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1
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Ind-additive functionals on random vectors

100%
Woyczyński W. A.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS 1. Introduction.......................................................................................................................................................................... 5 2. Preliminaries....................................................................................................................................................................... 6 3. Random vector measures................................................................................................................................................ 9 4. Random integrals of operator-valued functions........................................................................................................... 14 5. Ind-additive functionals...................................................................................................................................................... 21 6. A description of operator-valued functions that are integrable with respect to the homogeneous random vector measure.................................................................................................................. 22 7. Vector lattices and additive functionals........................................................................................................................... 26 8. Representation of additive functionals on finite-dimensional vector lattices and on F-lattices of typo M..................................................................................................................................................... 28 9. Representation of additive functionals on Orlicz spaces and $L_p$-type lattices having a Freudenthal unit...................................................................................................................................................... 30 10. Representation of ind-additive functionals on non-Gaussian vectors................................................................... 35 References............................................................................................................................................................................... 37
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Nonlocal quadratic evolution problems

61%
Biler P., Woyczyński W. A.
Banach Center Publications
|
2000
|
tom 52
|
nr 1
11-24
EN
Nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered. The inertial type nonlinearity is quadratic and nonlocal while the diffusive term, also nonlocal, is anomalous and fractal, i.e., represented by a fractional power of the Laplacian. Conditions for global in time existence versus finite time blow-up are studied. Self-similar solutions are constructed for certain homogeneous initial data. Monte Carlo approximation schemes by interacting particle systems are also mentioned.
3
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A Lost Opportunity: Recovering the End of Major League Baseball's 1994 Strike Shortened Season

49%
Hass Z., Woyczyński W. A., Yanosko C., Becker E.
Mathematica Applicanda
|
2012
|
tom 40
|
nr 2
EN
The 1994 Major League Baseball (MLB) Season ended prematurely when the players went on strike on August 12th, due to a labor disagreement with team owners. This paper describes the model estimation for predicting the runs scored in each of the unplayed games and gives the results of 1,000 simulations. Of particular interest are the Cleveland Indians and the Montreal Expos. The Expos were on pace to have the best season in franchise history (and the best record in the league), while the Indians were poised to begin a very successful run that could have ended the city's World Championship drought dating from 1948.
4
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Coalescing stochastic processes in retrival from semantic memory

49%
Queau P.-Y., Woyczyński W. A., Lerner A. J.
Mathematica Applicanda
|
2015
|
tom 43
|
nr 2
PL
Praca proponuje model procesów koalescencyjnych w celu wyjaśnienia mechnizmów odsku pojęć i nazw z pamięci semantycznej. Model jest pretestowany używając dobrze znanego eksperymentalnego Testu Biegłości Kategorycznej, który jest standartowym narzędziem neurologów badających pacjentów z objawami demencji. Możliwości modelowania opartego na procesach L´evy’ego i ułamkowych procesach Poissona są rownież zbadane.
EN
Semantic memory retrieval is one of the most fundamental cognitive functions in humans. It is not fully understood and researchers from various fields of science struggle to find a model that would correlate well with experimental results and help understanding the complex background processes involved. To study such a phenomenon we need a relevant experimental protocol which can isolate the basic cognitive functions of interest from other perturbations. A variety of existing medical tests can provide such information, and the one we analyze  is the Category Fluency Test (CFT).  It was originally designed to measure frontal brain lobe  damages in  injured patients, and it tests directly the semantic memory retrieval, which is affected in cases of injury but can be also influenced  by dementia, Alzheimer syndrome, or just aging. This paper introduces a new paradigm in analysis of  the temporal structure of  CFT responses  by utilizing  coalescent  stochastic process model. We believe that this particular  model is relevant  to how  this cognitive function  operates and can lead to a better understanding of the background processes. The method turns out to be better  at separating the two cognitively different  groups studied here than the Weibull model from our previous paper Meyer et al.(2012), and could potentially be used for early diagnostics of dementia or Alzheimer's disease. Two other models, one based on the concept of Levy processes,  and one related to  the fractional Poisson model,  are also explored.
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Multilinear forms in Pareto-like random variables and product random measures

49%
Rosiński J., Woyczyński W. A.
Colloquium Mathematicum
|
1987
|
tom 51
|
nr 1
303-313
6
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Positive-coefficient elements of Hardy-Orlicz spaces

42%
Woyczyński W. A.
Colloquium Mathematicum
|
1970
|
tom 21
|
nr 1
103-110
7
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Additive functionals on Orlicz spaces

30%
Woyczyński W. A.
Colloquium Mathematicum
|
1968
|
tom 19
|
nr 2
319-326
8
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Remarks on eigenvalues of infinite matrices

30%
Woyczyński W. A.
Colloquium Mathematicum
|
1968
|
tom 19
|
nr 1
103-106
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