Centre for Advanced Research in Applied Mathematics and Statistics, MAHE, Manipal, India
The present conference ICLAA 2023, Manipal India, the fifth in its sequel, shall provide a platform for leading Mathematicians and Statisticians, working around the globe in the theme area to discuss several research issues and to introduce new innovations. The main goal of the conference is to bring experts, young researchers, and students together to present recent developments in this dynamic and important field. The conference also aims to stimulate research and support the interaction among the scientists by creating an environment for the participants to exchange ideas and to initiate collaborations and professional partnerships.
On behalf of the Scientific Advisory Committee, and the Local Organizing Committee, we have much pleasure in extending a cordial invitation to participate in this conference.
The theme of the conference shall focus on but not limited to
Linear Algebra and Graph Theory are important branches of Mathematics having applications in every branch of science. The topic ‘Matrix Methods in Statistics’ is a branch of Linear Algebra and Matrix Theory containing a variety of challenging problems in Linear Statistical Models and Statistical Inference, having applications in various branches of Applied Statistics such as Natural Sciences, Medicine, Economics, Electrical Engineering, Markov Chains, Digital Signal Processing, Pattern Recognition and Neural Network, to name a few. Advances in Combinatorial Matrix Theory are motivated by a wide range of their applications in the subjects such as Networks, Chemistry, Genetics, Bioinformatics, Computer Science, and Information Technology. The areas of Classical Matrix Theory and Combinatorial Matrix Theory interact with each other, which is evident from the interplay between Graphs and Matrices. Generalized Inverses of Matrices such as the Incidence Matrix and Laplacian Matrix are mathematically interesting and have great practical significance. Covariance Matrices play an important role in the study of uncertainty associated with data related to measurements, which is an important part of applied Mathematics and Statistics.
This conference is in sequel to the conferences CMTGIM 2012, ICLAA 2014, ICLAA 2017, and ICLAA 2020(21) held in Manipal during January 2012, December 2014, December 2017, and December 2021, respectively. The present conference shall provide an avenue for leading Mathematicians, Statisticians, and scientists working in the applied area, who are working around the globe in the theme area to get together in the physical space, interact each other, discuss several research issues and to introduce new innovations. The ICLAA 2023, Manipal, India is expected to stimulate research and benefit the young scholars from the interaction with leading linear algebraists. The physical participation in the conference will be creating an environment for experts and young scholars to exchange ideas, and to initiate collaborations and professional partnerships. Besides organizing invited talks from eminent speakers, organizers invite the participants to present their research work in the sessions of contributory talks.
The conference is with three special sessions namely, ‘Special Matrices’, ‘Matrix Methods in Statistics’, and ‘Matrices, Graphs, and Applications’. These three sessions are dedicated to the great linear algebraists- Abraham Berman, Simo Puntanen, Ravindra B Bapat, and Steve J Kirkland who have been associated with the ICLAA series for last several years.
Research presented at the conference will get an opportunity of possible publication in one of the special issues dedicated to the conference in the following journals, subject to acceptance after the standard peer review process adopted by the journals.
Papers by nonparticipants are also welcome for submitting the articles which are in the focus of the conference. Due to the limitation of the number of articles in the special issue, qualified articles presented at the conference are considered with priority.
To encourage research and motivate young researchers, the best paper award competition will be conducted under the following three themes:
Eligibility: Full research articles (need not be original) on any of the above-mentioned themes are invited from the researchers (presenting authors) belonging to any of the following categories:
The presenting authors are required to submit No Objection Certificate from the coauthors, along with the paper. Format for No Objection Certificate can be downloaded here: Click here.
All original papers selected for presentations are eligible for the further review process in the appropriate conference publications. Authors may opt not to publish the presented paper in the special issues related to ICLAA 2023.
Note: One may submit an extended abstract of a paper instead of full paper for the possible consideration for presentation in Best Paper Award contest. However, full paper should be submitted before the presentation.
How to submit: Please send the articles before the deadline to iclaa2023.mahe@gmail.com or kmprasad63@gmail.com with the subject line ‘Article for BP Award’. For any future query related to the submitted manuscript, use the manuscript ID in the subject line.
Template for submitting abstract for Best Paper Award: Click here.
Template for submitting article for Best Paper Award: Click here.
Last date for submission of extended abstract: October 31, 2023.
The Preconference workshop `International Workshop on Special Matrices, Graphs, and Applications’ will be held during December 11-17, 2023. The workshop is aimed at training young students, scholars, and faculty interested in the focus area of special matrices, graphs, and their applications. Sessions in the workshop include lectures, tutorials and discussion on recent research trends in special matrices and graphs by Abraham Berman, Ravindra B. Bapat, S. K. Neogy, and other leading personalities of the subject. Conference participants may seek participation in the workshop. The number of participants in the workshop is restricted. Participants who could gain the benefit from the course will be chosen as the applications arrive. The course conducted in the workshop will carry a credit of two.
Workshop and conference are organized by the CARAMS, MAHE in association with Department of Mathematics, MIT, MAHE and Department of Data Science, PSPH, MAHE.
Ravindra B Bapat
Chair, Scientific Committee
ICLAA 2023
Narayana Sabhahit
(Pro Vice Chancellor -Tech. & Sci., MAHE)
Chair, Local Organizing Committee
ICLAA 2023
Centre for Advanced Research in Applied Mathematics and Statistics (CARAMS) was established in September 2018 at Manipal Academy of Higher Education, Manipal. MAHE, Manipal, an institution of eminence, is a deemed to be university and comprised of students from fifty seven nations around the globe. CARAMS has been established with the objectives of fostering advanced research and training in Mathematics, Statistics, and their applications. Also, it organizes national and international workshops and conferences in the focus area which help the promotion of Mathematics and Statistics in the university and also in the region.
CARAMS, MAHE offers a welcoming and inclusive environment to all participants in its activities, including all its meetings and conferences, irrespective of gender, gender identity or expression, sexual orientation, race, colour, national or ethnic origin, religion or religious belief, age, marital status, disabilities, and field of expertise.
CARAMS strives to foster an apolitical atmosphere that encourages the free expression and exchange of ideas, free from all forms of discrimination, harassment, and retaliation, and that is welcoming and safe to all members and to those who participate in its activities.
If you feel harassed or unsafe in any way because of the actions, words, pictures, or expressions of any other member or participant, we encourage you to bring this to the attention of the CARAMS or MAHE authority.
For details about publications of ICLAA 2023, please visit: Publications of ICLAA 2023
Timeline for the submission of paper for journal publications, please visit Publication section.
Category | Conference | Workshop | ||
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Early Bird Registration Fee | Late Registration Fee | Early Bird Registration Fee | Late Registration Fee | |
Foreign Delegates (FD) | 350 $/ 330 € # | 400 $/ 370 € # | 110 $/ 100 € # | 135 $/ 125 € # |
Foreign Accompanying | 110 $/ 100 € | 110 $/ 100 € | 110 $/ 100 € | 135 $/ 125 € |
Indian Scholar/Faculty (ISF) | 4000 INR + GST # | 4500 INR + GST # | 1000 INR + GST * | 1500 INR + GST * |
ISF Accompanying | 1000 INR + GST | 1000 INR + GST | – | – |
Indian Students ** | 1000 INR + GST * | 1000 INR + GST * | 1000 INR + GST * | 1000 INR + GST * |
# : The registration fee covers accommodation at Hostel/International Guest House, MAHE, registration kit, breakfast at venue, working lunch, and welcome dinner on 17th December.
* : The amount excludes accommodation charges, which is to be paid as per norm.
** : Indian students or research scholars not having any financial support of fellowship/salary. (Participants registering under this category must produce a letter of recommendation from their supervisor/HOD stating that the candidate has no fund support from any funding agencies. Kindly mail the recommendation letters to carams@manipal.edu or to km.prasad@manipal.edu.)
After successful registration, INDIAN PARTICIPANTS may pay the registration fee via the payment link (For the payment link visit My Page -> Event registered -> Select the event -> Payment).
After successful registration, FOREIGN PARTICIPANTS are required to mail their name and permanent address to carams.mahe@gmail.com to get the necessary invoice, against which one may pay the registration fee through bank transfer. Immediately after the payment, kindly send the transaction details to complete the registration procedure.
Accommodation from the organizer will be arranged, if any, for the duration starting from the evening before the event and up to morning after the event.
CARAMS aims at supporting the travel and registration of senior and young scientists not having the fund
support to present the paper, on the request made before November 30, 2023. However, such support (which
could be partial) will be provided depending on the fund support received from the different organizations.
Research Interests:
Perturbation theory for linear operators, Structured perturbation theory for matrices, Nonlinear eigenvalue problems, Multiparameter eigenvalue problems. Read more
Achievements:
Currently Prof. Rafikul Alam is working as a professor in the department of Mathematics, Indian Institute of Technology… Read more
Let $ M, D, K$ be $n\times n$ matrices such that $M$ and $K$ are positive semidefinite and $D$ is Hermitian. Consider the quadratic eigenvalue problem (QEP) $$P(\lambda)v := (\lambda^2 M + \lambda D + K)v= 0$$associated with a damped mass-spring system. The mass matrix $M$ is usually positive definite. However, there are applications where $M$ is positive semidefite and $K$ is positive definite. In such a case, $\infty$ is an eigenvalue of $P(\lambda)$. The presence of an infinite eigenvalue poses computational difficulty in solving the QEP. We describe a structure-preserving deflation strategy that deflates the eigenvalue $\infty$ and produces a reduced order model $ \widehat{P}(\lambda) := \lambda^2\widehat{M} + \lambda \widehat{D} + \widehat{K},$ where both $\widehat{M}$ and $\widehat{K}$ are positive definite and $\widehat{D}$ is Hermitian. We also discuss hyperbolicity and inertia of $P(\lambda).$ The damping matrix $D$ usually has low rank because of which $P(\lambda)$ has undamped (purely imaginary) eigenvalues. We analyze the effect of damping on the purely imaginary eigenvalues of $P(\lambda)$ and present a structure-preserving deflation strategy that deflates all the purely imaginary eigenvalues of $P(\lambda)$ and produces a reduced order model $ \widetilde{P}(\lambda) := \lambda^2\widetilde{M} + \lambda \widetilde{D} + \widetilde{K}.$ We also analyze removal of purely imaginary eigenvalues of $P(\lambda)$ via low rank perturbation of the damping matrix $D$.
Research Interests:
Matrices and Graphs, Nonnegative Matrices, Matrix Inequalities and Generalized Inverses Read more
Achievements:
He has published more than 140 research papers in these areas in reputed national and international journals and… Read more
Research Interests:
Analysis, Probability Theory, Applied Mathematics, Sequential analysis, Statistical inference, and Time series Read more
Achievements:
Dr. Sudeep R. Bapat had his schooling and undergraduate education in New Delhi. He obtained his Bachelors degree… Read more
A two-stage sequential procedure to estimate the parameters of a cumulative exposure model under an accelerated testing scenario is discussed. We focus on a step-stress model where the stress level is updated after a pre-specified number of failures occur, which is also random. This is termed as the ‘random stress change time’ in the literature. To obtain maximum precision, a certain variance optimality criterion is applied. A pseudo real data example from reliability studies is also analyzed to outline the performance of the proposed methodology.
Research Interests:
Matrices, Graphs and the connections between the two Read more
Achievements:
Abraham Berman received his B.Sc. (1966) and M.Sc. (1968) in mathematics from the Technion. In 1970 he received… Read more
The talk is a survey of some applications of matrix theory to graph theory and of graph theory to matrix theory.
Here are some examples: Every doubly nonnegative realization of a graph G is completely positive if and only if the line graph of G is perfect.
Graphs of pyramids are determined by their spectrum.
Construction of pairs of non regular non isomorphic graphs that are cospectral with respect to the adjacency matrix, the Laplacian, the sign less Laplacian and the normalized Laplacian.
Research Interests:
Generalized Inverses of Matrices and Linear Complimentarity Problem Read more
Achievements:
N.Eagambaram completed his M. Sc. in Statistics from Annamalai University in 1976. He worked as Lecturer in Statistics… Read more
Given a positive semi-definite matrix $G$ and another matrix $X$, we present a method of obtaining disjoint symmetric matrices $G_X$ and $G − G_X$ where range of $G_X$ is the intersection of the ranges of $G$ and $X$. $G_X$ is called a section of $G$. Properties of $G_X$ and its applications in quadratic minimization and Gauss Markov Model are given in this talk.
Research Interests:
Matrix Theory, Discrete Mathematics, Graph Theory, Combinatorial Matrix Analysis Read more
Achievements:
He has written a book titled 'Totally Nonnegative Matrices' which was published by Princeton University Press. He has… Read more
A matrix is called totally positive (TP) if all of its minors are positive. For over a century this class of matrices (and extensions to kernels, sequences, and distributions) has been studied and interesting applications continue to be developed. Recent interest on this topic stems from classifying entry-wise transformations that preserve TP matrices. While studying a particular instance of this problem we were lead to a new determinantal inequality associated with TP matrices. In verifying this inequality, we developed a technique which has proven useful for investigating families of additive and multiplicative determinantal inequalities (and identities) for TP matrices. I will discuss some of the history and recent research, which is joint with a PIMS PDF Dr. P.K. Vishwakarma.
Research Interests:
Mathematical Statistics, Medicine, Health Sciences, Psychology, Human Development, Political Science, History, the Humanities, Social Sciences, Zoology, Botany, Marine… Read more
Achievements:
Stephen J. Haslett is a former Professor and Director of the Statistical Consulting Unit. He is a Fellow… Read more
The initial results on necessary and sufficient conditions for BLUEs of estimable functions of parameters in a linear fixed effect model to remain un-altered despite changes in error covariance structure are given by Rao (1971). Rao’s results can be extended to any full rank or singular error covariance so that not only are the BLUEs in the linear model retained, but so is their covariance or their errors sum of squares. For submodels, where a full linear model is made smaller by reducing the number of regressors, block diagonal or diagonal matrices can provide insight into conditions for the full model and its entire set of submodels each to retain some or all of their BLUEs (Haslett, Istalo, Markiewicz, et al. (2023); Haslett, Puntanen (2023)) as well as retain the covariance of these BLUEs. Such error covariance changes can produce a wide variety of new cloned data sets, none of which seem to have any resemblance to the original data but which nevertheless have the same BLUEs and BLUE covariances for each submodel as for the original data. The results have application in data confidentiality, encryption, genetics and residual analysis.
Research Interests:
Algebra, Linear Algebra Read more
Achievements:
Distinguished Professor S. K. Jain served Ohio University, Department of Mathematics from 1970 to 2009. He also served… Read more
This talk will be related to the study of matrix algebras having the property that each singular element can be expressed as a product of idempotents – a subject that had and has been of interest to several mathematicians. For example, Howie was the first who showed that a non-invertible map on a finite set can be expressed a product of idempotent maps. This led to consider specific algebras having this property. Erdos, Victoria Gould, Fountain, Laffey, Lam, Leroy, O’Meara and many others studied as to when a given associative algebra has this property. Besides its intrinsic interest of studying structure of such algebras , this is also related to a long standing open question recently noted by Leroy-Jain, whether a von Neumann regular ring is always separative.
Research Interests:
Algebraic Graph Theory: Linear Algebra and its Applications to Graph Theory, Adjacency and Laplacian Spectra of Graphs. Read more
Achievements:
Debajit Kalita received his MSc degree from Gauhati University and a Ph.D. degree from IIT Guwahati. He has… Read more
In this talk, the class of bicyclic graphs with a unique perfect matching have been taken into consideration. This class is designated as $\mathcal{B}$. We identify all the graphs $B$ in $\mathcal{B}$ such that the diagonal entries of the inverse of the adjacency matrix of $B$ are all zero. We provide criteria for the adjacency of two vertices in the inverse of the graph $B\in\mathcal{B}$. Additionally, we describe the structure of those graphs in $\mathcal{B}$, whose inverse is a tree or a unicyclic graph.
Research Interests:
Algebraic and Spectral Graph Theory, Matrix Theory, Combinatorics Read more
Achievements:
Rajesh Kannan is a assistant professor in the department of Mathematics, Indian Institute of Technology Hyderabad. He has… Read more
The $\textit{eccentricity matrix}$ $\mathcal{E}(G)$ of a connected graph $G$ is obtained from the distance matrix of $G$ by keeping the largest nonzero entries in each row and each column, and leaving zeros in the remaining ones. The eigenvalues of $\mathcal{E}(G)$ are the $\mathcal{E}$-$\textit{eigenvalues}$ of $G$. It is well known that the distance matrices of tress are invertible and the determinant depends only on the number of vertices. We show that the eccentricity matrix of tree $T$ is invertible if and only if either $T$ is star or $P_4$. Also we show that any tree with odd diameter has $4$ distinct $\mathcal{E}$-eigenvalues, and any tree with even diameter has the same number of positive and negative $\mathcal{E}$-eigenvalues (which is equal to the number of ’diametrically distinguished’ vertices). Finally, we will discuss about the trees with $\mathcal{E}$-eigenvalues are symmetric with respect to the origin.
Research Interests:
Positivity and analysis, representation theory of Lie algebras, combinatorics and discrete mathematics Read more
Achievements:
Prof. Apoorva Khare is currently working as an Associate Professor in Mathematics at the Indian Institute of Science,… Read more
In this talk we discuss finite and infinite totally positive (TP) matrices, including the origins of their study — which date back morally to the 1600s, and mathematically to the 1800s. After discussing examples and basic properties of these matrices, we will see early results by Laguerre, Fekete (in correspondence with Polya), Schoenberg, and Motzkin. These results characterize total positive — and more broadly, strictly sign regular (SSR) — $n \times n$ matrices, via the variation diminishing property (VD) for all vectors of length $n$. We will end with recent results of P.N.\ Choudhury (including with coauthors) which reveal other characterizations of TP. In particular, to deduce that a matrix is TP/SSR, it suffices to consider the VD property for just a single vector for each square submatrix.
Research Interests:
Theory and Applications of Nonnegative Matrices, Combinatorial Matrix Theory, Spectral Graph Theory Read more
Achievements:
Prof. Kirkland has been published more than 130 journal articles, and author of 4 books. He is the… Read more
A square nonnegative matrix T is called stochastic if all of its row sums are equal to 1. Under mild conditions, it turns out that there is a positive row vector w^T (called the stationary distribution for T) whose entries sum to 1 such that the powers of T converge to the outer product of w^T with the all-ones vector. Further, the nature of that convergence is governed by the eigenvalues of T.
In this talk we explore how the stationary distribution for a stochastic matrix exerts an influence on the corresponding eigenvalues. We do so by considering the region in the complex plane comprised of all eigenvalues of all stochastic matrices with a given stationary distribution. We establish a few properties of that region, and of the variant that arises by considering the so-called reversible stochastic matrices. For the reversible version of the problem, the graphs associated with the reversible stochastic matrices are a useful tool.
Research Interests:
Arithmetical Function, Positive Definite Functions, Circulant Matrix, Jacobian Matrix, GCD Matrix Read more
Achievements:
Read more
In 1876 H. J. S. Smith defined an LCM matrix as follows: let $S=\{x_1,x_2,\ldots,x_n\}$ be a set of positive integers with $x_1$<$x_2$<$\cdots$<$x_n$. The LCM matrix $[S]$ on the set $S$ is the $n\times n$ matrix with $\mathrm{lcm}(x_i,x_j)$ as its $ij$ entry. During the last 30 years singularity of LCM matrices has interested many authors. In 1992 Bourque and Ligh ended up conjecturing that if the GCD closedness of the set $S$ (which means that $\gcd(x_i,x_j)\in S$ for all $i,j\in\{1,2,\ldots,n\}$), suffices to guarantee the invertibility of the matrix $[S]$. However, a few years later this conjecture was proven false first by Haukkanen et al. and then by Hong. It turned out that the conjecture holds only on GCD closed sets with at most 7 elements but not in general for larger sets. The GCD closedness of the set $S$ also makes it possible to study the invertibility and inertia of the corresponding LCM matrix by using a certain lattice theoretic method, see Altinisik, E. et al.(2017), Haukkanen, P. et al. (2020), M. Mattila et al. (2023) and Korkee, I. et al. (2018). However, this same lattice theoretic method can be applied to study the so called power LCM matrices on a GCD closed set $S$, which are simply the Hadamard powers of the ordinary LCM matrix $[S]$. In this presentation we shall make use of this lattice theoretic method and present some interesting results about singular power LCM matrices. The content of this talk is based on the articles Haukkanen, P. et al. (2015) and M. Mattila et al. (2023).
Research Interests:
Topological Graph Theory, Graph minors, Graph coloring, Algebraic graph theory, Graph algorithms Read more
Achievements:
Bojan Mohar is a professor at Department of Mathematics, Simon Fraser University, Canada. Topological Graph Theory, Graph minors,… Read more
Let $\lambda_1(T)\ge \lambda_2(T)\ge \cdots \ge\lambda_n(T)$ be the eigenvalues of an $n$-vertex tree $T$. Trees for which $\lambda_1(T)$ or $\lambda_2(T)$ is largest or smallest possible among all $n$-vertex trees have been classified. In this talk the speaker will discuss extremal trees for linear combinations
$\alpha \lambda_1(T)+ \beta \lambda_2 (T)$, where $\alpha, \beta \in \mathbb{R}$. This is joint work with Hitesh Kumar, Shivaramakrishna Pragada, and Harmony Zhan.
Research Interests:
Applied Statistics, Linear Programming, Nonlinear Programming, Non-cooperative games, Stochastic games, Statistical Quality Control, Six Sigma, Quality Management. Read more
Achievements:
Based on his research and teaching interests, in applied statistics and matrix methods, he has published several research… Read more
In this talk a new matrix class $\bar{L}(d)$ is discussed which are obtained as a limit of a sequence of $L(d)$ matrices introduced by Garcia. Various properties and characterizations of this new matrix class are discussed. Role of this new matrix class in pivoting algorithms are also explained. An application of this new matrix class that arises from general quadratic programs and polymatrix games is also discussed. Finally, an example is presented related to the existence of equilibrium in polymatrix games.
Research Interests:
Spectral Graph Theory, Linear and Multi-linear Algebra Read more
Achievements:
He is a member of the editorial board of reputable journals like Linear Multilinear algebra. Also has a… Read more
Research Interests:
Matrix methods in statistics, Generalized inverses, Canonical correlations Read more
Achievements:
He was a Senior Researcher of the Academy of Finland in 1992--1995. His main research interest lies on… Read more
In this talk I will consider my Indian experiences since 1980s: meetings with statisticians, mathematicians and the scenary, with several photographic glimpses.
Research Interests:
Game theory, Linear and non-linear programming, matrix theory, applied statistics, operations research Read more
Achievements:
Being a dynamic emeritus professor at the University of Illinois at Chicago has published more than 60 remarkable… Read more
A closed convex cone $K$ with the origin as an extreme point in $\mathbb{R}^n$ induces a partial order in $\mathbb{R}^n$. A cone $K$ is called minihedral, if the partial order induces the lattice structure. Any lattice cone with interior in $\mathbb{R}^n$ admits a basis with the property that the Cone is simply the collection of all nonnegative linear combinations of basis vectors. It is through this theorem of Yudin, that we show that any linear transformation $A$ which leaves this cone invariant with a fixed vector in the interior of the cone can be represented as a stochastic matrix with respect to a suitable basis in $K$. The theorem has extensions to stochastic operators and coordinate free representation of Positive operators as doubly stochastic matrices, with appropriate conditions.
This is a joint work with S. Natarajan and K. Viswanath
Research Interests:
Complementarity problems on symmetric cones, spectral properties of non-negative matrices and their generalizations Read more
Achievements:
He has published 14 research papers in reputed national and international journals. He has publications in linear algebra… Read more
Will be updated soon.
Research Interests:
Geometry of Banach spaces, Vector Measures, Tensor Product spaces, L^1-predual theory, Choquet theory, Function algebras, and approximation theory Read more
Achievements:
Prof. TSSRK Rao had his undergraduate education in Vijayawada. He obtained B.Sc. and M.Sc. from Andhra University and… Read more
Let X be an infinite dimensional Banach space. In this talk, we give an exposition on the problem of how finite dimensional perturbation of a subspace effects several proximinality related properties of the subspace. We also illustrate conditions on a Banach space X so that all finite codimensional subspaces of a certain type of proximinality occur as finite dimensional perturbations of some standard type of subspaces .
Research Interests:
Multivariate Analysis, Probability and Statistics, Regression Analysis, Mathematical Statistics and its applications Read more
Achievements:
He received a PhD from Stockholm University (1986). He was adviser for 18 undergraduate (master) theses in Mathematical… Read more
Penalized estimation methods will be considered (Ridge estimation). If there is a model including parameters and an estimation function, e.g., the least squares function, so called penalized estimators can be obtained. This means that the estimation function is modified by adding some ”fitting” term. However, in this presentation of the subject, restrictions are put on the parameters instead of the estimation function which in turn also will lead to a penalized estimation function. Indeed the two different approaches are very similar. The results will often be the same but interpretations can differ. In some way, from a likelihood point of view, it is more natural to put restrictions on the parameters in a model than on the estimation function. Our approach is based on convex optimization theory.
Research Interests:
Network Analysis, Graph Theory and its applications, Fuzzy logic and its applications to pattern recognition, Topology , Geometry… Read more
Achievements:
He has more than 250 publications and more than 20 books. Most of these books are prescribed as… Read more
Let $G$ be a simple graph of order $n$. The nullity $\eta(G)$ of $G$ is the algebraic multiplicity of $0$ as an eigen value of the adjacency matrix of $G$. A graph $G$ with $\eta(G) > 0$ is called a singular graph. For a bipartite graph $G$ (corresponding to an alterant hydrocarbon) if $\eta(G) > 0$, then it indicates that the molecule which such a graph represents is unstable. A characterization of graphs for which $\eta(G) > 0$ still remains open. In this talk we present a survey of results on $\eta(G)$ and indicate open problems and directions for further research.
Research Interests:
Linear and non-linear preservers, geometry of matrices, symmetries of effect algebras Read more
Achievements:
Peter Šemrl deals mainly with the area of Discrete mathematics, narrowing it down to issues related to the… Read more
Local order isomorphisms of matrix and operator domains will be discussed. A connection with Loewner’s theorem and the fundamental theorem of chronogeometry will be explained. The first one characterizes operator monotone functions while the second one describes the general form of bijective preservers of light-likeness on the classical Minkowski space.
Research Interests:
Functional Analysis, Harmonic Analysis, Quantum Information Theory Read more
Achievements:
Ajit Iqbal Singh (nee Ajit Kaur Chilana) earned her BA Hons (Mathematics) in 1963 and MA (Mathematics) (1965),… Read more
Let $m,n \ge 2$ be natural numbers. If $\xi$ and $\eta$ are vectors of length $m$ and $n$ respectively, their tensor product $\zeta = \xi \otimes \eta$ can be identified with the $ m \times n$ matrix $A = \xi \eta^t$, where $t$ is the transpose, leading to treating the tensor product $\mathcal{H}=\mathbb{C}^m \otimes \mathbb{C}^n$ as the linear space $\mathcal{M}_{m,n}$ of complex $m \times n$ matrices. Vectors $\zeta$ in $\mathcal{H}$ of the form $\xi \otimes \eta$ are called product or separable vectors and all others are called entangled vectors, the latter lot corresponds to matrices with rank $\ge 2$. Quantum Entanglement is an important and useful concept in Quantum Information Theory (QIT). Multipartite set-up $\mathcal{H} = \overunderset{k}{j=1}{\otimes} \mathcal{H}_j$ with $\mathcal{H}_j=\mathbb{C}^{d_j}$, $d_j \ge 2$ for $1 \le j \le k$ can be conveniently described as the linear space of complex polynomials in $k$ variables $\mathbf{X}=(X_j)^k_{j=1}$ with degree in $X_j$ less than or equal to $d_j-1$ for $1\le j \le k$ and it provides a simple approach to study quantum entanglement. Subspaces $\mathcal{S}$ of $\mathcal{H}$ that are completely entangled in the sense that all non-zero vectors in $\mathcal{S}$ are entangled have been well studied and two basic methods for their construction come from use of Unextendable Product Bases (UPB) and use of Van der Monde matrices by taking orthogonal complements of their linear spans $\mathcal{U}$ and $\mathcal{F}$ respectively. Examples of $\mathcal{U}$ having only finitely many well-specified product vectors and linear span of a single vector from UPB or $\mathcal{F}$ and the corresponding $\mathcal{S}$ with the same property are of interest in QTT. The talk will illustrate the related development over the decades including the recent one by us and others.
Research Interests:
Infinite Linear Programming, Generalized Inverses of Operators over Hilbert Spaces, Nonnegative Generalized Inverses, Generalizations of Matrix Monotonicity, Linear… Read more
Achievements:
K. C. Sivakumar is a Professor at Department of Mathematics, Indian Institute of Technology Madras. He obtained his… Read more
For real square matrices, it is known that, if $A$ is a singular irreducible $M$-matrix, then the only nonnegative vector that belongs to the range space of is the zero vector. In this talk, we present an analogue of this result for the Lyapunov and the Stein operators, on the space of real symmetric matrices.
Research Interests:
Matrix Theory, Graphs, Combinatorics, Combinatorial Optimization, Discrete Mathematics Read more
Achievements:
Currently a professor at IIT Bombay, Sivaramakrishnan has published more than 25 research articles in reputed national and… Read more
Associated to the $\textit{Four point condition}$ (4PC henceforth) and a tree $T$ on $n$ vertices are two matrices, the $ \text{Max}_{T} $ and the $ \text{Min}_{T} $. Both are $\binom{n}{2} \times \binom{n}{2}$ matrices.
The rows and columns of both matrices are indexed by pairs $\{i,j\}$ of vertices. The entry of the matrix $ \text{Min}_{T} $ in the row indexed by $\{i,j\}$ and column $\{k,l\}$ is the minimum value among the three terms in $S_{i,j,k,l} = \{d_{i,j} + d_{k,l}, d_{i,l} + d_{j,k}, d_{i,k} + d_{j,l} \}$. Replacing the word “minimum” by “maximum” in the previous sentence gives us the $ \text{Max}_{T} $ matrix.
Though some work has been done about the $ \text{Min}_{T} $ matrix, there is not much known about the $ \text{Max}_{T} $ matrix. We show results about the rank, give an algorithm that outputs a basis $B$ for the row space of $ \text{Max}_{T} $ and give the determinant of $ \text{Max}_{T}[B,B] $.
This is joint work with Ali Azimi, Rakesh Jana and Mukesh Nagar.
Research Interests:
Combinatorics, Graph theory Read more
Achievements:
Murali K. Srinivasan is working as a professor at the Indian Institute of Technology Bombay. He has published… Read more
Inspired by Biane’s map from involutions to Motzkin paths we define a map from subspaces to Motzkin paths, using Gauss elimination. As an application we revisit Vogt and Voigt’s remarkable solution to the Greene-Kleitman problem of constructing an explicit symmetric chain decomposition of the subspace lattice. We give a highly elegant and simpler reformulation of Vogt and Voigt’s solution.
This is joint work with Jonathan Farley.
carams.mahe@gmail.com