arXiv subjects

Vesselin Dimitrov

Publications and source records attributed to Vesselin Dimitrov.

17 recordsLinked to original sources

arXiv2026

A dual-polarization whitened-template trigger for real-time radio detection of extensive air showers

Autonomous radio stations require a first-stage trigger that rejects measured background while preserving weak extensive-air-shower pulses under tight hardware constraints. We present a dual-polarization trigger based on a 16-sample whitened pulse template evaluated continuously on the orthogonal north-south and east-west channels of an Auger Engineering Radio Array station. The template is derived from detector-folded air-shower pulses and whitened using the covariance of measured background. Responses from both polarizations are combined within a fixed timing radius and compared with a calibrated threshold. On an independent test set, the trigger reaches an efficiency of 0.97, with a 95 percent confidence interval of 0.96 to 0.98, at a frame-equivalent candidate rate of 3.39 kHz. At the same operating point, an unwhitened dual-polarization template reaches 0.41 efficiency and an amplitude trigger reaches 0.16. Efficiency remains at least 0.94 in every populated signal-to-noise bin. Replay of 159.29 ms of continuous measured background yields a score-cluster rate of 6.64 kHz, below the 71.4 kHz capacity of the downstream module. The FPGA implementation accepts one dual-polarization sample per clock, closes timing at 200 MHz, and uses 2377 lookup tables, 5330 registers, and 32 digital signal-processing blocks. Register-transfer-level simulation agrees bit for bit with the reference implementation for 400 traces. These results show that background covariance, pulse morphology, and dual-polarization consistency can be combined in a compact real-time radio trigger.

astro-ph.IM↗

arXiv2026

Hybrid neural denoising for resource-efficient near- and sub-threshold radio triggering of extensive air showers

Autonomous radio self-triggering for extensive air showers must reject variable radio-frequency interference while preserving sensitivity to weak pulses and remaining compatible with station-level edge hardware. This work presents a hybrid neural trigger in which waveform recovery and signal classification are treated as a single deployment-constrained problem. A compact convolutional denoiser maps a noisy single-channel trace to a cleaned estimate of the air-shower pulse, which is then evaluated by a compact classifier. The method is tested with measured high-interference background traces and detector-folded air-shower pulses from the Pierre Auger Offline simulation chain, with signals concentrated in the near- and sub-threshold regime. Model selection and deployment are linked through hyperparameter optimisation, quantisation-aware training, fixed-point quantisation, hls4ml firmware export, high-level synthesis, and register-transfer-level validation. The denoiser alone turns a simple peak-envelope decision into an efficient weak-pulse trigger, showing that the cleaned waveform carries trigger-relevant information beyond a final classifier score. In the full denoiser-classifier chain, the hybrid trigger improves signal-background separation and efficiency at fixed false-positive rates: at a false-positive rate of 10^-4, it retains about 41% of held-out signal traces in the weak-signal benchmark, while the classical peak-envelope trigger retains none. The cleaned waveform preserves timing and peak-amplitude structure for station-level diagnostics, feature extraction, and selective readout. The firmware meets timing on representative FPGA targets with microsecond-scale latency and compact arithmetic-resource demand. These results establish hybrid neural denoising as a practical route toward radio-only triggering for weak and inclined air-shower signals in noisy environments.

astro-ph.IM↗

arXiv2025

Quantization Effects of Artificial Neural Networks for Embedded Edge-Computing Applications

This paper examines the use of Quantized Neural Networks (QNNs) for two resource-constrained scientific applications: automated calibration of semi- conductor quantum bits (qubits) and scientific particle detectors. We evaluate the trade-offs between Post-Training Quantization (PTQ), Quantization-Aware Train- ing (QAT), and ultra-low-bit Binary Neural Networks (BNNs) with respect to la- tency and resource usage. Our results demonstrate that PTQ and QAT are easily implementable solutions achieving a four-fold reduction in memory usage for U- shaped CNN (U-Net) architectures, whereas BNNs are better suitable for use cases with challenging latency requirements. For the training of non-differentiable custom BNNs , we propose a novel, hardware-constrained learning approach using Genetic Algorithms (GAs). We showcase a Look-Up Table (LUT)-based BNN architecture suitable for direct conversion to Very High-Speed Integrated Circuit Hardware De- scription Language (VHDL) via the HCL4BNN framework. This method achieves nanosecond-scale inference latencies at 10 ns to 15 ns without requiring specialized Digital Signal Processor (DSP) or Block RAM (BRAM) resources.

cs.NE↗

arXiv2025

Arithmetic holonomy bounds and effective Diophantine approximation

In this paper, we explore several threads arising from our recent joint work on arithmetic holonomy bounds, which were originally devised to prove new irrationality results based on the method of Ap\'ery limits. We propose a new method to address effective Diophantine approximation on the projective line and the multiplicative group. This method, and all our other results in the paper, emerged from quantifying our holonomy bounds in a way that directly yields effective measures of irrationality and linear independence. Applying these to a dihedral algebraic construction, we derive good effective irrationality measures for high order roots of an algebraic number, in an approach that might be considered a multivalent continuation of the classical hypergeometric method of Thue, Siegel, and Baker. A well-known Dirichlet approximation argument of Bombieri allows one to derive from this the classical effective Diophantine theorems, hitherto only approachable by Baker's linear forms in logarithms or by Bombieri's equivariant Thue--Siegel method. These include the algorithmic resolution of the two-variable $S$-unit equation, the Thue--Mahler equation, and the hyperelliptic and superelliptic equations, as well as the Baker--Feldman effective power sharpening of Liouville's theorem. We also give some other applications, including irrationality measures for the classical $L(2,\chi_{-3})$ and the $2$-adic $\zeta(5)$, and a new proof of the transcendence of $\pi$. Due to space limitations, a full development of these ideas will be deferred to future work.

math.NT↗

arXiv2024

The linear independence of $1$, $\zeta(2)$, and $L(2,\chi_{-3})$

We prove the irrationality of the classical Dirichlet L-value $L(2,\chi_{-3})$. The argument applies a new kind of arithmetic holonomy bound to a well-known construction of Zagier. In fact our work also establishes the $\mathbf{Q}$-linear independence of $1$, $\zeta(2)$, and $L(2,\chi_{-3})$. We also give a number of other applications of our method to other problems in irrationality.

math.NT↗

arXiv2021

The Unbounded Denominators Conjecture

We prove the unbounded denominators conjecture in the theory of noncongruence modular forms for finite index subgroups of SL_2(Z). Our result includes also Mason's generalization of the original conjecture to the setting of vector-valued modular forms, thereby supplying a new path to the congruence property in rational conformal field theory. The proof involves a new arithmetic holonomicity bound of a potential-theoretic flavor, together with Nevanlinna's second main theorem, the congruence subgroup property of SL_2(Z[1/p]), and a close description of the Fuchsian uniformization D(0,1)/\Gamma_N of the Riemann surface C \setminus \mu_N.

math.NT↗

arXiv2021

A consequence of the relative Bogomolov conjecture

We propose a formulation of the relative Bogomolov conjecture and show that it gives an affirmative answer to a question of Mazur's concerning the uniformity of the Mordell-Lang conjecture for curves. In particular we show that the relative Bogomolov conjecture implies the uniform Manin-Mumford conjecture for curves. The proof is built up on our previous work "Uniformity in Mordell-Lang for curves".

math.NT↗

arXiv2021

Uniformity in Mordell-Lang for curves

Consider a smooth, geometrically irreducible, projective curve of genus $g \ge 2$ defined over a number field of degree $d \ge 1$. It has at most finitely many rational points by the Mordell Conjecture, a theorem of Faltings. We show that the number of rational points is bounded only in terms of $g$, $d$, and the Mordell-Weil rank of the curve's Jacobian, thereby answering in the affirmative a question of Mazur. In addition we obtain uniform bounded, in $g$ and $d$, for the number of geometric torsion points of the Jacobian which lie in the image of an Abel-Jacobi map. Both estimates generalize our previous work for $1$-parameter families. Our proof uses Vojta's approach to the Mordell Conjecture, and the key new ingredient is the generalization of a height inequality due to the second- and third-named authors.

math.NT↗

arXiv2019

A proof of the Schinzel-Zassenhaus conjecture on polynomials

We prove that if $P(X) \in \mathbb{Z}[X]$ is an integer polynomial of degree $n$ and having $P(0) = 1$, then either $P(X)$ is a product of cyclotomic polynomials, or else at least one of the complex roots of $P$ belongs to the disk $|z| \leq 2^{ - 1 / (4n) }$. We also obtain a relative version of this result over the compositum $\mathbb{Q}^{\mathrm{ab}} \cdot \mathbb{Q}^{\mathrm{t.}p}$ of all abelian and all totally $p$-adic extensions of $\mathbb{Q}$, for any fixed prime~$p$, and apply it to prove a $\mathbb{Q}^{\mathrm{ab}} \cdot \mathbb{Q}^{\mathrm{t.}p}$-relative canonical height lower bound on the multiplicative group. Another extension is given to a uniform positive height lower bound, inverse-proportional to the total number of singular points, on holonomic power series in $\mathbb{Q}[[X]]$ and not of the form $p(X) / (X^k-1)^m$, where $p(X) \in \mathbb{Q}[X]$, with a further application to existence of a small critical value for certain rational functions.

math.NT↗

arXiv2019

Galois orbits of torsion points near atoral sets

We prove that the Galois equidistribution of torsion points of the algebraic torus $\mathbb{G}_{m}^d$ extends to the singular test functions of the form $\log{|P|}$, where $P$ is a Laurent polynomial having algebraic coefficients that vanishes on the unit real $d$-torus in a set whose Zariski closure in $\mathbb{G}_m^d$ has codimension at least $2$. Our result includes a power saving quantitative estimate of the decay rate of the equidistribution. It refines an ergodic theorem of Lind, Schmidt, and Verbitskiy, of which it also supplies a purely Diophantine proof. As an application, we confirm Ih's integrality finiteness conjecture on torsion points for a class of atoral divisors of $\mathbb{G}_m^d$.

math.NT↗

arXiv2019

Uniform bound for the number of rational points on a pencil of curves

Consider a one-parameter family of smooth, irreducible, projective curves of genus $g\ge 2$ defined over a number field. Each fiber contains at most finitely many rational points by the Mordell Conjecture, a theorem of Faltings. We show that the number of rational points is bounded only in terms of the family and the Mordell--Weil rank of the fiber's Jacobian. Our proof uses Vojta's approach to the Mordell Conjecture furnished with a height inequality due to the second- and third-named authors. In addition we obtain uniform bounds for the number of torsion in the Jacobian that lie each fiber of the family.

math.NT↗

arXiv2017

Convergence to the Mahler measure and the distribution of periodic points for algebraic Noetherian $\mathbb{Z}^d$-actions

For every $P \in \mathbb{Z}[x_1^{\pm 1}, \ldots, x_d^{\pm 1}] \setminus \{0\}$, and every $\varepsilon > 0$, we prove that there are a computable function $M = M(d,\varepsilon,°{P},h(P)) < \infty$ and a finite union $Z = Z(d,\varepsilon,°{P},h(P))$ of proper torsion cosets $\boldsymbolμ T \subsetneq \mathbb{G}_m^d$ such that, for every $N \in \mathbb{N}$, $Z$ contains all but at most $M$ of the torsion points $\boldsymbolζ \in μ_N^d$ satisfying $|P(\boldsymbolζ)| < e^{-\varepsilon ϕ(N)}$. This extends a well known structural theorem from torsion points lying exactly on a variety to torsion points lying very near to the subvariety. As a consequence, we prove that the averages of $\log{|P(\mathbf{x})|}$ over $μ_N^d$ converge as $N \to \infty$ to the Mahler measure of $P$. By the work of B. Kitchens, D. Lind, K. Schmidt and T. Ward, the convergence consequence amounts to the following statement in dynamics: For every Noetherian $\mathbb{Z}^d$-action $T : \mathbb{Z}^d \to \mathrm{Aut}(X)$ by automorphisms of a compact abelian group $X$ having a finite topological entropy $h(T)$, the exponential growth rate of the number of connected components of the group $\mathrm{Per}_N(T)$ of $N \cdot \mathbb{Z}^d$-periodic points of $(X,T)$ exists as $N \to \infty$, and equals the topological entropy $h(T)$. Moreover, it follows that all weak-$*$ limit measures of the push-forwards of the Haar measures on $\mathrm{Per}_N(T)$, under any a sequence of positive integers $N$, are measures of maximum entropy $h(T)$. Our main arithmetic result extends to Diophantine approximation by points of sufficiently small canonical height. It is best possible in such a generality, where an exceptional set is an inevitable feature.

math.DS↗

arXiv2016

Finiteness of local torsion for abelian t-modules

Let $C/\mathbb{F}_q$ be a regular projective curve, $\infty \in C$ a closed point, $A := Γ(C - \{\infty\}, \mathcal{O}_C)$, and $K := K(C)$ the fraction field of $A$. Consider a finite extension $L/K$, a place $v$ of $L$, and an abelian $A$-module $M$ (in the sense of Anderson) over $L_v$. We prove that the $L_v$-rational torsion submodule $M(L_v)_{\mathrm{tors}}$ of $M$ is a finite $A$-module.

math.NT↗

arXiv2016

Effectivity in Mochizuki's work on the $abc$-conjecture

This note outlines a constructive proof of a proposition in Mochizuki's paper "Arithmetic elliptic curves in general position," making a direct use of computable non-critical Belyi maps to effectively reduce the full $abc$-conjecture to a restricted form. Such a reduction means that an effective $abc$-theorem is implied by Theorem 1.10 of Mochizuki's final IUT paper ("Inter-universal Teichmuller theory IV: log-volume computations and set-theoretic foundations").

math.NT↗

arXiv2015

Silverman's conjecture for additive polynomial mappings

Let $F : \mathrm{End}_{\mathbb{F_p}}(\mathbb{G}_{a/K}^d)$ be an additive polynomial mapping over a global function field $K/\mathbb{F}_q$, and let $P \in \mathbb{G}_a^d(K)$. Following Silverman, consider $δ:= \lim_{n \in \mathbb{N}} (°{F^{n}})^{1/n}$ the dynamic degree of $F$ and $α(P) := \limsup_{n \in \mathbb{N}} h_K(F^{n}P)^{1/n}$ the arithmetic degree of $F$ at $P$. We have $α(P) \leq δ$, and extending a conjecture of Silverman from the number field case, it is expected that equality holds if the orbit of $P$ is Zariski-dense. We prove a weaker form of this conjecture: if $δ> 1$ and the orbit of $P$ is Zariski-dense, then also $α(P) > 1$. We obtain furthermore a more precise result concerning the growth along the orbit of $P$ of the heights of the individual coordinates, and formulate a few related open problems motivated by our results, including a generalization "with moving targets" of Faltings's theorem back in the number field case.

math.NT↗

arXiv2013

A lower bound on the orbit growth of a regular self-map of affine space

We show that if $f : \mathbb{A}_{\bar{\mathbb{Q}}}^r \to \mathbb{A}_{\bar{\mathbb{Q}}}^r$ is a regular self-map and $P \in \mathbb{A}^r(\bar{\mathbb{Q}})$ has $\limsup_{n \in \mathbb{N}} \frac{\log{h_{\mathrm{aff}}(f^nP)}}{\log{n}} < 1/r$, where $h_{\textrm{aff}}$ is the affine Weil height, then $\mathbb{N}$ partitions into a finite set and finitely many full arithmetic progressions, on each of which the coordinates of $f^nP$ are polynomials in $n$. In particular, if $(f^nP)_{n \in \mathbb{N}}$ is a Zariski-dense orbit, then either $n = 1$ and $f$ is of the shape $t \mapsto ζt + c$, $ζ\in μ_{\infty}$, or else $\limsup_{n \in \mathbb{N}} \frac{\log{h_{\mathrm{aff}}(f^nP)}}{\log{n}} \geq 1/r$. This inequality is the exponential improvement of the trivial lower bound obtained from counting the points of bounded height in $\mathbb{A}^r(K)$.

math.NT↗

arXiv2013

A note on a generalization of the Hadamard quotient theorem

We consider a generalization of the "Hadamard quotient theorem" of Pourchet and van der Poorten. A particular case of our conjecture states that if $f := \sum_{n \geq 0} a(n)x^n$ and $g := \sum_{n \geq 0} b(n)x^n$ represent, respectively, an algebraic and a rational function over a global field $K$ such that $b(n) \neq 0$ for all $n$ and the coefficients of the power series $h := \sum_{n \geq 0} a(n)/b(n)x^n$ are contained in a finitely generated ring, then $h$ is algebraic. We prove this conjecture if either (i) $g$ has a simple pole of a strictly maximal absolute value at some place; or (ii) or poles of $g$ are simple, there is a positive density $δ> 0$ of places which split completely in the field generated by the poles of g$ and at which all $b(n)$ are units, and with $d := [K(t,f):K(f)]$, the local radii of convergence $R_v$ of $h$ at the places $v$ of $K$ satisfy $\sum_v \log^+{R_v^{-1}} \leq δ/12d^4$.

math.NT↗