arXiv subjects

Prateek R. Srivastava

Publications and source records attributed to Prateek R. Srivastava.

6 recordsLinked to original sources

arXiv2026

The Truncated Octahedral Graph Has Bondage Number Five

For a graph G, its bondage number b(G) is the minimum number of edges whose deletion increases its domination number. Dunbar, Haynes, Teschner, and Volkmann conjectured in 1998 that every nontrivial planar graph satisfies b(G) <= Delta(G) + 1. We show that the truncated octahedral graph T has gamma(T) = 8 and b(T) = 5. Since T is planar and cubic, this gives b(T) = 5 > 4 = Delta(T) + 1 and disproves the conjecture. The finite parts of the verification are exhaustive: the direct verifier checks candidate dominating sets of sizes six, seven, and eight and all 58,905 four-edge sets. The targeted discovery search and an independently written verifier are described, and the complete C++20 verifier is included in the source archive.

math.CO↗

arXiv2026

A Ten-Vertex Counterexample to a Conjecture on Unstable Graphs

Mizzi conjectured that every nontrivially unstable graph contains cycles C_k and C_{2k} for some odd k. We give a connected, nonbipartite, vertex-determining counterexample on ten vertices. Its instability is certified by an explicit nontrivial two-fold automorphism, and its complete set of simple-cycle lengths is {5,5,6}.

math.CO↗

arXiv2023

Broadband Diffractive Solar Sail

The transverse radiation pressure force and acceleration is compared for two parametrically optimized designs: prismatic and two-pillar metasurface gratings. The numerical results were cross-verified with both Maxwell stress tensor and modal analysis. Solar blackbody irradiance was assumed for wavelengths ranging from 0.33 [um] to the grating cutoff at 1.5 [um], encompassing 83% of the solar constant. This multi-objective optimizer study found that neither design comprised Si3N4 performed as well as those corresponding to a low refractive index, low mass density material. The predicted transverse acceleration of the optimized low-index metasurface grating is compared to that of a state-of-the-art reflective solar sail.

physics.optics↗

arXiv2023

High Forward Thrust Metasurface Beam-Riding Sail

The radiation pressure force and torque on a one-dimensional bi-grating composed of a Si-SiO_2 high contrast binary metagrating is analyzed for the purpose of stable beam riding whereupon a high power laser having an expanding Gaussian irradiance distribution propels the grating in outer space, free from gravitational forces. The binary metagrating structure has been simultaneously optimized to afford high forward thrust, and corrective restoring forces and torques in the event of small linear and angular disturbances. We demonstrate that stability may be enhanced at the expense of forward thrust. The validity of our metamaterial findings is reinforced owing to good agreements between finite-difference time-domain and finite element numerical methods. To reduce mass and enhance forward acceleration this laser-driven sail was designed to be free of a stabilizing boom.

physics.optics↗

arXiv2021

On Data-Driven Prescriptive Analytics with Side Information: A Regularized Nadaraya-Watson Approach

We consider generic stochastic optimization problems in the presence of side information which enables a more insightful decision. The side information constitutes observable exogenous covariates that alter the conditional probability distribution of the random problem parameters. A decision maker who adapts her decisions according to the observed side information solves an optimization problem where the objective function is specified by the conditional expectation of the random cost. If the joint probability distribution is unknown, then the conditional expectation can be approximated in a data-driven manner using the Nadaraya-Watson (NW) kernel regression. While the emerging approximation scheme has found successful applications in diverse decision problems under uncertainty, it is largely unknown whether the scheme can provide any reasonable out-of-sample performance guarantees. In this paper, we establish guarantees for the generic problems by leveraging techniques from moderate deviations theory. Our analysis motivates the use of a variance-based regularization scheme which, in general, leads to a non-convex optimization problem. We adopt ideas from distributionally robust optimization to obtain tractable formulations. We present numerical experiments for newsvendor and wind energy commitment problems to highlight the effectiveness of our regularization scheme.

math.OC↗

arXiv2021

A Robust Spectral Clustering Algorithm for Sub-Gaussian Mixture Models with Outliers

We consider the problem of clustering datasets in the presence of arbitrary outliers. Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number of outliers. In this paper, we develop a provably robust spectral clustering algorithm that applies a simple rounding scheme to denoise a Gaussian kernel matrix built from the data points and uses vanilla spectral clustering to recover the cluster labels of data points. We analyze the performance of our algorithm under the assumption that the "good" data points are generated from a mixture of sub-gaussians (we term these "inliers"), while the outlier points can come from any arbitrary probability distribution. For this general class of models, we show that the misclassification error decays at an exponential rate in the signal-to-noise ratio, provided the number of outliers is a small fraction of the inlier points. Surprisingly, this derived error bound matches with the best-known bound for semidefinite programs (SDPs) under the same setting without outliers. We conduct extensive experiments on a variety of simulated and real-world datasets to demonstrate that our algorithm is less sensitive to outliers compared to other state-of-the-art algorithms proposed in the literature.

stat.ML↗