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Hemant Kumar Singh

Publications and source records attributed to Hemant Kumar Singh.

At least 19 recordsLinked to original sources

Real-time Unsupervised Object Discovery from Asynchronous Event Streams

Event cameras capture pixel-level intensity changes with microsecond resolution to produce highly sparse asynchronous data streams. For visual perception in latency-critical environments, we propose a lightweight, training-free framework for discovery of moving objects based on spatio-temporal clustering. This framework is driven by two core contributions. First, a linear-time Spatio-temporal Probabilistic Event Filter (SPEF) that introduces an adaptive event acceptance threshold to distinguish salient motion structures from background noise. Second, an Event Morton Code Clustering (EMCC) module that bypasses expensive distance matrix computation to efficiently group events for unsupervised discovery of moving objects. On the E-MLB dataset benchmark, SPEF achieves the best denoising performance among classical filtering methods and remains competitive with learning-based approaches without requiring any offline training. On object discovery, EMCC achieves the highest overall accuracy and lowest execution time across the FRED and eTraM datasets, outperforming established density-based clustering baselines by a substantial margin. Overall, this work establishes a new performance benchmark for classical object discovery in event data, providing a highly scalable, training-free solution for resource-constrained visual perception. The code is available at https://github.com/PrathamShenwai/SPEF_EMCC

cs.CV

Confidence-based Ranking with Adaptive Sampling for Noisy Black-Box Optimisation

Real-world optimization problems often involve black-box functions and uncertainties in their evaluation, widely referred to as noisy optimization problems (NOPs). Evolutionary algorithms (EA), including Evolutionary Strategies (ES) and genetic algorithms (GA) have been commonly adopted to solve these problems in the contemporary literature. An ongoing challenge is the computational expense involved, given the number of evaluations required for good fitness estimation and ranking. Two fundamental methods commonly used for fitness estimation for NOPs are implicit averaging and explicit averaging. Explicit averaging uses resampling of solutions to improve the estimates, while implicit averaging typically uses a large population size with low resampling. Implicit averaging has been shown to have theoretical advantages for certain cases, which has motivated some recent approaches to use them. However, a recent study demonstrated that its performance is highly dependent on certain assumptions about the function, such as steepness and constant noise level, which may not apply for majority of the real world problems. Moreover, most existing algorithms have only considered homoscedastic noise, where the amplitude of variation is uniform across the entire search space, as opposed to more generic case of heteroscedastic noise. To address these issues, we introduce a set of heteroscedastic test problems and propose a novel confidence ranking method that employs a computationally efficient explicit averaging strategy with sampling budget adaptation. It is implemented within the Covariance Matrix Adaptation ES (CMA-ES) and GA frameworks to demonstrate its effectiveness and versatility. The resulting algorithm is evaluated on a range of problems with both homoscedastic and heteroscedastic noise, and it demonstrates superior performance compared to state-of-the-art approaches.

cs.NE

Furtherness in finite topological spaces

In this paper, we introduce a novel distance-like notion of furtherness for finite topological spaces, demonstrating that every finite space can be viewed as an asymmetric pseudometric space. In particular, we show that every finite T0 space is asymmetric metric space. The topology induced by the forward balls coincides with the original topology of the space, while the backward balls induce the opposite topology. To capture essential information about each finite space, we construct a furtherness Matrix, which gives significant structural details of the finite space. As an application, we introduce the notion of center and radius of subsets of finite topological spaces.

math.GN

ISS-Geo142: A Benchmark for Geolocating Astronaut Photography from the International Space Station

This paper introduces ISS-Geo142, a curated benchmark for geolocating astronaut photography captured from the International Space Station (ISS). Although the ISS position at capture time is known precisely, the specific Earth locations depicted in these images are typically not directly georeferenced, making automated localization non-trivial. ISS-Geo142 consists of 142 images with associated metadata and manually determined geographic locations, spanning a range of spatial scales and scene types. On top of this benchmark, we implement and evaluate three geolocation pipelines: a neural network based approach (NN-Geo) using VGG16 features and cross-correlation over map-derived Areas of Interest (AOIs), a Scale-Invariant Feature Transform based pipeline (SIFT-Match) using sliding-window feature matching on stitched high-resolution AOIs, and TerraByte, an AI system built around a GPT-4 model with vision capabilities that jointly reasons over image content and ISS coordinates. On ISS-Geo142, NN-Geo achieves a match for 75.52\% of the images under our evaluation protocol, SIFT-Match attains high precision on structurally rich scenes at substantial computational cost, and TerraByte establishes the strongest overall baseline, correctly geolocating approximately 90\% of the images while also producing human-readable geographic descriptions. The methods and experiments were originally developed in 2023; this manuscript is a revised and extended version that situates the work relative to subsequent advances in cross-view geo-localization and remote-sensing vision--language models. Taken together, ISS-Geo142 and these three pipelines provide a concrete, historically grounded benchmark for future work on ISS image geolocation.

cs.CV

Free Circle Actions on the Product of Three Spheres

The orbit spaces of free S^0-actions on the mod 2 cohomology product of three spheres, S^n x S^m x S^l, 1 <= n <= m <= l have been determined in [6]. In this paper, we extend these findings to free S^1-actions on the rational cohomology product of three spheres. This extension also builds upon the work of Dotzel et al. [7], who studied free circle actions on the rational cohomology product of two spheres. Additionally, we establish Borsuk-Ulam type theorems.

math.AT

Center and radius of a subset of metric space

In this paper, we introduce a notion of the center and radius of a subset A of metric space X. In the Euclidean spaces, this notion can be seen as the extension of the center and radius of open/closed balls. The center and radius of a finite product of subsets of metric spaces, and a finite union of subsets of a metric space are also determined. For any subset A of metric space X, there is a natural question to identify the open balls of X with the largest radius that are entirely contained in A. To answer this question, we introduce a notion of quasi-center and quasi-radius of a subset A of metric space X. We prove that the center of the largest open balls contained in A belongs to the quasi-center of A, and its radius is equal to the quasi-radius of A. In particular, for the Euclidean spaces, we see that the center of largest open balls contained in A belongs to the center of A, and its radius is equal to the radius of A.

math.GN

Decomposition of Difficulties in Complex Optimization Problems Using a Bilevel Approach

Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at tackling one or more difficulty in an optimization problem. For instance, evolutionary algorithms have a niche in handling complexities like discontinuity, non-differentiability, discreteness and non-convexity. However, evolutionary algorithms may get computationally expensive for mathematically well behaved problems with large number of variables for which classical mathematical programming approaches are better suited. In this paper, we demonstrate a decomposition strategy that allows us to synergistically apply two complementary approaches at the same time on a complex optimization problem. Evolutionary algorithms are useful in this context as their flexibility makes pairing with other solution approaches easy. The decomposition idea is a special case of bilevel optimization that separates the difficulties into two levels and assigns different approaches at each level that is better equipped at handling them. We demonstrate the benefits of the proposed decomposition idea on a wide range of test problems.

cs.NE

Finitistic Spaces with Orbit Space a Product of Projective Spaces

Let G = Z2 act freely on a nitistic space X. If the mod 2 cohomology of X is isomorphic to the real projective space RP^{2n+1} (resp. complex projective space CP^{2n+1}) then the mod 2 cohomology of orbit spaces of these free actions are RP1 x CPn (resp. RP2 x HPn) [7]. In this paper, we have discussed converse of these results. We have showed that if the mod 2 cohomology of the orbit space X/G is RP1 x CPn (resp. RP2 x HPn) then the mod 2 cohomology of X is RP^{2n+1} or S1 x CPn (resp. CP^{2n+1} or S2 x HPn). A partial converse of free involutions on the product of projective spaces RPn x RP2m+1 (resp. CPn x CP2m+1) are also discussed.

math.AT

Fixed Point Sets of Involutions on the Product of Three Spheres

Let G = Z2 act on a finitistic space X having mod 2 cohomology of the product of three spheres S^n x S^m x S^l. In this paper, we have determined the fixed point sets of involutions on X. This generalizes J. C. Su [12] results for involutions on the product of two sphere S^n x S^m.

math.AT

Finitistic Spaces with the Orbit Space FP^n x S^m

Let G = S^d, d = 0, 1 or 3, act freely on a finitistic connected space X. This paper gives the cohomology classification of X if a mod 2 or rational cohomology of the orbit space X/G is isomorphic to the product of a projective space and sphere FP^n x S^m, where F = R, C or H, respectively. For a free involution on X, a lower bound of covering dimension of the coincidence set of a continuous map f: X -> R^k is also determined.

math.AT

Orbit spaces of free involutions on the product of three spheres

In this paper, we have determined the orbit spaces of free involutions on a finitistic space having mod 2 cohomology of the product of three spheres $\mathbb{S}^n\times \mathbb{S}^m \times \mathbb{S}^l, 1 \leq n \leq m \leq l$. This paper generalizes the results proved by Dotzel et al. [6] for free involutions on the product of two sphere $\mathbb{S}^n \times \mathbb{S}^m,1\leq n\leq m.$

math.AT

Involution on the product of projective space and sphere

Let $G=\mathbb{Z}_2$ act on a finite CW-complex $X$ having mod 2 cohomology isomorphic to the product of projective space and sphere $\mathbb{F}P^n\times \mathbb{S}^m,$ where $\mathbb{F}=\mathbb{R}$ or $\mathbb{C}.$ In this paper, we have determined the connected fixed point sets and the orbit spaces of free involutions on $X.$ As an application, we derive the Borsuk-Ulam type results.

math.AT

Fixed point sets and orbit spaces of wedge of three spheres

Let $X$ be a finite CW-complex having mod $p$ cohomology isomorphic to a wedge of three spheres $\mathbb{S}^n\vee \mathbb{S}^m \vee \mathbb{S}^l,~ 1\leq n \leq m \leq l$. The aim of this paper is to determine the fixed point sets of actions of the cyclic group of prime order on $X.$ We also classify the orbit spaces of free actions of $G=\mathbb{Z}_p, p$ a prime or $G=\mathbb{S}^d,~d=1,3,$ on $X$ and derive the Borsuk-Ulam type results.

math.AT

A Simple Evolutionary Algorithm for Multi-modal Multi-objective Optimization

In solving multi-modal, multi-objective optimization problems (MMOPs), the objective is not only to find a good representation of the Pareto-optimal front (PF) in the objective space but also to find all equivalent Pareto-optimal subsets (PSS) in the variable space. Such problems are practically relevant when a decision maker (DM) is interested in identifying alternative designs with similar performance. There has been significant research interest in recent years to develop efficient algorithms to deal with MMOPs. However, the existing algorithms still require prohibitive number of function evaluations (often in several thousands) to deal with problems involving as low as two objectives and two variables. The algorithms are typically embedded with sophisticated, customized mechanisms that require additional parameters to manage the diversity and convergence in the variable and the objective spaces. In this letter, we introduce a steady-state evolutionary algorithm for solving MMOPs, with a simple design and no additional userdefined parameters that need tuning compared to a standard EA. We report its performance on 21 MMOPs from various test suites that are widely used for benchmarking using a low computational budget of 1000 function evaluations. The performance of the proposed algorithm is compared with six state-of-the-art algorithms (MO Ring PSO SCD, DN-NSGAII, TriMOEA-TA&R, CPDEA, MMOEA/DC and MMEA-WI). The proposed algorithm exhibits significantly better performance than the above algorithms based on the established metrics including IGDX, PSP and IGD. We hope this study would encourage design of simple, efficient and generalized algorithms to improve its uptake for practical applications.

cs.NE

Fixed point Free Actions of Spheres and Equivariant maps

This paper generalizes the concept of index and co-index and some related results for free actions of G = S0 on a paracompact Hausdorff space which were introduced by Conner and Floyd. We define the index and co-index of a finitistic free G-space X, where G = Sd , d = 1 or 3 and prove that the index of X is not more than the mod 2 cohomology index of X. We observe that the index and co-index of a (2n + 1)-sphere (resp. (4n+3)-sphere) for the action of componentwise multiplication of G = S1 (resp. S3) is n. We also determine the orbit spaces of free actions of G = S3 on a finitistic space X with the mod 2 cohomology and the rational cohomology product of spheres. The orbit spaces of circle actions on the mod 2 cohomology X is also discussed. Using these calculation, we obtain an upper bound of the index of X and the Borsuk-Ulam type results.

math.AT

Cohomology Classification of Spaces with Free S3 Actions

This paper gives the cohomology classification of finitistic spaces X equipped with free actions of the group G = S3 and the orbit space X/G is the integral or mod 2 cohomology quaternion projective space HPn. We have proved that X is the integral or mod 2 cohomology (4n+3)-sphere or the product of 3-sphere and quaternion projective space HPn. Similar results for G = S1 actions are also discussed.

math.AT

Free Action of Finite Groups on Spaces of Cohomology Type (0, b)

Let G be a finite group acting freely on a finitistic space X having cohomology type (0, b) (for example, S^n x S^{2n} is a space of type (0, 1) and the one-point union S^n V S^{2n} V S^{3n} is a space of type (0, 0)). It is known that a finite group G which contains Zp + Zp + Zp, p a prime, can not act freely on S^n x S^{2n}. In this paper, we show that if a finite group G acts freely on a space of type (0, 1), where n is odd, then G can not contain Zp + Zp, p an odd prime. For spaces of cohomology type (0, 0), we show that every p-subgroup of G is either cyclic or a generalized quaternion group. Moreover, for n even, it is shown that Z2 is the only group which can act freely on X.

math.AT