Volume 16, 2004
Proceedings of the X International Summer Conference on Probability and Statistics and Seminar on Statistical Data Analysis, Sozopol, 2003
GUEST EDITORS: N.Yanev, D. Vandev
Dimitar Atanasov
Sofia University, Department of Mathematics and Informatics,
5 J. Boucher Str.1407 Sofia, Bulgaria,
email: datanasov@fmi.unisofia.bg
The probability that a device will work properly after a certain period of time can be studied using the StrehlerMildvan model. Let us suppose that the functionality of a device depends on an unknown parameter X, which decreases progressively in time. The device stops working if X goes below a certain given value.
We can use the method of maximum likelihood to estimate the parameters of the model and to estimate the probability of proper work at a future moment using the survival function.
This model can be modified in order to improve its robust performance. We will consider the breakdown properties of the model using the WLTE(k) Estimators and the theory of d fullness of the set of subcompact functions.
KEY WORDS: robust statistics
2000 AMS Subject Classification: 62F35, 62F15
Verica Bakeva
The Faculty of the Natural Sciences and Mathematics,
Institute of Informatics, P.O.Box 162
Skopje, Republic of Macedonia,
email:verica@pmf.ukim.edu.mk
This paper is a review of some applications of probabilistic models in
cryptography, coding theory and tests for pseudorandom number generators
(PRNG). Using quasigroup transformations, we design streams
cyphers and errorcorrecting codes with suitable properties. Some tests
for pseudorandom number generators are designed, too . They are based on
random walk on discrete coordinate plane.
KEY WORDS:
quasigroups, stream cypher, tests for pseudorandom number
generators, errorcorrecting codes.
2000 AMS Subject Classification: 94A29, 94B70
KEY WORDS: concentration function, confidence density, confidence residual highest density region 2000 AMS Subject Classification: 60E10, 62G15, 62M20 


Recent Results for Supercritical Controlled Branching Processes with Control Random Functions^{1}
Miguel González, Manuel Molina and Inés del Puerto
Department of Mathematics. University of Extremadura. 06071 Badajoz.
Spain.
In this paper we are concerned with the controlled branching processes with random control functions. Recently, we have considered them under the condition of asymptotically linear growth of the mathematical expectations associated to the random control variables. We present a review of the main results obtained until now, mainly, in the supercritical case.
2000 AMS Subject Classification: 60J80, 60F05
References

^{1}This work is supported by the Ministerio de Ciencia y Tecnología and the FEDER through the Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica, grant BFM200306074.



Branching Particle Representations of a Class of Semilinear Equations
José Alfredo LópezMimbela
Centro de Investigación en Matemáticas We review several probabilistic techniques that were developed in a series of papers to study blowup properties of positive (mild) solutions of semilinear equations of the form : ¶ u(t,x)/¶ t =Au(t,x)+u^{b }(t,x), u(0,x)=f(x) where A is the generator of a strong Markov process in a locally compact space S, b > 1 is an integer, and f:S® [0, +¥ ) is bounded and measurable, The emphasis is on probabilistic representation of positive solutions, and on qualitative properties of solutions.
References
KEY WORDS: Markov branching process, semilinear partial differential equation, global and nonglobal solutions, mild solutions 2000 AMS Subject Classification: 60J80, 60J85 





A Stochastic Approach for Finding of Semantically Related Words
Veska Noncheva^{1}^{4}, Pablo Gamallo^{2} and Alexandre Agustini^{2}^{5}
^{1}Dept. of Applied Mathematics, Plovdiv University
email: bojkova@math.bas.bg Semantically related words are modelled as words having the same probability distribution on the set of ssyntatic contexts occuring in text corpora. A learning algorithm for finding of clusters of semantically related words is developed. In that algorithm c^{2} statistics is used as a performance measure.
2. Pablo Gamallo, Caroline Gasperin, Alexandre Agustini, and Gabriel P. Lopes. Syntacticbased methods for measuring word similarity. In V. Mautner, R. Moucek, and K. Moucek, editors, Text, Speech, and Discourse (TSD2001), pages 116125. Berlin:Springer Verlag, 2001. 3. Gregory Grefenstette. Explorations in Automatic Thesaurus Discovery. Kluwer Academic Publishers, USA, 1994. 4. Z. Harris. Distributional structure. In J.J. Katz, editor, The Philosophy of Linguistics, pages 2647. New York: Oxford University Press, 1995. 5. Dekang Lin. Automatic retrieval and clustering of similar words. In COLINGACL'98, Montreal, 1998. 6. N. Marqes and G.P. Lopes. Tagging with small training corpora. In F. Hoffmann, D. Hand, N. Adams, D. Fisher, and G. Guimaraes, editors, Advances in Intelligent Data Analysis, pages 6272. LNCS, Springer Verlag, 2001. 7. Noncheva V., J.F.Silva, and G. Lopes. Automatic acquisition of word interaction patterns from corpora. In 10th Conference of the European Chapter of the Association for Computation Linguistics, EACL03 Workshop on Language Modeling for Text Entry Methods, Budapest, Bulgaria, 2003.
KEY WORDS: syntatic context, semantic preferences, c^{2 }goodness of fit test. 2000 AMS Subject Classification: 62P99, 68T50 






^{6} Research supported by contracts: PROENBIS: GTC1200143031 and WINE DB: G6RDCT200100646
Comparing Several Methods of Discriminant Analysis on the Case of Wine Data^{7}
Dimitar Vandev^{1}, Ute Römisch^{2}
^{1}Sofia University
The main problem of this European wine project (WINEDB) is the identification of the geographical origin based on chemicoanalytical measurements. At first the type of data collected in preparation of this project will be analysed. Then different procedures of Discriminant Analysis are described. Our special attention will be focused to some new techniqies as Support Vector Mashines (also known as Kernel Mashines)  procedures from the field of Mashine Learning. We test traditional techniques of Linear, Quadratic and Nonparametric Discriminant Analysis as well as the Support Vector Mashines on the base of our data and comment the results. KEY WORDS: application linear quadratic discriminant analysis SVM 2000 AMS Subject Classification: 62H30, 62J20, 62P12, 68T99 
^{7}The research is
supported by contracts: PROENBIS: GTC1200143031 and WINE DB:
G6RDCT200100646

^{3} Research supported by the Consejería de Educación, Ciencia y Tecnología de la Junta de Extremadura and the Fondo Social Europeo, grant TEM02/0007. The paper is also supported by Grant MM1101/02 by the National Foundation for Scientific Investigations, Bulgaria.
^{4} Supported by a grant from the PRAXIS XXI project, FCT, Portugal
^{5}Supported by a
grant from CAPES, Brazil