arXiv subjects

Suraj Kumar

Publications and source records attributed to Suraj Kumar.

30 records · Page 2Linked to original sources

arXiv2025

Rees algebra and almost linearly presented ideals in three variables

Let $R=\k[x,y,z]$ and $I=(f_0,\dots,f_{n-1})$ be a height two perfect ideal which is almost linearly presented (that is, all but the last column have linear entries, but the last column has entries which are homogeneous of degree $2$). Further we suppose that after modulo an ideal generated by two variables, the presentation matrix has rank one. Also, the ideal $I$ satisfies $\Gs{2}$ but not $\Gs{3}$, then we obtain explicit formulas for the defining ideal of the Rees algebra $\rees(I)$ of $I$.

math.AC↗

arXiv2025

Minimizing Communication for Parallel Symmetric Tensor Times Same Vector Computation

In this article, we focus on the parallel communication cost of multiplying the same vector along two modes of a $3$-dimensional symmetric tensor. This is a key computation in the higher-order power method for determining eigenpairs of a $3$-dimensional symmetric tensor and in gradient-based methods for computing a symmetric CP decomposition. We establish communication lower bounds that determine how much data movement is required to perform the specified computation in parallel. The core idea of the proof relies on extending a key geometric inequality for $3$-dimensional symmetric computations. We demonstrate that the communication lower bounds are tight by presenting an optimal algorithm where the data distribution is a natural extension of the triangle block partition scheme for symmetric matrices to 3-dimensional symmetric tensors.

cs.DC↗

arXiv2025

Enhanced $A^{*}$ Algorithm for Mobile Robot Path Planning with Non-Holonomic Constraints

In this paper, a novel method for path planning of mobile robots is proposed, taking into account the non-holonomic turn radius constraints and finite dimensions of the robot. The approach involves rasterizing the environment to generate a 2D map and utilizes an enhanced version of the $A^{*}$ algorithm that incorporates non-holonomic constraints while ensuring collision avoidance. Two new instantiations of the $A^{*}$ algorithm are introduced and tested across various scenarios and environments, with results demonstrating the effectiveness of the proposed method.

cs.RO↗

arXiv2024

Discrete time model predictive control for humanoid walking with step adjustment

This paper presents a Discrete-Time Model Predictive Controller (MPC) for humanoid walking with online footstep adjustment. The proposed controller utilizes a hierarchical control approach. The high-level controller uses a low-dimensional Linear Inverted Pendulum Model (LIPM) to determine desired foot placement and Center of Mass (CoM) motion, to prevent falls while maintaining the desired velocity. A Task Space Controller (TSC) then tracks the desired motion obtained from the high-level controller, exploiting the whole-body dynamics of the humanoid. Our approach differs from existing MPC methods for walking pattern generation by not relying on a predefined foot-plan or a reference center of pressure (CoP) trajectory. The overall approach is tested in simulation on a torque-controlled Humanoid Robot. Results show that proposed control approach generates stable walking and prevents fall against push disturbances.

cs.RO↗

arXiv2024

Communication Lower Bounds and Optimal Algorithms for Symmetric Matrix Computations

In this article, we focus on the communication costs of three symmetric matrix computations: i) multiplying a matrix with its transpose, known as a symmetric rank-k update (SYRK) ii) adding the result of the multiplication of a matrix with the transpose of another matrix and the transpose of that result, known as a symmetric rank-2k update (SYR2K) iii) performing matrix multiplication with a symmetric input matrix (SYMM). All three computations appear in the Level 3 Basic Linear Algebra Subroutines (BLAS) and have wide use in applications involving symmetric matrices. We establish communication lower bounds for these kernels using sequential and distributed-memory parallel computational models, and we show that our bounds are tight by presenting communication-optimal algorithms for each setting. Our lower bound proofs rely on applying a geometric inequality for symmetric computations and analytically solving constrained nonlinear optimization problems. The symmetric matrix and its corresponding computations are accessed and performed according to a triangular block partitioning scheme in the optimal algorithms.

cs.DC↗

arXiv2024

Strongly correlated multi-electron bunches from interaction with quantum light

Strongly correlated electron systems are a cornerstone of modern physics, being responsible for groundbreaking phenomena from superconducting magnets to quantum computing. In most cases, correlations in electrons arise exclusively due to Coulomb interactions. In this work, we reveal that free electrons interacting simultaneously with a light field can become highly correlated via mechanisms beyond Coulomb interactions. In the case of two electrons, the resulting Pearson correlation coefficient (PCC) for the joint probability distribution of the output electron energies is enhanced over 13 orders of magnitude compared to that of electrons interacting with the light field in succession (one after another). These highly correlated electrons are the result of momentum and energy exchange between the participating electrons via the external quantum light field. Our findings pave the way to the creation and control of highly correlated free electrons for applications including quantum information and ultra-fast imaging.

quant-ph↗

arXiv2023

TPMCF: Temporal QoS Prediction using Multi-Source Collaborative Features

Recently, with the rapid deployment of service APIs, personalized service recommendations have played a paramount role in the growth of the e-commerce industry. Quality-of-Service (QoS) parameters determining the service performance, often used for recommendation, fluctuate over time. Thus, the QoS prediction is essential to identify a suitable service among functionally equivalent services over time. The contemporary temporal QoS prediction methods hardly achieved the desired accuracy due to various limitations, such as the inability to handle data sparsity and outliers and capture higher-order temporal relationships among user-service interactions. Even though some recent recurrent neural-network-based architectures can model temporal relationships among QoS data, prediction accuracy degrades due to the absence of other features (e.g., collaborative features) to comprehend the relationship among the user-service interactions. This paper addresses the above challenges and proposes a scalable strategy for Temporal QoS Prediction using Multi-source Collaborative-Features (TPMCF), achieving high prediction accuracy and faster responsiveness. TPMCF combines the collaborative-features of users/services by exploiting user-service relationship with the spatio-temporal auto-extracted features by employing graph convolution and transformer encoder with multi-head self-attention. We validated our proposed method on WS-DREAM-2 datasets. Extensive experiments showed TPMCF outperformed major state-of-the-art approaches regarding prediction accuracy while ensuring high scalability and reasonably faster responsiveness.

cs.SE↗

arXiv2023

ARRQP: Anomaly Resilient Real-time QoS Prediction Framework with Graph Convolution

In the realm of modern service-oriented architecture, ensuring Quality of Service (QoS) is of paramount importance. The ability to predict QoS values in advance empowers users to make informed decisions. However, achieving accurate QoS predictions in the presence of various issues and anomalies, including outliers, data sparsity, grey-sheep instances, and cold-start scenarios, remains a challenge. Current state-of-the-art methods often fall short when addressing these issues simultaneously, resulting in performance degradation. In this paper, we introduce a real-time QoS prediction framework (called ARRQP) with a specific emphasis on improving resilience to anomalies in the data. ARRQP utilizes the power of graph convolution techniques to capture intricate relationships and dependencies among users and services, even when the data is limited or sparse. ARRQP integrates both contextual information and collaborative insights, enabling a comprehensive understanding of user-service interactions. By utilizing robust loss functions, ARRQP effectively reduces the impact of outliers during the model training. Additionally, we introduce a sparsity-resilient grey-sheep detection method, which is subsequently treated separately for QoS prediction. Furthermore, we address the cold-start problem by emphasizing contextual features over collaborative features. Experimental results on the benchmark WS-DREAM dataset demonstrate the framework's effectiveness in achieving accurate and timely QoS predictions.

cs.LG↗

arXiv2023

Communication Lower Bounds and Optimal Algorithms for Multiple Tensor-Times-Matrix Computation

Multiple Tensor-Times-Matrix (Multi-TTM) is a key computation in algorithms for computing and operating with the Tucker tensor decomposition, which is frequently used in multidimensional data analysis. We establish communication lower bounds that determine how much data movement is required to perform the Multi-TTM computation in parallel. The crux of the proof relies on analytically solving a constrained, nonlinear optimization problem. We also present a parallel algorithm to perform this computation that organizes the processors into a logical grid with twice as many modes as the input tensor. We show that with correct choices of grid dimensions, the communication cost of the algorithm attains the lower bounds and is therefore communication optimal. Finally, we show that our algorithm can significantly reduce communication compared to the straightforward approach of expressing the computation as a sequence of tensor-times-matrix operations.

cs.DC↗

arXiv2022

Roadmap on spatiotemporal light fields

Spatiotemporal sculpturing of light pulse with ultimately sophisticated structures represents the holy grail of the human everlasting pursue of ultrafast information transmission and processing as well as ultra-intense energy concentration and extraction. It also holds the key to unlock new extraordinary fundamental physical effects. Traditionally, spatiotemporal light pulses are always treated as spatiotemporally separable wave packet as solution of the Maxwell's equations. In the past decade, however, more generalized forms of spatiotemporally nonseparable solution started to emerge with growing importance for their striking physical effects. This roadmap intends to highlight the recent advances in the creation and control of increasingly complex spatiotemporally sculptured pulses, from spatiotemporally separable to complex nonseparable states, with diverse geometric and topological structures, presenting a bird's eye viewpoint on the zoology of spatiotemporal light fields and the outlook of future trends and open challenges.

physics.optics↗

arXiv2022

Tight Memory-Independent Parallel Matrix Multiplication Communication Lower Bounds

Communication lower bounds have long been established for matrix multiplication algorithms. However, most methods of asymptotic analysis have either ignored the constant factors or not obtained the tightest possible values. Recent work has demonstrated that more careful analysis improves the best known constants for some classical matrix multiplication lower bounds and helps to identify more efficient algorithms that match the leading-order terms in the lower bounds exactly and improve practical performance. The main result of this work is the establishment of memory-independent communication lower bounds with tight constants for parallel matrix multiplication. Our constants improve on previous work in each of three cases that depend on the relative sizes of the aspect ratios of the matrices.

cs.DC↗

arXiv2019

Performance Models for Data Transfers: A Case Study with Molecular Chemistry Kernels

With increasing complexity of hardwares, systems with different memory nodes are ubiquitous in High Performance Computing (HPC). It is paramount to develop strategies to overlap the data transfers between memory nodes with computations in order to exploit the full potential of these systems. In this article, we consider the problem of deciding the order of data transfers between two memory nodes for a set of independent tasks with the objective to minimize the makespan. We prove that with limited memory capacity, obtaining the optimal order of data transfers is a NP-complete problem. We propose several heuristics for this problem and provide details about their favorable situations. We present an analysis of our heuristics on traces, obtained by running 2 molecular chemistry kernels, namely, Hartree-Fock (HF) and Coupled Cluster Single Double (CCSD) on 10 nodes of an HPC system. Our results show that some of our heuristics achieve significant overlap for moderate memory capacities and are very close to the lower bound of makespan.

cs.PF↗