scholarly journals Contextuality Analysis of Impossible Figures

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 981
Author(s):  
Víctor H. Cervantes ◽  
Ehtibar N. Dzhafarov
Keyword(s):  
Random Variables ◽  
Physical Object ◽  
The Other ◽  
Deterministic Systems ◽  
Random Variability ◽  
Impossible Figures ◽  
Lack Of Knowledge

This paper has two purposes. One is to demonstrate contextuality analysis of systems of epistemic random variables. The other is to evaluate the performance of a new, hierarchical version of the measure of (non)contextuality introduced in earlier publications. As objects of analysis we use impossible figures of the kind created by the Penroses and Escher. We make no assumptions as to how an impossible figure is perceived, taking it instead as a fixed physical object allowing one of several deterministic descriptions. Systems of epistemic random variables are obtained by probabilistically mixing these deterministic systems. This probabilistic mixture reflects our uncertainty or lack of knowledge rather than random variability in the frequentist sense.

Probability Spaces and the Theory of Error of Measurement

1971 ◽  
Vol 28 (1) ◽  
pp. 291-301 ◽  
Author(s):  
Donald W. Zimmerman
Keyword(s):  
Probability Model ◽  
Random Variables ◽  
Measurement Procedure ◽  
Psychological Tests ◽  
Random Variability ◽  
Probability Spaces ◽  
True Values ◽  
Suitable Product ◽  
Error Of Measurement

A model of variability in measurement, which is sufficiently general for a variety of applications and which includes the main content of traditional theories of error of measurement and psychological tests, can be derived from the axioms of probability, without introducing “true values” and “errors.” Beginning with probability spaces (Ω, P1) and (φ, P2), the set Ω representing the outcomes of a measurement procedure and the set * representing individuals or experimental objects, it is possible to construct suitable product probability spaces and collections of random variables which can yield all results needed to describe random variability and reliability. This paper attempts to fill gaps in the mathematical derivations in many classical theories and at the same time to overcome limitations in the language of “true values” and “errors” by presenting explicitly the essential constructions required for a general probability model.

scholarly journals On a characterization theorem on a-adic solenoids

2019 ◽  
Vol 489 (3) ◽  
pp. 227-231
Author(s):  
G. M. Feldman
Keyword(s):  
Gaussian Distribution ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
The Other ◽  
Independent Random Variables ◽  
Linear Forms ◽  
The Real

According to the Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given the other. We prove an analogue of this theorem for linear forms of two independent random variables taking values in an -adic solenoid containing no elements of order 2. Coefficients of the linear forms are topological automorphisms of the -adic solenoid.

Analysis of the M x/G/1 queue by N-policy and multiple vacations

1994 ◽  
Vol 31 (02) ◽  
pp. 476-496
Author(s):  
Ho Woo Lee ◽  
Soon Seok Lee ◽  
Jeong Ok Park ◽  
K. C. Chae
Keyword(s):  
Performance Measures ◽  
Queue Length ◽  
Time Distribution ◽  
Queueing System ◽  
Random Variables ◽  
System Size ◽  
The Other ◽  
Waiting Time Distribution ◽  
Multiple Vacations ◽  
Linear Cost

We consider an Mx /G/1 queueing system with N-policy and multiple vacations. As soon as the system empties, the server leaves for a vacation of random length V. When he returns, if the queue length is greater than or equal to a predetermined value N(threshold), the server immediately begins to serve the customers. If he finds less than N customers, he leaves for another vacation and so on until he finally finds at least N customers. We obtain the system size distribution and show that the system size decomposes into three random variables one of which is the system size of ordinary Mx /G/1 queue. The interpretation of the other random variables will be provided. We also derive the queue waiting time distribution and other performance measures. Finally we derive a condition under which the optimal stationary operating policy is achieved under a linear cost structure.

A characterization of the negative exponential distribution with application to reliability theory

1981 ◽  
Vol 18 (3) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

Wondering about John Clare

2020 ◽  
pp. 74-89
Author(s):  
Erica McAlpine
Keyword(s):  
The Other ◽  
Or Education ◽  
John Clare ◽  
The One ◽  
Lack Of Knowledge

This chapter focuses on a word used wrongly by a poet who often took pride in his own wrongness. Unlike Browning and Wordsworth, John Clare paid little attention to details like spelling and punctuation: he depended on editors for clean copy. So what should readers make of his writing “wander” with an “o” in one poem and an “a” in another? Or of his invoking both meanings—wondering and wandering—in a single poem, but spelling them the same? Resisting the urge to gloss over this mistake, either by shrugging it off as a careless misspelling or by treating the words as yoked, the chapter disentangles the idea of mistake from carelessness on the one hand and lack of knowledge or education on the other. It calls for the possibility of blundering even amid competing editorial concerns over what constitutes a draft and when to edit for consistency, suggesting that readers have much to gain by distinguishing Clare's feigned errors from his unwilling mistakes.

scholarly journals On strict sub-Gaussianity, optimal proxy variance and symmetry for bounded random variables

2020 ◽  
Vol 24 ◽  
pp. 39-55
Author(s):  
Julyan Arbel ◽  
Olivier Marchal ◽  
Hien D. Nguyen
Keyword(s):  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Random Variables ◽  
The Other ◽  
Bounded Support ◽  
Uniform Distributions ◽  
Standard Variance ◽  
Per Se ◽  
The One ◽  
The Relationship

We investigate the sub-Gaussian property for almost surely bounded random variables. If sub-Gaussianity per se is de facto ensured by the bounded support of said random variables, then exciting research avenues remain open. Among these questions is how to characterize the optimal sub-Gaussian proxy variance? Another question is how to characterize strict sub-Gaussianity, defined by a proxy variance equal to the (standard) variance? We address the questions in proposing conditions based on the study of functions variations. A particular focus is given to the relationship between strict sub-Gaussianity and symmetry of the distribution. In particular, we demonstrate that symmetry is neither sufficient nor necessary for strict sub-Gaussianity. In contrast, simple necessary conditions on the one hand, and simple sufficient conditions on the other hand, for strict sub-Gaussianity are provided. These results are illustrated via various applications to a number of bounded random variables, including Bernoulli, beta, binomial, Kumaraswamy, triangular, and uniform distributions.

A characterization of the negative exponential distribution with application to reliability theory

1981 ◽  
Vol 18 (03) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

Asymptotic properties of super-critical branching processes II: Crump-Mode and Jirina processes

1975 ◽  
Vol 7 (01) ◽  
pp. 66-82 ◽  
Author(s):  
N. H. Bingham ◽  
R. A. Doney
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Regular Variation ◽  
Branching Processes ◽  
Asymptotic Properties ◽  
Random Variables ◽  
The Other ◽  
Continuous State Space ◽  
Continuous State ◽  
Integer Exponent

We obtain results connecting the distribution of the random variablesYandWin the supercritical generalized branching processes introduced by Crump and Mode. For example, if β > 1,EYβandEWβconverge or diverge together and regular variation of the tail of one ofY, Wwith non-integer exponent β > 1 is equivalent to regular variation of the other. We also prove analogous results for the continuous-time continuous state-space branching processes introduced by Jirina.

Difficulties and Advantages of Supersonic Civil Transport—A Discussion

1965 ◽  
Vol 69 (658) ◽  
pp. 691-691
Author(s):  
B. S. Shenstone
Keyword(s):  
Side Effects ◽  
The Other ◽  
Sonic Boom ◽  
High Speeds ◽  
Civil Aircraft ◽  
The Usa ◽  
Lack Of Knowledge

THE SST project is the largest, most expensive and most dubious project ever undertaken in the development of civil aircraft. It is dubious because of the concern about the side effects of supersonic flying on a regular basis, the main one being the sonic boom. Apparently the more one learns about the sonic boom, the more intractable it appears.The project is unique in that in Europe it was instigated by, and financed by, the Governments for airlines and not by airlines. A similar, although not exactly the same, pattern is followed in the USA.Another main characteristic of the SST is that no airline has ever asked for it, but the project existing has tempted a few airlines to put in tentative orders, which has encouraged other airlines out of fear to put in other orders.The general run of technical unknowns is pretty well-known, one of them being how to get rid of the heat caused by the friction of the air at the high speeds involved. However, probably the greatest doubt lies in the improbability that the SST will be able to be profitable in operation. I agree that it is possible to make any given number of calculations on this matter, all with reasonable degrees of honesty, and half of them will show that airlines will make money and the other half will show the opposite. This is merely a measure of our lack of knowledge of these aircraft.

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