We present a self-consistent electronic structure calculation method based on the {\it Exact Muffin-Tin Orbitals} (EMTO) Theory developed by O. K. Andersen, O. Jepsen and G. Krier (in {\it Lectures on Methods of Electronic Structure Calculations}, Ed. by V. Kumar, O.K. Andersen, A. Mookerjee, Word Scientific, 1994 pp. 63-124) and O. K. Andersen, C. Arcangeli, R. W. Tank, T. Saha-Dasgupta, G. Krier, O. Jepsen, and I. Dasgupta, (in {\it Mat. Res. Soc. Symp. Proc.} {\bf 491}, 1998 pp. 3-34). The EMTO Theory can be considered as an {\it improved screened} KKR (Korringa-Kohn-Rostoker) method which is able to treat large overlapping potential spheres. Within the present implementation of the EMTO Theory the one electron equations are solved exactly using the Green's function formalism, and the Poisson's equation is solved within the {\it Spherical Cell Approximation} (SCA). To demonstrate the accuracy of the SCA-EMTO method test calculations have been carried out.

L. Vitos H. L. Skriver B. Johansson J. Kollár

The Ma-Dasgupta real-space renormalization methods allow to study disordered systems which are governed by strong disorder fixed points. After a general introduction to the qualitative ideas and to the quantitative renormalization rules, we describe the explicit exact results that can be obtained in various one-dimensional models, either classical or quantum, either for dynamics or statics. The main part of this dissertation is devoted to statistical physics models, with special attention to (i) the off-equilibrium dynamics of a particle diffusing in a Brownian potential or in a trap landscape, (ii) the coarsening dynamics and the equilibrium of classical disordered spin chains, (iii) the delocalization transition of a random polymer at an interface. The last part of the dissertation deals with two disordered quantum spin chains which exhibit a zero-temperature phase transition as the disorder varies, namely (a) the random antiferromagnetic S=1 spin chain, (b) the random transverse field Ising chain.

Cecile Monthus

We construct a duality cycle which provides a complete supergravity description of geometric transitions in type II theories via a flop in M-theory. This cycle connects the different supergravity descriptions before and after the geometric transitions. Our construction reproduces many of the known phenomena studied earlier in the literature and allows us to describe some new and interesting aspects in a simple and elegant fashion. A precise supergravity description of new torsional manifolds that appear on the type IIA side with branes and fluxes and the corresponding geometric transition are obtained. A local description of new G_2 manifolds that are circle fibrations over non-Kahler manifolds is presented.

Melanie Becker Keshav Dasgupta Anke Knauf Radu Tatar

We studied a doping series of (110)-oriented AlAs quantum wells (QWs) and observed transport evidence of single anisotropic-mass valley occupancy for the electrons in a 150 \AA wide QW. Our calculations of strain and quantum confinement for these samples predict single anisotropic-mass valley occupancy for well widths $W$ greater than 53 \AA. Below this, double-valley occupation is predicted such that the longitudinal mass axes are collinear. We observed mobility anisotropy in the electronic transport along the crystallographic directions in the ratio of 2.8, attributed to the mass anisotropy as well as anisotropic scattering of the electrons in the X-valley of AlAs.

S. Dasgupta S. Birner C. Knaak M. Bichler A. Fontcuberta i Morral G. Abstreiter M. Grayson

Ontology Learning has been the subject of intensive study for the past decade. Researchers in this field have been motivated by the possibility of automatically building a knowledge base on top of text documents so as to support reasoning based knowledge extraction. While most works in this field have been primarily statistical (known as light-weight Ontology Learning) not much attempt has been made in axiomatic Ontology Learning (called heavy-weight Ontology Learning) from Natural Language text documents. Heavy-weight Ontology Learning supports more precise formal logic-based reasoning when compared to statistical ontology learning. In this paper we have proposed a sound Ontology Learning tool DLOL_(IS-A) that maps English language IS-A sentences into their equivalent Description Logic (DL) expressions in order to automatically generate a consistent pair of T-box and A-box thereby forming both regular (definitional form) and generalized (axiomatic form) DL ontology. The current scope of the paper is strictly limited to IS-A sentences that exclude the possible structures of: (i) implicative IS-A sentences, and (ii) "Wh" IS-A questions. Other linguistic nuances that arise out of pragmatics and epistemic of IS-A sentences are beyond the scope of this present work. We have adopted Gold Standard based Ontology Learning evaluation on chosen IS-A rich Wikipedia documents.

Sourish Dasgupta Ankur Padia Kushal Shah Rupali KaPatel Prasenjit Majumder

We present a high accuracy Monte Carlo simulation study of the Isotropic - Nematic phase transition of a lattice dispersion model of biaxial liquid crystals. The NI coexistence curve terminating at the Landau critical point have been determined using multiple histogram reweighting technique. A close investigation reveals a sharp departure in the nature of the $N$-$I$ coexistence curve in temperature- biaxiality parameter phase diagram in comparison to the earlier theoretical (either mean-field or computer simulation) predictions.The coexitence curve shows a change in curvature with increasing value of the degree molecular biaxiality.

Nababrata Ghoshal Soumyajit Pramanick Sudeshna DasGupta Soumen Kumar Roy

The flexibility and wide applicability of the Fisher randomization test (FRT) makes it an attractive tool for assessment of causal effects of interventions from modern-day randomized experiments that are increasing in size and complexity. This paper provides a theoretical inferential framework for FRT by establishing its connection with confidence distributions Such a connection leads to development of (i) an unambiguous procedure for inversion of FRTs to generate confidence intervals with guaranteed coverage, (ii) generic and specific methods to combine FRTs from multiple independent experiments with theoretical guarantees and (iii) new insights on the effect of size of the Monte Carlo sample on the results of FRT. Our developments pertain to finite sample settings but have direct extensions to large samples. Simulations and a case example demonstrate the benefit of these new developments.

Xiaokang Luo Tirthankar Dasgupta Minge Xie Regina Liu

Voting is the aggregation of individual preferences in order to select a winning alternative. Selection of a winner is accomplished via a voting rule, e.g., rank-order voting, majority rule, plurality rule, approval voting. Which voting rule should be used? In social choice theory, desirable properties of voting rules are expressed as axioms to be satisfied. This thesis focuses on axioms concerning strategic manipulation by voters. Sometimes, voters may intentionally misstate their true preferences in order to alter the outcome for their own advantage. For example, in plurality rule, if a voter knows that their top-choice candidate will lose, then they might instead vote for their second-choice candidate just to avoid an even less desirable result. When no coalition of voters can strategically manipulate, then the voting rule is said to satisfy the axiom of Strategy-Proofness. A less restrictive axiom is Weak Strategy-Proofness (as defined by Dasgupta and Maskin (2019)), which allows for strategic manipulation by all but the smallest coalitions. Under certain intuitive conditions, Dasgupta and Maskin (2019) proved that the only voting rules satisfying Strategy-Proofness are rank-order voting and majority rule. In my thesis, I generalize their result, by proving that rank-order voting and majority rule are surprisingly still the only voting rules satisfying Weak Strategy-Proofness.

Anne Carlstein

Spin-orbit coupling (SOC) offers a large variety of novel and extraordinary magnetic and electronic properties in otherwise `ordinary pool' of heavy ion oxides. Here we present a detailed study on an apparently isolated hexagonal 2$H$ spin-chain $d^4$ iridate Sr$_3$LiIrO$_6$ (SLIO) with geometric frustration. Our structural studies clearly reveal perfect Li-Ir chemical order in this compound. Our combined experimental and {\it ab-initio} electronic structure investigations establish a magnetic ground state with finite Ir$^{5+}$ magnetic moments in this compound, contrary to the anticipated nonmagnetic $J$=0 state. Furthermore, the dc magnetic susceptibility ($\chi$), heat capacity ($C_p$) and spin-polarized density functional theory (DFT) studies unravel that despite having noticeable antiferromagnetic correlation among the Ir$^{5+}$ local moments, this SLIO system evades any kind of magnetic ordering down to at least 2 K due to geometrical frustration, arising from the comparable interchain Ir-O-O-Ir superexchange interaction strengths, hence promoting SLIO as a potential quantum spin liquid candidate.

Abhisek Bandyopadhyay A. Chakraborty S. Bhowal Vinod Kumar M. M. Sala A. Efimenko C. Meneghini I. Dasgupta T. Saha Dasgupta A. V. Mahajan Sugata Ray

Let $\mathscr{L}$ denote the $\mathbf{Q}$-vector space of logarithms of algebraic numbers. In this expository work, we provide an introduction to the study of ranks of matrices with coefficients in $\mathscr{L}$. We begin by considering a slightly different question, namely we present a proof of a weak form of Baker's Theorem. This states that a collection of elements of $\mathscr{L}$ that is linearly independent over $\mathbf{Q}$ is in fact linear independent over $\overline{\mathbf{Q}}$. Next we recall Schanuel's Conjecture and prove Ax's analogue of it over $\mathbf{C}((t))$. We then consider arbitrary matrices with coefficients in $\mathscr{L}$ and state the Structural Rank Conjecture, which gives a conjecture for the rank of a general matrix with coefficients in $\mathscr{L}$. We prove the theorem of Waldschmidt and Masser, which provides a lower bound giving a partial result toward the Structural Rank Conjecture. We conclude by stating a new conjecture that we call the Matrix Coefficient Conjecture, which gives a necessary condition for a square matrix with coefficients in $\mathscr{L}$ to be singular.

Samit Dasgupta