# Keynote Speakers

Prof. João
Tiago Praça Nunes Mexia

Universidade Nova de Lisboa,
Portugal

João Tiago Praça Nunes Mexia was born in Lisbon in June of 1939. The most part of his career was as Full Professor at the FCT/UNL-Faculty for Sciences and Technology of the New University of Lisbon. At that time he supervised the teaching of Statistics at FCT/UNL and directed the Research Center in Mathematics of the University (CMA-Center for Mathematics and its Applications) from 1999 to 2009. In 2009 he became Emeritus Professor. Until now he supervised 19 Ph.D. and co-supervised 12 Ph.D. His research is centered on Linear Statistical Inference, having almost 100 papers published in International Journals.

Prof. Alexandr
Boichuk

National Academy of Sciences of
Ukraine, Ukraine

Alexander Andreevych Boichuk is a Ukrainian mathematician, doctor of physical and mathematical sciences, professor, corresponding member of the National Academy of Sciences of Ukraine (since 2012), head of the laboratory boundary-value problems of differential equations of the Institute of Mathematics of the National Academy of Sciences of Ukraine, was awarded the State Prize of Ukraine in Science and Technology and Mitropolskiy Prize (2013). Professor A. Boichuk is an expert on the theory of the boundary value problems with the normally solvable operators in the linear part. For the first time defined the conditions for the solvability and spent the classification of the resonant cases a wide class of nonlinear boundary value problems for systems of ordinary differential and difference equations, delay equations, equations with impulsive and singularly perturbed equations for which the proposed use of the apparatus of generalized inverse operators. A. Boichuk is the author of over 110 scientific papers including three monographs. Under his guidance prepared 11 candidates of sciences.

Speech Title: "Boundary Value Problems of a Nonlinear Lyapunov Equation and Homoclinic Chaos"

Abstract: The report is devoted to obtaining a necessary and sufficient conditions of the existence of bounded on the whole axis solutions of a nonlinear evolution boundary value problems under assumption that corresponding homogeneous equation admits an exponential dichotomy on the semi-axes. We illustrate obtaining results for the Lyapunov type equation. We seek bounded solution of the nonlinear boundary value problem which turns in one of bounded solutions of the generating linear boundary value problem for the Lyapunov equation. It is shown that with using of proposed in report so called equation for generating operators we can obtain conditions of homoclinic chaos. We find connections between the well-known Palmer theorem and Melnikov function.

Prof. Carlos
A. Braumann

University of Évora, Portugal

Carlos A. Braumann is Emeritus Professor and member of the research centre CIMA at the University of Évora (UE), Portugal, where he has been Vice-Rector in 1987-94 and Rector in 2010-14. His publications are mostly on Stochastic Differential Equations and its applications in several areas (population dynamics, fisheries, animal growth, demography, finance). He got his Ph.D. in 1979 at the Stony Brook University and his habilitation in Stochastic Processes at the UE in 1988. He is an elected member of the International Statistical Institute since 1992, a former President of the European Society for Mathematical and Theoretical Biology (2009-12) and of the Portuguese Statistical Society (2006-09 and 2009-12), and a former member of the European Regional Committee of the Bernoulli Society (2008-12).

Speech
Title: "Individual
Growth Modelling with
Stochastic Differential
Equations"

Authors: Carlos A. Braumann,
Patrícia A. Filipe, and
Gonçalo Jacinto

Abstract: Common growth
curves for the weight X(t)
of an animal at age t can be
described by a differential
equation of the form
dY(t)=β(α-Y(t))dt, where
Y(t)=h(X(t)) and h is an
appropriate strictly
increasing continuously
differentiable function,
α=h(A) (A= maturity weight
of the animal), and β>0 is a
rate of approach to
maturity. Adjustment to data
was usually done through
non-linear regression
inappropriate methodology
that ignores the growth
dynamics and the influence
of environmental
fluctuations on it. Instead,
we use instead stochastic
differential equations
(SDEs) models
dY(t)=β(α-Y(t))dt+σdW(t),
where W(t) is a standard
Wiener process and σ is an
intensity parameter of the
fluctuations. We have
previously studied
estimation, prediction and
optimization issues using
cattle weight data from
females of Mertolengo cattle
breed. In the present work,
we have adjusted and applied
the methodologies to the
weight data of males of
Mertolengo cattle breed and
Alentejana cattle breed.
Since model parameters may
vary from animal to animal
and that variability can be
partially explained by their
genetic differences, we
introduce the extension of
the study to SDE mixed
models. These mixed models
incorporate the individual
genetic values that are
available at the databases
of the producer
associations.

Acknowledgements: The
authors belong to the
research centre Centro de
Investigação em Matemática e
Aplicações (CIMA),
Universidade de Évora,
supported by FCT (Fundação
para a Ciência e a
Tecnologia, Portugal,
project UID/MAT/04674/2019).

# Invited Speakers

Prof.
Alexander Bulinski

Moscow State University, Russia

Alexander Bulinski, Professor of the Moscow State University, Dr. Sc. Phys. Math. (Habilitation) is a Member of the Board of the Moscow Mathematical Society since 2000, was a Member of the European Committee of the Bernoulli Society (2002-2006). He is an author of 5 books and numerous research papers. His main results pertain to the theory of stochastic processes and random fields. Various statistical applications of limit theorems are also in the scope of his activity. A.Bulinski belongs to the scientific school of Professor A.N.Kolmogorov being his former PhD student. He was awarded the State Scholarship for prominent scientists and International Science Foundation Diploma ``for outstanding contribution to world science and education''. He is a winner of the Lomonosov prize in Science. A.Bulinski is a Member of the Editorial Boards of 6 journals. He was Invited Professor in France, Germany, Sweden, Netherlands, UK etc. Under his scientific direction 15 PhD-theses were written and 4 are in preparation. He was Keynote Speaker and Invited Speaker, as well as a member of Program Committees, at various International conferences. A.Bulinski is a Member of the Expert Council for Higher Qualification Committee of Russia, Head of the Federal Teaching Union on Mathematics and Mechanics in the Higher Education System of Russia.

Speech Title: "Statistical Estimation of Mutual Information and Applications"

Abstract: Statistical
estimation of mutual
information is important for
various applications. Such
estimates are employed, for
instance, in machine
learning, feature selection
and identification of
textures inhomogeneities. In
this regard one can refer,
e.g., to the book by
V.Bolon-Canedo and
A.Alonso-Betanzos (2018),
see also a review by
J.R.Vergara and P.A.Estevez
(2014). We develop the quite
recent papers by A.Bulinski,
A.Dimitrov (2018) and
A.Bulinski, A.Kozhevin
(2018), concerning the
Shannon entropy, to study
statistical estimation of
mutual information and the
Kullback-Leibler divergence.
We investigate the
asymptotic properties of
proposed estimates
constructed by means of
i.i.d. (vector-valued)
observations. For this
purpose we apply the
techniques involving the
nearest neighbor statistics.
Special attention is payed
to results of computer
simulations in the framework
of mixed models (see, e.g.
F.Coelho, A.P.Braga,
M.Verleysen (2016), W.Gao,
S.Kannan, P.Viswanath
(2018)) comprising the
widely used logistic
regression. In contrast to
previous works we do not
suppose that the set of a
response variable values is
endowed with nontrivial
metric. This is essential in
many cases for analysis of
medical and biological data.