Technical Note: Parameterised-Response Zero-Intelligence (PRZI) Traders

Previously, dynamic-assignment Blahut-Arimoto (DAB) was used to find capacity-achieving probability mass functions (PMFs) for binomial channels and molecular channels. As it turns out, DAB can efficiently identify capacity-achieving PMFs for a wide variety of channels. This paper applies DAB to power-constrained (PC) additive white Gaussian Noise (AWGN) Channels and amplitude-constrained (AC) AWGN Channels.This paper modifies DAB to include a power constraint and finds low-cardinality PMFs that approach capacity on PC-AWGN Channels. While a continuous Gaussian PDF is well-known to be capacity-achieving on the PC-AWGN channel, DAB identifies low-cardinality PMFs within 0.01 bits of the mutual information provided by a Gaussian PDF. Recall the results of Ozarow and Wyner requiring a constellation cardinality of ⌈2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C+1</sup> ⌉ to approach capacity C to within the asymptotic shaping loss of 1.53 dB at high SNR. PMF’s found by DAB approach capacity with essentially no shaping loss with cardinality less than 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C+1.2</sup> . As expected, DAB’s numerical approach identifies PMFs with better mutual information vs. SNR performance than the analytical approaches to finite-support constellations examined by Wu and Verdu.This paper also uses DAB to find capacity-achieving PMFs with small cardinality support sets for AC-AWGN Channels. The resulting evolution of capacity-achieving PMFs as a function of SNR is consistent with the approximate cardinality transition points of Sharma and Shamai.

Provides a game theoretical perspective on the problem of international pollution control. Presents background for those unfamiliar with game theory. Explores how cooperation can be established between countries to fight international pollution, analyzing static games with discrete strategy space; finite dynamic games with discrete strategy space; infinite dynamic games with discrete strategy space; whether, and under what conditions, the linkage of two or more issues may be conducive to cooperation; a simple static global emission game with continuous strategy space; finite dynamic games with continuous strategy space and static representations of dynamic games; bargaining over a uniform emission reduction quota and a uniform emission tax; the global emission game in the context of an infinite time horizon; and the coalition formation process in an N-country world.

Recent advances in random access (RA) have highlighted the performance improvement yield by the joint use of proactive replication of packets and successive interference cancellation (SIC). Users send multiple replicas and collisions are resolved via iterative cancellation of the interference. The optimal choice for the number of replicas is drawn from a properly designed probability mass function (PMF). Selfish uncoordinated users are prone to choose the maximum number of replicas and diverge from the designed PMF. Exploiting game theoretic tools, we describe such scenario as a noncooperative game. Properly setting the cost per replica transmission, we are able to drive the Nash equilibrium to the designed PMF and thus hinder the users to diverge. Numerical results complement the study, showing the practical impact of the proposed solution.

Random number generators (RNG) are essential elements in many cryptographic systems. True random number generators (TRNG) rely upon sources of randomness from natural processes such as those arising from quantum mechanics phenomena. We demonstrate that a quantum computer can serve as a high-quality, weakly random source for a generalized user-defined probability mass function (PMF). Specifically, QC measurement implements the process of variate sampling according to a user-specified PMF resulting in a word comprised of electronic bits that can then be processed by an extractor function to address inaccuracies due to non-ideal quantum gate operations and other system biases. We introduce an automated and flexible method for implementing a TRNG as a programmed quantum circuit that executes on commercially-available, gate-model quantum computers. The user specifies the desired word size as the number of qubits and a definition of the desired PMF. Based upon the user specification of the PMF, our compilation tool automatically synthesizes the desired TRNG as a structural OpenQASM file containing native gate operations that are optimized to reduce the circuit's quantum depth. The resulting TRNG provides multiple bits of randomness for each execution/measurement cycle; thus, the number of random bits produced in each execution is limited only by the size of the QC. We provide experimental results to illustrate the viability of this approach.

This paper presents a novel video-based face recognition algorithm by using a sequential sampling and updating scheme, named sequential sample consensus. The proposed algorithm aims at providing a sequential scheme that can be applied to streaming video data. Different from existing approaches, the training video sequences serve as the sample space, and the person’s identity in the testing sequence is characterized using an identity probability mass function (PMF) that is sequentially updated. For each testing frame, samples are randomly drawn from the sample space, and the numbers of samples for each identity are determined by the identity PMF. The testing frame is evaluated against the drawn samples to calculate the weights, and the sample weights are used for updating the identity PMF. Benefiting from the sampling procedure, the change in both the numbers and the weights of the samples for each individual leads to quick reaction of the algorithm. The proposed algorithm is robust against misclassification caused by pose variations, and sensitive to identity switching during recognition. The algorithm is evaluated using both public and self-made datasets, and shows better performance than other video-based face recognition approaches.

Let $\mathcal{P}_{n}$ be the set of all probability mass functions (PMFs) $(p_{1},p_{2}, \ldots, p_{n})$ that satisfy $p_{i} > 0$ for $1\leq i\leq n$ . Define the minimum expected length function $\mathcal{L}_{D}:\mathcal{P}_{n}\rightarrow \mathbb{R}$ such that $\mathcal{L}_{D}(P)$ is the minimum expected length of a prefix code, formed out of an alphabet of size D, for the discrete memoryless source having $P$ as its source distribution. It is well-known that the function $\mathcal{L}_{D}$ attains its maximum value at the uniform distribution. Further, when $n$ is of the form $D^{m}$ , with $m$ being a positive integer, PMFs other than the uniform distribution at which $\mathcal{L}_{D}$ attains its maximum value are known. However, a complete characterization of all such PMFs at which the minimum expected length function attains its maximum value has not been done so far. This is done in this paper.

The conflation of a finite number of probability distributions P 1 , … , P n P_1,\dots , P_n is a consolidation of those distributions into a single probability distribution Q = Q ( P 1 , … , P n ) Q=Q(P_1,\dots , P_n) , where intuitively Q Q is the conditional distribution of independent random variables X 1 , … , X n X_1,\dots , X_n with distributions P 1 , … , P n P_1,\dots , P_n , respectively, given that X 1 = ⋯ = X n X_1=\cdots =X_n . Thus, in large classes of distributions the conflation is the distribution determined by the normalized product of the probability density or probability mass functions. Q Q is shown to be the unique probability distribution that minimizes the loss of Shannon information in consolidating the combined information from P 1 , … , P n P_1,\dots , P_n into a single distribution Q Q , and also to be the optimal consolidation of the distributions with respect to two minimax likelihood-ratio criteria. In that sense, conflation may be viewed as an optimal method for combining the results from several different independent experiments. When P 1 , … , P n P_1,\dots , P_n are Gaussian, Q Q is Gaussian with mean the classical weighted-mean-squares reciprocal of variances. A version of the classical convolution theorem holds for conflations of a large class of a.c. measures.

This work proposes a decision-theoretic approach to problems involving interaction between robot systems and human users, with the goal of estimating the human state from observations of its behavior, and taking actions that encourage desired behaviors. The approach is based on the Partially Observable Markov Decision Process (POMDP) framework, which determines an optimal policy (mapping beliefs onto actions) in the presence of uncertainty on the effects of actions and state observations, extended with information rewards (POMDP-IR) to optimize the information-gathering capabilities of the system. The POMDP observations consist of human gestures and spoken sentences, while the actions are split into robot behaviors (such as speaking to the human) and information-reward actions to gain more information about the human state. Under the proposed framework, the robot system is able to actively gain information and react to its belief on the state of the human (expressed as a probability mass function over the discrete state space), effectively encouraging the human to improve his/her behavior, in a socially acceptable manner. Results of applying the method to a real scenario of interaction between a robot and humans are presented, supporting its practical use.

In this paper the Type II Non-central Polya-Aeppli distribution is introduced. It is a sum of two independent variables, one that is an Inflated-parameter binomial distributed and another one, a Polya-Aeppli distributed. The probability mass function, moments, recursion formulas and some properties of the defined distribution are derived.In this paper the Type II Non-central Polya-Aeppli distribution is introduced. It is a sum of two independent variables, one that is an Inflated-parameter binomial distributed and another one, a Polya-Aeppli distributed. The probability mass function, moments, recursion formulas and some properties of the defined distribution are derived.

Probability mass functions forecasting of occupants’ sensation votes under the effects of temperature, illuminance, and sound level based on ANN

A method is presented for analyzing flow through a porous medium whose parameters are random functions. Such a medium is conceptualized as an ensemble of media with an associated probability mass function. The flow problem in each member of this ensemble is deterministic in the usual sense. All the solutions belong to a particular Hilbert space, and hence they can be written in terms of linear combinations of its basis functions. This is similar to the Galerkin formulation except that the coefficients in the linear combination are no longer deterministic quantities but random functions. The finite element method in conjunction with a Taylor series expansion is used to get the first two moments of the solution approximately. The method does not require specification of full probability mass functions of the parameters but only their first two moments, and spatial correlations can be easily accounted for. However, it is assumed that the probability mass functions are peaked at the expected value and are smooth in its vicinity. A sample problem is solved to illustrate the procedure. It is observed that the result is sensitive to the element size in the numerical scheme and the variances and spatial correlations of parameters. The expected value of the hydraulic head is found to differ significantly from the results that would have been obtained if the problem had been solved deterministically.

ABSTRACTThe main contribution of this paper is a new definition of expected value of belief functions in the Dempster–Shafer (D–S) theory of evidence. Our definition shares many of the properties of the expectation operator in probability theory. Also, for Bayesian belief functions, our definition provides the same expected value as the probabilistic expectation operator. A traditional method of computing expected of real-valued functions is to first transform a D–S belief function to a corresponding probability mass function, and then use the expectation operator for probability mass functions. Transforming a belief function to a probability function involves loss of information. Our expectation operator works directly with D–S belief functions. Another definition is using Choquet integration, which assumes belief functions are credal sets, i.e. convex sets of probability mass functions. Credal sets semantics are incompatible with Dempster's combination rule, the center-piece of the D–S theory. In general, our definition provides different expected values than, e.g. if we use probabilistic expectation using the pignistic transform or the plausibility transform of a belief function. Using our definition of expectation, we provide new definitions of variance, covariance, correlation, and other higher moments and describe their properties.

In this paper, we introduce a new probability mass function by discretizing the continuous failure model of the generalized odd Lindley–Weibull distribution, which is called the discrete generalized odd Lindley–Weibull (DGOL-W) distribution. This new probability mass function is characterized by a very flexible probability function: reverse J-shape, right-skewed shape, left-skewed shape, and close to symmetric shape. The proposed distribution has five special models, i.e., the discrete generalized odd Lindley-exponential, discrete generalized odd Lindley–Rayleigh, discrete odd Lindley–Weibull, discrete odd Lindley-exponential, and discrete odd Lindley–Rayleigh distributions. Some properties of the proposed distribution are introduced. The maximum likelihood estimation is used to estimate the unknown parameters of the DGOL-W distribution. Applications are illustrated, which show that the model is suited for use in various data sets, i.e., the mean and variance of the count data are equal, over-dispersion count data, and under-dispersion count data. Based on the results, we have shown that the DGOL-W distribution provides a better fit compared to the Poisson, discrete Lindley and four sub-models of DGOL-W distribution for count data.

Design of delay timers based on estimated probability mass functions of alarm durations

The objective of item difficulty modeling (IDM) is to predict the statistical parameters of an item (e.g., difficulty) based on features extracted directly from the item (e.g., number of words). This paper utilizes neural networks (NNs) to predict a discrete item characteristic curve (ICC). The presented approach exploits one-to-one mapping from monotonically non-decreasing discrete ICCs to probability mass functions (PMFs). An NN was trained using soft labels for each item (by mapping ICCs to PMFs), with a softmax output layer representing PMF and the Kullback-Leibler divergence representing a loss function. Results of a cross-validation of the NN on 1742 retired logical reasoning items from the Law School Admission Test are presented and discussed.KeywordsItem difficulty modelingItem response modelingItem characteristic curveNeural networksMachine learningNatural language processingSemantic similarity