Institute of Mathematics AS CR, v. v. i.

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A regression method of estimation for generalized extreme value distribution

Author: Anand R.
Chandran C.
Publication venue: Institute of Information Theory and Automation AS CR
Publication date: 01/01/2025
Field of study

summary:This study focuses on parameter estimation for the generalized extreme value distribution (GEVD) using the regression method described by [Van2012median]. A regression equation is derived from the cumulative distribution function and the scale parameter is estimated by applying the iterative re-weighted least squares in this regression equation. For estimating the shape parameter, a profile likelihood is constructed based on this regression equation. A comparison study of the regression method with other existing estimators derived from the method of moments, maximum likelihood, probability-weighted moments, l-moments, and maximum product spacing is performed for the GEVD. Also, the left truncated GEVD is considered and the behaviour of its hazard function is studied. The parameter estimates of the left truncated GEVD is also derived using the regression method. An extensive simulation study is conducted and the efficiencies of the estimation techniques are analysed. The bootstrap confidence intervals for the estimators are also constructed. Finally, a real data analysis is carried out to illustrate the applicability of the models and estimation techniques

New gravitational algorithms for the detection of overlapping and disjoint communities in weighted complex networks

Author: Kartli Nermin
Çetin Pelin
Ayhan Selin
Publication venue: Institute of Information Theory and Automation AS CR
Publication date: 01/01/2025
Field of study

summary:The excessive increase in the amount of data caused a rise in the number of vertices and edges in the graph models. This gave rise to the concept of complex networks. Complex networks are present in almost every area of life, in social networks, natural sciences, drug discovery, etc. Detection of overlapping or disjoint communities in complex networks is an important problem. In this study, we propose two new algorithms to detect overlapping and disjoint communities in weighted complex networks. We assume that the weights represent how close the vertices are to each other in some sense. First, we calculate the similarity of the vertices to each other using the universal gravitational law, then place similar vertices in overlapping communities. Then, for each vertex in multiple communities, we calculate the attraction force of each community where this vertex is located. We leave the vertex in the community that attracts the vertex more and delete it from the others. The results of experiments conducted on complex networks consisting of real and artificial data show the efficiency of the proposed algorithms

Subclass of analytic functions related with Miller-Ross-type Poisson distribution series

Author: Frasin Basem Aref
Publication venue: Matematický ústav AV ČR
Publication date: 01/01/2025
Field of study

summary:The purpose of the present paper is to find a necessary and sufficient condition for the Miller-Ross-type Poisson distribution series to be in the class

\mathcal {P}^{\ast }(\alpha ,\beta ,\gamma )

of analytic functions with negative coefficients. Also, we investigate several inclusion properties of the classes of Janowski type close-to-starlike functions, Janowski type close-to-convex functions and Janowski type quasi-convex functions associated with the operator

\mathbb {I}_{\theta ,\epsilon }^{s}

defined by this distribution. Further, we consider an integral operator related to the Miller-Ross-type Poisson distribution series. Several corollaries and consequences of the main results are also considered

The CR geometry of the three-segment snake

Author: Frelik Tymon
Publication venue: Department of Mathematics, Faculty of Science of Masaryk University, Brno
Publication date: 01/01/2025
Field of study

summary:We study the geometry associated with the kinematics of a planar robot known as the three-segment snake, whose velocity distribution belongs to a class of

(2,3,5)

distributions. We discover that, under certain assumptions on its construction parameters, the snake may be endowed with a CR structure of CR dimension 1 and real codimension 3. We solve the associated Cartan equivalence problem and find the invariants of the snake’s CR structure

Analysis and optimal control of a fractional tuberculosis model

Author: Dicko Hamadoum
Traoré Ali
Ouedraogo Rosaire
Publication venue: Matematický ústav AV ČR
Publication date: 01/01/2025
Field of study

summary:A fractional model is developed to study the transmission dynamics of tuberculosis disease. The use of a fractional model provides a memory effect and long-term dynamics often observed in chronic infectious diseases such as tuberculosis, which is characterized by a prolonged incubation period and risks of reactivation. The basic reproduction number is computed and we derive the qualitative stability analysis of equilibria. A sensitivity analysis is conducted to assess the impact of the model parameters. Three control strategies are applied, namely treatment, vaccination, and infection rate management, to minimize the number of infected individuals. Numerical simulations are carried out to illustrate the theoretical results obtained

Global weak solutions to a 3D self-consistent chemotaxis-Stokes system with nonlinear resource consumption

Author: Ri Kwang-Ok
Kim Yong-Ho
Paek Jong-Chol
Hong Song-Chol
Publication venue: Matematický ústav AV ČR
Publication date: 01/01/2025
Field of study

summary:We study the self-consistent chemotaxis-fluid system with nonlinear resource consumption

\begin {cases} n_{t}+u\cdot \nabla n=\Delta n^m -\nabla \cdot (n \nabla c)+\nabla \cdot (n\nabla \phi ), & x\in \Omega ,\ t>0, \\ c_{t}+u\cdot \nabla c=\Delta c-n^\alpha c, & x\in \Omega ,\ t>0, \\ u_t+ \nabla P=\Delta u-n\nabla \phi +n \nabla c,& x\in \Omega ,\ t>0,\\ \nabla \cdot u=0,& x\in \Omega ,\ t>0,\\ \end {cases}

under no-flux boundary conditions in a bounded domain

\Omega \subset \mathbb {R}^3

with smooth boundary. It is proved that this system possesses a global weak solution provided

m>1

and

\alpha > \frac {4}{3}

An accelerated gradient descent method based on a non-monotone backtracking line search scheme for unconstrained optimization and image restoration problems

Author: Ashrafi Ali
Mirzaei Seyed Hamzeh
Publication venue: Matematický ústav AV ČR
Publication date: 01/01/2025
Field of study

summary:This study introduces an accelerated gradient descent method based on a non-monotone backtracking line search scheme. A simple adaptive quadratic model is enhanced by utilizing a real, positive definite scalar matrix derived from the Taylor expansion of the objective function, rather than relying on the exact Hessian. The global and superlinear convergence of the defined model is established under appropriate conditions. Numerical experiments on a set of standard unconstrained optimization problems and image restoration problems show that the new algorithm outperforms other comparable methods in terms of efficiency and robustness

Multi-argument specialization semilattices

Author: Lipparini Paolo
Publication venue: Matematický ústav AV ČR
Publication date: 01/01/2025
Field of study

summary:If

X

is a closure space with closure

K

, we consider the semilattice

(\mathcal P(X), \cup )

endowed with a further relation

x \sqsubseteq \{ y_1, y_2, \dots , y_n\}

between elements of

\mathcal P(X)

and finite subsets of

\mathcal P(X)

, whose interpretation is

x \subseteq Ky_1 \cup Ky_2 \cup \dots \cup Ky_n

. \endgraf We present axioms for such multi-argument specialization semilattices and show that this list of axioms is sound and complete for substructures of closure spaces, namely, a model satisfies the axioms if and only if it can be embedded into the structure associated to a closure space as in the previous sentence. As a main tool for the proof, we provide a canonical embedding of a multi-argument specialization semilattice into (the structure associated to) a closure semilattice

Positive solution for infinitely impulsive singular third-order $\phi$ -Laplacian BVPs on the half line with first-order derivative dependence

Author: Benmezaï Abdelhamid
Belal Dhehbiya
Bachouche Kamal
Publication venue: Matematický ústav AV ČR
Publication date: 01/01/2025
Field of study

summary:We are concerned in this paper with the existence of positive solutions to the

\phi

-Laplacian third-order boundary value problem

\begin {cases} -(\phi (u''))'(t)=f(t,u(t),u'(t))\text { for a.e. }t\in J, \\ u(0)=0,\ u'(0)=a\text {, }\lim \limits _{t\rightarrow \infty }u''(t)=0, \\ \Delta u(t_{k})=I_{1,k}(u(t_{k}),u'(t_{k})),\ k=1,2,\ldots ,\\ \Delta u'(t_{k})=I_{2,k}(u(t_{k}),u'(t_{k})),\ k=1,2,\ldots , \\ -\Delta \phi (u'')(t_{k})=I_{3,k}(u(t_{k}),u'(t_{k})),\ k=1,2,\ldots ,\end {cases}

where

a\geq 0,

J=(0,\infty )

0<t_{1}<t_{2}<\ldots <t_{k}\ldots

t_{k}\rightarrow \infty

k\rightarrow \infty

\Delta u(t_{k})=u(t_{k}^{+})-u(t_{k}^{-})

and

J^{\ast }=J\backslash \{t_{k}\colon k\geq 1\}

. The function

\phi \colon \mathbb {R}\rightarrow \mathbb {R}

is an increasing homeomorphism such that

\phi (0)=0

I_{i,k}\in C(I^{2},[0,\infty ))

for

i=1,2,3

and

k\geq 1

, and the nonlinearity

f\colon J^{3}\rightarrow \mathbb {R}^{+}

is a Caratheodory function.\\ By means of a Guo-Krasnoselskii type fixed point theorem, we prove an existence result for at least one positive solution

On forbidden configuration of pseudomodular lattices

Author: Dhake Manoj
Ballal Sachin
Kharat Vilas
Shewale Rupesh S.
Publication venue: Matematický ústav AV ČR
Publication date: 01/01/2025
Field of study

summary:We characterize the pseudomodular lattices by means of a forbidden configuration

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Institute of Mathematics AS CR, v. v. i.

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