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A systematic study of the attenuation of electromagnetic radiation in Nuclear Track Detectors (NTDs) is carried out. The attenuation of gamma-ray, X-ray, UV, visible, and infrared radiation in NTDs are investigated using NaI(Tl) detector, Gas Electron Multiplier (GEM) detector, UV-Vis spectrophotometer, and FTIR spectrophotometer respectively. The values of some important parameters (e.g., optical depth, attenuation coefficient, etc.) of three commercially available NTDs (PET, Makrofol r and CR-39 r ), at the relevant region of the electromagnetic spectrum, is determined. The details of the experimental techniques and the results are also presented in this paper., Comment: 10 pages

For the purpose of analyzing observed phenomena, it has been convenient, and thus far sufficient, to regard gravity as subject to the deterministic principles of classical physics, with the gravitational field obeying Newton's law or Einstein's equations. Here we treat the gravitational field as a quantum field and determine the implications of such treatment for experimental observables. We find that falling bodies in gravity are subject to random fluctuations ("noise") whose characteristics depend on the quantum state of the gravitational field. We derive a stochastic equation for the separation of two falling particles. Detection of this fundamental noise, which may be measurable at gravitational wave detectors, would vindicate the quantization of gravity, and reveal important properties of its sources., Comment: 5 pages + 3 pages of supplemental material, 2 figures

We develop a formalism to calculate the response of a model gravitational wave detector to a quantized gravitational field. Coupling a detector to a quantum field induces stochastic fluctuations ("noise") in the length of the detector arm. The statistical properties of this noise depend on the choice of quantum state of the gravitational field. We characterize the noise for vacuum, coherent, thermal, and squeezed states. For coherent states, corresponding to classical gravitational configurations, we find that the effect of gravitational field quantization is small. However, the standard deviation in the arm length can be enhanced -- possibly significantly -- when the gravitational field is in a non-coherent state. The detection of this fundamental noise could provide direct evidence for the quantization of gravity and for the existence of gravitons., Comment: 34 pages, 1 figure

Recently, remarkable progress in recovering the Page curve of an evaporating black hole (BH) in Jackiw-Teitelboim gravity has been achieved through use of Quantum Extremal surfaces (QES). Multi-boundary Wormhole (MbW) models have been crucial in parallel model building in three dimensions. Motivated by this we here use the latter models to compute the subregion complexity of the Hawking quanta of the evaporating BH in AdS$_{3}$ and obtain the Page curve associated with this information theoretic measure. We use three- and $n$-boundary wormhole constructions to elucidate our computations of volumes below the Hubeny-Rangamani-Takayanagi (HRT) surfaces at different times. Time is represented by the growing length of the throat horizons corresponding to smaller exits of the multi-boundary wormhole and the evaporating bigger exit shrinks with evolving time. We track the change in choice of HRT surfaces with time and plot the volume with time. The smooth transition of Page curve is realized by a discontinuous jump at Page time in volume subregion complexity plots and the usual Page transition is realized as a phase transition due to the inclusion of the island in this context. We discuss mathematical intricacies and physical insights regarding the inclusion of the extra volume at Page time. The analysis is backed by calculations and lessons from kinematic space and tensor networks., Comment: Modified Version (52 pages, 18 figures). Accepted for publication in JHEP

Several applications in the scientific simulation of physical systems can be formulated as control/optimization problems. The computational models for such systems generally contain hyperparameters, which control solution fidelity and computational expense. The tuning of these parameters is non-trivial and the general approach is to manually `spot-check' for good combinations. This is because optimal hyperparameter configuration search becomes impractical when the parameter space is large and when they may vary dynamically. To address this issue, we present a framework based on deep reinforcement learning (RL) to train a deep neural network agent that controls a model solve by varying parameters dynamically. First, we validate our RL framework for the problem of controlling chaos in chaotic systems by dynamically changing the parameters of the system. Subsequently, we illustrate the capabilities of our framework for accelerating the convergence of a steady-state CFD solver by automatically adjusting the relaxation factors of discretized Navier-Stokes equations during run-time. The results indicate that the run-time control of the relaxation factors by the learned policy leads to a significant reduction in the number of iterations for convergence compared to the random selection of the relaxation factors. Our results point to potential benefits for learning adaptive hyperparameter learning strategies across different geometries and boundary conditions with implications for reduced computational campaign expenses. \footnote{Data and codes available at \url{https://github.com/Romit-Maulik/PAR-RL}}

Clinicians face several significant barriers to search and synthesize accurate, succinct, updated, and trustworthy medical information from several literature sources during the practice of medicine and patient care. In this talk, we will be presenting our research behind the development of a Focused Clinical Search Service, powered by a Healthcare Knowledge Graph, to interpret the query intent behind clinical search queries and retrieve relevant medical snippets from a diverse corpus of medical literature., Comment: Under Review as a Podium Talk at the AMIA Informatics Summit 2021

Have you ever looked at an Instagram model, or a model in a fashion e-commerce web-page, and thought \textit{"Wish I could get a list of fashion items similar to the ones worn by the model!"}. This is what we address in this paper, where we propose a novel computer vision based technique called \textbf{ShopLook} to address the challenging problem of recommending similar fashion products. The proposed method has been evaluated at Myntra (www.myntra.com), a leading online fashion e-commerce platform. In particular, given a user query and the corresponding Product Display Page (PDP) against the query, the goal of our method is to recommend similar fashion products corresponding to the entire set of fashion articles worn by a model in the PDP full-shot image (the one showing the entire model from head to toe). The novelty and strength of our method lies in its capability to recommend similar articles for all the fashion items worn by the model, in addition to the primary article corresponding to the query. This is not only important to promote cross-sells for boosting revenue, but also for improving customer experience and engagement. In addition, our approach is also capable of recommending similar products for User Generated Content (UGC), eg., fashion article images uploaded by users. Formally, our proposed method consists of the following components (in the same order): i) Human keypoint detection, ii) Pose classification, iii) Article localisation and object detection, along with active learning feedback, and iv) Triplet network based image embedding model., Comment: Accepted at the IEEE International Conference on Multimedia Information Processing and Retrieval (MIPR) 2021

In this paper, we study a novel technique that exploits the interaction between speaker traits and linguistic content to improve both speaker verification and utterance verification performance. We implement an idea of speaker-utterance dual attention (SUDA) in a unified neural network. The dual attention refers to an attention mechanism for the two tasks of speaker and utterance verification. The proposed SUDA features an attention mask mechanism to learn the interaction between the speaker and utterance information streams. This helps to focus only on the required information for respective task by masking the irrelevant counterparts. The studies conducted on RSR2015 corpus confirm that the proposed SUDA outperforms the framework without attention mask as well as several competitive systems for both speaker and utterance verification., Comment: Accepted by Interspeech 2020

We construct natural operators connecting the cohomology of the moduli spaces of stable Higgs bundles with different ranks and genera which, after numerical specialization, recover the topological mirror symmetry conjecture of Hausel-Thaddeus concerning $\mathrm{SL}_n$- and $\mathrm{PGL}_n$-Higgs bundles. This provides a complete description of the cohomology of the moduli space of stable $\mathrm{SL}_n$-Higgs bundles in terms of the tautological classes, and gives a new proof of the Hausel-Thaddeus conjecture, proven recently by Gr\"ochenig-Wyss-Ziegler via p-adic integration. Our method is to relate the decomposition theorem for the Hitchin fibration, using vanishing cycle functors, to the decomposition theorem for the twisted Hitchin fibration whose supports are simpler., Comment: 53 pages. Various corrections. Final version accepted at Forum of Mathematics Pi

Adjoint-based optimization methods are attractive for aerodynamic shape design primarily due to their computational costs being independent of the dimensionality of the input space and their ability to generate high-fidelity gradients that can then be used in a gradient-based optimizer. This makes them very well suited for high-fidelity simulation based aerodynamic shape optimization of highly parametrized geometries such as aircraft wings. However, the development of adjoint-based solvers involve careful mathematical treatment and their implementation require detailed software development. Furthermore, they can become prohibitively expensive when multiple optimization problems are being solved, each requiring multiple restarts to circumvent local optima. In this work, we propose a machine learning enabled, surrogate-based framework that replaces the expensive adjoint solver, without compromising on predicting predictive accuracy. Specifically, we first train a deep neural network (DNN) from training data generated from evaluating the high-fidelity simulation model on a model-agnostic, design of experiments on the geometry shape parameters. The optimum shape may then be computed by using a gradient-based optimizer coupled with the trained DNN. Subsequently, we also perform a gradient-free Bayesian optimization, where the trained DNN is used as the prior mean. We observe that the latter framework (DNN-BO) improves upon the DNN-only based optimization strategy for the same computational cost. Overall, this framework predicts the true optimum with very high accuracy, while requiring far fewer high-fidelity function calls compared to the adjoint-based method. Furthermore, we show that multiple optimization problems can be solved with the same machine learning model with high accuracy, to amortize the offline costs associated with constructing our models., Comment: 25 pages, 13 figures

The rigid body attitude estimation problem is treated using the discrete-time Lagrange-d'Alembert principle. Three different possibilities are considered for the multi-rate relation between angular velocity measurements and direction vector measurements for attitude: 1) integer relation between sampling rates, 2) time-varying sampling rates, 3) non-integer relation between sampling rates. In all cases, it is assumed that angular velocity measurements are sampled at a higher rate compared to the inertial vectors. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. At instants when direction vector measurements are absent, a discrete-time model for attitude kinematics is used to propagate past measurements. A discrete-time Lagrangian is constructed as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. An additional dissipation term is introduced and the discrete-time Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation to obtain an optimal filtering scheme. A discrete-time Lyapunov analysis is carried out to show that the optimal filtering scheme is asymptotically stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. These numerical simulations exhibit convergence of the estimated states to a bounded neighborhood of the actual states., Comment: arXiv admin note: substantial text overlap with arXiv:2007.08185

Introduction of electric field in the D-brane worldvolume induces a horizon in the open string geometry perceived by the brane fluctuations. We study the holographic entanglement entropy (HEE) and subregion complexity (HSC) in these asymptotically AdS geometries in three, four and five dimensions aiming to capture these quantities in the flavor sector introduced by the D-branes. Both the strip and spherical subregions have been considered. We show that the Bekenstein-Hawking entropy associated with the open string horizon, which earlier failed to reproduce the thermal entropy in the boundary, now precisely matches with the entanglement entropy at high temperatures. We check the validity of embedding function theorem while computing the HEE and attempt to reproduce the first law of entanglement thermodynamics, at least at leading order. On the basis of obtained results, we also reflect upon consequences of applying Ryu-Takayanagi proposal on these non-Einstein geometries., Comment: 36 pages, 2 figures, Published in JHEP

Non-intrusive reduced-order models (ROMs) have recently generated considerable interest for constructing computationally efficient counterparts of nonlinear dynamical systems emerging from various domain sciences. They provide a low-dimensional emulation framework for systems that may be intrinsically high-dimensional. This is accomplished by utilizing a construction algorithm that is purely data-driven. It is no surprise, therefore, that the algorithmic advances of machine learning have led to non-intrusive ROMs with greater accuracy and computational gains. However, in bypassing the utilization of an equation-based evolution, it is often seen that the interpretability of the ROM framework suffers. This becomes more problematic when black-box deep learning methods are used which are notorious for lacking robustness outside the physical regime of the observed data. In this article, we propose the use of a novel latent-space interpolation algorithm based on Gaussian process regression. Notably, this reduced-order evolution of the system is parameterized by control parameters to allow for interpolation in space. The use of this procedure also allows for a continuous interpretation of time which allows for temporal interpolation. The latter aspect provides information, with quantified uncertainty, about full-state evolution at a finer resolution than that utilized for training the ROMs. We assess the viability of this algorithm for an advection-dominated system given by the inviscid shallow water equations.

A geometric estimator is proposed for the rigid body attitude under multi-rate measurements using discrete-time Lyapunov stability analysis in this work. The angular velocity measurements are assumed to be sampled at a higher rate compared to the attitude. The attitude determination problem from two or more vector measurements in the body-fixed frame is formulated as Wahba's problem. In the case when measurements are absent, a discrete-time model for attitude kinematics is assumed in order to propagate the measurements. A discrete-time Lyapunov function is constructed as the sum of a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential energy-like term obtained from Wahba's cost function. A filtering scheme is obtained by discrete-time stability analysis using a suitable Lyapunov function. The analysis shows that the filtering scheme is exponentially stable in the absence of measurement noise and the domain of convergence is almost global. For a realistic evaluation of the scheme, numerical experiments are conducted with inputs corrupted by bounded measurement noise. Simulation results exhibit convergence of the estimated states to a bounded neighborhood of the actual states.

Poincar\'e maps for toroidal magnetic fields are routinely employed to study gross confinement properties in devices built to contain hot plasmas. In most practical applications, evaluating a Poincar\'e map requires numerical integration of a magnetic field line, a process that can be slow and that cannot be easily accelerated using parallel computations. We show that a novel neural network architecture, the H\'enonNet, is capable of accurately learning realistic Poincar\'e maps from observations of a conventional field-line-following algorithm. After training, such learned Poincar\'e maps evaluate much faster than the field-line integration method. Moreover, the H\'enonNet architecture exactly reproduces the primary physics constraint imposed on field-line Poincar\'e maps: flux preservation. This structure-preserving property is the consequence of each layer in a H\'enonNet being a symplectic map. We demonstrate empirically that a H\'enonNet can learn to mock the confinement properties of a large magnetic island by using coiled hyperbolic invariant manifolds to produce a sticky chaotic region at the desired island location. This suggests a novel approach to designing magnetic fields with good confinement properties that may be more flexible than ensuring confinement using KAM tori., Comment: 28 pages, 26 figures

Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant interest in the use of techniques borrowed from machine learning to reduce the computational expense and/or improve the accuracy of predictions for these systems. These rely on the identification of a basis that reduces the dimensionality of the problem and the subsequent use of time series and sequential learning methods to forecast the evolution of the reduced state. Often, however, machine-learned predictions after reduced-basis projection are plagued by issues of stability stemming from incomplete capture of multiscale processes as well as due to error growth for long forecast durations. To address these issues, we have developed a \emph{non-autoregressive} time series approach for predicting linear reduced-basis time histories of forward models. In particular, we demonstrate that non-autoregressive counterparts of sequential learning methods such as long short-term memory (LSTM) considerably improve the stability of machine-learned reduced-order models. We evaluate our approach on the inviscid shallow water equations and show that a non-autoregressive variant of the standard LSTM approach that is bidirectional in the PCA components obtains the best accuracy for recreating the nonlinear dynamics of partial observations. Moreover---and critical for many applications of these surrogates---inference times are reduced by three orders of magnitude using our approach, compared with both the equation-based Galerkin projection method and the standard LSTM approach.

Depending on their type, supernova remnants may have ejecta material with high abundance of heavy elements such as carbon or oxygen. In addition, core-collapse supernovae explode in the wind material of their progenitor star that may also have a high abundance of heavy elements. Hadronic collisions in these enriched media spawn the production of gamma rays, neutrinos, and secondary electrons with spectra that cannot be scaled from those calculated for pp collisions, potentially leading to erroneous results. We used Monte-Carlo event generators to calculate the differential production rate of particles such as gamma rays, neutrinos, and secondary electrons for H, He, C, and O nuclei as projectiles and as target material. The cross sections and the multiplicity spectra are separately computed for each of the 16 combinations of projectile and target. We describe characteristic effects of heavy nuclei in the shape and normalization of the spectra of various particles produced., Comment: Final version; accepted for publication in Astroparticle Physics

Let $X$ be a smooth threefold with a simple normal crossings divisor $D$. We construct the Donaldson-Thomas theory of the pair $(X|D)$ enumerating ideal sheaves on $X$ relative to $D$. These moduli spaces are compactified by studying subschemes in expansions of the target geometry, and the moduli space carries a virtual fundamental class leading to numerical invariants with expected properties. We formulate punctual evaluation, rationality and wall-crossing conjectures, in parallel with the standard theory. Our formalism specializes to the Li-Wu theory of relative ideal sheaves when the divisor is smooth, and is parallel to recent work on logarithmic Gromov-Witten theory with expansions., Comment: v4: 71 pages. Expository changes. Final version to appear in Forum of Mathematics, Pi

While the biomedical community has published several "open data" sources in the last decade, most researchers still endure severe logistical and technical challenges to discover, query, and integrate heterogeneous data and knowledge from multiple sources. To tackle these challenges, the community has experimented with Semantic Web and linked data technologies to create the Life Sciences Linked Open Data (LSLOD) cloud. In this paper, we extract schemas from more than 80 publicly available biomedical linked data graphs into an LSLOD schema graph and conduct an empirical meta-analysis to evaluate the extent of semantic heterogeneity across the LSLOD cloud. We observe that several LSLOD sources exist as stand-alone data sources that are not inter-linked with other sources, use unpublished schemas with minimal reuse or mappings, and have elements that are not useful for data integration from a biomedical perspective. We envision that the LSLOD schema graph and the findings from this research will aid researchers who wish to query and integrate data and knowledge from multiple biomedical sources simultaneously on the Web., Comment: Under Review at Nature Scientific Data

We develop a novel computational method for evaluating the extreme excursion probabilities arising from random initialization of nonlinear dynamical systems. The method uses excursion probability theory to formulate a sequence of Bayesian inverse problems that, when solved, yields the biasing distribution. Solving multiple Bayesian inverse problems can be expensive; more so in higher dimensions. To alleviate the computational cost, we build machine-learning-based surrogates to solve the Bayesian inverse problems that give rise to the biasing distribution. This biasing distribution can then be used in an importance sampling procedure to estimate the extreme excursion probabilities., Comment: arXiv admin note: text overlap with arXiv:2001.11904

A novel image analysis algorithm as applied to images of Nuclear Track Detectors (NTD) is presented. This process, involving sequential application of deconvolution and convolution techniques, followed by the application of Artificial Neural Network (ANN), is identifying the etch-pit openings in NTD images with a higher degree of success compared to other conventional image analysis techniques.

We show that when the gravitational field is treated quantum-mechanically, it induces fluctuations -- noise -- in the lengths of the arms of gravitational wave detectors. The characteristics of the noise depend on the quantum state of the gravitational field, and can be calculated exactly in several interesting cases. For coherent states the noise is very small, but it can be greatly enhanced in thermal and (especially) squeezed states. Detection of this fundamental noise would constitute direct evidence for the quantization of gravity and the existence of gravitons., Comment: First prize in the Gravity Research Foundation Essay Competition. 6 pages. Published version

Transfer learning has been shown to be effective in many applications in which training data for the target problem are limited but data for a related (source) problem are abundant. In this paper, we apply transfer learning to the prediction of anti-cancer drug response. Previous transfer learning studies for drug response prediction focused on building models that predict the response of tumor cells to a specific drug treatment. We target the more challenging task of building general prediction models that can make predictions for both new tumor cells and new drugs. We apply the classic transfer learning framework that trains a prediction model on the source dataset and refines it on the target dataset, and extends the framework through ensemble. The ensemble transfer learning pipeline is implemented using LightGBM and two deep neural network (DNN) models with different architectures. Uniquely, we investigate its power for three application settings including drug repurposing, precision oncology, and new drug development, through different data partition schemes in cross-validation. We test the proposed ensemble transfer learning on benchmark in vitro drug screening datasets, taking one dataset as the source domain and another dataset as the target domain. The analysis results demonstrate the benefit of applying ensemble transfer learning for predicting anti-cancer drug response in all three applications with both LightGBM and DNN models. Compared between the different prediction models, a DNN model with two subnetworks for the inputs of tumor features and drug features separately outperforms LightGBM and the other DNN model that concatenates tumor features and drug features for input in the drug repurposing and precision oncology applications. In the more challenging application of new drug development, LightGBM performs better than the other two DNN models.

We consider the use of probabilistic neural networks for fluid flow {surrogate modeling} and data recovery. This framework is constructed by assuming that the target variables are sampled from a Gaussian distribution conditioned on the inputs. Consequently, the overall formulation sets up a procedure to predict the hyperparameters of this distribution which are then used to compute an objective function given training data. We demonstrate that this framework has the ability to provide for prediction confidence intervals based on the assumption of a probabilistic posterior, given an appropriate model architecture and adequate training data. The applicability of the present framework to cases with noisy measurements and limited observations is also assessed. To demonstrate the capabilities of this framework, we consider canonical regression problems of fluid dynamics from the viewpoint of reduced-order modeling and spatial data recovery for four canonical data sets. The examples considered in this study arise from (1) the shallow water equations, (2) a two-dimensional cylinder flow, (3) the wake of NACA0012 airfoil with a Gurney flap, and (4) the NOAA sea surface temperature data set. The present results indicate that the probabilistic neural network not only produces a machine-learning-based fluid flow {surrogate} model but also systematically quantifies the uncertainty therein to assist with model interpretability.

By combining various cancer cell line (CCL) drug screening panels, the size of the data has grown significantly to begin understanding how advances in deep learning can advance drug response predictions. In this paper we train >35,000 neural network models, sweeping over common featurization techniques. We found the RNA-seq to be highly redundant and informative even with subsets larger than 128 features. We found the inclusion of single nucleotide polymorphisms (SNPs) coded as count matrices improved model performance significantly, and no substantial difference in model performance with respect to molecular featurization between the common open source MOrdred descriptors and Dragon7 descriptors. Alongside this analysis, we outline data integration between CCL screening datasets and present evidence that new metrics and imbalanced data techniques, as well as advances in data standardization, need to be developed.

Developing surrogate geophysical models from data is a key research topic in atmospheric and oceanic modeling because of the large computational costs associated with numerical simulation methods. Researchers have started applying a wide range of machine learning models, in particular neural networks, to geophysical data for forecasting without these constraints. Constructing neural networks for forecasting such data is nontrivial, however, and often requires trial and error. To address these limitations, we focus on developing proper-orthogonal-decomposition-based long short-term memory networks (POD-LSTMs). We develop a scalable neural architecture search for generating stacked LSTMs to forecast temperature in the NOAA Optimum Interpolation Sea-Surface Temperature data set. Our approach identifies POD-LSTMs that are superior to manually designed variants and baseline time-series prediction methods. We also assess the scalability of different architecture search strategies on up to 512 Intel Knights Landing nodes of the Theta supercomputer at the Argonne Leadership Computing Facility.

Given the importance of public support for policy change and implementation, public policymakers and researchers have attempted to understand the factors associated with this support for climate change mitigation policy. In this article, we compare the feasibility of using different supervised learning methods for regression using a novel socio-economic data set which measures public support for potential climate change mitigation policies. Following this model selection, we utilize gradient boosting regression, a well-known technique in the machine learning community, but relatively uncommon in public policy and public opinion research, and seek to understand what factors among the several examined in previous studies are most central to shaping public support for mitigation policies in climate change studies. The use of this method provides novel insights into the most important factors for public support for climate change mitigation policies. Using national survey data, we find that the perceived risks associated with climate change are more decisive for shaping public support for policy options promoting renewable energy and regulating pollutants. However, we observe a very different behavior related to public support for increasing the use of nuclear energy where climate change risk perception is no longer the sole decisive feature. Our findings indicate that public support for renewable energy is inherently different from that for nuclear energy reliance with the risk perception of climate change, dominant for the former, playing a subdued role for the latter.

The closure problem in fluid modeling is a well-known challenge to modelers aiming to accurately describe their system of interest. Over many years, analytic formulations in a wide range of regimes have been presented but a practical, generalized fluid closure for magnetized plasmas remains an elusive goal. In this study, as a first step towards constructing a novel data based approach to this problem, we apply ever-maturing machine learning methods to assess the capability of neural network architectures to reproduce crucial physics inherent in popular magnetized plasma closures. We find encouraging results, indicating the applicability of neural networks to closure physics but also arrive at recommendations on how one should choose appropriate network architectures for given locality properties dictated by underlying physics of the plasma.

Let $p$ be a prime number. We prove that the $P=W$ conjecture for $\mathrm{SL}_p$ is equivalent to the $P=W$ conjecture for $\mathrm{GL}_p$. As a consequence, we verify the $P=W$ conjecture for genus 2 and $\mathrm{SL}_p$. For the proof, we compute the perverse filtration and the weight filtration for the variant cohomology associated with the $\mathrm{SL}_p$-Hitchin moduli space and the $\mathrm{SL}_p$-twisted character variety, relying on Gr\"ochenig-Wyss-Ziegler's recent proof of the topological mirror conjecture by Hausel-Thaddeus. Finally we discuss obstructions of studying the cohomology of the $\mathrm{SL}_n$-Hitchin moduli space via compact hyper-K\"ahler manifolds., Comment: 18 Pages

A common strategy for the dimensionality reduction of nonlinear partial differential equations relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that an encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent-space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD Galerkin technique.

The MoEDAL trapping detector, consists of approximately 800 kg of aluminium volumes. It was exposed during Run-2 of the LHC program to 6.46 fb^-1 of 13 TeV proton-proton collisions at the LHCb interaction point. Evidence for dyons (particles with electric and magnetic charge) captured in the trapping detector was sought by passing the aluminium volumes comprising the detector through a SQUID magnetometer. The presence of a trapped dyon would be signalled by a persistent current induced in the SQUID magnetometer. On the basis of a Drell-Yan production model, we exclude dyons with a magnetic charge ranging up to 5 Dirac charges, and an electric charge up to 200 times the fundamental electric charge for mass limits in the range 790 - 3130 GeV., Comment: arXiv admin note: text overlap with arXiv:1903.08491

The (F1,D2,D8) brane configuration with $Lif_4^{(2)}\times {S}^1\times S^5$ geometry is a known Lifshitz vacua supported by massive $B_{\mu\nu}$ field in type IIA theory. This system allows exact IR excitations which couple to massless modes of the fundamental string. Due to these massless modes the solutions have a flow to a dilatonic $Lif_4^{(3)}\times S^1\times S^5$ vacua in IR. We study the entanglement entropy on the boundary of this spacetime for the strip and the disc subsystems. To our surprise net entropy density of the excitations at first order is found to be independent of the typical size of subsystems. We interpret our results in the light of first law of entanglement thermodynamics., Comment: 22 pages, 5 figures; accepted for publication in Phys. Rev. D

In open agent systems, the set of agents that are cooperating or competing changes over time and in ways that are nontrivial to predict. For example, if collaborative robots were tasked with fighting wildfires, they may run out of suppressants and be temporarily unavailable to assist their peers. We consider the problem of planning in these contexts with the additional challenges that the agents are unable to communicate with each other and that there are many of them. Because an agent's optimal action depends on the actions of others, each agent must not only predict the actions of its peers, but, before that, reason whether they are even present to perform an action. Addressing openness thus requires agents to model each other's presence, which becomes computationally intractable with high numbers of agents. We present a novel, principled, and scalable method in this context that enables an agent to reason about others' presence in its shared environment and their actions. Our method extrapolates models of a few peers to the overall behavior of the many-agent system, and combines it with a generalization of Monte Carlo tree search to perform individual agent reasoning in many-agent open environments. Theoretical analyses establish the number of agents to model in order to achieve acceptable worst case bounds on extrapolation error, as well as regret bounds on the agent's utility from modeling only some neighbors. Simulations of multiagent wildfire suppression problems demonstrate our approach's efficacy compared with alternative baselines., Comment: Pre-print with appendices for AAAI 2020

Fluid flow in the transonic regime finds relevance in aerospace engineering, particularly in the design of commercial air transportation vehicles. Computational fluid dynamics models of transonic flow for aerospace applications are computationally expensive to solve because of the high degrees of freedom as well as the coupled nature of the conservation laws. While these issues pose a bottleneck for the use of such models in aerospace design, computational costs can be significantly minimized by constructing special, structure-preserving surrogate models called reduced-order models. Such models are known to incur huge off-line costs, however, which can sometimes outweigh their potential benefits. Furthermore, their prediction accuracy is known to be poor under transonic flow conditions. In this work, we propose a machine learning method to construct reduced-order models via deep neural networks, and we demonstrate its ability to preserve accuracy with significantly lower offline and online costs. In addition, our machine learning methodology is physics-informed and constrained through the utilization of an interpretable encoding by way of proper orthogonal decomposition. Application to the inviscid transonic flow past the RAE2822 airfoil under varying freestream Mach numbers and angles of attack, as well as airfoil shape parameters with a deforming mesh, shows that the proposed approach adapts to high-dimensional parameter variation well. Notably, the proposed framework precludes knowledge of numerical operators utilized in the data generation phase, thereby demonstrating its potential utility in fast exploration of design space for diverse engineering applications.

The Reynolds-averaged Navier-Stokes (RANS) equations for steady-state assessment of incompressible turbulent flows remain the workhorse for practical computational fluid dynamics (CFD) applications. Consequently, improvements in speed or accuracy have the potential to affect a diverse range of applications. We introduce a machine learning framework for the {surrogate modeling of steady-state turbulent eddy viscosities for RANS simulations, given the initial conditions. This modeling strategy} is assessed for parametric interpolation, while numerically solving for the pressure and velocity equations to steady state, thus representing a framework that is hybridized with machine learning. We achieve {competitive} steady-state results with a significant reduction in solution time when compared to those obtained by the Spalart-Allmaras one-equation model. This is because the proposed methodology allows for considerably larger relaxation factors for the steady-state velocity and pressure solvers. Our assessments are made for a backward-facing step with considerable mesh anisotropy and separation to represent a practical CFD application. For test experiments with \textcolor{black}{either} varying inlet velocity conditions or step heights we see time-to-solution reductions around a factor of 5. The results represent an opportunity for the rapid exploration of parameter spaces that prove prohibitive when utilizing turbulence closure models with multiple coupled partial differential equations. \blfootnote{Code available publicly at \texttt{https://github.com/argonne-lcf/TensorFlowFoam}}.

This paper addresses the problem of exploring a region using the Hilbert's space-filling curve in the presence of obstacles. No prior knowledge of the region being explored is assumed. An online algorithm is proposed which can implement evasive strategies to avoid obstacles comprising a single or two blocked unit squares placed side by side and successfully explore the entire region. The strategies are specified by the change in the waypoint array which robot going to follow. The fractal nature of the Hilbert's space-filling curve has been exploited in proving the validity of the solution.

We study the topology of Hitchin fibrations via abelian surfaces. We establish the P=W conjecture for genus $2$ curves and arbitrary rank. In higher genus and arbitrary rank, we prove that P=W holds for the subalgebra of cohomology generated by even tautological classes. Furthermore, we show that all tautological generators lie in the correct pieces of the perverse filtration as predicted by the P=W conjecture. In combination with recent work of Mellit, this reduces the full conjecture to the multiplicativity of the perverse filtration. Our main technique is to study the Hitchin fibration as a degeneration of the Hilbert-Chow morphism associated with the moduli space of certain torsion sheaves on an abelian surface, where the symmetries induced by Markman's monodromy operators play a crucial role., Comment: 47 pages. Minor revision. Accepted at Journal of the American Mathematical Society

We consider a randomized urn model with objects of finitely many colors. The replacement matrices are random, and are conditionally independent of the color chosen given the past. Further, the conditional expectations of the replacement matrices are close to an almost surely irreducible matrix. We obtain almost sure and $L^1$ convergence of the configuration vector, the proportion vector and the count vector. We show that first moment is sufficient for i.i.d.\ replacement matrices independent of past color choices. This significantly improves the similar results for urn models obtained in Athreya and Ney (1972) requiring $L\log_+ L$ moments. For more general adaptive sequence of replacement matrices, a little more than $L\log_+ L$ condition is required. Similar results based on $L^1$ moment assumption alone has been considered independently and in parallel in Zhang (2018). Finally, using the result, we study a delayed elephant random walk on the nonnegative orthant in $d$ dimension with random memory., Comment: References updated. Slightly reorganized. Published in Statistics and Probability Letters