problem with a Kullback-Leibler regularizer at each time step. The usage of an exponential family parametrization makes the estimation at each time point a convex optimization problem, guaranteeing that the solution we find is optimal. We test three different distributions: inverse Gaussian, gamma, and log-normal. We find that the inverse Gaussian fits the distribution of interbeat intervals from clinical electrocardiogram data the best when evaluated using the Kolmogorov-Smirnov statistic. We then show in simulations as well as in clinical data the model's ability to successfully detect outliers.Clinical relevance-Identification of heartbeat timings can be difficult in noisy settings. In addition, ectopic beats and arrhythmic events can produce irregular timings. This outlier detection is one method to help identify timings that are statistically unlikely.

Simulation cloning is a technique in which cloned simulations whose state spaces differ partially from their parent simulation due to intervening events are spawned at runtime and concurrently advanced. It is a powerful method to carry out what-if analysis by speculatively exploring and evaluating the impact of various permutations of intervening cascade of events. Due to the exponential growth in the number of possible clones even for a small number of distinct intervening events, the practical efficacy of the approach is often severely limited by the maximum available memory of the computing host. In this paper, we introduce a novel speculative simulation cloning framework that executes a simulation cloning campaign capable of efficiently exploring an exponentially large space of clone simulations created by permutation of intervening events under a finite memory constraint. We provide a theoretical analysis of the runtime characteristics of our proposed approach and highlight its novel advantages such as memory-aware and as-long-as-needed execution. In support of our analytical findings and to demonstrate its practical feasibility, we implement a prototype of the cloning framework on a shared memory system and report its performance characteristics in the context of a heat diffusion simulation, and a power grid simulation subject to cascading disruptions from geomagnetic disturbances.

Multifractal signals are characterized by a local Holder exponent that may change completely from point to point. We show that wavelet methods are an extremely efficient tool for determining the exact Holder exponent of a function, or at least, for getting some information about this Holder exponent, such as the Spectrum of Singularities. We construct functions that have a given Holder exponent in a deterministic setting and also in a probabilistic setting (we then obtain the Multifractional Brownian Motion); we also study the Multifractal Formalism for Functions and give some results about its validity.

Summarizes some recent work in the field of universal data compression, both from a probabilistic and a deterministic point of view. In the probabilistic setting, the data x to be compressed is generated by a source from a certain class {P(x|/spl theta/),/spl theta//spl isin//spl Lambda/}. The capacity C of the channel from /spl theta/ to a is well known to be the minimum attainable redundancy of universal lossless codes w.r.t. this class, both in the minimax sense and in the Bayesian (maximin) sense. We show that C is essentially a lower bound also in a stronger sense, that is, for most sources in the class. This extends Rissanen's lower bound for parametric families. In the deterministic setting, an individual sequence is assumed without any statistical assumptions, and we seek a universal lossless encoder that is essentially no worse than the best encoder in a certain class of encoders, e.g., finite-state (FS) encoders, block encoders, etc. We characterize the the minimum attainable redundancy of universal coding w.r.t the best encoder in this class. For the class of FS encoders, we derive a bound that holds for most sequences in a certain sense, which is analogous to the classical probabilistic minimum description length (MDL) principle. The bound is attainable sequentially by a suitable arithmetic code, and therefore a deterministic significance of the predictive MDL concept is established. Finally, we extend this approach to lossy compression and obtain results in the same spirit for block-to-block and block-to-variable length codes.

A language is called (m,n)-verbose if there exists a Turing machine that enumerates for any n words at most m possibilities for their characteristic string. This notion is compared with (m,n)-fa-verboseness, where instead of a Turing machine a finite automaton is used. By use of a new diagonalisation method, where finite automata trick Turing machines, it is shown that all (m,n)-verbose languages are (h,k)-verbose iff all (m,n)-fa-verbose languages are (h,k)-fa-verbose. In other words, Turing machines and finite automata behave exactly the same way with respect to inclusion of verboseness classes. This identical behaviour implies that the nonspeedup theorem also holds for finite automata. As an application of the theoretical framework, a lower bound is derived on the number of bits that need to be communicated to finite automata protocol checkers for nonregular protocols.

Bounded rationality aims to understand the effects of how limited rationality affects decision-making. The traditional models in game theory and multiagent system research, such as finite automata or unrestricted Turing machine, fall short of capturing how intelligent agents make decision in realistic applications. To address this problem, we model bounded rational agents as restricted Turing machines: restrictions on running time and on storage space. We study our model under the context of two-person repeated games. In the case where the running time of Turing machines is restricted, we show that computing the best response of a given strategy is much harder than the strategy itself. In the case where the storage space of the Turing machines is restricted, we show the best response of a space restricted strategy can not be implemented by machines within the same size (up to a constant factor). Finally, we study how these restrictions affect the set of Nash equilibria in infinitely repeated games.We show restricting the agent’s computational resources will give rise to new Nash equilibria.

This article introduces the Doubly Stochastic Sequential Assignment Problem (DSSAP), an extension of the Sequential Stochastic Assignment Problem (SSAP), where sequentially arriving tasks are assigned to workers with random success rates. A given number of tasks arrive sequentially, each with a random value coming from a known distribution. On a task arrival, it must be assigned to one of the available workers, each with a random success rate coming from a known distribution. Optimal assignment policies are proposed for DSSAP under various assumptions on the random success rates. The optimal assignment algorithm for the general case of DSSAP, where workers have distinct success rate distribution, has an exponential running time. An approximation algorithm that achieves a fraction of the maximum total expected reward in a polynomial time is proposed. The results are illustrated by several numerical experiments. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 124–137, 2016

A sequential stochastic assignment problem in a stationary Markov chain, where the states are not known explicitly, is considered. This is an optimization problem in a partially observable Markov chain, and an optimal policy and the total expected reward under this policy are obtained. Here we specify the learning procedure by the Bayes' theorem, and the optimal policy is not always a critical number policy. As a special case of this problem, a problem of optimal selections is considered, and a relation to former results of a sequential stochastic assignment problem is observed.

In general, a nondeterministic automaton or machine (for example a finite automaton, pushdown automaton or Turing machine) is called unambiguous if each input is accepted by at most one run or computation. Each deterministic automaton is obviously unambiguous. However, in many settings, unambiguous automata are more expressive or admit more succinct automata than deterministic models, while preserving some good algorithmic properties. The aim of this talk is to survey some classical and some more recent results on unambiguous finite automata over different kind of input structures, namely finite words, infinite words, finite trees, and infinite trees.

Recently, related to the open problem of whether deterministic and nondeterministic space (especially lower-level) complexity classes are separated, the inkdot Turing machine was introduced. An inkdot machine is a conventional Turing machine capable of dropping an inkdot on a given input tape for a landmark, but not to pick it up nor further erase it. In this paper, we introduce a finite state version of the inkdot machine as a weak recognizer of the properties of digital pictures, rather than a Turing machine supplied with a one-dimensional working tape. We first investigate the sufficient spaces of three-way Turing machines to simulate two-dimensional inkdot finite automaton, as preliminary results. Next, we investigate the basic properties of two-dimensional inkdot automaton, i.e. the hierarchy based on the number of inkdots and the relationship of two-dimensional inkdot automata to other conventional two-dimensional automata. Finally, we investigate the recognizability of connected pictures of two-dimensional inkdot finite machines.

Reliability-based topology optimization of uncertain building systems subject to stochastic excitation

We determine the descriptional complexity (smallest number of states, up to constant factors) of recognizing languages {1^n} and {1^{t n} : t = 0, 1, 2, ...} with state-based finite machines of various kinds. This task is understood as counting to n and modulo n, respectively, and was previously studied for classes of finite-state automata by Kupferman, Ta-Shma, and Vardi (2001). We show that for Turing machines it requires log(n)/log(log(n)) states in the worst case, and individual values are related to Kolmogorov complexity of the binary encoding of n. For deterministic pushdown and counter automata, the complexity is log(n) and sqrt(n), respectively; for alternating counter automata, we show an upper bound of log(n). For visibly pushdown automata, i.e., if the stack movements are determined by input symbols, we consider languages {a^n b^n} and {a^{t n} b^{t n} : n t = 0, 1, 2, ...} and determine their complexity, of sqrt(n) and min(n_1 + n_2), respectively, with minimum over all factorizations n = n_1 n_2.

A greedy and distributable approach to the Lexicographic Bottleneck Assignment Problem with conditions on exactness

The sequential and stochastic assignment problem (SSAP) has wide applications in logistics, finance, and health care management, and has been well studied in the literature. It assumes that jobs with unknown values arrive according to a stochastic process. Upon arrival, a job's value is made known and the decision-maker must immediately decide whether to accept or reject the job and, if accepted, to assign it to a resource for a reward. The objective is to maximize the expected reward from the available resources. The optimal assignment policy has a threshold structure and can be computed in polynomial time. In reality, there exist situations in which the decision-maker may postpone the accept/reject decision. In this research, we study the value of postponing decisions by allowing a decision-maker to hold a number of jobs which may be accepted or rejected later. While maintaining this queue of arrivals significantly complicates the analysis, optimal threshold policies exist under mild assumptions when the resources are homogeneous. We illustrate the benefits of delaying decisions through higher profits and lower risk in both cases of homogeneous and heterogeneous resources.

Evaluating the capabilities of a satellite communication system (SCS) is challenging due to its complexity and ambiguity. It is difficult to accurately analyze uncertain situations, making it difficult for experts to determine appropriate evaluation values. To address this problem, this paper proposes an innovative approach by extending the Dempster-Shafer evidence theory (DST) to the probabilistic hesitant fuzzy evidence theory (PHFET). The proposed approach introduces the concept of probabilistic hesitant fuzzy basic probability assignment (PHFBPA) to measure the degree of support for propositions, along with a combination rule and decision approach. Two methods are developed to generate PHFBPA based on multi-classifier and distance techniques, respectively. In order to improve the consistency of evidence, discounting factors are proposed using an entropy measure and the Jousselme distance of PHFBPA. In addition, a model for evaluating the degree of satisfaction of SCS capability requirements based on PHFET is presented. Experimental classification and evaluation of SCS capability requirements are performed to demonstrate the effectiveness and stability of the PHFET method. By employing the DST framework and probabilistic hesitant fuzzy sets, PHFET provides a compelling solution for handling ambiguous data in multi-source information fusion, thereby improving the evaluation of SCS capabilities.