scholarly journals Entropy Optimization, Maxwell–Boltzmann, and Rayleigh Distributions

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 754
Author(s):  
Nicy Sebastian ◽  
Arak M. Mathai ◽  
Hans J. Haubold
Keyword(s):  
Communication Theory ◽  
Complex Domain ◽  
Cauchy Matrix ◽  
The Real ◽  
Entropy Optimization ◽  
Engineering Statistics

In physics, communication theory, engineering, statistics, and other areas, one of the methods of deriving distributions is the optimization of an appropriate measure of entropy under relevant constraints. In this paper, it is shown that by optimizing a measure of entropy introduced by the second author, one can derive densities of univariate, multivariate, and matrix-variate distributions in the real, as well as complex, domain. Several such scalar, multivariate, and matrix-variate distributions are derived. These include multivariate and matrix-variate Maxwell–Boltzmann and Rayleigh densities in the real and complex domains, multivariate Student-t, Cauchy, matrix-variate type-1 beta, type-2 beta, and gamma densities and their generalizations.

Of ants and academics: The computational power of external representation

1997 ◽  
Vol 20 (1) ◽  
pp. 78-79
Author(s):  
Jon Oberlander
Keyword(s):  
Real World ◽  
External Representation ◽  
External Representations ◽  
Computational Power ◽  
The Real

Clark & Thornton speculate that intervening in the real world might be a way of transforming type-2 problems into type-1, but they state that they are not aware of any definite cases. It is argued that the active construction of external representations often performs exactly this function, and that recoding via the real world is therefore common, if not ubiquitous.

scholarly journals Application of Type-1 and Type-2 Fuzzy Logic Controller for The Real Swarm Robot

2019 ◽  
Vol 15 (06) ◽  
pp. 83 ◽  
Author(s):  
Ade Silvia Handayani ◽  
Nyayu Latifah Husni ◽  
Siti Nurmaini ◽  
Irsyadi Yani
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Logic Controller ◽  
Complex Problem ◽  
The Real ◽  
Advantages And Disadvantages ◽  
Path Navigation ◽  
Swarm Robot ◽  
Interval Type

Navigation is one of the typical problem domains occurred in studying swarm robot. This task needs a special ability in avoiding obstacles.  This research presents the navigation techniques using type 1 fuzzy logic and interval type 2 fuzzy logic. A comparison of those two fuzzy logic performances in controlling swarm robot as tools for complex problem modeling, especially for path navigation is presented in this paper.  Each hierarchical of fuzzy logic shows its advantages and disadvantages.  For testing the robustness of type-1 fuzzy logic and interval type-2 fuzzy logic algorithms, 3 robots for the real swarm robot experiment are used.  Each is equipped with one compass sensor, three distance sensors, and one X-Bee communication module.  The experimental results show that type-2 fuzzy logic has better performance than type-1 fuzzy logic.

A continuous functional with noncollapsing hierarchy

1978 ◽  
Vol 43 (3) ◽  
pp. 487-491
Author(s):  
Dag Normann
Keyword(s):  
Continuous Functional ◽  
Standard Methods ◽  
The Real ◽  
Arbitrary Type ◽  
Ordinal Notations ◽  
Primitive Recursive

In [5] S. S. Wainer introduces a hierarchy for arbitrary type-2-functionals. Given F, he defines a set of ordinal notations OF, and for each a ∈ OF, a function fa recursive in F and an ordinal ∣a∣F < For any f recursive in F there is an a ∈ OF such that f is primitive recursive in fa.Let ρF be the least ordinal α such that for any f recursive in F there is an α ∈ OF with ∣a∣F ≤ α such that f is primitive recursive in fa. If ρF < the hierarchy breaks down. In Bergstra and Wainer [2] ρF is described as “the real ordinal of the 1-section of F”.Using standard methods (originally due to Kleene) one may prove that if F is normal, then ρF = Feferman has proved that if F is recursive, then ρF = ω2.Let 1-section (F) = l-sc(F) = {f; f is recursive in F} where f is a total object of type 1.Grilliot [4] proved that F ↾ 1-sc(F) is continuous if and only if F is not normal.Let h be an associate for a given functional F, and assume that h is recursive in the jump of an element of 1-sc(F).

Type 2 Diabetes Overtakes Type 1 in Hispanic Girls

2008 ◽  
Vol 38 (15) ◽  
pp. 18
Author(s):  
SHERRY BOSCHERT
Keyword(s):  
Type 2 Diabetes

Molecular analysis of FVIII gene in severe HA patients of Costa Rica

2010 ◽  
Vol 30 (S 01) ◽  
pp. S150-S152
Author(s):  
G. Jiménez-Cruz ◽  
M. Mendez ◽  
P. Chaverri ◽  
P. Alvarado ◽  
W. Schröder ◽  
...  
Keyword(s):  
Factor Viii ◽  
Coagulation Factor ◽  
Costa Rican ◽  
Factor Viii Gene ◽  
Intron 22 Inversion ◽  
Intron 1 ◽  
Polymerase Chain ◽  
Inversion Analysis

SummaryHaemophilia A (HA) is X-chromosome linked bleeding disorders caused by deficiency of the coagulation factor VIII (FVIII). It is caused by FVIII gene intron 22 inversion (Inv22) in approximately 45% and by intron 1 inversion (Inv1) in 5% of the patients. Both inversions occur as a result of intrachromosomal recombination between homologous regions, in intron 1 or 22 and their extragenic copy located telomeric to the FVIII gene. The aim of this study was to analyze the presence of these mutations in 25 HA Costa Rican families. Patients, methods: We studied 34 HA patients and 110 unrelated obligate members and possible carriers for the presence of Inv22or Inv1. Standard analyses of the factor VIII gene were used incl. Southern blot and long-range polymerase chain reaction for inversion analysis. Results: We found altered Inv22 restriction profiles in 21 patients and 37 carriers. It was found type 1 and type 2 of the inversion of Inv22. During the screening for Inv1 among the HA patient, who were Inv22 negative, we did not found this mutation. Discussion: Our data highlight the importance of the analysis of Inv22 for their association with development of inhibitors in the HA patients and we are continuous searching of Inv1 mutation. This knowledge represents a step for genetic counseling and prevention of the inhibitor development.

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