arXiv subjects

Md. Shariful Islam

Publications and source records attributed to Md. Shariful Islam.

10 recordsLinked to original sources

arXiv2026

The Position-wise Prime Digit Distribution Theorem: A Formal Proof of Position-wise Digit Equidistribution in the Prime Numbers

We state and prove the Theorem: for primes $p < 10^n$ with base-$10$ expansion $p = \sum_{k=0}^{n(p)-1} d_k(p) 10^k$, the positional digit probabilities $P_n(d \mid k)$ satisfy \[ \lim_{n \to \infty} P_n(d \mid k) = \begin{cases} 1/10, & k \ge 1,\ d \in \{0,\dots,9\}, \\[4pt] 1/9, & k = \mathrm{lead},\ d \in \{1,\dots,9\}. \end{cases} \] The limiting behavior splits cleanly into two distinct mechanisms: an arithmetic regime for interior digits and an Archimedean regime for the leading digit. For fixed interior positions ($k \ge 1$), digit extraction modulo $10^{k+1}$ reduces the problem to prime counts in reduced residue classes, where uniform distribution follows from Siegel--Walfisz (with Bombieri--Vinogradov allowing $k$ to grow with $n$). For the leading digit, the $1/9$ limit is not a Benford-type scale invariance, but arises from the local near-constancy of the prime density $1/\log t$ within single decades combined with a Toeplitz-type error averaging. Explicit classical and conditional error bounds are recorded for both regimes.

math.NT↗

arXiv2026

Cross-Corpus Evaluation of Generalizable Vulnerability Detection in IoT Firmware

IoT firmware vulnerability detection is constrained by ecosystem heterogeneity, resource-limited platforms, and benchmark quality limitations. Existing datasets are often synthetic or general-purpose and lack human-verified, contamination-screened annotations, leaving cross-corpus generalization across training sources, architectures, and curriculum design underexplored. In this study, we have introduced IoTVulBench, a human-verified benchmark for cross-corpus firmware vulnerability detection. IoTVulBench was built from GitHub repositories, validated by three expert reviewers, and evaluated on a contamination-screened held-out target across five architectures, two tuning methods, and three curriculum strategies, with ensemble, distillation, and robustness analyses. Models trained on IoTVulBench reached the highest Matthews Correlation Coefficient (MCC) among undersampling-matched single-source datasets, at 0.58 versus 0.44 for PrimeVul and 0.39 for D2A. Staged curriculum learning raised MCC to 0.69, and a diversity-optimized ensemble reached 0.73. This gain represents a 0.42 MCC improvement over the strongest reference comparator, a static analyzer with an MCC of 0.31, and a 0.29 MCC improvement over the strongest single-source dataset, PrimeVul. At a 0.5% false-positive rate, the model missed only 21% of vulnerabilities versus 71% for the comparator. The model also retained 86% of its performance under identifier renaming, with strong calibration. These results indicate that domain-matched training data and curriculum design, rather than model scale alone, drive generalization in firmware vulnerability detection, and yield both a benchmark and deployment-ready configurations for IoT security.

cs.CR↗

arXiv2026

A Structured Cyber Threat Intelligence Dataset Using STIX 2.1 Entities and MITRE ATT&CK Mappings

Cyber threat intelligence (CTI) reports are typically written in unstructured formats, which complicates the extraction and analysis of important entities and adversarial behaviors. Although existing CTI research provides extraction tools, knowledge-graph frameworks, and MITRE ATT&CK mapped datasets, curated report-level datasets that preserve complex entity relationships and normalized adversarial behaviors remain limited. To address this limitation, this study presents a manually constructed dataset of 150 English-language CTI reports, each represented as STIX 2.1 based graphs, which includes 4,777 STIX entities, 5,817 STIX relationships in total, and 1,273 STIX attack-pattern entities (adversarial behaviors) mapped to 269 unique MITRE ATT&CK Enterprise techniques and sub-techniques. Twenty five randomly sampled reports were independently assessed by two cybersecurity researchers, which shows substantial inter-rater agreement. Disagreements were subsequently adjudicated to establish a gold-standard reference dataset. Four locally deployed open-source LLMs were evaluated as automated judges against this adjudicated reference sample. Qwen3.6:27B achieved the strongest overall performance, with a maximum kappa score of 0.803, micro-F1 scores exceeding 92%, and false-positive rates below 5%. The dataset provides a benchmark for CTI information extraction, knowledge-graph construction, incident analysis, and threat attribution. The findings further indicate that locally deployed LLMs can support human reviewers in identifying annotation inconsistencies, but expert validation remains essential.

cs.CR↗

arXiv2026

The Prime Digit Distribution Conjecture: A Formal Proof of Average Digit Equidistribution in the Prime Numbers

Let $S_n=\{p\in\mathbb{P}:p<10^n\}$, $N_n$ denote the total number of decimal digits occurring in the primes of $S_n$, $C_n(d)$ be the number of occurrences of a digit $d\in\{0,\ldots,9\}$ among those digits, and $P_n(d)$ be the probability of occurrence of a digit, $d$ among those digits. We prove that \[ P_n(d)=\frac{C_n(d)}{N_n} =\frac{1}{10} +O\!\left(\frac{\log n}{n}\right), \qquad n\to\infty, \] uniformly for every decimal digit $d$. The argument is entirely unconditional and combines the Prime Number Theorem, the Erd\H{o}s--Tur\'an discrepancy inequality, and classical Vaughan--Vinogradov estimates for exponential sums over primes. The principal step establishes quantitative equidistribution for interior digit positions, while the logarithmically many exceptional positions near the ends of the decimal expansion are shown to have asymptotically negligible influence after averaging over all digit positions and prime lengths. Consequently, the decimal digits occurring in primes, when pooled over all positions and all primes below $10^n$, become asymptotically equidistributed. We also clarify the precise scope of the theorem by distinguishing this averaged equidistribution result from the substantially stronger and presently unresolved questions concerning pointwise digit equidistribution, normality, and higher-order digit correlations in the sequence of prime numbers.

math.NT↗

arXiv2025

Experimental Demonstration of Software-Orchestrated Quantum Network Applications over a Campus-Scale Testbed

To fulfill their promise, quantum networks must transform from isolated testbeds into scalable infrastructures for distributed quantum applications. In this paper, we present a prototype orchestrator for the Argonne Quantum Network (ArQNet) testbed that leverages design principles of software-defined networking (SDN) to automate typical quantum communication experiments across buildings in the Argonne campus connected over deployed, telecom fiber. Our implementation validates a scalable architecture supporting service-level abstraction of quantum networking tasks, distributed time synchronization, and entanglement verification across remote nodes. We present a prototype service of continuous, stable entanglement distribution between remote sites that ran for 12 hours, which defines a promising path towards scalable quantum networks.

quant-ph↗

arXiv2025

Tunable Coloration in Core-Shell Plasmonic Nanopixels Based on Organic Conductive Polymers: A First-Principles and FDTD Study

From raindrops to planets, the scattering of electromagnetic fields introduces exciting phenomena that can be utilized for display devices. Here, we designed an electrochromic nanoparticle on mirror (eNPoM) structure with core-shell geometries for low-power nanoscale pixels with rapid coloration abilities based on four electrochromic organic conducting polymers utilizing the first-principles calculations based on density functional theory (DFT) and the finite-difference time-domain (FDTD) simulations. Au nanoparticles are coated with electrochromic conductive polymers (such as PANI, PEDOT, PPy, and PTh) and positioned on the metal mirror. The electric field enhancement and the impact of shell thickness are analyzed. Dielectric properties of all polymers resulting from atomistic calculation were utilized for FDTD simulation, which helps to correlate the direct relationship between polymer structure and optical properties. Notably, the study reveals significant wavelength tunability of 100nm, 40nm, 70nm, and over 40nm using PANI, PEDOT, PPy, and PTh shells, respectively. Additionally, the potential for RGB color production using a TiN layer on the mirror is explored. For the first time, complex structures such as bow tie and gear were utilized to model the nanopixels studied and a significant absorption peak shift was observed. Chromaticity coordinates in the CIE 1931 color space and CIELAB2000 color difference quantify color change capabilities during the redox cycle, and a comparative analysis of organic and inorganic materials highlights the prospects of the proposed plasmonic nanopixels.

physics.optics↗

arXiv2024

A Deep Learning Approach to Detect Complete Safety Equipment For Construction Workers Based On YOLOv7

In the construction sector, ensuring worker safety is of the utmost significance. In this study, a deep learning-based technique is presented for identifying safety gear worn by construction workers, such as helmets, goggles, jackets, gloves, and footwears. The recommended approach uses the YOLO v7 (You Only Look Once) object detection algorithm to precisely locate these safety items. The dataset utilized in this work consists of labeled images split into training, testing and validation sets. Each image has bounding box labels that indicate where the safety equipment is located within the image. The model is trained to identify and categorize the safety equipment based on the labeled dataset through an iterative training approach. We used custom dataset to train this model. Our trained model performed admirably well, with good precision, recall, and F1-score for safety equipment recognition. Also, the model's evaluation produced encouraging results, with a mAP@0.5 score of 87.7\%. The model performs effectively, making it possible to quickly identify safety equipment violations on building sites. A thorough evaluation of the outcomes reveals the model's advantages and points up potential areas for development. By offering an automatic and trustworthy method for safety equipment detection, this research makes a contribution to the fields of computer vision and workplace safety. The proposed deep learning-based approach will increase safety compliance and reduce the risk of accidents in the construction industry

cs.CV↗

arXiv2024

Aluminium nanoparticle-based ultra-wideband high-performance polarizer

The polarizer-based device industry is expanding quickly, requiring high-quality research on nanoscale wideband polarizers. Here, we investigated the possibility of utilizing Al dimer nanostructures on broad-band polarizers. Metals are always considered promising candidates for reflection-based polarizer development because of their high extinction ratio. This study proposes a nanoparticle polarizer comprised of semi-immersed Al nanodimers with a 200 nm radius on a CaF_2 substrate. Our proposed polarizer has effective polarization anisotropy in the near-infrared (NIR) and THz range. This study includes calculating performance parameters for the extraction of the proposed polarizer, including insertion loss, extinction ratio (ER), Mueller matrix values, and polarization ellipse diagram. The finite-difference time-domain (FDTD) simulation-based results suggested obtaining more than 55 dB extinction ratio for the 0.2 to 9 THz range. The average extinction ratio and insertion loss over the 1-1665 micrometer wavelength were 29.01 dB and ~1 dB, respectively. We have reviewed recent reports of similar nanoparticle and wire grid-based polarizers to evaluate our Al nanodimer-based polarizer and performed a comparative analysis. The idea of Al dimer and the insight gained from the results extracted from the rigorous simulation report suggested a great opportunity for developing micro-scale metallic wideband polarizers.

physics.optics↗

arXiv2022

Morse-Novikov cohomology on foliated manifolds

The idea of Lichnerowicz or Morse-Novikov cohomology groups of a manifold has been utilized by many researchers to study important properties and invariants of a manifold. Morse-Novikov cohomology is defined using the differential $d_ω=d+ω\wedge$, where $ω$ is a closed $1$-form. We study Morse-Novikov cohomology relative to a foliation on a manifold and its homotopy invariance and then extend it to more general type of forms on a Riemannian foliation. We study the Laplacian and Hodge decompositions for the corresponding differential operators on reduced leafwise Morse-Novikov complexes. In the case of Riemannian foliations, we prove that the reduced leafwise Morse-Novikov cohomology groups satisfy the Hodge theorem and Poincar{é} duality. The resulting isomorphisms yield a Hodge diamond structure for leafwise Morse-Novikov cohomology.

math.DG↗

arXiv2021

Binomial Coefficients in a Row of Pascal's Triangle from Extension of Power of Eleven: Newton's Unfinished Work

The aim of this paper is to find a general formula to generate any row of Pascal's triangle as an extension of the concept of $\left(11\right)^{n}$. In this study, the visualization of each row of Pascal's triangle has been presented by extending the concept of the power of 11 to the power of 101, 1001, 10001, and so on. We briefly discuss how our proposed concept works for any $n$ by inserting an appropriate number of zeros between $1$ and $1$ (eleven), that is the concept of $\left(11\right)^{n}$ has been extended to $\left(1\Theta1\right)^{n}$, where $Θ$ represents the number of zeros. We have proposed a formula for obtaining the value of $Θ$. The proposed concept has been verified with Pascal's triangle and matched successfully. Finally, Pascal's triangle for a large n has been presented considering the $51^{\text{st}}$ row as an example.

math.HO↗