Homogeneous Relaxation at Strong Coupling from Gravity

Homogeneous relaxation is a ubiquitous phenomenon in semiclassical kinetic theories where the quasiparticles are distributed uniformly in space, and the equilibration involves only their velocity distribution. For such solutions, the hydrodynamic variables remain constant. We construct asymptotically AdS solutions of Einstein's gravity dual to such processes at strong coupling, perturbatively in the amplitude expansion, where the expansion parameter is the ratio of the amplitude of the non-hydrodynamic shear-stress tensor to the pressure. At each order, we sum over all time derivatives through exact recursion relations. We argue that the metric has a regular future horizon, order by order in the amplitude expansion, provided the shear-stress tensor follows an equation of motion. At the linear order, this equation of motion implies that the metric perturbations are composed of zero wavelength quasinormal modes. Our method allows us to calculate the non-linear corrections to this equation perturbatively in the amplitude expansion. We thus derive a special case of our previous conjecture on the regularity condition on the boundary stress tensor that endows the bulk metric with a regular future horizon, and also refine it further. We also propose a new outlook for heavy-ion phenomenology at RHIC and ALICE.Comment: 60 pages, a section titled "Outlook for RHIC and ALICE" has been added, accepted for publication in Physical Review

The holographic spectral function in non-equilibrium states

We develop holographic prescriptions for obtaining spectral functions in non-equilibrium states and space-time dependent non-equilibrium shifts in the energy and spin of quasi-particle like excitations. We reproduce strongly coupled versions of aspects of non-equilibrium dynamics of Fermi surfaces in Landau's Fermi-liquid theory. We find that the incoming wave boundary condition at the horizon does not suffice to obtain a well-defined perturbative expansion for non-equilibrium observables. Our prescription, based on analysis of regularity at the horizon, allows such a perturbative expansion to be achieved nevertheless and can be precisely formulated in a universal manner independent of the non-equilibrium state, provided the state thermalizes. We also find that the non-equilibrium spectral function furnishes information about the relaxation modes of the system. Along the way, we argue that in a typical non-supersymmetric theory with a gravity dual, there may exist a window of temperature and chemical potential at large N, in which a generic non-equilibrium state can be characterized by just a finitely few operators with low scaling dimensions, even far away from the hydrodynamic limit.Comment: revtex; 43 pages, 2 figures; typos corrected, accepted for publication in PR

Software simulation of MC68000

The introduction of the Motorola MC68000 family of microprocessors ushered in a new era of microprocessors. These are single-chip microprocessors designed to function as the central processing units of sophisticated computer systems. The prime objective of this thesis work is to develop a simulator for the MC68000 microprocessor mainly for educational purposes. The simulator would help in any test or research work utilizing 68000 assembly programs in the future. Most of the instructions in the 68000 family are implemented. Both the user mode and supervisory mode programs can be written and run against the simulator. Besides supporting most of the MC68000 features the simulator also has additional features to help debugging

String Theory and Water Waves

We uncover a remarkable role that an infinite hierarchy of non-linear differential equations plays in organizing and connecting certain {hat c}<1 string theories non-perturbatively. We are able to embed the type 0A and 0B (A,A) minimal string theories into this single framework. The string theories arise as special limits of a rich system of equations underpinned by an integrable system known as the dispersive water wave hierarchy. We observe that there are several other string-like limits of the system, and conjecture that some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain how these and several string-like special points arise and are connected. In some cases, the framework endows the theories with a non-perturbative definition for the first time. Notably, we discover that the Painleve IV equation plays a key role in organizing the string theory physics, joining its siblings, Painleve I and II, whose roles have previously been identified in this minimal string context.Comment: 49 pages, 4 figure

DIAGNOSE: Avoiding Out-of-distribution Data using Submodular Information Measures

Avoiding out-of-distribution (OOD) data is critical for training supervised machine learning models in the medical imaging domain. Furthermore, obtaining labeled medical data is difficult and expensive since it requires expert annotators like doctors, radiologists, etc. Active learning (AL) is a well-known method to mitigate labeling costs by selecting the most diverse or uncertain samples. However, current AL methods do not work well in the medical imaging domain with OOD data. We propose Diagnose (avoiDing out-of-dIstribution dAta usinG submodular iNfOrmation meaSurEs), a novel active learning framework that can jointly model similarity and dissimilarity, which is crucial in mining in-distribution data and avoiding OOD data at the same time. Particularly, we use a small number of data points as exemplars that represent a query set of in-distribution data points and a private set of OOD data points. We illustrate the generalizability of our framework by evaluating it on a wide variety of real-world OOD scenarios. Our experiments verify the superiority of Diagnose over the state-of-the-art AL methods across multiple domains of medical imaging.Comment: Accepted to MICCAI 2022 MILLanD Worksho

Widespread presence of direction-reversing neurons in the mouse visual system

Direction selectivity, the preference of motion in one direction over the opposite, is a fundamental property of visual neurons across species. We find that a substantial proportion of direction selective neurons in the mouse visual system reverse their preferred direction of motion in response to drifting gratings at different spatiotemporal parameters. A spatiotemporally asymmetric filter model recapitulates our experimental observations