A partial order on classical and quantum states

In this work we extend the work done by Bob Coecke and Keye Martin in their paper “Partial Order on Classical States and Quantum States (2003)”. We review basic notions involving elementary domain theory, the set of probability measures on a finite set {a1, a2, ..., an}, which we identify with the standard (n-1)-simplex ∆n and Shannon Entropy. We consider partial orders on ∆n, which have the Entropy Reversal Property (ERP) : elements lower in the order have higher (Shannon) entropy or equivalently less information . The ERP property is important because of its applications in quantum information theory. We define a new partial order on ∆n, called Stochastic Order , using the well-known concept of majorization order and show that it has the ERP property and is also a continuous domain. In contrast, the bayesian order on ∆n defined by Coecke and Martin has the ERP property but is not continuous

Strategic Default and Moral Hazard in Real Estate: Insights from Machine Learning Applications

Strategic default has been the achilles heel in academic finance for decades. By definition, whether a default has occurred due to strategic motive is unobservable. Moreover, a household has only so many avenues of conducting a strategic default. I use the context of commercial mortgages as property value as well property cashflow co-determine the default decision of these borrowers. I tease out the different strategic aspects of default from the ones emanating from liquidity constraints. The recent advances in Deep Neural Network (DNN), the advent of big data and the computational power associated with it has enabled me to disentangle the motive of default. Also, agency conflicts of brokers during origination of a mortgage loan and the moral hazards thereof has been documented based on the soft information about the borrowers. However, there have been few, if any paper, which retains the soft information about the borrowers, post origination, during the life of the loans. There has been a plethora of research about the biases generated towards foreclosures and other adverse outcomes post securitization for the last decade. But the soft information about the borrowers obtained by the brokers have been lost during the pooling process in securitization and there have been famous papers on the loss of information during the securitization process which happens at arms’ length from the original lender. I bridge this gap by using novel data on proprietary call transcripts (textual data) between borrowers and servicers. I am also in the process of procuring audio files which can capture mood, content, tone of these communications. My dissertation documents the use of machine learning (ML) techniques in commercial and residential real estate to answer long-standing questions, which could not previously be answered due to paucity of data and computational resources. In the first chapter, Irun a horserace of Deep Neural Network with other ML models and parametric models to provide a new identification strategy to disentangle liquidity-constrained default and incentives for strategic default. The second chapter attempts to answer the most pressing current socio-economic issue in the United States. Specifically, I compute the social, racial and dollar cost of the CARES Act and find these adhoc policies are as expensive as direct payment of $2,000 to households, if not worse. Finally, in the third chapter I create a novel framework to ingest quantified time-varying soft information from call transcript text data about borrowers in ML models on hard information. I alleviate the information asymmetry between the borrowers and issuers, increase mortgage market efficiency and mitigate the conflict of interest between master servicers and special servicers. There has been recent literature on the applications of supervised, unsupervised and reinforcement learning in mainstream academic finance. But, very little work is done in the highly illiquid opaque real estate literature using the cutting edge methods in Machine Learning. I take a fresh look at some of the long-debated questions in the literature using some of the machine learning techniques. I am also able to able to use the current COVID-19 pandemic as an exogenous shock for robustness check in most of my current research

Berry Curvature Dipole and its Strain Engineering in Layered Phosphorene

The emergence of the fascinating non-linear Hall effect intrinsically depends on the non-zero value of the Berry curvature dipole. In this work, we predict that suitable strain engineering in layered van der Waals material phosphorene can give rise to a significantly large Berry curvature dipole. Using symmetry design principles, and a combination of feasible strain and staggered on-site potentials, we show how a substantial Berry curvature dipole may be engineered at the Fermi level. We discover that monolayer phosphorene exhibits the most intense Berry curvature dipole peak near 11.8% strain, which is also a critical point for the topological phase transition in pristine phosphorene. Furthermore, we have shown that the necessary strain value to achieve substantial Berry curvature dipole can be reduced by increasing the number of layers. We have revealed that strain in these van der Waals systems not only alters the magnitude of Berry curvature dipole to a significant value but allows control over its sign. We are hopeful that our predictions will pave way to realize the non-linear Hall effect in such elemental van der Waals systems.Comment: Accepted for publication in "Materials Today Electronics" (2023

Electronic and optical properties of B-N doped carbon nanotubes and graphene: A first principles Study

2D materials as well as quasi-1D materials exhibit fascinating optical and electronic properties. Boron (B) and nitrogen (N) doping are of particular interest due to their expected modification of electronic hence optical properties. We have performed density functional theory (DFT) computations in the low frequency limit to calculate the band structure and dielectric constant of the B-N doped single wall carbon nanotubes (SWCNT) systems. Graphene sheet has been doped with individual B, N atoms along with the simultaneous B-N codoping with varying concentrations. Controllable band gaps have been observed to be induced in the systems for different concentrations of three different foreign species. Besides, the Raman spectrum of the B/N doped Tetragonal graphene (T-graphene) systems has been computed for characterization purpose. Among transition metals, doped in T-graphene system, Sc shows significant spin polarization. Further, the electronic structure and the relevant density of state (DOS) at Fermi energy of B-N doped T-graphene can be judiciously used for the electronic transport. Our theoretical results will serve as an important reference to fabricate various optoelectronic devices with nanoscale dimensions using B/N substitution in the carbon network

Atypical presentation of scrub typhus encephalitis with cerebral hemorrhage

Scrub typhus, an arthropod borne infection caused by the rickettsial organism Orientia tsutsugamushi, is a fairly common disease in north-eastern sub-Himalayan India, particularly the forest areas, and is known to manifest with varied presentations ranging from non-specific fever to severe multi-organ complications. Hemorrhagic manifestations described in the literature are mostly gastrointestinal and genitourinary, secondary to vasculitis and/or thrombocytopenia, but reports of cerebral hemorrhage have been extremely rare. We report a case from sub-Himalayan eastern India where a 23 years old male tea plantation worker presented with recurrent convulsions with magnetic resonance imaging (MRI) brain showing multiple parenchymal hemorrhages with encephalitis involving both the cerebral hemispheres. Although patient developed fever and acute kidney injury later in the course, these were not the presenting complaints despite fever being the most consistent sign of a scrub typhus infection. We suggest consideration of scrub typhus as a differential diagnosis of a cerebral hemorrhage in endemic regions

The kk-essence scalar field in the context of Supernova Ia Observations

A $k$-essence scalar field model having (non canonical) Lagrangian of the form $L=-V(\phi)F(X)$ where $X=1/2g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi$ with constant $V(\phi)$ is shown to be consistent with luminosity distance-redshift data observed for type Ia Supernova. For constant $V(\phi)$, $F(X)$ satisfies a scaling relation which is used to set up a differential equation involving the Hubble parameter $H$, the scale factor $a$ and the $k$-essence field $\phi$. $H$ and $a$ are extracted from SNe Ia data and using the differential equation the time dependence of the field $\phi$ is found to be: $\phi(t) \sim \lambda_0 + \lambda_1 t + \lambda_2 t^2$. The constants $\lambda_i$ have been determined. The time dependence is similar to that of the quintessence scalar field (having canonical kinetic energy) responsible for homogeneous inflation. Furthermore, the scaling relation and the obtained time dependence of the field $\phi$ is used to determine the $X$-dependence of the function $F(X)$.Comment: 8 pages, 5 figures, Late

Effect and Characterization of Stone–Wales Defects on Graphene Quantum Dot: A First-Principles Study

A first principles based density functional theory (DFT) has been employed to identify the signature of Stone⁻Wales (SW) defects in semiconducting graphene quantum dot (GQD). Results show that the G mode in the Raman spectra of GQD has been red shifted to 1544.21 cm − 1 in the presence of 2.08% SW defect concentration. In addition, the intensity ratio between a robust low intense contraction⁻elongation mode and G mode is found to be reduced for the defected structure. We have also observed a Raman mode at 1674.04 cm − 1 due to the solo contribution of the defected bond. The increase in defect concentration, however, reduces the stability of the structures. As a consequence, the systems undergo structural buckling due to the presence of SW defect generated additional stresses. We have further explored that the 1615.45 cm − 1 Raman mode and 1619.29 cm − 1 infra-red mode are due to the collective stretching of two distinct SW defects separated at a distance 7.98 Å. Therefore, this is the smallest separation between the SW defects for their distinct existence. The pristine structure possesses maximum electrical conductivity and the same reduces to 0.37 times for 2.08% SW defect. On the other hand, the work function is reduced in the presence of defects except for the structure with SW defects separated at 7.98 Å. All these results will serve as an important reference to facilitate the potential applications of GQD based nano-devices with inherent topological SW defects

Electrically switchable giant Berry curvature dipole in silicene, germanene and stanene

The anomalous Hall effect in time-reversal symmetry broken systems is underpinned by the concept of Berry curvature in band theory. However, recent experiments reveal that the nonlinear Hall effect can be observed in non-magnetic systems without applying an external magnetic field. The emergence of nonlinear Hall effect under time-reversal symmetric conditions can be explained in terms of non-vanishing Berry curvature dipole arising from inversion symmetry breaking. In this work, we availed realistic tight-binding models, first-principles calculations, and symmetry analyses to explore the combined effect of transverse electric field and strain, which leads to a giant Berry curvature dipole in the elemental buckled honeycomb lattices -- silicene, germanene, and stanene. The external electric field breaks the inversion symmetry of these systems, while strain helps to attain an asymmetrical distribution of Berry curvature of a single valley. Furthermore, the topology of the electronic wavefunction switches from the band inverted quantum spin Hall state to normal insulating one at the gapless point. This band gap closing at the critical electric field strength is accompanied by an enhanced Berry curvature and concomitantly a giant Berry curvature dipole at the Fermi level. Our results predict the occurrence of an electrically switchable nonlinear electrical and thermal Hall effect in a new class of elemental systems that can be experimentally verified.Comment: To appear in 2D Material