Finite-order universal portfolios generated by probability mass functions

2015 ◽  
Author(s):  
Choon Peng Tan ◽  
Sin Yen Chu ◽  
Wei Yeing Pan
Keyword(s):  
Finite Order ◽  
Universal Portfolios ◽  
Probability Mass ◽  
Mass Functions

scholarly journals Stochastic methods defeat regular RSA exponentiation algorithms with combined blinding methods

2021 ◽  
Vol 15 (1) ◽  
pp. 408-433
Author(s):  
Margaux Dugardin ◽  
Werner Schindler ◽  
Sylvain Guilley
Keyword(s):  
State Of The Art ◽  
Stochastic Methods ◽  
Rsa Algorithm ◽  
Montgomery Ladder ◽  
Channel Information ◽  
Probability Mass ◽  
The Cost ◽  
Noisy Measurements ◽  
Mass Functions ◽  
Larger Sample

Abstract Extra-reductions occurring in Montgomery multiplications disclose side-channel information which can be exploited even in stringent contexts. In this article, we derive stochastic attacks to defeat Rivest-Shamir-Adleman (RSA) with Montgomery ladder regular exponentiation coupled with base blinding. Namely, we leverage on precharacterized multivariate probability mass functions of extra-reductions between pairs of (multiplication, square) in one iteration of the RSA algorithm and that of the next one(s) to build a maximum likelihood distinguisher. The efficiency of our attack (in terms of required traces) is more than double compared to the state-of-the-art. In addition to this result, we also apply our method to the case of regular exponentiation, base blinding, and modulus blinding. Quite surprisingly, modulus blinding does not make our attack impossible, and so even for large sizes of the modulus randomizing element. At the cost of larger sample sizes our attacks tolerate noisy measurements. Fortunately, effective countermeasures exist.

scholarly journals Scholarly Book Review on Bayesian Statistics for Beginners: A Step-by-Step Approach

2020 ◽  
pp. 1-4
Author(s):  
Eahsan Shahriary ◽  
Amir Hajibabaee
Keyword(s):  
Bayesian Statistics ◽  
Open Source Software ◽  
Probability Density Functions ◽  
Bayesian Probability ◽  
Density Functions ◽  
Scholarly Book ◽  
Real World Applications ◽  
Probability Mass ◽  
Mass Functions

This book offers the students and researchers a unique introduction to Bayesian statistics. Authors provide a wonderful journey in the realm of Bayesian Probability and aspire readers to become Bayesian statisticians. The book starts with Introduction to Probability and covers Bayes’ Theorem, Probability Mass Functions, Probability Density Functions, The Beta-Binomial Conjugate, Markov chain Monte Carlo (MCMC), and Metropolis-Hastings Algorithm. The book is very well written, and topics are very to the point with real-world applications but does not provide examples for computing using common open-source software.

scholarly journals Two Useful Discrete Distributions to Model Overdispersed Count Data

2020 ◽  
Vol 43 (1) ◽  
pp. 21-48
Author(s):  
Josmar Mazucheli ◽  
Wesley Bertoli ◽  
Ricardo Puziol Oliveira
Keyword(s):  
Infinite Series ◽  
Count Data ◽  
Survival Function ◽  
Continuous Distribution ◽  
Discrete Distributions ◽  
Mathematical Expressions ◽  
Probability Mass ◽  
The Difference ◽  
Discrete Analogues ◽  
Mass Functions

The methods to obtain discrete analogues of continuous distributions have been widely considered in recent years. In general, the discretization process provides probability mass functions that can be competitive with the traditional model used in the analysis of count data, the Poisson distribution. The discretization procedure also avoids the use of continuous distribution in the analysis of strictly discrete data. In this paper, we seek to introduce two discrete analogues for the Shanker distribution using the method of the infinite series and the method based on the survival function as alternatives to model overdispersed datasets. Despite the difference between discretization methods, the resulting distributions are interchangeable. However, the distribution generated by the method of infinite series method has simpler mathematical expressions for the shape, the generating functions and the central moments. The maximum likelihood theory is considered for estimation and asymptotic inference concerns. A simulation study is carried out in order to evaluate some frequentist properties of the developed methodology. The usefulness of the proposed models is evaluated using real datasets provided by the literature.

Probability Mass Functions for Years to Final Separation from the Labor Force Induced by the Markov Model

2003 ◽  
Vol 16 (1) ◽  
pp. 51-86 ◽  
Author(s):  
Gary R. Skoog ◽  
James E. Ciecka
Keyword(s):  
Markov Model ◽  
Labor Force ◽  
Probability Mass ◽  
Mass Functions

Abstract No abstract available.

Joint distributions of successes, failures and patterns in enumeration problems

2000 ◽  
Vol 32 (3) ◽  
pp. 866-884 ◽  
Author(s):  
S Chadjiconstantinidis ◽  
D. L. Antzoulakos ◽  
M. V. Koutras
Keyword(s):  
Joint Distribution ◽  
Joint Probability ◽  
Fixed Number ◽  
Composite Pattern ◽  
Joint Distributions ◽  
Special Cases ◽  
Enumeration Problems ◽  
Binomial Type ◽  
Probability Mass ◽  
Mass Functions

Let ε be a (single or composite) pattern defined over a sequence of Bernoulli trials. This article presents a unified approach for the study of the joint distribution of the number Sn of successes (and Fn of failures) and the number Xn of occurrences of ε in a fixed number of trials as well as the joint distribution of the waiting time Tr till the rth occurrence of the pattern and the number STr of successes (and FTr of failures) observed at that time. General formulae are developed for the joint probability mass functions and generating functions of (Xn,Sn), (Tr,STr) (and (Xn,Sn,Fn),(Tr,STr,FTr)) when Xn belongs to the family of Markov chain imbeddable variables of binomial type. Specializing to certain success runs, scans and pattern problems several well-known results are delivered as special cases of the general theory along with some new results that have not appeared in the statistical literature before.

scholarly journals Urn models for regulated gene expression yield physically intuitive solutions for probability distributions of single-cell counts

2020 ◽  
Author(s):  
Krishna Choudhary ◽  
Atul Narang
Keyword(s):  
Gene Expression ◽  
Gene Regulation ◽  
Single Cell ◽  
Hypergeometric Functions ◽  
Probability Distributions ◽  
Time Intervals ◽  
Probability Mass ◽  
Regulated Gene Expression ◽  
Short Time ◽  
Mass Functions

AbstractFitting the probability mass functions from analytical solutions of stochastic models of gene expression to the count distributions of mRNA and protein molecules in single cells can yield valuable insights into mechanisms of gene regulation. Solutions of chemical master equations are available for various kinetic schemes but, even for the models of regulation with a basic ON-OFF switch, they take complex forms with generating functions given as hypergeometric functions. Gene expression studies that have used these to fit the data have interpreted the parameters as burst size and frequency. However, this is consistent with the hypergeometric functions only if a gene stays active for short time intervals separated by relatively long intervals of inactivity. Physical insights into the probability mass functions are essential to ensure proper interpretations but are lacking for models of gene regulation. We fill this gap by developing urn models for regulated gene expression, which are of immense value to interpret probability distributions. Our model consists of a master urn, which represents the cytosol. We sample RNA polymerases and ribosomes from it and assign them to recipient urns of two or more colors, which represent time intervals with a homogeneous propensity for gene expression. Colors of the recipient urns represent sub-systems of the promoter states, and the assignments to urns of a specific color represent gene expression. We use elementary principles of discrete probability theory to derive the solutions for a range of kinetic models, including the Peccoud-Ycart model, the Shahrezaei-Swain model, and models with an arbitrary number of promoter states. For activated genes, we show that transcriptional lapses, which are events of gene inactivation for short time intervals separated by long active intervals, quantify the transcriptional dynamics better than bursts. Our approach reveals the physics underlying the solutions, which has important implications for single-cell data analysis.

A Novelty in Blahut-Arimoto T ype Algorithms: Optimal Control over Noisy Commu nication Channels

2020 ◽  
Author(s):  
Makan Zamanipour
Keyword(s):  
Optimal Control ◽  
Channel Coding ◽  
Joint Source Channel Coding ◽  
Mathematical Expressions ◽  
Type Algorithm ◽  
Theoretic Problem ◽  
Probability Mass ◽  
Information Constraints ◽  
First Time ◽  
Mass Functions

A probability-theoretic problem under information constraints for the concept of optimal control over a noisy-memoryless channel is considered. For our \textit{Observer-Controller} block, i.e., the lossy joint-source-channel-coding (JSCC) scheme, after providing the relative mathematical expressions, we propose a \textit{Blahut-Arimoto}-type algorithm $-$ which is, to the best of our knowledge, for the first time. The algorithm efficiently finds the probability-mass-functions (PMFs) required for .......................................

Two Approaches for Workflow Scheduling with Quality of Service in the Grid

2012 ◽  
pp. 1265-1288
Author(s):  
Fangpeng Dong ◽  
Selim G. Akl
Keyword(s):  
Resource Sharing ◽  
Completion Time ◽  
Scheduling Algorithm ◽  
Workflow Scheduling ◽  
Performance Change ◽  
Probability Mass ◽  
Grid Resources ◽  
Mass Functions ◽  
Algorithm Level

Over the past decade, Grid Computing has earned its reputation by facilitating resource sharing in larger communities and providing non-trivial services. However, for Grid users, Grid resources are not usually dedicated, which results in fluctuations of available performance. This situation raises concerns about the quality of services (QoS). The meaning of QoS varies with different concerns of different users. Objective functions that drive job schedulers in the Grid may be different from each other as well. Some are system-oriented, which means they make schedules to favor system metrics such as throughput, load-balance, resource revenue and so on. To narrow the scope of the problem to be discussed in this chapter and to make the discussion substantial, the scheduling objective function considered is minimizing the total completion time of all tasks in a workflow (also known as the makespan). Correspondingly, the meaning of QoS is restricted to the ability that scheduling algorithms can shorten the makespan of a workflow in an environment where resource performance is vibrant. This chapter introduces two approaches that can provide QoS features at the workflow scheduling algorithm level in the Grid. One approach is based on a workflow rescheduling technique, which can reallocate resources for tasks when a resource performance change is observed. The other copes with the stochastic performance change using pre-acquired probability mass functions (PMF) and produces a probability distribution of the final schedule length, which will then be used to handle the different QoS concerns of the users.

Basic probability theory

2019 ◽  
pp. 121-140
Author(s):  
Thomas P. Trappenberg
Keyword(s):  
Machine Learning ◽  
Probability Theory ◽  
Random Numbers ◽  
Density Functions ◽  
Approximation Techniques ◽  
Basic Probability ◽  
Probability Mass ◽  
Learning Probability ◽  
Mass Functions ◽  
Modern Machine

The discussion provides a refresher of probability theory, in particular with respect to the formulations that build the theoretical language of modern machine learning. Probability theory is the formalism of random numbers, and this chapter outlines what these are and how they are characterized by probability density or probability mass functions. How such functions have traditionally been characterized is covered, and a review of how to work with such mathematical objects such as transforming density functions and how to measure differences between density function is presented. Definitions and basic operations with multiple random variables, including the Bayes law, are covered. The chapter ends with an outline of some important approximation techniques of so-called Monte Carlo methods.

Probability and random variables

2019 ◽  
pp. 38-59
Author(s):  
M. D. Edge
Keyword(s):  
Probability Density ◽  
Random Variables ◽  
Bayes Theorem ◽  
Probability Density Functions ◽  
Density Functions ◽  
Conditional Probabilities ◽  
Discrete Random Variables ◽  
New Information ◽  
Probability Mass ◽  
Mass Functions

This chapter considers the rules of probability. Probabilities are non-negative, they sum to one, and the probability that either of two mutually exclusive events occurs is the sum of the probability of the two events. Two events are said to be independent if the probability that they both occur is the product of the probabilities that each event occurs. Bayes’ theorem is used to update probabilities on the basis of new information, and it is shown that the conditional probabilities P(A|B) and P(B|A) are not the same. Finally, the chapter discusses ways in which distributions of random variables can be described, using probability mass functions for discrete random variables and probability density functions for continuous random variables.

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