Sagar Shah | Searcharxiv

arXiv2025

Leaky Zero Forcing on Induced Subgraphs of $d$-dimensional Grid Graphs with an Application to Hopi Rectangles

We study zero forcing and $\ell$-leaky zero forcing on induced subgraphs of $d$-dimensional grid graphs. Using $\ell$-leaky forts, we prove structural results showing that for $\ell \le 2d-1$, every nonempty $\ell$-leaky fort in an induced subgraph of $P_{n_1}\square\cdots\square P_{n_d}$ intersects the boundary of the graph. These results give general bounds and, in certain settings, exact values for the $\ell$-leaky forcing number of induced subgraphs. Motivated by this framework, we introduce an integer lattice based definition of the Hopi rectangle graphs $HD(a,b)$ as induced subgraphs of $P_{a+b}\square P_{a+b}$. For this particular family of graphs, we show that the zero forcing number equals the maximum nullity, and we completely characterize the $\ell$-leaky forcing number for all $\ell\ge 1$.

math.CO↗

arXiv2025

CyberSOCEval: Benchmarking LLMs Capabilities for Malware Analysis and Threat Intelligence Reasoning

Today's cyber defenders are overwhelmed by a deluge of security alerts, threat intelligence signals, and shifting business context, creating an urgent need for AI systems to enhance operational security work. While Large Language Models (LLMs) have the potential to automate and scale Security Operations Center (SOC) operations, existing evaluations do not fully assess the scenarios most relevant to real-world defenders. This lack of informed evaluation impacts both AI developers and those applying LLMs to SOC automation. Without clear insight into LLM performance in real-world security scenarios, developers lack a north star for development, and users cannot reliably select the most effective models. Meanwhile, malicious actors are using AI to scale cyber attacks, highlighting the need for open source benchmarks to drive adoption and community-driven improvement among defenders and model developers. To address this, we introduce CyberSOCEval, a new suite of open source benchmarks within CyberSecEval 4. CyberSOCEval includes benchmarks tailored to evaluate LLMs in two tasks: Malware Analysis and Threat Intelligence Reasoning--core defensive domains with inadequate coverage in current benchmarks. Our evaluations show that larger, more modern LLMs tend to perform better, confirming the training scaling laws paradigm. We also find that reasoning models leveraging test time scaling do not achieve the same boost as in coding and math, suggesting these models have not been trained to reason about cybersecurity analysis, and pointing to a key opportunity for improvement. Finally, current LLMs are far from saturating our evaluations, showing that CyberSOCEval presents a significant challenge for AI developers to improve cyber defense capabilities.

cs.CR↗

arXiv2010

Step-Frequency Radar with Compressive Sampling (SFR-CS)

Step-frequency radar (SFR) is a high resolution radar approach, where multiple pulses are transmitted at different frequencies, covering a wide spectrum. The obtained resolution directly depends on the total bandwidth used, or equivalently, the number of transmitted pulses. This paper proposes a novel SFR system, namely SFR with compressive sampling (SFRCS), that achieves the same resolution as a conventional SFR, while using significantly reduced bandwidth, or equivalently, transmitting significantly fewer pulses. This bandwidth reduction is accomplished by employing compressive sampling ideas and exploiting the sparseness of targets in the range velocity space.

cs.IT↗