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The coronene molecules have been bombarded by protons of energy by 75 to 300 keV. The time of flight mass spectrum has been recorded using a two stage Wiley McLaren type spectrometer. A large enhancement in the doubly and triply ionized recoil ion is observed compared to the singly ionized one. The single, double and triple ionization yields have also been calculated using the continuum distorted wave eikonal initial state (CDW EIS) theoretical model and are compared with the experimental results. Experimental double to single ionization yield ratios and triple to single ionization yield ratios have been compared with the theoretical ratios which are found to be much higher w.r. t. the gas atoms. Evaporation peaks due to the loss of several neutral C2H2 and C3H3 are observed corresponding to their parent singly, doubly and triply charge coronene ions. Small fragmentation peaks CnHx+ (n = 3 to 7) are present in the spectra due to higher energy transfer by the projectile to the molecule. The hydrogen losses are observed in the cation, di-cation and tri-cation coronene peak structures. A maximum of the 7 H losses are detected which depends on the beam energy., Comment: After careful consideration, I have decided to withdraw this paper due to significant improvements needed in the paper and require extensive revisions. I plan to address these issues and resubmit a corrected version in the future."

To avoid failures on out-of-distribution data, recent works have sought to extract features that have an invariant or stable relationship with the label across domains, discarding "spurious" or unstable features whose relationship with the label changes across domains. However, unstable features often carry complementary information that could boost performance if used correctly in the test domain. In this work, we show how this can be done without test-domain labels. In particular, we prove that pseudo-labels based on stable features provide sufficient guidance for doing so, provided that stable and unstable features are conditionally independent given the label. Based on this theoretical insight, we propose Stable Feature Boosting (SFB), an algorithm for: (i) learning a predictor that separates stable and conditionally-independent unstable features; and (ii) using the stable-feature predictions to adapt the unstable-feature predictions in the test domain. Theoretically, we prove that SFB can learn an asymptotically-optimal predictor without test-domain labels. Empirically, we demonstrate the effectiveness of SFB on real and synthetic data., Comment: NeurIPS 2023 Camera-Ready

The dynamical aspect of accelerating cosmological model has been studied in this paper in the context of modified symmetric teleparallel gravity, the $f(Q)$ gravity. Initially, we have derived the dynamical parameters for two well known forms of $f(Q)$ such as: (i) log-square-root form and (ii) exponential form. The equation of state (EoS) parameter for the dark energy in the $f(Q)$ gravity in both the models emerges into a dynamical quantity. At present model-I shows the quintessence behavior and behave like the $\Lambda$CDM at the late time whereas model-II shows phantom behaviour. Further, the dynamical system analysis has been performed to determine the cosmological behaviour of the models along with its stability behaviour. For both the models the critical points are obtained and analysed the stability at each critical points with phase portraits. The evolutionary behaviour of density parameters for the matter-dominated, radiation-dominated, and dark energy phases are also shown for both the models., Comment: 13 pages, 9 figures

Eye-tracking has potential to provide rich behavioral data about human cognition in ecologically valid environments. However, analyzing this rich data is often challenging. Most automated analyses are specific to simplistic artificial visual stimuli with well-separated, static regions of interest, while most analyses in the context of complex visual stimuli, such as most natural scenes, rely on laborious and time-consuming manual annotation. This paper studies using computer vision tools for "attention decoding", the task of assessing the locus of a participant's overt visual attention over time. We provide a publicly available Multiple Object Eye-Tracking (MOET) dataset, consisting of gaze data from participants tracking specific objects, annotated with labels and bounding boxes, in crowded real-world videos, for training and evaluating attention decoding algorithms. We also propose two end-to-end deep learning models for attention decoding and compare these to state-of-the-art heuristic methods., Comment: To be published in Proceedings of the NeurIPS 2022 Gaze Meets ML Workshop

Domain generalization (DG) seeks predictors which perform well on unseen test distributions by leveraging data drawn from multiple related training distributions or domains. To achieve this, DG is commonly formulated as an average- or worst-case problem over the set of possible domains. However, predictors that perform well on average lack robustness while predictors that perform well in the worst case tend to be overly-conservative. To address this, we propose a new probabilistic framework for DG where the goal is to learn predictors that perform well with high probability. Our key idea is that distribution shifts seen during training should inform us of probable shifts at test time, which we realize by explicitly relating training and test domains as draws from the same underlying meta-distribution. To achieve probable DG, we propose a new optimization problem called Quantile Risk Minimization (QRM). By minimizing the $\alpha$-quantile of predictor's risk distribution over domains, QRM seeks predictors that perform well with probability $\alpha$. To solve QRM in practice, we propose the Empirical QRM (EQRM) algorithm and provide: (i) a generalization bound for EQRM; and (ii) the conditions under which EQRM recovers the causal predictor as $\alpha \to 1$. In our experiments, we introduce a more holistic quantile-focused evaluation protocol for DG and demonstrate that EQRM outperforms state-of-the-art baselines on datasets from WILDS and DomainBed., Comment: NeurIPS 2022 camera-ready (+ minor corrections)

We show that the hypergeometric groups corresponding to the seven pairs of the parameters $\alpha$, $\beta$ where $\alpha$ = (0, 0, 0, 0, 0, 0) and $\beta$ is any of the parameters (1/2, 1/2, 1/2, 1/2, 1/2, 1/2), (1/2, 1/2, 1/2, 1/2, 1/3, 2/3), (1/2, 1/2, 1/2, 1/2, 1/4, 3/4), (1/2, 1/2, 1/2, 1/2, 1/6, 5/6), (1/2, 1/2, 1/3, 2/3, 1/3, 2/3), (1/2, 1/2, 1/3, 2/3, 1/4, 3/4), (1/2, 1/2, 1/5, 2/5, 3/5, 4/5) are thin., Comment: Final version; accepted for publication in Glasgow Mathematical Journal

Traditional models of active learning assume a learner can directly manipulate or query a covariate $X$ in order to study its relationship with a response $Y$. However, if $X$ is a feature of a complex system, it may be possible only to indirectly influence $X$ by manipulating a control variable $Z$, a scenario we refer to as Indirect Active Learning. Under a nonparametric model of Indirect Active Learning with a fixed budget, we study minimax convergence rates for estimating the relationship between $X$ and $Y$ locally at a point, obtaining different rates depending on the complexities and noise levels of the relationships between $Z$ and $X$ and between $X$ and $Y$. We also identify minimax rates for passive learning under comparable assumptions. In many cases, our results show that, while there is an asymptotic benefit to active learning, this benefit is fully realized by a simple two-stage learner that runs two passive experiments in sequence., Comment: To appear in proceedings of the 26th International Conference on Artificial Intelligence and Statistics (AISTATS)

We show that the hypergeometric groups associated to the pairs of the parameters $\left(0,0,\frac{1}{3}, \frac{2}{3}\right)$, $\left(\frac{1}{2},\frac{1}{2},\frac{1}{4},\frac{3}{4}\right)$; and $\left(0,\frac{1}{12}, \frac{5}{12},\frac{7}{12},\frac{11}{12}\right), \left(\frac{1}{2},\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3}\right)$ are arithmetic., Comment: 9 pages

Two-electron one-photon transitions have been successfully observed for the Ne projectile and Al target at low energy regime. Experimental energy values of two-electron one-photon transitions are compared with previously reported theoretical and experimental values. Ionization cross-section of two-electron one-photon transition is reported.

The vast majority of statistical theory on binary classification characterizes performance in terms of accuracy. However, accuracy is known in many cases to poorly reflect the practical consequences of classification error, most famously in imbalanced binary classification, where data are dominated by samples from one of two classes. The first part of this paper derives a novel generalization of the Bayes-optimal classifier from accuracy to any performance metric computed from the confusion matrix. Specifically, this result (a) demonstrates that stochastic classifiers sometimes outperform the best possible deterministic classifier and (b) removes an empirically unverifiable absolute continuity assumption that is poorly understood but pervades existing results. We then demonstrate how to use this generalized Bayes classifier to obtain regret bounds in terms of the error of estimating regression functions under uniform loss. Finally, we use these results to develop some of the first finite-sample statistical guarantees specific to imbalanced binary classification. Specifically, we demonstrate that optimal classification performance depends on properties of class imbalance, such as a novel notion called Uniform Class Imbalance, that have not previously been formalized. We further illustrate these contributions numerically in the case of $k$-nearest neighbor classification, Comment: Parts of this paper have been revised from arXiv:2004.04715v2 [math.ST]

The K x-ray spectra of different targets (Cu, Zn, and Ge) induced by 3 to 5 MeV/u Si projectile ions have been measured to determine the K-shell ionization cross-section. A significant difference is observed between the measurements and theoretical estimates, where the theoretical ones are about 28-35% of the experimental results. Such difference is reduced to a good extent 51-56% if multiple ionization effects are taken into account. Remaining discrepancy may be attributed to the electron capture contribution., Comment: 7 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2103.08299

To have a better understanding of a physical process, a comparison of ex-perimental data with theoretical values is mandatory. The comparison ismeaningful if the uncertainty in the experiment is accounted well. However,it is seldom seen, especially for a complex phenomenon. We take a test casethrough L subshell ionization of atoms by particle impact. Experimentally,x-ray production cross-sections are measured, but ionization cross-sectionsare calculated theoretically. Furthermore, the uncertainty of the x-ray pro-duction cross-section is mainly statistics and detector-efficiency driven. Butionization cross-section involves many other factors because of the relation-ship between the production and ionization cross section, having wide uncer-tainty spectrum. Consequently, determining the measurement uncertainty inL subshell ionization cross-section is always difficult. We have studied thisissue in the simplest way, where the rule of weighted propagation of rela-tive uncertainty is utilised. We notice that larger uncertainties are involvedin atomic parameters relevant to L1(2s1/2) subshell than those associatedwith the other two L2(2p1/2) and L3(2p3/2) subshells. Hence, comparisonbetween theory and experiment would give higher emphasis onL2andL3subshell ionization cross sections. We believe this work aware us that theappropriate uncertainty evaluation is extremely important for providing theright judgment on the data., Comment: 31 pages, 2 figures

Continuum-armed bandits (a.k.a., black-box or $0^{th}$-order optimization) involves optimizing an unknown objective function given an oracle that evaluates the function at a query point, with the goal of using as few query points as possible. In the most well-studied case, the objective function is assumed to be Lipschitz continuous and minimax rates of simple and cumulative regrets are known in both noiseless and noisy settings. This paper studies continuum-armed bandits under more general smoothness conditions, namely Besov smoothness conditions, on the objective function. In both noiseless and noisy conditions, we derive minimax rates under simple and cumulative regrets. Our results show that minimax rates over objective functions in a Besov space are identical to minimax rates over objective functions in the smallest H\"older space into which the Besov space embeds.

We propose a novel approach that integrates machine learning into compartmental disease modeling to predict the progression of COVID-19. Our model is explainable by design as it explicitly shows how different compartments evolve and it uses interpretable encoders to incorporate covariates and improve performance. Explainability is valuable to ensure that the model's forecasts are credible to epidemiologists and to instill confidence in end-users such as policy makers and healthcare institutions. Our model can be applied at different geographic resolutions, and here we demonstrate it for states and counties in the United States. We show that our model provides more accurate forecasts, in metrics averaged across the entire US, than state-of-the-art alternatives, and that it provides qualitatively meaningful explanatory insights. Lastly, we analyze the performance of our model for different subgroups based on the subgroup distributions within the counties.

We study minimax convergence rates of nonparametric density estimation in the Huber contamination model, in which a proportion of the data comes from an unknown outlier distribution. We provide the first results for this problem under a large family of losses, called Besov integral probability metrics (IPMs), that includes $\mathcal{L}^p$, Wasserstein, Kolmogorov-Smirnov, and other common distances between probability distributions. Specifically, under a range of smoothness assumptions on the population and outlier distributions, we show that a re-scaled thresholding wavelet series estimator achieves minimax optimal convergence rates under a wide variety of losses. Finally, based on connections that have recently been shown between nonparametric density estimation under IPM losses and generative adversarial networks (GANs), we show that certain GAN architectures also achieve these minimax rates.

We study statistical properties of the k-nearest neighbors algorithm for multiclass classification, with a focus on settings where the number of classes may be large and/or classes may be highly imbalanced. In particular, we consider a variant of the k-nearest neighbor classifier with non-uniform class-weightings, for which we derive upper and minimax lower bounds on accuracy, class-weighted risk, and uniform error. Additionally, we show that uniform error bounds lead to bounds on the difference between empirical confusion matrix quantities and their population counterparts across a set of weights. As a result, we may adjust the class weights to optimize classification metrics such as F1 score or Matthew's Correlation Coefficient that are commonly used in practice, particularly in settings with imbalanced classes. We additionally provide a simple example to instantiate our bounds and numerical experiments., Comment: 62 pages, 4 figures, 2 tables

Our computations show that there is a total of $40$ pairs of degree six coprime polynomials $f,g$ where $f(x)=(x-1)^6$, $g$ is a product of cyclotomic polynomials, $g(0)=1$ and $f,g$ form a primitive pair. The aim of this article is to determine whether the corresponding $40$ symplectic hypergeometric groups with a maximally unipotent monodromy follow the same dichotomy between arithmeticity and thinness that holds for the $14$ symplectic hypergeometric groups corresponding to the pairs of degree four polynomials $f,g$ where $f(x)=(x-1)^4$ and $g$ is as described above. As a result we prove that at least $18$ of these $40$ groups are arithmetic in $\mathrm{Sp}(6)$. In addition, we extend our search to all degree six symplectic hypergeometric groups. We find that there is a total of $458$ pairs of polynomials (up to scalar shifts) corresponding to such groups. For $211$ of them, the absolute values of the leading coefficients of the difference polynomials $f-g$ are at most $2$ and the arithmeticity of the corresponding groups follows from Singh and Venkataramana, while the arithmeticity of one more hypergeometric group follows from Detinko, Flannery and Hulpke. In this article, we show the arithmeticity of $160$ of the remaining $246$ hypergeometric groups., Comment: 25 Pages, 4 Tables. Author's list has been updated. The article has been reorganized. New results have been found and incorporated

The real-time statistics on key consumer parameters and key utility parameters earmark the implementation of demand response (DR) under the smart grid (SG) paradigm. Advanced metering infrastructure (AMI) enables monitoring and control over both key parameters to reflect reliable information on SG. Firstly, this paper aims at a physical realization of an AMI, which comprises a meter data management system (MDMS) supported by smart meters. Secondly, a sliding window based non-intrusive load monitoring algorithm is proposed to illustrate the power consumption pattern. The MDMS features an incremental block--rate tariff structure given by Tamil Nadu state electricity board for the estimation and prediction of electricity bill. Finally, an implementation perspective is presented describing the features of its constituents both theoretically and experimentally, which could envision a consumer-facing grid and exert the proposed self--DR scheme., Comment: Presented in the 2019 International Conference on Electronics, Computing and Communication Technologies (IEEE CONECCT) organized by IEEE Bangalore Section, held at IIIT Bangalore during 26-27 July, 2019

The state of charge (SoC) and the rate of charging/discharging current are the vital parameters associated with a battery by which its accurate runtime can be estimated. This paper aims to design a controller which comprises of a field-programmable gate array, back to back connected dc-dc converters, and a resistive touch display based graphical user interface (GUI). The controller estimates SoC and performs constant current charging or discharging of the battery. The implementation of GUI is to input the reference charging/discharging current from the user and to display the SoC. This research delves into battery and obtains its internal parameters by conducting hybrid pulse power characterization test. Furthermore, the obtained internal parameters are processed through an extended Kalman filter which yields the SoC. This controller has large applications in the renewable energy system, battery testing system, smart residential energy management systems, and micro-grids., Comment: Presented in 2018 15th IEEE India Council International Conference (INDICON)

Under Smart Grid environment, the consumers may respond to incentive--based smart energy tariffs for a particular consumption pattern. Demand Response (DR) is a portfolio of signaling schemes from the utility to the consumers for load shifting/shedding with a given deadline. The signaling schemes include Time--of--Use (ToU) pricing, Maximum Demand Limit (MDL) signals etc. This paper proposes a DR algorithm which schedules the operation of home appliances/loads through a minimization problem. The category of loads and their operational timings in a day have been considered as the operational parameters of the system. These operational parameters determine the dynamic priority of a load, which is an intermediate step of this algorithm. The ToU pricing, MDL signals, and the dynamic priority of loads are the constraints in this formulated minimization problem, which yields an optimal schedule of operation for each participating load within the consumer provided duration. The objective is to flatten the daily load curve of a smart home by distributing the operation of its appliances in possible low--price intervals without violating the MDL constraint. This proposed algorithm is simulated in MATLAB environment against various test cases. The obtained results are plotted to depict significant monetary savings and flattened load curves., Comment: This paper was accepted and presented in 2019 IEEE PES GTD Grand International Conference and Exposition Asia (GTD Asia). Furthermore, the conference proceedings has been published in IEEE Xplore

In many learning situations, resources at inference time are significantly more constrained than resources at training time. This paper studies a general paradigm, called Differentiable ARchitecture Compression (DARC), that combines model compression and architecture search to learn models that are resource-efficient at inference time. Given a resource-intensive base architecture, DARC utilizes the training data to learn which sub-components can be replaced by cheaper alternatives. The high-level technique can be applied to any neural architecture, and we report experiments on state-of-the-art convolutional neural networks for image classification. For a WideResNet with $97.2\%$ accuracy on CIFAR-10, we improve single-sample inference speed by $2.28\times$ and memory footprint by $5.64\times$, with no accuracy loss. For a ResNet with $79.15\%$ Top1 accuracy on ImageNet, we improve batch inference speed by $1.29\times$ and memory footprint by $3.57\times$ with $1\%$ accuracy loss. We also give theoretical Rademacher complexity bounds in simplified cases, showing how DARC avoids overfitting despite over-parameterization.

We study the problem of estimating a nonparametric probability density under a large family of losses called Besov IPMs, which include, for example, $\mathcal{L}^p$ distances, total variation distance, and generalizations of both Wasserstein and Kolmogorov-Smirnov distances. For a wide variety of settings, we provide both lower and upper bounds, identifying precisely how the choice of loss function and assumptions on the data interact to determine the minimax optimal convergence rate. We also show that linear distribution estimates, such as the empirical distribution or kernel density estimator, often fail to converge at the optimal rate. Our bounds generalize, unify, or improve several recent and classical results. Moreover, IPMs can be used to formalize a statistical model of generative adversarial networks (GANs). Thus, we show how our results imply bounds on the statistical error of a GAN, showing, for example, that GANs can strictly outperform the best linear estimator., Comment: Advances in Neural Information Processing Systems. 2019

In the present scenario rate of utilization of electrical energy is continuously increasing, to preserve the non-renewable energy resources, efficient consumption of electrical energy is one of the most important needs of this era. Smart Energy Meter (SEM) plays a vital role in efficient use of electrical energy in consumer premises. Accuracy in the measurement of current is one of the key factors to be considered while measuring energy consumption. This paper introduces Arduino based low cost single-phase SEM and proposes a linear regression based technique for accurate measurement of current. The proposed current measurement approach gives accurate measurement for linear as well as highly non-linear loads. The SEM built in the laboratory has data transfer capability and also embedded with Demand Response (DR) feature. Block Rate Tariff structure used by Tamil Nadu Generation and Distribution Company is considered to incorporate DR that warns the consumers whenever their energy consumption reaches the boundary of a block., Comment: Presented at 2017 IEEE Region 10 Symposium (TENSYMP), Cochin, Kerala, India