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Articles 1 - 30 of 466
Full-Text Articles in Mathematics
C*-Extreme Quantum Instruments; Completion And Disintegration Of Completely Positive Maps, Arghya Chongdar
C*-Extreme Quantum Instruments; Completion And Disintegration Of Completely Positive Maps, Arghya Chongdar
Doctoral Theses
This thesis develops a comprehensive operator-algebraic framework for the study of completely positive (CP) instruments, with contributions spanning convexity theory, integration theory, completion problems, and disintegration theory. We begin by laying the foundational groundwork in the theory of C*-algebras and von Neumann algebras, introducing key structures such as CP maps, positive operator-valued measures (POVMs), and CP instruments, along with their dilation-theoretic properties. Pure and decomposable instruments are characterized via minimal bi-dilations, and CP instruments are realized as bivariate maps, providing a rigorous quantum analogue of classical joint measures. The thesis then investigates convexity-theoretic aspects of instruments. A structural characterization of …
Projective Corepresentations And Cohomology Of Compact Quantum Groups, Kiran Maity
Projective Corepresentations And Cohomology Of Compact Quantum Groups, Kiran Maity
Doctoral Theses
In this thesis, we briefly review various types of projective corepresentations of compact quantum groups and prove the existence of suitable envelopes for them. We also study the associated invariant (dual) 2-cohomology and calculate it in a few concrete examples
Restricted Mean Value Property On Riemannian Manifolds And Carleson's Problem On Damek-Ricci Spaces, Utsav Dewan
Restricted Mean Value Property On Riemannian Manifolds And Carleson's Problem On Damek-Ricci Spaces, Utsav Dewan
Doctoral Theses
One of the most key aspects of Harmonic Analysis is the study of the boundary behaviour of solutions of Partial Differential Equations. The central theme of this thesis is to study such problems for some suitable classes of Riemannian manifolds. We first study the restricted mean value property (RMVP for short) in the context of Riemannian manifolds. For a pre-compact domain D with smooth boundary in a Riemannian manifold M, we first prove that any real-valued, bounded, continuous function u satisfying the RMVP in D, having boundary limits in a full measure subset of the boundary, is harmonic in D. …
On Algebraic Aspects And Functoriality Of The Set Of Unbounded Operators Affiliated With A Von Neumann Algebra, Indrajit Ghosh
On Algebraic Aspects And Functoriality Of The Set Of Unbounded Operators Affiliated With A Von Neumann Algebra, Indrajit Ghosh
Doctoral Theses
In quantum theory, physically meaningful observables such as position and momentum are modeled by unbounded self-adjoint operators on Hilbert spaces. To study such operators in a rigorous mathematical framework, Murray and von Neumann introduced the concept of affiliation with a von Neumann algebra, giving rise to what are now known as Murray–von Neumann affiliated operators. For a single (unbounded) self-adjoint operator, its spectral projections span an abelian von Neumann algebra to which the operator is affiliated. If we want a common framework to study families of (unbounded) self-adjoint operators which do not necessarily commute with each other, it is instructive …
Second Moment Of Degree Three L-Functions, Sampurna Pal
Second Moment Of Degree Three L-Functions, Sampurna Pal
Doctoral Theses
Let $F$ be a Hecke-Maa\ss\ cusp form for $SL(3,\mathbb{Z})$. In this dissertation, we obtain a non-trivial upper bound of the second moment of $L(F,s)$ in the $t$-aspect: $$ \int_{T}^{2T}|L(F,1/2+it)|^2 dt\ll_{F,\epsilon} T^{3/2-3/32+\epsilon}.$$ Immediate corollaries include improvements over the existing results on the Subconvexity bound for self-dual $GL(3)$ $L$-functions in the $t$-aspect and for self-dual $GL(3)\times GL(2)$ $L$-functions in the $GL(2)$ spectral aspect, the error term in the Rankin-Selberg problem, and the zero density estimate for $GL(3)$ $L$-functions.
Dynamics Of Random Graphs And Interacting Particle Systems, Aritra Mandal
Dynamics Of Random Graphs And Interacting Particle Systems, Aritra Mandal
Doctoral Theses
The talk will be based on the thesis which has broadly two objectives. In the first part of the thesis we study a certain random dynamics of discrete sparse graphs on n vertices(based on the Moran model) and understand the limit as n goes to infinity. In the second part of the thesis we provide a trajectorial representation for a semi linear parabolic partial differential equation. In this talk we will mainly focus on the results concerning the dynamics of sparse graphs. We will begin with the preliminaries of the sparse graphs and convergences. Following which we will define the …
Crystallization Of The Quantized Function Algebras Of Suq(N + 1), Manabendra Giri
Crystallization Of The Quantized Function Algebras Of Suq(N + 1), Manabendra Giri
Doctoral Theses
The $q$-deformation of a connected, simply connected Lie group $G$ is typically studied through two Hopf algebras associated with it: the quantized universal enveloping algebra $\mathcal{U}_q(\mathfrak{g})$ and the quantized function algebra $\mathcal{O}(G_q)$. If $G$ has a compact real form $K$, one can use the Cartan involution to give a $*$-structure on $\mathcal{O}(G_q)$. The QFA $\mathcal{O}(G_q)$ with this $*$ structure is denoted by $\mathcal{O}(K_q)$ and its $C^*$-completion by $C(K_q)$. Here we study the crystal limits of $\mathcal{O}(SU_q(n+1))$ and $C(SU_q(n+1))$ and classify all irreducible representations of the crystallized algebras. We also prove that the crystallized algebra carries a natural bialgebra structure.
Some Studies On Mathematical Morphology In Remotely Sensed Data Analysis, Geetika Barman
Some Studies On Mathematical Morphology In Remotely Sensed Data Analysis, Geetika Barman
Doctoral Theses
The application of Mathematical Morphology (MM) techniques has proven to be beneficial in the extraction of shapebased and texture-based features during remote sensing image analysis. The characteristics of these techniques, such as nonlinear adaptability and comprehensive lattice structure, make them useful for contextual spatial feature analysis. Despite the advancements, there are still persistent challenges, including the curse of dimensionality, maintaining spatial correlation, and the adaptability of morphological operators in higher dimensions. The focus of this thesis is to explore the potential of MM-based methods to analyse spatial features in addressing these challenges, specifically in the context of spatialcontextual feature analysis …
C∗-Extreme Maps And Nest Algebras, Manish Kumar Dr.
Randomized Algorithms For Resource Allocation In Device To Device Communication., Subhankar Ghosal Dr.
Randomized Algorithms For Resource Allocation In Device To Device Communication., Subhankar Ghosal Dr.
Doctoral Theses
In device to device (D2D) communication, two users residing in close proximity can directly communicate between them, through a common channel, without the need of a base station. A pair of D2D users forms a link and a channel needs to be allocated to it. The interference relationship among the active links at time t is modelled as an interference graph g(t). To establish interference-free communication, we have to assign a channel vector C(t) and a power vector corresponding to the active links such that the required signal to interference plus noise ratio (SINR) is satisfied for each link. Since …
On Moments Of Certain Families Of L-Functions, Gopal Maiti
On Moments Of Certain Families Of L-Functions, Gopal Maiti
Doctoral Theses
In this thesis, I described the notion of moments of L-functions in some families. Then I discussed some problems on estimating moments of L-functions. As applications, I showed some simultaneous non-vanishing and correlation results of certain product L-functions over number fields as well as function fields.
Morphological Network: Network With Morphological Neurons., Ranjan Mondal Dr.
Morphological Network: Network With Morphological Neurons., Ranjan Mondal Dr.
Doctoral Theses
Image processing with traditional approaches mainly use the tools of linear systems. However, linear approaches are not well suited and may even fail to solve problems involving geometrical aspects of the image. Thus, nonlinear geometric approaches like morphological operations are very popular in those cases. Morphological operations are nonlinear operations based on a set and lattice-theoretic methodology for image analysis that are capable of describing the geometrical structure of image objects quantitatively. It is suitable for various problems in image processing, computer vision, and pattern recognition. While solving problems with morphology, a particular structuring element is defined. Structuring elements have …
Constructions And Analyses Of Efficient Symmetric-Key Primitives For Authentication And Encryption., Sebati Ghosh Dr.
Constructions And Analyses Of Efficient Symmetric-Key Primitives For Authentication And Encryption., Sebati Ghosh Dr.
Doctoral Theses
In symmetric key cryptography there are two fundamental objectives, viz. 1. confidentiality or secrecy of message from unexpected party and 2. authentication of message which includes authenticating the source of the message as well as integrity of the message against any unwanted modification. Let us first concentrate on confidentiality. In classical symmetric key cryptography two parties, say Alice and Bob, first secretly exchange a key-pair (e, d). Later, if Alice wishes to send a secret message m ∈ M to Bob, she computes c = Ee(m) and transmits c to Bob. Upon receiving c, Bob computes Dd(c) = m and …
Computing Well-Structured Subgraphs In Geometric Intersection Graphs., Satyabrata Jana Dr.
Computing Well-Structured Subgraphs In Geometric Intersection Graphs., Satyabrata Jana Dr.
Doctoral Theses
For a set of geometric objects, the associative geometric intersection graph is the graph with a vertex for each object and an edge between two vertices if and only if the corresponding objects intersect. Geometric intersection graphs are very important due to their theoretical properties and applicability. Based on the different geometric objects, several types of geometric intersection graphs are defined. Given a graph G, an induced (either vertex or edge) subgraph H ⊆ G is said to be an well-structured subgraph if H satisfies certain properties among the vertices in H. This thesis studies some well-structured subgraphs finding problems …
Essays On The Economics Of Conflict., Ranajoy Guha Neogi Dr.
Essays On The Economics Of Conflict., Ranajoy Guha Neogi Dr.
Doctoral Theses
The thesis encompasses three chapters which provide policy-relevant insights into the domain of conflict economics. The research endeavour goes deep into exploring the underlying linkages of varied economic and non-economic factors (e.g., culture, religion and myriads of ethnic factors) leading to the multiple facets of economic outcomes. The analyses in the thesis, which fall in the realm of applied microeconomic theory, are facilitated by different tools of game theory and public economics. Although the focuses of these chapters lie in the domain of economics of conflict (and its policy implications under different situations), each chapter addresses the conflicts engendered in …
Essays In Multidimensional Mechanism Design., Kolagani Paramahamsa Dr.
Essays In Multidimensional Mechanism Design., Kolagani Paramahamsa Dr.
Doctoral Theses
This thesis analyzes three problems where a monopolistic seller is selling to an agent with multidimensional private information. While our understanding of such problems is comprehensive if the agent's private information is one-dimensional, problems with multidimensional private information are known to be ubiquitous but analytically notorious. The three chapters in this thesis make progress in understanding optimal mechanism design in such multidimensional screening problems. In the first problem, the seller is selling an object to an agent who exhibits behavioral preferences, in a departure from the standard rational models. Behavioral preferences arise because the agent is budget constrained and needs …
Efficient Handover Mechanisms For Heterogeneous Networks., Shankar Kumar Ghosh Dr.
Efficient Handover Mechanisms For Heterogeneous Networks., Shankar Kumar Ghosh Dr.
Doctoral Theses
In this thesis, some analytical frameworks have been developed to analyze the effect of different system parameters on handover performances in heterogeneous network (HetNet) and based on such frameworks, some efficient handover algorithms have been proposed. The study starts with an analytical framework to investigate the effect of resource allocation mechanisms, upper layer mobility management protocols (MMPs) and handover decision metrics on user perceived throughput. This analysis reveals that among other factors, handover decision metric plays a crucial role in determining user perceived throughput in HetNet. Subsequently, we develop two handover decision metrics for ultra dense networks (UDN) and unlicensed …
Essays On Social Networks, Workplace Ties And Labor Productivity., Swati Sharma Dr.
Essays On Social Networks, Workplace Ties And Labor Productivity., Swati Sharma Dr.
Doctoral Theses
The role of social contacts in finding jobs, career mobility and other labor market outcomes is well acknowledged both theoretically and empirically in labor economics. The existence of individuals’ social networks at their workplace is a pervasive phenomenon, leading to the widespread use of social ties for information, influence and referrals on both sides of the labor market. The central theme of this thesis is to examine the interplay of ‘off-workplace socio-economic interdependence’ and outcomes at the workplace. Understanding this interdependence has the potential to devise policies which can impact labor productivity, especially in developing countries. This thesis divided into …
Zero-Knowledge Proof, Deniability And Their Applications In Blockchain, E-Voting And Deniable Secret Handshake Protocols., Somnath Panja Dr.
Zero-Knowledge Proof, Deniability And Their Applications In Blockchain, E-Voting And Deniable Secret Handshake Protocols., Somnath Panja Dr.
Doctoral Theses
In this thesis, we propose a cryptographic technique for an authenticated, end-to-end verifiable and secret ballot election. Currently, almost all verifiable e-voting systems require trusted authorities to perform the tallying process except for the DRE-i and DRE-ip systems. We have shown a weaknesses in the DRE-ip system and proposed a solution. We have modified the DRE-ip system so that no adversary can create and post a valid ballot on the public bulletin board without detection. We provide security proofs to prove the security properties of the proposed scheme. We propose two methods to store these ballots using blockchain and cloud …
Mathematical Formulations For Complex Resource Scheduling Problems., T. R. Lalita Dr.
Mathematical Formulations For Complex Resource Scheduling Problems., T. R. Lalita Dr.
Doctoral Theses
This thesis deals with development of effective models for large scale real-world resource scheduling problems. Efficient utilization of resources is crucial for any organization or industry as resources are often scarce. Scheduling them in an optimal way can not only take care of the scarcity but has potential economic benefits. Optimal utilization of resources reduces costs and thereby provides a competitive edge in the business world. Resources can be of different types such as human (personnel-skilled and unskilled), financial(budgets), materials, infrastructures(airports and seaports with designed facilities, windmills, warehouses’ area, hotel rooms etc) and equipment (microprocessors, cranes, machinery, aircraft simulators for …
Many-Objective Evolutionary Algorithms: Objective Reduction, Decomposition And Multi-Modality., Monalisa Pal Dr.
Many-Objective Evolutionary Algorithms: Objective Reduction, Decomposition And Multi-Modality., Monalisa Pal Dr.
Doctoral Theses
Evolutionary Algorithms (EAs) for Many-Objective Optimization (MaOO) problems are challenging in nature due to the requirement of large population size, difficulty in maintaining the selection pressure towards global optima and inability of accurate visualization of high-dimensional Pareto-optimal Set (in decision space) and Pareto-Front (in objective space). The quality of the estimated set of Pareto-optimal solutions, resulting from the EAs for MaOO problems, is assessed in terms of proximity to the true surface (convergence) and uniformity and coverage of the estimated set over the true surface (diversity). With more number of objectives, the challenges become more profound. Thus, better strategies have …
Interplay Between Education And Identity: Inter Caste Marriages, Gendered Stream Choice And Caste Peer Effects., Komal Sahai Dr.
Interplay Between Education And Identity: Inter Caste Marriages, Gendered Stream Choice And Caste Peer Effects., Komal Sahai Dr.
Doctoral Theses
No abstract provided.
On Class Imbalanced Learning:Design Of Non-Parametricclassifiers, Performance Indices, And Deep Oversampling Strategies., Sankha Mullick Dr.
On Class Imbalanced Learning:Design Of Non-Parametricclassifiers, Performance Indices, And Deep Oversampling Strategies., Sankha Mullick Dr.
Doctoral Theses
The relevance of classification is almost endless in the everyday application of machine learning. However, the performance of a classifier is only limited to the fulfillment of the inherent assumptions it makes about the training examples. For example, to facilitate unbiased learning a classifier is expected to be trained with an equal number of labeled data instances from all of the classes. However, in a large number of practical applications such as anomaly detection, semantic segmentation, disease prediction, etc. it may not be possible to gather an equal number of diverse training points for all the classes. This results in …
Optimal Eavesdropping In Quantum Cryptography, Atanu Acharyya Dr.
Optimal Eavesdropping In Quantum Cryptography, Atanu Acharyya Dr.
Doctoral Theses
Quantum key distribution (QKD) has raised some promise for more secured communication than its classical counterpart. It allows the legitimate parties to detect eavesdropping which introduces error in the channel. If disturbed, there are ways to distill a secure key within some threshold error-rate. The amount of information gained by an attacker is generally quantified by (Shannon) mutual information. Knowing the maximum amount of information that an intruder can gain is important for post-processing purposes, and we mainly focus on that side in the thesis. Renyi information is also useful especially when post-processing is considered. The scope of this thesis …
Locally Dependent Natural Image Priors For Non-Blind And Blind Image Deconvolution., Kaustav Nandy Dr.
Locally Dependent Natural Image Priors For Non-Blind And Blind Image Deconvolution., Kaustav Nandy Dr.
Doctoral Theses
Degradation of photographic images is a common phenomenon that can occur due to several reasons. Astronomical images may be degraded due to atmospheric factors or telescope optics. Photographs taken using standard digital cameras may be blurred due to lack of focus, due to motion of the subject, due to low resolution, or due to camera shake during relatively long exposures. Often one wishes to correct for the effect of such degradation and recover the original image, and this has been a long-standing research problem in digital imaging. Effective solutions depend critically on the context of the problem and the type …
A Brief Treatise On Bayesian Inverse Regression., Debashis Chatterjee Dr.
A Brief Treatise On Bayesian Inverse Regression., Debashis Chatterjee Dr.
Doctoral Theses
Inverse problems, where in a broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific disciplines. However, apart from the class of traditional inverse problems, there exists another class of inverse problems, which qualify as more authentic class of inverse problems, but unfortunately did not receive as much attention.In a nutshell, the other class of inverse problems can be described as the problem of predicting the covariates corresponding to given responses and the rest of the data. …
Secret Sharing And Its Variants, Matroids,Combinatorics., Shion Samadder Chaudhury Dr.
Secret Sharing And Its Variants, Matroids,Combinatorics., Shion Samadder Chaudhury Dr.
Doctoral Theses
The main focus of this thesis is secret sharing. Secret Sharing is a very basic and fundamental cryptographic primitive. It is a method to share a secret by a dealer among different parties in such a way that only certain predetermined subsets of parties can together reconstruct the secret while some of the remaining subsets of parties can have no information about the secret. Secret sharing was introduced independently by Shamir [139] and Blakely [20]. What they introduced is called a threshold secret sharing scheme. In such a secret sharing scheme the subsets of parties that can reconstruct a secret …
Some Nonparametric Hybrid Predictive Models : Asymptotic Properties And Applications., Tanujit Chakraborty Dr.
Some Nonparametric Hybrid Predictive Models : Asymptotic Properties And Applications., Tanujit Chakraborty Dr.
Doctoral Theses
Prediction problems like classification, regression, and time series forecasting have always attracted both the statisticians and computer scientists worldwide to take up the challenges of data science and implementation of complicated models using modern computing facilities. But most traditional statistical and machine learning models assume the available data to be well-behaved in terms of the presence of a full set of essential features, equal size of classes, and stationary data structures in all data instances, etc. Practical data sets from the domain of business analytics, process and quality control, software reliability, and macroeconomics, to name a few, suffer from various …
Three Essays On The Political Economics Of Conflict., Dripto Bakshi Dr.
Three Essays On The Political Economics Of Conflict., Dripto Bakshi Dr.
Doctoral Theses
A standard practice in the sociological and comparative-politics literature is to interpret ethnicity broadly as identity cleavages deriving from non-class categories such as language, religion, race and caste. In recent decades, conflicts between ‘ethnic’ communities, i.e., groups divided along non-class identity dimensions such as race, language, and, in particular, religion, have attained increasing salience in many countries. In response to this, a large analytical and empirical literature has developed both in political science and in political economics that seeks to explicate various aspects of this phenomenon. This thesis aims to throw light on two major aspects of ethnic conflicts. (1) …
Some Contributions To Free Probability And Random Matrices., Sukrit Chakraborty Dr.
Some Contributions To Free Probability And Random Matrices., Sukrit Chakraborty Dr.
Doctoral Theses
No abstract provided.