scholarly journals Infinite Choice and Probability Distributions. An Open Problem: The Real Hotel

2021 ◽  
Vol 339 ◽  
pp. 2-8
Author(s):  
Jan Friso Groote
Keyword(s):  
Open Problem ◽  
Probability Distributions ◽  
The Real

Computer Aided Tolerance Analysis of Parts and Assemblies

1989 ◽  
Author(s):  
R. T. Scott ◽  
G. A. Gabriele
Keyword(s):  
Real World ◽  
Probability Distributions ◽  
Three Dimensional ◽  
Tolerance Analysis ◽  
The Real ◽  
Assembly Tolerance ◽  
Computer Aided ◽  
Probability Information ◽  
Exact Constraint

Abstract An exact constraint scheme based on the physical contacting constraints of real part mating features is used to represent the process of assembling the parts. To provide useful probability information about how assembly dimensions are distributed when the parts are assembled as intended, the real world constraints that would prevent interference are ignored. This work addresses some limitations in the area of three dimensional assembly tolerance analysis. As a result of this work, the following were demonstrated: 1. Assembly of parts whose assembly mating features are subjected to variation; 2. Assemble parts using a real world set of exact constraints; 3. Provide probability distributions of assembly dimensions.

Uniform conditional variability ordering of probability distributions

1985 ◽  
Vol 22 (03) ◽  
pp. 619-633 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Probability Distribution ◽  
Real Line ◽  
Convex Functions ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Queueing Network ◽  
Network Models ◽  
Scalar Multiplication ◽  
Closed Queueing Network ◽  
The Real

Variability orderings indicate that one probability distribution is more spread out or dispersed than another. Here variability orderings are considered that are preserved under conditioning on a common subset. One density f on the real line is said to be less than or equal to another, g, in uniform conditional variability order (UCVO) if the ratio f(x)/g(x) is unimodal with the model yielding a supremum, but f and g are not stochastically ordered. Since the unimodality is preserved under scalar multiplication, the associated conditional densities are ordered either by UCVO or by ordinary stochastic order. If f and g have equal means, then UCVO implies the standard variability ordering determined by the expectation of all convex functions. The UCVO property often can be easily checked by seeing if f(x)/g(x) is log-concave. This is illustrated in a comparison of open and closed queueing network models.

A case study in authorship attribution: The Mondrigo1

2021 ◽  
pp. 1-8
Author(s):  
Gerardo Sierra ◽  
Tonatiuh Hernández-García ◽  
Helena Gómez-Adorno ◽  
Gemma Bel-Enguix
Keyword(s):  
Unsupervised Learning ◽  
Open Problem ◽  
Authorship Attribution ◽  
The Real ◽  
Supervised And Unsupervised Learning ◽  
Single Author ◽  
Svm Algorithm ◽  
Mexican Government

In this paper, we present authorship attribution methods applied to ¡El Mondrigo! (1968), a controversial text supposedly created by order of the Mexican Government to defame a student strike. Up to now, although the authorship of the book has been attributed to several journalists and writers, it could not be demonstrated and remains an open problem. The work aims at establishing which one of the most commonly attributed writers is the real author. To do that, we implement methods based on stylometric features using textual distance, supervised, and unsupervised learning. The distance-based methods implemented in this work are Kilgarriff and Delta of Burrows, an SVM algorithm is used as the supervised method, and the k-means algorithm as the unsupervised algorithm. The applied methods were consistent by pointing out a single author as the most likely one.

Density of Real Zeros of the Tutte Polynomial

2018 ◽  
Vol 27 (3) ◽  
pp. 398-410
Author(s):  
SEONGMIN OK ◽  
THOMAS J. PERRETT
Keyword(s):  
Open Problem ◽  
Dense Subset ◽  
Tutte Polynomial ◽  
The Real ◽  
Real Zeros ◽  
Density Result ◽  
Positive Volume ◽  
Tutte Polynomials

The Tutte polynomial of a graph is a two-variable polynomial whose zeros and evaluations encode many interesting properties of the graph. In this article we investigate the real zeros of the Tutte polynomials of graphs, and show that they form a dense subset of certain regions of the plane. This is the first density result for the real zeros of the Tutte polynomial in a region of positive volume. Our result almost confirms a conjecture of Jackson and Sokal except for one region which is related to an open problem on flow polynomials.

A Poincaré limit theorem for wrapped probability distributions on compact symmetric spaces

1984 ◽  
Vol 95 (2) ◽  
pp. 329-334
Author(s):  
P. E. Jupp
Keyword(s):  
Limit Theorem ◽  
Uniform Distribution ◽  
Real Line ◽  
Symmetric Spaces ◽  
Probability Distributions ◽  
The Real ◽  
Compact Symmetric Spaces

In an article on the philosophy of chance, Poincaré[7] showed that the distribution of the stopping position of a needle pivoted about its centre tends to the uniform distribution on the circle as the distribution of the initial push becomes spread out along the real line. This result was formalized by Feller [2] and strengthened by Mardia [6] as follows.

scholarly journals Contracting and Involutive Negations of Probability Distributions

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2389
Author(s):  
Ildar Z. Batyrshin
Keyword(s):  
Fuzzy Logic ◽  
Uniform Distribution ◽  
Open Problem ◽  
Probability Distributions ◽  
Maximal Entropy ◽  
Involutive Negation

A dozen papers have considered the concept of negation of probability distributions (pd) introduced by Yager. Usually, such negations are generated point-by-point by functions defined on a set of probability values and called here negators. Recently the class of pd-independent linear negators has been introduced and characterized using Yager’s negator. The open problem was how to introduce involutive negators generating involutive negations of pd. To solve this problem, we extend the concepts of contracting and involutive negations studied in fuzzy logic on probability distributions. First, we prove that the sequence of multiple negations of pd generated by a linear negator converges to the uniform distribution with maximal entropy. Then, we show that any pd-independent negator is non-involutive, and any non-trivial linear negator is strictly contracting. Finally, we introduce an involutive negator in the class of pd-dependent negators. It generates an involutive negation of probability distributions.

scholarly journals Generalization of the Harmonic Weighted Mean Via Pythagorean Invariance Identity and Application

2020 ◽  
Vol 34 (1) ◽  
pp. 104-122
Author(s):  
Peter Kahlig ◽  
Janusz Matkowski
Keyword(s):  
Open Problem ◽  
Functional Equations ◽  
Harmonic Mean ◽  
Weighted Mean ◽  
Geometric Means ◽  
The Real ◽  
Weighted Arithmetic ◽  
Real Functions ◽  
Pythagorean Harmony

AbstractUnder some simple conditions on the real functions f and g defined on an interval I ⊂ (0, ∞), the two-place functions Af (x, y) = f (x) + y − f (y) and {G_g}\left({x,y} \right) = {{g\left(x \right)} \over {g\left(y \right)}}y generalize, respectively, A and G, the classical weighted arithmetic and geometric means. In this note, basing on the invariance identity G ∘ (H, A) = G (equivalent to the Pythagorean harmony proportion), a suitable weighted extension Hf,g of the classical harmonic mean H is introduced. An open problem concerning the symmetry of Hf,g is proposed. As an application a method of effective solving of some functional equations involving means is presented.

Uniform conditional variability ordering of probability distributions

1985 ◽  
Vol 22 (3) ◽  
pp. 619-633 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Probability Distribution ◽  
Real Line ◽  
Convex Functions ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Queueing Network ◽  
Network Models ◽  
Scalar Multiplication ◽  
Closed Queueing Network ◽  
The Real

Variability orderings indicate that one probability distribution is more spread out or dispersed than another. Here variability orderings are considered that are preserved under conditioning on a common subset. One density f on the real line is said to be less than or equal to another, g, in uniform conditional variability order (UCVO) if the ratio f(x)/g(x) is unimodal with the model yielding a supremum, but f and g are not stochastically ordered. Since the unimodality is preserved under scalar multiplication, the associated conditional densities are ordered either by UCVO or by ordinary stochastic order. If f and g have equal means, then UCVO implies the standard variability ordering determined by the expectation of all convex functions. The UCVO property often can be easily checked by seeing if f(x)/g(x) is log-concave. This is illustrated in a comparison of open and closed queueing network models.

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