Department of History

Ashoka University is a private university located in Sonipat, Haryana, India, focusing on liberal arts and sciences. It was established in 2014.&nbsp;It is guided by an academic council of academics and scholars from around the world. The council sets the university&#39;s academic standard, advising on matters of curriculum, faculty hiring and research.&nbsp;

Ashoka University offers a full-time 3 (+ 1) year undergraduate programme. The University comprises of&nbsp;2500 plus students, with a mix of both national and international students.&nbsp; &nbsp;

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Ashoka University

In this paper we consider Anderson models with a large number of sites with zero interaction. For such models we study the spectral statistics in the region of complete localization. We show that Poisson statistics holds for such energies, by proving the Minami estimate. © European Mathematical Society.

World University root node

Department of Mathematics

Fulltext

Journal of Spectral Theory

Spectral statistics for anderson models with sporadic potentials

Branching Brownian motion (BBM) is used as a population model where the location of a particle on the real line represents his or her fitness which evolves according to a Brownian motion due to mutations. In this context, the genealogical tree of the particles is important to understand the evolution of the population over time. The main goal of this article is to give an overview and motivations for some of the results on the genealogy of extremal particles of BBM. In the first part of this article, we discuss the results of L.-P. Arguin, A. Bovier and N. Kistler from [Genealogy of Extremal Particles of BBM, 2011] and [Poissonian Statistics in the Extremal Process of BBM, 2012]. Their articles give a partial answer to what the distribution of the limiting extremal process of BBM looks like. These two articles highlight, how genetical information can successfully be used to obtain rather extensive information for the limiting particle picture. In the second part, we discuss the results of J. Berestycki, N. Berestycki and J. Schweinsberg from [The Genealogy of BBM with Absorption, 2013]. BBM with absorption is related to a population model with selection. This article shows that the genealogy of the surviving particles (with a selective advantage), which are 'local' extremal particles, is then governed by a Bolthausen-Sznitman coalescent process. This result is in sharp contrast to the standard population models without selection.

Lecture Notes Series, Institute for Mathematical Sciences

The Genealogy of Extremal Particles of Branching Brownian Motion

Department of Environmental Studies

Labour and Environment confusions, conflicts closeness (Module VII)

Department of Philosophy

Journal of Value Inquiry

On the Alleged Laziness of Moral Realists

Model approaches to nuclear architecture have traditionally ignored the biophysical consequences of ATP-fueled active processes acting on chromatin. However, transcription-coupled activity is a source of stochastic forces that are substantially larger than the Brownian forces present at physiological temperatures. Here, we describe an approach to large-scale nuclear architecture in metazoans that incorporates cell-type-specific active processes. The model predicts the statistics of positional distributions, shapes, and overlaps of each chromosome. Simulations of the model reproduce common organizing principles underlying large-scale nuclear architecture across human cell nuclei in interphase. These include the differential positioning of euchromatin and heterochromatin, the territorial organization of chromosomes (including both gene-density-based and size-based chromosome radial positioning schemes), the nonrandom locations of chromosome territories, and the shape statistics of individual chromosomes. We propose that the biophysical consequences of the distribution of transcriptional activity across chromosomes should be central to any chromosome positioning code.

Department of Biology

Biophysical Journal

Nonequilibrium Biophysical Processes Influence the Large-Scale Architecture of the Cell Nucleus

We employed functional magnetic resonance imaging (fMRI) and diffuse tensor imaging (DTI) to study neural implications of silent reading of words in mutually comprehensible but visually and orthographically distinct languages for example Hindi and Urdu by independent groups of skilled readers. The fMRI results (conjunction analyses) showed the left inferior frontal gyrus (BA 44/45), bilateral inferior occipital (BA 18/19), bilateral superior parietal (BA 7), left pre-central region (BA 6), and bilateral inferior temporal gyrus (BA 20) as common regions for Hindi and Urdu readers. Some additional regions such as left ventral occipitotemporal, left middle frontal (BA 46), left middle occipital (BA18), and bilateral post-central regions (BA 3) were observed for Urdu readers. DTI results showed significantly higher FA value at the left inferior fronto-occipital fasciculus in Urdu speakers. Overall findings suggest strong engagement of ventral visual pathway in reading Urdu which has a visually complex deep orthography.

Other Publications

Reading and Writing

The effect of written scripts’ dissimilarity over ventral and dorsal reading pathway: combined fMRI &amp; DTI study

Drive-by sensing has emerged as a popular way to achieve fine-grained sensing of physical phenomena. However, for it to be effective at a city-scale, there is a need to optimally select a subset of vehicles from a larger available fleet. These chosen vehicles must maximize coverage of the entire city. Simultaneously, they must fulfill other deployment requirements specific to the sensing application such as reference-monitor colocation instances for gas sensors. In this paper, we describe a system to evaluate the coverage offered by different subsets of vehicles for sensor deployment based on historical vehicle mobility data. Our system allows evaluation of different vehicle selection algorithms, and also provides two in-built baselines - - i) Random-MP, and ii) MaxPoints - - for comparison. Finally, we provide visualizations showing coverage to gauge the efficacy of different vehicle selections. © 2019 Authors.

SenSys 2019 - Proceedings of the 17th Conference on Embedded Networked Sensor Systems

System for vehicle selection in drive-by sensing: Poster abstract

Users of web browsers today swim in a sea of haphazardly organized tabs, bookmarks, searches and downloads. This is because browsers operate at the level of individual web pages, and rarely understand the user’s high-level tasks. We propose to address this problem by compartmentalizing the web browsing experience across different tasks defined by the user. Wedescribe Sailboat, an extension for Google Chrome that explores this idea by making user-defined tasks first-class objects in the browsing experience. In Sailboat, different tasks have their own tabs, history, bookmarks and download folders, while maintaining a unified identity across compartments. Sailboat lets the user create and switch between tasks such as "Philosophy Paper", "Summer Internships", and "Trip to China". Users can encapsulate the browsing related to a task, archive it or share it with others, and come back to it months later. Sailboat also tracks and reflects the analytics of time spent on different tasks to aid productivity. Wedeployed Sailboat with several users, and studied how they engaged with it. Our users report that Sailboat aids organized browsing, reduces distractions, and is easy to get used to.

Compartmentalizing web browsing with Sailboat

A matrix is MDS or super-regular if and only if every square submatrices of it are nonsingular. MDS matrices provide perfect diffusion in block ciphers and hash functions. In this paper we provide a brief survey on cryptographically significant MDS matrices - a first to the best of our knowledge. In addition to providing a summary of existing results, we make several contributions. We exhibit some deep and nontrivial interconnections between different constructions of MDS matrices. For example, we prove that all known Vandermonde constructions are basically equivalent to Cauchy constructions. We prove some folklore results which are used in MDS matrix literature. Wherever possible, we provide some simpler alternative proofs. We do not discuss efficiency issues or hardware implementations; however, the theory accumulated and discussed here should provide an easy guide towards efficient implementations. © 2019 AIMS.

Advances in Mathematics of Communications

Cryptographically significant mds matrices over finite fields: A brief survey and some generalized results

On the space of positive definite matrices, we consider distance functions of the form 𝑑(𝐴,𝐵)=[tr𝒜(𝐴,𝐵)−tr𝒢(𝐴,𝐵)]1/2,<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mrow><mo>[</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="script">A</mi></mrow><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo><mo>−</mo><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="script">G</mi></mrow><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo><mo>]</mo></mrow><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup><mo>,</mo></math>&nbsp;where 𝒜(𝐴,𝐵)<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="script">A</mi></mrow><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo></math>&nbsp;is the arithmetic mean and 𝒢(𝐴,𝐵)<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="script">G</mi></mrow><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo></math>&nbsp;is one of the different versions of the geometric mean. When 𝒢(𝐴,𝐵)=𝐴1/2𝐵1/2<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="script">G</mi></mrow><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup></math>&nbsp;this distance is ‖𝐴1/2−𝐵1/2‖2,<math xmlns="http://www.w3.org/1998/Math/MathML"><mo fence="false" stretchy="false">‖</mo><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup><mo>−</mo><msup><mi>B</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup><msub><mo fence="false" stretchy="false">‖</mo><mn>2</mn></msub><mo>,</mo></math>&nbsp;and when 𝒢(𝐴,𝐵)=(𝐴1/2𝐵𝐴1/2)1/2<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="script">G</mi></mrow><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup><mi>B</mi><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup></math>&nbsp;it is the Bures–Wasserstein metric. We study two other cases: 𝒢(𝐴,𝐵)=𝐴1/2(𝐴−1/2𝐵𝐴−1/2)1/2𝐴1/2,<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="script">G</mi></mrow><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup><mo stretchy="false">(</mo><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup><mi>B</mi><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mo>−</mo><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup><msup><mi>A</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mrow></msup><mo>,</mo></math>&nbsp;the Pusz–Woronowicz geometric mean, and 𝒢(𝐴,𝐵)=exp(log𝐴+log𝐵2),<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="script">G</mi></mrow><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo><mo>=</mo><mi>exp</mi><mo>⁡</mo><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mo maxsize="1.2em" minsize="1.2em">(</mo></mrow></mstyle><mfrac><mrow><mi>log</mi><mo>⁡</mo><mi>A</mi><mo>+</mo><mi>log</mi><mo>⁡</mo><mi>B</mi></mrow><mn>2</mn></mfrac><mstyle scriptlevel="0"><mrow class="MJX-TeXAtom-ORD"><mo maxsize="1.2em" minsize="1.2em">)</mo></mrow></mstyle><mo>,</mo></math>&nbsp;the log Euclidean mean. With these choices, d(A,&nbsp;B) is no longer a metric, but it turns out that 𝑑2(𝐴,𝐵)<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>d</mi><mn>2</mn></msup><mo stretchy="false">(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo stretchy="false">)</mo></math>&nbsp;is a divergence. We establish some (strict) convexity properties of these divergences. We obtain characterisations of barycentres of m positive definite matrices with respect to these distance measures. One of these leads to a new interpretation of a power mean introduced by Lim and Palfia, as a barycentre. The other uncovers interesting relations between the log Euclidean mean and relative entropy.