arXiv subjects

A. Mani

Publications and source records attributed to A. Mani.

At least 19 recordsLinked to original sources

arXiv2025

Witnessing the Effective Entanglement in the COW Protocol

We present a rigorous mathematical framework for verifying effective entanglement in a Coherent One-Way (COW) quantum key distribution setup. In particular, we introduce a two-parameter family of entanglement witnesses, identify the parameter ranges where they constitute valid witnesses, and demonstrate their ability to reveal effective entanglement in the COW protocol. Additionally, we analyze previously obtained experimental data from a COW implementation and report clear signatures of effective entanglement.

quant-ph↗

arXiv2023

Studies on the proximity effect in Bi-based high-temperature superconductor/manganite heterostructures

The effect of proximity of the magnetism of the Pr-based manganite (Pr0.6Sr0.4MnO3) on the superconductivity of Bi-based high-temperature superconductor (Bi1.75Pb0.25Sr2Ca2Cu3O10+d) was studied based on the results obtained from the magnetotransport and magnetization measurements. Decrease in the values of the upper critical field (HC2(0)) and an increase in the width of the superconducting transition (Delta TC) of Bi1.75Pb0.25Sr2Ca2Cu3O10+d were observed in proximity with the manganite. The combined effect of magnetic exchange interaction arising from the manganite, the leakage of Cooper-pairs from the superconductor into the manganite, and the diffusion and transport of spin-polarized electrons from the manganite into the superconductor were found to modify the superconducting properties of Bi1.75Pb0.25Sr2Ca2Cu3O10+d. The stacking sequence of the individual layers in these heterostructures was found to dictate the ground state properties of the heterostructure. As a consequence of the proximity effect, the colossal-magnetoresistance (CMR) ratio as high as ~ 99 % observed in the heterostructure makes the thin film heterostructures promising candidates for potential technological applications.

cond-mat.supr-con↗

arXiv2021

Mereological Emptiness for the Signed Number Problem

It is well-known (at least in the education research literature) that primary school students face considerable difficulties in the understanding of negative integers (and numbers), related operations and their visualizations. In the present research, a proposal based on mereological principles is advanced towards solving aspects of the problem by the present author. Her proposal builds on the actual semantic content of what is taught expressed in algebraic terms, and natural types that can potentially be an explicit habit.

math.HO↗

arXiv2021

General Rough Modeling of Cluster Analysis

In this research, a general theoretical framework for clustering is proposed over specific partial algebraic systems by the present author. Her theory helps in isolating minimal assumptions necessary for different concepts of clustering information in any form to be realized in a situation (and therefore in a semantics). \emph{It is well-known that of the limited number of proofs in the theory of hard and soft clustering that are known to exist, most involve statistical assumptions}. Many methods seem to work because they seem to work in specific empirical practice. A new general rough method of analyzing clusterings is invented, and this opens the subject to clearer conceptions and contamination-free theoretical proofs. Numeric ideas of validation are also proposed to be replaced by those based on general rough approximation. The essence of the approach is explained in brief and supported by an example.

cs.AI↗

arXiv2020

Encoding the information in relative parameters

We investigate the problem of communicating three parameters in the absence of shared reference frame. We explore two methods in which the relative angles of spins are used to encode the parameters. In the first method we use three spins that carry the information in their relative angles while in the second method we use three disjoint spin-pairs and the information is sent through the relative angles of each individual pair. We show that in the first method, the information conveyed by each qubit is more than the second one, and that is while it requires fewer particles.

quant-ph↗

arXiv2020

The discrete Green's function paradigm for two-way coupled Euler-Lagrange simulation

We outline a methodology for the simulation of particle-laden flows whereby the dispersed and fluid phases are two-way coupled. The drag force which couples fluid and particle momentum depends on the undisturbed fluid velocity at the particle location, and this latter quantity requires modelling. We demonstrate that the undisturbed fluid velocity, in the low particle Reynolds number limit, can be related exactly to the discrete Green's function of the discrete Stokes equations. The method is general in that it can be extended to other partial differential equations which may be associated with particle-laden flows, such as the thermal energy equation or Maxwell's equations. In this work, we demonstrate the method of discrete Green's functions by obtaining these functions for the Navier-Stokes equations at low particle Reynolds number in a two-plane channel geometry. We perform verification at low and finite particle Reynolds number for the case of a point-particle settling under gravity parallel to a plane wall, for different wall normal separations. In comparing to other point-particle schemes the discrete Green's function approach is the most robust at low particle Reynolds number, accurate at all wall-normal separations and is the most accurate in the near wall region at finite Reynolds number. We discuss how the accuracy away from the wall at finite Reynolds number could be improved by appealing to Oseen-like discrete Green's functions. Finally we demonstrate that the discrete Green's function approach can have important implications on statistics of particle-laden turbulent channel flow.

physics.flu-dyn↗

arXiv2019

High Granular Operator Spaces, and Less-Contaminated General Rough Mereologies

Granular operator spaces and variants had been introduced and used in theoretical investigations on the foundations of general rough sets by the present author over the last few years. In this research, higher order versions of these are presented uniformly as partial algebraic systems. They are also adapted for practical applications when the data is representable by data table-like structures according to a minimalist schema for avoiding contamination. Issues relating to valuations used in information systems or tables are also addressed. The concept of contamination introduced and studied by the present author across a number of her papers, concerns mixing up of information across semantic domains (or domains of discourse). Rough inclusion functions (\textsf{RIF}s), variants, and numeric functions often have a direct or indirect role in contaminating algorithms. Some solutions that seek to replace or avoid them have been proposed and investigated by the present author in some of her earlier papers. Because multiple kinds of solution are of interest to the contamination problem, granular generalizations of RIFs are proposed, and investigated. Interesting representation results are proved and a core algebraic strategy for generalizing Skowron-Polkowski style of rough mereology (though for a very different purpose) is formulated. A number of examples have been added to illustrate key parts of the proposal in higher order variants of granular operator spaces. Further algorithms grounded in mereological nearness, suited for decision-making in human-machine interaction contexts, are proposed by the present author. Applications of granular \textsf{RIF}s to partial/soft solutions of the inverse problem are also invented in this paper.

cs.LO↗

arXiv2019

The power of a shared singlet state, compared with a shared reference frame

We show that a Shared Singlet State (SSS) can supersede a Shared Reference Frame (SRF) in certain quantum communication tasks, i.e. tasks in which two remote players are required to estimate certain parameters of a two particle state sent to them. This shows that task specific value of resources maybe some what different from their common values based on their exchange possibilities.

quant-ph↗

arXiv2019

Rough Contact in General Rough Mereology

Theories of rough mereology have originated from diverse semantic considerations from contexts relating to study of databases, to human reasoning. These ideas of origin, especially in the latter context, are intensely complex. In this research, concepts of rough contact relations are introduced and rough mereologies are situated in relation to general spatial mereology by the present author. These considerations are restricted to her rough mereologies that seek to avoid contamination.

cs.LO↗

arXiv2018

Dialectical Rough Sets, Parthood and Figures of Opposition-1

In one perspective, the main theme of this research revolves around the inverse problem in the context of general rough sets that concerns the existence of rough basis for given approximations in a context. Granular operator spaces and variants were recently introduced by the present author as an optimal framework for anti-chain based algebraic semantics of general rough sets and the inverse problem. In the framework, various sub-types of crisp and non-crisp objects are identifiable that may be missed in more restrictive formalism. This is also because in the latter cases concepts of complementation and negation are taken for granted - while in reality they have a complicated dialectical basis. This motivates a general approach to dialectical rough sets building on previous work of the present author and figures of opposition. In this paper dialectical rough logics are invented from a semantic perspective, a concept of dialectical predicates is formalised, connection with dialetheias and glutty negation are established, parthood analyzed and studied from the viewpoint of classical and dialectical figures of opposition by the present author. Her methods become more geometrical and encompass parthood as a primary relation (as opposed to roughly equivalent objects) for algebraic semantics.

math.LO↗

arXiv2017

Secure alignment of coordinate systems by using quantum correlation

We show that two parties far apart can use shared entangled states and classical communication to align their coordinate systems with a very high fidelity. Moreover compared with previous methods proposed for such a task, i.e. sending parallel or anti-parallel pairs or groups of spin states, our method has the extra advantages of using single qubit measurements and also being secure, so that third parties do not extract any information about the aligned coordinate system established between the two parties. The latter property is important in many other quantum information protocols in which measurements inevitably play a significant role.

quant-ph↗

arXiv2017

Approximations from Anywhere and General Rough Sets

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present author in her earlier papers. From the practical perspective, a few (as opposed to one) theoretical frameworks may be suitable for formulating the problem itself. \emph{Granular operator spaces} have been recently introduced and investigated by the present author in her recent work in the context of antichain based and dialectical semantics for general rough sets. The nature of the inverse problem is examined from number-theoretic and combinatorial perspectives in a higher order variant of granular operator spaces and some necessary conditions are proved. The results and the novel approach would be useful in a number of unsupervised and semi supervised learning contexts and algorithms.

math.LO↗

arXiv2017

Combinatorial Aspects of the Distribution of Rough Objects

The inverse problem of general rough sets, considered by the present author in some of her earlier papers, in one of its manifestations is essentially the question of when an agent's view about crisp and non crisp objects over a set of objects has a rough evolution. In this research the nature of the problem is examined from number-theoretic and combinatorial perspectives under very few assumptions about the nature of data and some necessary conditions are proved.

cs.AI↗

arXiv2017

Pure Rough Mereology and Counting

The study of mereology (parts and wholes) in the context of formal approaches to vagueness can be approached in a number of ways. In the context of rough sets, mereological concepts with a set-theoretic or valuation based ontology acquire complex and diverse behavior. In this research a general rough set framework called granular operator spaces is extended and the nature of parthood in it is explored from a minimally intrusive point of view. This is used to develop counting strategies that help in classifying the framework. The developed methodologies would be useful for drawing involved conclusions about the nature of data (and validity of assumptions about it) from antichains derived from context. The problem addressed is also about whether counting procedures help in confirming that the approximations involved in formation of data are indeed rough approximations?

cs.AI↗

arXiv2016

On Deductive Systems of AC Semantics for Rough Sets

Antichain based semantics for general rough sets were introduced recently by the present author. In her paper two different semantics, one for general rough sets and another for general approximation spaces over quasi-equivalence relations, were developed. These semantics are improved and studied further from a lateral algebraic logic perspective in this research. The main results concern the structure of the algebras and deductive systems in the context.

math.LO↗

arXiv2015

FOSS-Based Grid Computing

In this expository paper we will be primarily concerned with core aspects of Grids and Grid computing using free and open-source software with some emphasis on utility computing. It is based on a technical report entitled 'Grid-Computing Using GNU/Linux' by the present author. This article was written in 2006 and should be of historical interest.

cs.DC↗

arXiv2014

Algebraic Semantics of Proto-Transitive Rough Sets

Rough sets over generalized transitive relations like proto-transitive ones had been initiated by the present author in the year 2012. Subsequently, approximation of proto-transitive relations by other relations was investigated and the relation with rough approximations was developed towards constructing semantics that can handle fragments of structure. It was also proved that difference of approximations induced by some approximate relations need not induce rough structures. In this research we develop different semantics of proto transitive rough sets (PRAX) after characterizing the structure of rough objects and also develop a theory of dependence for general rough sets and use it to internalize the Nelson-algebra based approximate semantics developed earlier. The theory of rough dependence initiated later by the present author is extended in the process. This monograph is reasonably self-contained and includes proofs and extensions of representation of objects that were not part of earlier papers.

cs.AI↗

arXiv2014

Dialectics of Counting and the Mathematics of Vagueness

New concepts of rough natural number systems are introduced in this research paper from both formal and less formal perspectives. These are used to improve most rough set-theoretical measures in general Rough Set theory (\textsf{RST}) and to represent rough semantics. The foundations of the theory also rely upon the axiomatic approach to granularity for all types of general \textsf{RST} recently developed by the present author. The latter theory is expanded upon in this paper. It is also shown that algebraic semantics of classical \textsf{RST} can be obtained from the developed dialectical counting procedures. Fuzzy set theory is also shown to be representable in purely granule-theoretic terms in the general perspective of solving the contamination problem that pervades this research paper. All this constitutes a radically different approach to the mathematics of vague phenomena and suggests new directions for a more realistic extension of the foundations of mathematics of vagueness from both foundational and application points of view. Algebras corresponding to a concept of \emph{rough naturals} are also studied and variants are characterised in the penultimate section.

math.LO↗