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Eldar Sultanow

Publications and source records attributed to Eldar Sultanow.

15 recordsLinked to original sources
arXiv2025

Hearing the Sides: Recovering a Planar Rectangle from Eigenvalues

We present a direct, index-free method to recover the side lengths of a planar rectangle the spectrum of its Dirichelet Laplacian, assuming only access to a finite subset of eigenvalues. No modal indices $(m,n)$ are available, and the list may begin at an arbitrary unknown offset; in particular, the lowest eigenvalues may be missing, so classical formulas based on $\lambda_{1,0}$ and $\lambda_{0,1}$ cannot be used. Our reconstruction procedure extracts geometric information solely from the asymptotic density and oscillatory structure of the ordered spectrum. The area $ab$ is obtained from the high-frequency Weyl slope, while the fundamental lengths $2a$ and $2b$ appear as dominant periodic--orbit contributions in the Fourier transform of the spectral fluctuations. This separation of smooth and oscillatory components yields a robust, offset-agnostic recovery of both side lengths. The result is a fully index-free algorithm that reconstructs the geometry of a rectangular planar domain even when the spectrum is incomplete and all modal information is lost.

math.SP↗
arXiv2025

LLM vs. SAST: A Technical Analysis on Detecting Coding Bugs of GPT4-Advanced Data Analysis

Large language models (LLMs) are increasingly used for code understanding, yet their practical effectiveness for vulnerability detection relative to Static Application Security Testing (SAST) remains insufficiently quantified. We present a controlled comparative study between GPT-4 (Advanced Data Analysis) and two SAST tools (SonarQube and Cloud Defence) on 32 curated security scenarios representing common coding pitfalls. Each scenario is scored with a binary detection rule, the two SAST outputs are aggregated using a logical OR baseline, and paired outcomes are evaluated using McNemar's test for statistical significance. In our dataset, GPT-4 correctly detected 30 of 32 scenarios (93.75\%), while the aggregated SAST baseline detected 11 of 32. The paired comparison shows a statistically significant difference in detection performance in favour of GPT-4. We also discuss security considerations and operational constraints for integrating LLM-enhanced vulnerability scanning into secure software development workflows.

cs.CR↗
arXiv2025

Quantum Agents

This paper explores the intersection of quantum computing and agentic AI by examining how quantum technologies can enhance the capabilities of autonomous agents, and, conversely, how agentic AI can support the advancement of quantum systems. We analyze both directions of this synergy and present conceptual and technical foundations for future quantum-agentic platforms. Our work introduces a formal definition of quantum agents and outlines potential architectures that integrate quantum computing with agent-based systems. As a proof-of-concept, we develop and evaluate three quantum agent prototypes that demonstrate the feasibility of our proposed framework. Furthermore, we discuss use cases from both perspectives, including quantum-enhanced decision-making, quantum planning and optimization, and AI-driven orchestration of quantum workflows. By bridging these fields, we aim to chart a path toward scalable, intelligent, and adaptive quantum-agentic ecosystems.

quant-ph↗
arXiv2024

Quantum Error Propagation

Data poisoning attacks on machine learning models aim to manipulate the data used for model training such that the trained model behaves in the attacker's favour. In classical models such as deep neural networks, large chains of dot products do indeed cause errors injected by an attacker to propagate or accumulate. But what about quantum models? We hypothesise that, in quantum machine learning, error propagation is limited for two reasons. The first is that data, which is encoded in quantum computing, is in terms of qubits that are confined to the Bloch sphere. Second, quantum information processing happens via the application of unitary operators, which preserve norms. Testing this hypothesis, we investigate how extensive error propagation and, thus, poisoning attacks affect quantum machine learning.

quant-ph↗
arXiv2023

Enabling Quantum Cybersecurity Analytics in Botnet Detection: Stable Architecture and Speed-up through Tree Algorithms

For the first time, we enable the execution of hybrid machine learning methods on real quantum computers with 100 data samples and real-device-based simulations with 5,000 data samples, thereby outperforming the current state of research of Suryotrisongko and Musashi from 2022 who were dealing with 1,000 data samples and quantum simulators (pure software-based emulators) only. Additionally, we beat their reported accuracy of $76.8\%$ by an average accuracy of $91.2\%$, all within a total execution time of 1,687 seconds. We achieve this significant progress through two-step strategy: Firstly, we establish a stable quantum architecture that enables us to execute HQML algorithms on real quantum devices. Secondly, we introduce new hybrid quantum binary classification algorithms based on Hoeffding decision tree algorithms. These algorithms speed up the process via batch-wise execution, reducing the number of shots required on real quantum devices compared to conventional loop-based optimizers. Their incremental nature serves the purpose of online large-scale data streaming for DGA botnet detection, and allows us to apply hybrid quantum machine learning to the field of cybersecurity analytics. We conduct our experiments using the Qiskit library with the Aer quantum simulator, and on three different real quantum devices from Azure Quantum: IonQ, Rigetti, and Quantinuum. This is the first time these tools are combined in this manner.

quant-ph↗
arXiv2022

Machine Learning Class Numbers of Real Quadratic Fields

We implement and interpret various supervised learning experiments involving real quadratic fields with class numbers 1, 2 and 3. We quantify the relative difficulties in separating class numbers of matching/different parity from a data-scientific perspective, apply the methodology of feature analysis and principal component analysis, and use symbolic classification to develop machine-learned formulas for class numbers 1, 2 and 3 that apply to our dataset.

math.NT↗
arXiv2022

Predict better with less training data using a QNN

Over the past decade, machine learning revolutionized vision-based quality assessment for which convolutional neural networks (CNNs) have now become the standard. In this paper, we consider a potential next step in this development and describe a quanvolutional neural network (QNN) algorithm that efficiently maps classical image data to quantum states and allows for reliable image analysis. We practically demonstrate how to leverage quantum devices in computer vision and how to introduce quantum convolutions into classical CNNs. Dealing with a real world use case in industrial quality control, we implement our hybrid QNN model within the PennyLane framework and empirically observe it to achieve better predictions using much fewer training data than classical CNNs. In other words, we empirically observe a genuine quantum advantage for an industrial application where the advantage is due to superior data encoding.

quant-ph↗
arXiv2022

Which programming languages do hackers use? A survey at the German Chaos Computer Club

There are numerous articles about the programming languages most commonly used by hackers. Among them, however, there are hardly any scientific studies. One reason might be that hackers mainly operate anonymously and are difficult to reach. This paper aims to shed light on this interesting and relevant research question. In order to find answers, we conducted a survey among the members of the German Chaos Computer Club. As one of the world's largest organisations for information security and hacking, the club provides a good basis for our study. We examine the question of which programming languages are used by hackers as well as the importance of the programming language for their work. The paper offers first insights into the topic and can provide a starting point for further research.

cs.CR↗
arXiv2021

Rotating Binaries

This paper investigates the behaviour of rotating binaries. A rotation by $r$ digits to the left of a binary number $B$ exhibits in particular cases the divisibility $l\mid N_1(B)\cdot r+1$, where $l$ is the bit-length of $B$ and $N_1(B)$ is the Hamming weight of $B$, that is the number of ones in $B$. The integer $r$ is called the left-rotational distance. We investigate the connection between this rotational distance, the length and the Hamming weight of binary numbers. Moreover we follow the question under which circumstances the above mentioned divisibility is true. We have found out and will demonstrate that this divisibility occurs for $kn+c$ cycles.

math.NT↗
arXiv2021

The Farey Sequence and the Mertens Function

Franel and Landau derived an arithmetic statement involving the Farey sequence that is equivalent to the Riemann hypothesis. Since there is a relationship between the Mertens function and the Riemann hypothesis, there should be a relationship between the Mertens function and the Farey sequence. Functions of subsets of the fractions in Farey sequences that are analogous to the Mertens function are introduced. Mikolas proved that the sum of certain Mertens function values is 1. Results analogous to Mikolas theorem are the defining property of these functions. A relationship between the Farey sequence and the Riemann hypothesis other than the Franel-Landau theorem is postulated. This conjecture involves a theorem of Mertens and the second Chebyshev function.

math.NT↗
arXiv2021

Collatz Cycles and $3n+c$ Cycles

Halbeisen and Hungerbuhler determined optimal bounds for the length of rational Collatz cycles. Their methods are extended to $3n+c$ cycles. Another sequence having properties similar to those of Riemann zeta function zeros is introduced.

math.GM↗
arXiv2021

Bounds of the Mertens Function

In this paper, we derive new properties of the Mertens function and discuss a likely upper bound of the absolute value of the Mertens function $\sqrt{\log{x!}}>|M(x)|$ when $x>1$. Using this likely bound we show that we have a sufficient condition to prove the Riemann Hypothesis.

math.GM↗
arXiv2021

Sequences and Polynomial Congruence

In this paper, we shall find a new connection between $n$th degree polynomial mod $p$ congruence with $n$ roots and higher-order Fibonacci and Lucas sequences. We shall first discuss the recent work been done in sequences and their connection to polynomial congruence and then find out new relations between particular recurrence relation and the congruence of the sequences.

math.GM↗
arXiv2021

Collatz convergence is a Hydra game

The Collatz dynamic is known to generate a complex quiver of sequences over natural numbers which inflation propensity remains so unpredictable it could be used to generate reliable proof of work algorithms for the cryptocurrency industry. Here we establish an ad hoc equivalent of modular arithmetic for Collatz sequences to automatically demonstrate the convergence of infinite quivers of numbers, based on five arithmetic rules we prove apply on the entire Collatz dynamic and which we further simulate to gain insight on their graph geometry and computational properties. We then formally demonstrate these rules define an automaton that is playing a Hydra game on the graph of undecided numbers we also prove is embedded in 24N-7, proving that in ZFC the Collatz conjecture is true, before giving a promising direction to also prove it in Peano arithmetic.

math.GM↗