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Rahul Singh

Rahul Singh contributes to research discovery and scholarly infrastructure.

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preprint2026arXiv

Equivariant Chevalley, Giambelli, and Monk Formulae for the Peterson Variety

We present a formula for the Poincaré dual in the flag manifold of the equivariant fundamental class of any regular nilpotent or regular semisimple Hessenberg variety as a polynomial in terms of certain Chern classes. We then develop a type-independent proof of the Giambelli formula for the Peterson variety, and use this formula to compute the intersection multiplicity of a Peterson variety with an opposite Schubert variety corresponding to a Coxeter word. Finally, we develop an equivariant Chevalley formula for the cap product of a divisor class with a fundamental class, and a dual Monk rule, for the Peterson variety.

preprint2026arXiv

Extensible Post Quantum Cryptography Based Authentication

Cryptography underpins the security of modern digital infrastructure, from cloud services to health data. However, many widely deployed systems will become vulnerable after the advent of scalable quantum computing. Although quantum-safe cryptographic primitives have been developed, such as lattice-based digital signature algorithms (DSAs) and key encapsulation mechanisms (KEMs), their unique structural and performance characteristics make them unsuitable for existing protocols. In this work, we introduce a quantum-safe single-shot protocol for machine-to-machine authentication and authorization that is specifically designed to leverage the strengths of lattice-based DSAs and KEMs. Operating entirely over insecure channels, this protocol enables the forward-secure establishment of tokens in constrained environments. By demonstrating how new quantum-safe cryptographic primitives can be incorporated into secure systems, this study lays the groundwork for scalable, resilient, and future-proof identity infrastructures in a quantum-enabled world.

preprint2026arXiv

On Gaussian approximation for entropy-regularized Q-learning with function approximation

In this paper, we derive rates of convergence in the high-dimensional central limit theorem for Polyak--Ruppert averaged iterates generated by entropy-regularized asynchronous Q-learning with linear function approximation and a polynomial stepsize $k^{-ω}$, $ω\in (1/2,1)$. Assuming that the sequence of observed triples $(s_k,a_k,s_{k+1})_{k \geq 0}$ forms a uniformly geometrically ergodic Markov chain, and under suitable regularity conditions for the projected soft Bellman equation, we establish a Gaussian approximation bound in the convex distance with rate of order $n^{-1/4}$, up to polylogarithmic factors in $n$, where $n$ is the number of samples used by the algorithm. To obtain this result, we combine a linearization of the soft Bellman recursion with a Gaussian approximation for the leading martingale term. Finally, we derive high-order moment bounds for the algorithm's last iterate, which might be of independent interest.

preprint2026arXiv

Policy Gradient Methods for Non-Markovian Reinforcement Learning

We study policy gradient methods for reinforcement learning in non-Markovian decision processes (NMDPs), where observations and rewards depend on the entire interaction history. To handle this dependence, the agent maintains an internal state that is recursively updated to provide a compact summary of past observations and actions. In contrast to approaches that treat the agent state dynamics as fixed or learn it via predictive objectives, we propose a reward-centric formulation that jointly optimizes the agent state dynamics and the control policy to maximize the expected cumulative reward. To this end, we consider a class of Agent State-Markov (ASM) policies, comprising an agent state dynamics and a control policy that maps the agent state to actions. We establish a novel policy gradient theorem for ASM policies, extending the classical policy gradient results from the Markovian setting to episodic and infinite-horizon discounted NMDPs. Building on this gradient expression, we propose the Agent State-Markov Policy Gradient (ASMPG) algorithm, which leverages the recursive structure of the agent state dynamics for efficient optimization. We establish finite-time and almost sure convergence guarantees, and empirically demonstrate that, on a range of non-Markovian tasks, ASMPG outperforms baselines that learn state representations via predictive objectives.

preprint2022arXiv

Conormal Varieties of covexillary Schubert Varieties

A permutation is called covexillary if it avoids the pattern $3412$. We construct an open embedding of a covexillary matrix Schubert variety into a Grassmannian Schubert variety. As applications of this embedding, we show that the characteristic cycles of covexillary Schubert varieties are irreducible, and provide a new proof of Lascoux's model computing Kazhdan-Lusztig polynomials of vexillary permutations. Combining the above embedding with earlier work of the author on the conormal varieties of Grassmannian Schubert varieties, we develop an algebraic criterion identifying the conormal varieties of covexillary Schubert and matrix Schubert varieties as subvarieties of the respective cotangent bundles.

preprint2022arXiv

Quantifying Inherent Randomness in Machine Learning Algorithms

Most machine learning (ML) algorithms have several stochastic elements, and their performances are affected by these sources of randomness. This paper uses an empirical study to systematically examine the effects of two sources: randomness in model training and randomness in the partitioning of a dataset into training and test subsets. We quantify and compare the magnitude of the variation in predictive performance for the following ML algorithms: Random Forests (RFs), Gradient Boosting Machines (GBMs), and Feedforward Neural Networks (FFNNs). Among the different algorithms, randomness in model training causes larger variation for FFNNs compared to tree-based methods. This is to be expected as FFNNs have more stochastic elements that are part of their model initialization and training. We also found that random splitting of datasets leads to higher variation compared to the inherent randomness from model training. The variation from data splitting can be a major issue if the original dataset has considerable heterogeneity. Keywords: Model Training, Reproducibility, Variation

preprint2022arXiv

Reinforcement Learning for Finite-Horizon Restless Multi-Armed Multi-Action Bandits

We study a finite-horizon restless multi-armed bandit problem with multiple actions, dubbed R(MA)^2B. The state of each arm evolves according to a controlled Markov decision process (MDP), and the reward of pulling an arm depends on both the current state of the corresponding MDP and the action taken. The goal is to sequentially choose actions for arms so as to maximize the expected value of the cumulative rewards collected. Since finding the optimal policy is typically intractable, we propose a computationally appealing index policy which we call Occupancy-Measured-Reward Index Policy. Our policy is well-defined even if the underlying MDPs are not indexable. We prove that it is asymptotically optimal when the activation budget and number of arms are scaled up, while keeping their ratio as a constant. For the case when the system parameters are unknown, we develop a learning algorithm. Our learning algorithm uses the principle of optimism in the face of uncertainty and further uses a generative model in order to fully exploit the structure of Occupancy-Measured-Reward Index Policy. We call it the R(MA)^2B-UCB algorithm. As compared with the existing algorithms, R(MA)^2B-UCB performs close to an offline optimum policy, and also achieves a sub-linear regret with a low computational complexity. Experimental results show that R(MA)^2B-UCB outperforms the existing algorithms in both regret and run time.

preprint2022arXiv

Signed Graph Neural Networks: A Frequency Perspective

Graph convolutional networks (GCNs) and its variants are designed for unsigned graphs containing only positive links. Many existing GCNs have been derived from the spectral domain analysis of signals lying over (unsigned) graphs and in each convolution layer they perform low-pass filtering of the input features followed by a learnable linear transformation. Their extension to signed graphs with positive as well as negative links imposes multiple issues including computational irregularities and ambiguous frequency interpretation, making the design of computationally efficient low pass filters challenging. In this paper, we address these issues via spectral analysis of signed graphs and propose two different signed graph neural networks, one keeps only low-frequency information and one also retains high-frequency information. We further introduce magnetic signed Laplacian and use its eigendecomposition for spectral analysis of directed signed graphs. We test our methods for node classification and link sign prediction tasks on signed graphs and achieve state-of-the-art performances.

preprint2022arXiv

Understanding Metrics for Paraphrasing

Paraphrase generation is a difficult problem. This is not only because of the limitations in text generation capabilities but also due that to the lack of a proper definition of what qualifies as a paraphrase and corresponding metrics to measure how good it is. Metrics for evaluation of paraphrasing quality is an on going research problem. Most of the existing metrics in use having been borrowed from other tasks do not capture the complete essence of a good paraphrase, and often fail at borderline-cases. In this work, we propose a novel metric $ROUGE_P$ to measure the quality of paraphrases along the dimensions of adequacy, novelty and fluency. We also provide empirical evidence to show that the current natural language generation metrics are insufficient to measure these desired properties of a good paraphrase. We look at paraphrase model fine-tuning and generation from the lens of metrics to gain a deeper understanding of what it takes to generate and evaluate a good paraphrase.

preprint2021arXiv

Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection

I propose kernel ridge regression estimators for nonparametric dose response curves and semiparametric treatment effects in the setting where an analyst has access to a selected sample rather than a random sample; only for select observations, the outcome is observed. I assume selection is as good as random conditional on treatment and a sufficiently rich set of observed covariates, where the covariates are allowed to cause treatment or be caused by treatment -- an extension of missingness-at-random (MAR). I propose estimators of means, increments, and distributions of counterfactual outcomes with closed form solutions in terms of kernel matrix operations, allowing treatment and covariates to be discrete or continuous, and low, high, or infinite dimensional. For the continuous treatment case, I prove uniform consistency with finite sample rates. For the discrete treatment case, I prove root-n consistency, Gaussian approximation, and semiparametric efficiency.

preprint2021arXiv

Learning Augmented Index Policy for Optimal Service Placement at the Network Edge

We consider the problem of service placement at the network edge, in which a decision maker has to choose between $N$ services to host at the edge to satisfy the demands of customers. Our goal is to design adaptive algorithms to minimize the average service delivery latency for customers. We pose the problem as a Markov decision process (MDP) in which the system state is given by describing, for each service, the number of customers that are currently waiting at the edge to obtain the service. However, solving this $N$-services MDP is computationally expensive due to the curse of dimensionality. To overcome this challenge, we show that the optimal policy for a single-service MDP has an appealing threshold structure, and derive explicitly the Whittle indices for each service as a function of the number of requests from customers based on the theory of Whittle index policy. Since request arrival and service delivery rates are usually unknown and possibly time-varying, we then develop efficient learning augmented algorithms that fully utilize the structure of optimal policies with a low learning regret. The first of these is UCB-Whittle, and relies upon the principle of optimism in the face of uncertainty. The second algorithm, Q-learning-Whittle, utilizes Q-learning iterations for each service by using a two time scale stochastic approximation. We characterize the non-asymptotic performance of UCB-Whittle by analyzing its learning regret, and also analyze the convergence properties of Q-learning-Whittle. Simulation results show that the proposed policies yield excellent empirical performance.

preprint2021arXiv

Low-Power Status Updates via Sleep-Wake Scheduling

We consider the problem of optimizing the freshness of status updates that are sent from a large number of low-power sources to a common access point. The source nodes utilize carrier sensing to reduce collisions and adopt an asynchronized sleep-wake scheduling strategy to achieve a target network lifetime (e.g., 10 years). We use age of information (AoI) to measure the freshness of status updates, and design sleep-wake parameters for minimizing the weighted-sum peak AoI of the sources, subject to per-source battery lifetime constraints. When the sensing time (i.e., the time duration of carrier sensing) is zero, this sleep-wake design problem can be solved by resorting to a two-layer nested convex optimization procedure; however, for positive sensing times, the problem is non-convex. We devise a low-complexity solution to solve this problem and prove that, for practical sensing times that are short, the solution is within a small gap from the optimum AoI performance. When the mean transmission time of status-update packets is unknown, we devise a reinforcement learning algorithm that adaptively performs the following two tasks in an ``efficient way'': a) it learns the unknown parameter, b) it also generates efficient controls that make channel access decisions. We analyze its performance by quantifying its ``regret'', i.e., the sub-optimality gap between its average performance and the average performance of a controller that knows the mean transmission time. Our numerical and NS-3 simulation results show that our solution can indeed elongate the batteries lifetime of information sources, while providing a competitive AoI performance.

preprint2021arXiv

Straggler-Resilient Distributed Machine Learning with Dynamic Backup Workers

With the increasing demand for large-scale training of machine learning models, consensus-based distributed optimization methods have recently been advocated as alternatives to the popular parameter server framework. In this paradigm, each worker maintains a local estimate of the optimal parameter vector, and iteratively updates it by waiting and averaging all estimates obtained from its neighbors, and then corrects it on the basis of its local dataset. However, the synchronization phase can be time consuming due to the need to wait for \textit{stragglers}, i.e., slower workers. An efficient way to mitigate this effect is to let each worker wait only for updates from the fastest neighbors before updating its local parameter. The remaining neighbors are called \textit{backup workers.} To minimize the globally training time over the network, we propose a fully distributed algorithm to dynamically determine the number of backup workers for each worker. We show that our algorithm achieves a linear speedup for convergence (i.e., convergence performance increases linearly with respect to the number of workers). We conduct extensive experiments on MNIST and CIFAR-10 to verify our theoretical results.

preprint2020arXiv

A Partially Observable MDP Approach for Sequential Testing for Infectious Diseases such as COVID-19

The outbreak of the novel coronavirus (COVID-19) is unfolding as a major international crisis whose influence extends to every aspect of our daily lives. Effective testing allows infected individuals to be quarantined, thus reducing the spread of COVID-19, saving countless lives, and helping to restart the economy safely and securely. Developing a good testing strategy can be greatly aided by contact tracing that provides health care providers information about the whereabouts of infected patients in order to determine whom to test. Countries that have been more successful in corralling the virus typically use a ``test, treat, trace, test'' strategy that begins with testing individuals with symptoms, traces contacts of positively tested individuals via a combinations of patient memory, apps, WiFi, GPS, etc., followed by testing their contacts, and repeating this procedure. The problem is that such strategies are myopic and do not efficiently use the testing resources. This is especially the case with COVID-19, where symptoms may show up several days after the infection (or not at all, there is evidence to suggest that many COVID-19 carriers are asymptotic, but may spread the virus). Such greedy strategies, miss out population areas where the virus may be dormant and flare up in the future. In this paper, we show that the testing problem can be cast as a sequential learning-based resource allocation problem with constraints, where the input to the problem is provided by a time-varying social contact graph obtained through various contact tracing tools. We then develop efficient learning strategies that minimize the number of infected individuals. These strategies are based on policy iteration and look-ahead rules. We investigate fundamental performance bounds, and ensure that our solution is robust to errors in the input graph as well as in the tests themselves.

preprint2020arXiv

Accelerating computational modeling and design of high-entropy alloys

With huge design spaces for unique chemical and mechanical properties, we remove a roadblock to computational design of {high-entropy alloys} using a metaheuristic hybrid Cuckoo Search (CS) for "on-the-fly" construction of Super-Cell Random APproximates (SCRAPs) having targeted atomic site and pair probabilities on arbitrary crystal lattices. Our hybrid-CS schema overcomes large, discrete combinatorial optimization by ultrafast global solutions that scale linearly in system size and strongly in parallel, e.g. a 4-element, 128-atom model [a $10^{73+}$ space] is found in seconds -- a reduction of 13,000+ over current strategies. With model-generation eliminated as a bottleneck, computational alloy design can be performed that is currently impossible or impractical. We showcase the method for real alloys with varying short-range order. Being problem-agnostic, our hybrid-CS schema offers numerous applications in diverse fields.

preprint2020arXiv

Dynamics of a long chain in turbulent flows: Impact of vortices

We show and explain how a long bead-spring chain, immersed in a homogeneous, isotropic turbulent flow, preferentially samples vortical flow structures. We begin with an elastic, extensible chain which is stretched out by the flow, up to inertial-range scales. This filamentary object, which is known to preferentially sample the circular coherent vortices of two-dimensional (2D) turbulence, is shown here to also preferentially sample the intense, tubular, vortex filaments of 3D turbulence. In the 2D case, the chain collapses into a tracer inside vortices. In 3D, on the contrary, the chain is extended even in vortical regions, which suggests that it follows axially-stretched tubular vortices by aligning with their axes. This physical picture is confirmed by examining the relative sampling behaviour of the individual beads, and by additional studies on an inextensible chain with adjustable bending-stiffness. A highly-flexible, inextensible chain also shows preferential sampling in 3D, provided it is longer than the dissipation scale, but not much longer than the vortex tubes. This is true also for 2D turbulence, where a long inextensible chain can occupy vortices by coiling into them. When the chain is made inflexible, however, coiling is prevented and the extent of preferential sampling in 2D is considerably reduced. In 3D, on the contrary, bending stiffness has no effect, because the chain does not need to coil in order to thread a vortex tube and align with its axis.

preprint2020arXiv

Improving Robustness via Risk Averse Distributional Reinforcement Learning

One major obstacle that precludes the success of reinforcement learning in real-world applications is the lack of robustness, either to model uncertainties or external disturbances, of the trained policies. Robustness is critical when the policies are trained in simulations instead of real world environment. In this work, we propose a risk-aware algorithm to learn robust policies in order to bridge the gap between simulation training and real-world implementation. Our algorithm is based on recently discovered distributional RL framework. We incorporate CVaR risk measure in sample based distributional policy gradients (SDPG) for learning risk-averse policies to achieve robustness against a range of system disturbances. We validate the robustness of risk-aware SDPG on multiple environments.

preprint2020arXiv

Incremental inference of collective graphical models

We consider incremental inference problems from aggregate data for collective dynamics. In particular, we address the problem of estimating the aggregate marginals of a Markov chain from noisy aggregate observations in an incremental (online) fashion. We propose a sliding window Sinkhorn belief propagation (SW-SBP) algorithm that utilizes a sliding window filter of the most recent noisy aggregate observations along with encoded information from discarded observations. Our algorithm is built upon the recently proposed multi-marginal optimal transport based SBP algorithm that leverages standard belief propagation and Sinkhorn algorithm to solve inference problems from aggregate data. We demonstrate the performance of our algorithm on applications such as inferring population flow from aggregate observations.

preprint2020arXiv

Kernel Instrumental Variable Regression

Instrumental variable (IV) regression is a strategy for learning causal relationships in observational data. If measurements of input X and output Y are confounded, the causal relationship can nonetheless be identified if an instrumental variable Z is available that influences X directly, but is conditionally independent of Y given X and the unmeasured confounder. The classic two-stage least squares algorithm (2SLS) simplifies the estimation problem by modeling all relationships as linear functions. We propose kernel instrumental variable regression (KIV), a nonparametric generalization of 2SLS, modeling relations among X, Y, and Z as nonlinear functions in reproducing kernel Hilbert spaces (RKHSs). We prove the consistency of KIV under mild assumptions, and derive conditions under which convergence occurs at the minimax optimal rate for unconfounded, single-stage RKHS regression. In doing so, we obtain an efficient ratio between training sample sizes used in the algorithm's first and second stages. In experiments, KIV outperforms state of the art alternatives for nonparametric IV regression.

preprint2020arXiv

Learning in Networked Control Systems

We design adaptive controller (learning rule) for a networked control system (NCS) in which data packets containing control information are transmitted across a lossy wireless channel. We propose Upper Confidence Bounds for Networked Control Systems (UCB-NCS), a learning rule that maintains confidence intervals for the estimates of plant parameters $(A_{(\star)},B_{(\star)})$, and channel reliability $p_{(\star)}$, and utilizes the principle of optimism in the face of uncertainty while making control decisions. We provide non-asymptotic performance guarantees for UCB-NCS by analyzing its "regret", i.e., performance gap from the scenario when $(A_{(\star)},B_{(\star)},p_{(\star)})$ are known to the controller. We show that with a high probability the regret can be upper-bounded as $\tilde{O}\left(C\sqrt{T}\right)$\footnote{Here $\tilde{O}$ hides logarithmic factors.}, where $T$ is the operating time horizon of the system, and $C$ is a problem dependent constant.

preprint2020arXiv

Mather classes and conormal spaces of Schubert varieties in cominuscule spaces

Let $G/P$ be a complex cominuscule flag manifold. We prove a type independent formula for the torus equivariant Mather class of a Schubert variety in $G/P$, and for a Schubert variety pulled back via the natural projection $G/Q \to G/P$. We apply this to find formulae for the local Euler obstructions of Schubert varieties, and for the torus equivariant localizations of the conormal spaces of these Schubert varieties. We conjecture positivity properties for the local Euler obstructions and for the Schubert expansion of Mather classes. We check the conjectures in many cases, by utilizing results of Boe and Fu about the characteristic cycles of the intersection homology sheaves of Schubert varieties. We also conjecture that certain `Mather polynomials' are unimodal in general Lie type, and log concave in type A.

preprint2020arXiv

Model Robustness with Text Classification: Semantic-preserving adversarial attacks

We propose algorithms to create adversarial attacks to assess model robustness in text classification problems. They can be used to create white box attacks and black box attacks while at the same time preserving the semantics and syntax of the original text. The attacks cause significant number of flips in white-box setting and same rule based can be used in black-box setting. In a black-box setting, the attacks created are able to reverse decisions of transformer based architectures.

preprint2020arXiv

Multi-marginal optimal transport and probabilistic graphical models

We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular, an entropy regularized multi-marginal optimal transport is equivalent to a Bayesian marginal inference problem for probabilistic graphical models with the additional requirement that some of the marginal distributions are specified. This relation on the one hand extends the optimal transport as well as the probabilistic graphical model theories, and on the other hand leads to fast algorithms for multi-marginal optimal transport by leveraging the well-developed algorithms in Bayesian inference. Several numerical examples are provided to highlight the results.

preprint2020arXiv

Performance of closed orbit feedback systems with spatial model mismatch

Closed orbit feedback (COFB) systems used for the global orbit correction rely on the pseudo-inversion of the orbit response matrix (ORM). A mismatch between the model ORM used in the controller and the actual machine ORM can affect the performance of the feedback system. In this paper, the typical sources of such model mismatch such as acceleration ramp ORM variation, intensity-dependent tune shift and beta beating are considered in simulation studies. Their effect on the performance and the stability margins are investigated for both the slow and fast regimes of a COFB system operation. The spectral radius stability condition is utilized instead of the small gain theorem to arrive at the theoretical limits of COFB stability and comparisons with simulations for SIS18 of GSI and experiments at the Cooler synchrotron (COSY) in the Forschungzentrum Jülich (FZJ) are also presented.

preprint2020arXiv

Sample-based Distributional Policy Gradient

Distributional reinforcement learning (DRL) is a recent reinforcement learning framework whose success has been supported by various empirical studies. It relies on the key idea of replacing the expected return with the return distribution, which captures the intrinsic randomness of the long term rewards. Most of the existing literature on DRL focuses on problems with discrete action space and value based methods. In this work, motivated by applications in robotics with continuous action space control settings, we propose sample-based distributional policy gradient (SDPG) algorithm. It models the return distribution using samples via a reparameterization technique widely used in generative modeling and inference. We compare SDPG with the state-of-art policy gradient method in DRL, distributed distributional deterministic policy gradients (D4PG), which has demonstrated state-of-art performance. We apply SDPG and D4PG to multiple OpenAI Gym environments and observe that our algorithm shows better sample efficiency as well as higher reward for most tasks.

preprint2019arXiv

Elasto-inertial Chains in a Two-dimensional Turbulent Flow

The interplay of inertia and elasticity is shown to have a significant impact on the transport of filamentary objects, modelled by bead-spring chains, in a two-dimensional turbulent flow. We show how elastic interactions amongst inertial beads result in a non-trivial sampling of the flow, ranging from entrapment within vortices to preferential sampling of straining regions. This behavior is quantified as a function of inertia and elasticity and is shown to be very different from free, non-interacting heavy particles, as well as inertialess chains [Picardo et al., Phys. Rev. Lett. 121, 244501 (2018)]. In addition, by considering two limiting cases, of a heavy-headed and a uniformly-inertial chain, we illustrate the critical role played by the mass distribution of such extended objects in their turbulent transport.

preprint2019arXiv

Room temperature large spontaneous exchange bias in hard-soft antiferromagnetic composite BiFeO3-TbMnO3

We report the presence of giant spontaneous exchange bias (HSEB) in a hard and soft antiferromagnetic composite of BiFeO3-TbMnO3 (BFO-TMO in 7:3 and 8:2 ratio). The HSEB varies between 5-778Oe, but persists up to room temperature with a maximum near a spin reorientation transition temperature observed from magnetization vs. temperature measurement in Zero-field cooled (ZFC) and Field cooled (FC) modes. Isothermal remnant magnetization measurements at room temperature indicate the presence of an interfacial layer of a 2 dimensional dilute antiferromagnet in a field (2D DAFF). A stable value of the exchange bias has been observed via training effect measurements which signify the role of interfacial exchange coupling in the system. Based on the experimental results we explain the presence of the giant spontaneous exchange bias on the basis of a strong strain-mediated magnetoelectriccoupling induced exchange interaction and the creation of 2D DAFF layer at the interface. Theproperties of this layer are defined by canting and pinning of BFO spins at the interface with TMO due to Fe and Mn interaction. X-ray Magnetic Circular Dichroism (XMCD) confirms the presence of canted antiferromagnetic ordering of BiFeO3, charge transfer between Mn ions and different magnetically coupled layers which play vital role in getting the exchange bias.

preprint2019arXiv

Smoothing of the slowly extracted coasting beam from a synchrotron

Slow extraction of beam from synchrotrons or storage rings as required by many fixed target experiments is performed by controlled excitation and feeding of a structural lattice resonance. Due to the sensitive nature of this resonant extraction process, the temporal structure of the extracted beam is modulated by the minuscule current fluctuations present on the quadrupole magnet power supplies. Such a modulation lead to pile-ups in detectors and a significant reduction in accumulated event statistics. This contribution proposes and experimentally demonstrates that by an introduction of further modulation on quadrupole currents with a specific amplitude and frequency, the inherent power supply fluctuations are mitigated leading to a smoothening of the beam temporal structure. The slow extraction beam dynamics associated with this method are explained along with the operational results.

preprint2018arXiv

Conormal Varieties on the Cominuscule Grassmannian

Let $G$ be a simply connected, almost simple group over an algebraically closed field $\mathbf k$, and $P$ a maximal parabolic subgroup corresponding to omitting a cominuscule root. We construct a compactification $ϕ:T^*G/P\rightarrow X(u)$, where $X(u)$ is a Schubert variety corresponding to the loop group $LG$. Let $N^*X(w)\subset T^*G/P$ be the conormal variety of some Schubert variety $X(w)$ in $G/P$; hence we obtain that the closure of $ϕ(N^*X(w))$ in $X(u)$ is a $B$-stable compactification of $N^*X(w)$. We further show that this compactification is a Schubert subvariety of $X(u)$ if and only if $X(w_0w)\subset G/P$ is smooth, where $w_0$ is the longest element in the Weyl group of $G$. This result is applied to compute the conormal fibre at the zero matrix in any determinantal variety.

preprint2018arXiv

Conormal Varieties on the Cominuscule Grassmannian - II

Let $X_w$ be a Schubert subvariety of a cominuscule Grassmannian $X$, and let $μ:T^*X\rightarrow\mathcal N$ be the Springer map from the cotangent bundle of $X$ to the nilpotent cone $\mathcal N$. In this paper, we construct a resolution of singularities for the conormal variety $T^*_XX_w$ of $X_w$ in $X$. Further, for $X$ the usual or symplectic Grassmannian, we compute a system of equations defining $T^*_XX_w$ as a subvariety of the cotangent bundle $T^*X$ set-theoretically. This also yields a system of defining equations for the corresponding orbital varieties $μ(T^*_XX_w)$. Inspired by the system of defining equations, we conjecture a type-independent equality, namely $T^*_XX_w=π^{-1}(X_w)\capμ^{-1}(μ(T^*_XX_w))$. The set-theoretic version of this conjecture follows from this work and previous work for any cominuscule Grassmannian of type A, B, or C.

preprint2018arXiv

Finite Groups Generated in Low Real Codimension

We study the intersection lattice of the arrangement $\mathcal{A}^G$ of subspaces fixed by subgroups of a finite linear group $G$. When $G$ is a reflection group, this arrangement is precisely the hyperplane reflection arrangement of $G$. We generalize the notion of finite reflection groups. We say that a group $G$ is generated (resp. strictly generated) in codimension $k$ if it is generated by its elements that fix point-wise a subspace of codimension at most $k$ (resp. precisely $k$). If $G$ is generated in codimension two, we show that the intersection lattice of $\mathcal{A}^G$ is atomic. We prove that the alternating subgroup $\mathsf{Alt}(W)$ of a reflection group $W$ is strictly generated in codimension two, moreover, the subspace arrangement of $\mathsf{Alt}(W)$ is the truncation at rank two of the reflection arrangement $\mathcal{A}^W$. Further, we compute the intersection lattice of all finite subgroups of $GL_3(\mathbb{R})$, and moreover, we emphasize the groups that are "minimally generated in real codimension two", i.e, groups that are strictly generated in codimension two but have no real reflection representations. We also provide several examples of groups generated in higher codimension.

preprint2018arXiv

Tuning Bandgap and Energy Stability of Organic-Inorganic Halide Perovskites through Surface Engineering

Organohalide perovskite with a variety of surface structures and morphologies have shown promising potential owing to the choice of the type of heterostructure dependent stability. We systematically investigate and discuss the impact of 2-dimensional molybdenum-disulphide (MoS2), molybdenum-diselenide (MoSe2), tungsten-disulphide (WS2), tungsten-diselenide (WSe2), boron- nitiride (BN) and graphene monolayers on band-gap and energy stability of organic-inorganic halide perovskites. We found that MAPbI3ML deposited on BN-ML shows room temperature stability (-25 meV~300K) with an optimal bandgap of ~1.6 eV. The calculated absorption coefficient also lies in the visible-light range with a maximum of 4.9 x 104 cm-1 achieved at 2.8 eV photon energy. On the basis of our calculations, we suggest that the encapsulation of an organic-inorganic halide perovskite monolayers by semiconducting monolayers potentially provides greater flexibility for tuning the energy stability and the bandgap.

preprint2017arXiv

Cotangent Bundles of Partial Flag Varieties and Conormal Varieties of their Schubert Divisors

Let $P$ be a parabolic subgroup in $G=SL_n(\mathbf k)$, for $\mathbf k$ an algebraically closed field. We show that there is a $G$-stable closed subvariety of an affine Schubert variety in an affine partial flag variety which is a natural compactification of the cotangent bundle $T^*G/P$. Restricting this identification to the conormal variety $N^*X(w)$ of a Schubert divisor $X(w)$ in $G/P$, we show that there is a compactification of $N^*X(w)$ as an affine Schubert variety. It follows that $N^*X(w)$ is normal, Cohen-Macaulay, and Frobenius split.

Rahul Singh

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33 published item(s)

Equivariant Chevalley, Giambelli, and Monk Formulae for the Peterson Variety

Extensible Post Quantum Cryptography Based Authentication

On Gaussian approximation for entropy-regularized Q-learning with function approximation

Policy Gradient Methods for Non-Markovian Reinforcement Learning

Conormal Varieties of covexillary Schubert Varieties

Quantifying Inherent Randomness in Machine Learning Algorithms

Reinforcement Learning for Finite-Horizon Restless Multi-Armed Multi-Action Bandits

Signed Graph Neural Networks: A Frequency Perspective

Understanding Metrics for Paraphrasing

Generalized Kernel Ridge Regression for Causal Inference with Missing-at-Random Sample Selection

Learning Augmented Index Policy for Optimal Service Placement at the Network Edge

Low-Power Status Updates via Sleep-Wake Scheduling

Straggler-Resilient Distributed Machine Learning with Dynamic Backup Workers

A Partially Observable MDP Approach for Sequential Testing for Infectious Diseases such as COVID-19

Accelerating computational modeling and design of high-entropy alloys

Dynamics of a long chain in turbulent flows: Impact of vortices

Improving Robustness via Risk Averse Distributional Reinforcement Learning

Incremental inference of collective graphical models

Kernel Instrumental Variable Regression

Learning in Networked Control Systems

Mather classes and conormal spaces of Schubert varieties in cominuscule spaces

Model Robustness with Text Classification: Semantic-preserving adversarial attacks

Multi-marginal optimal transport and probabilistic graphical models

Performance of closed orbit feedback systems with spatial model mismatch

Sample-based Distributional Policy Gradient

Elasto-inertial Chains in a Two-dimensional Turbulent Flow

Room temperature large spontaneous exchange bias in hard-soft antiferromagnetic composite BiFeO3-TbMnO3

Smoothing of the slowly extracted coasting beam from a synchrotron

Conormal Varieties on the Cominuscule Grassmannian

Conormal Varieties on the Cominuscule Grassmannian - II

Finite Groups Generated in Low Real Codimension

Tuning Bandgap and Energy Stability of Organic-Inorganic Halide Perovskites through Surface Engineering

Cotangent Bundles of Partial Flag Varieties and Conormal Varieties of their Schubert Divisors