arXiv subjects

Benjamin Weiss

Publications and source records attributed to Benjamin Weiss.

At least 19 recordsLinked to original sources

arXiv2026

On-Detector Machine Learning for Beam-Induced Background Rejection at a 10 TeV Muon Collider

A 10 TeV Muon Collider is a compelling candidate for a future energy-frontier facility, offering unprecedented opportunities to explore the fundamental laws of particle physics. Muon decays in the collider ring produce intense beam-induced background (BIB) that can overwhelm detector occupancy and exceed readout bandwidth constraints. We investigate the potential of on-detector Machine Learning for BIB rejection in the vertex detector, exploiting pixel cluster shapes to distinguish background from collision products. We study three classes of lightweight neural-network architectures, and evaluate their implementation feasibility using high-level synthesis. Selected architectures achieve 88 to 90% data reduction at 99% signal efficiency, while requiring hardware resources compatible with potential ASIC implementation. These results demonstrate the potential of performing substantial BIB rejection directly in the pixel readout, providing a strategy for meeting the tracker readout requirements at a future Muon Collider.

hep-ex↗

arXiv2026

Invertibility, Often

By using a similar pattern of arguments, we show that in four categories the collection of isomorphisms forms a residual subset of the space of morphisms. We first consider surjective continuous mappings on Cantor spaces. Next, we look at measure preserving maps on Polish measure spaces. We then consider the $L^1$ representations of nonsingular maps on Polish measure spaces. Finally, we examine continuous, measure preserving maps on Cantor spaces equipped with so-called good measures.

math.DS↗

arXiv2026

On-chip probabilistic inference for charged-particle tracking at the sensor edge

Modern scientific instruments operate under increasingly extreme constraints on bandwidth, latency, and power. Inference at the sensor edge determines experimental data collection efficiency by deciding which information to save for further analysis. Particle tracking detectors at the Large Hadron Collider exemplify this challenge: pixelated silicon sensors generate rich spatiotemporal ionization patterns, yet most of this information is discarded due to data-rate limitations. Concurrently, advancements in co-design tools provide rapid turn-around for incorporating machine learning into application-specific integrated circuits, motivating designs for particle detectors with new integrated technologies. We demonstrate that neural networks embedded in the front-end electronics can infer charged-particle kinematic parameters from a single silicon layer. We regress hit positions and incident angles with calibrated uncertainties, while satisfying stringent constraints on numerical precision, latency, and silicon area. Our results establish a path toward probabilistic inference directly at the edge, opening new opportunities for intelligent sensing in high-rate scientific instruments.

physics.ins-det↗

arXiv2026

On a theorem Dan Rudolph: Part II: Amenable groups

We prove an analog of Rudolph's theorem for actions of countable amenable groups, which asserts that among invariant measures with entropy at least c on the $G$-shift $(\Lambda^G,\sigma)$, a typical measure has entropy $c$ and is Bernoulli. We also address a relative version of this theorem.

math.DS↗

arXiv2025

Characterization of a 28 nm $\textit{smartpixels}$ ASIC With On-Chip ML for Particle Tracking Detectors

We present a 28 nm CMOS pixel readout integrated circuit implementing in-pixel analog signal processing and on-chip machine learning data filtering for particle tracking detectors. Our ASIC comprises two $32 \times 8$ pixel matrices with a pixel pitch of $25 \times 25~\mu\mathrm{m}^2$, in which each pixel integrates a charge-sensitive amplifier with synchronous auto-zero offset cancellation and a 2-bit flash ADC with programmable thresholds. Two analog front-end architectures, single-ended and differential, are implemented and characterized. Digitized pixel data are combined into row-wise projections and processed by an on-chip, fully combinational neural network classifier for data reduction. Measurements at room temperature using charge injection demonstrate an equivalent noise charge of $54.6~\mathrm{e}^{-}$ and a threshold dispersion of $\sim$78.2~\unit{\electron} at nominal bias, linear response up to several~\unit{\kilo\electron}, and stable operation at a 10~MHz clock frequency. The neural network output is compared with offline RTL predictions and agrees for $99.06\%$ of $1.5 \times 10^{5}$ test inputs.

physics.ins-det↗

arXiv2025

Some Generic Properties of Processes

For a given ergodic measure preserving transformation T of a standard measure space each finite labelled partition defines an ergodic stationary process. There is a complete metric on the space of partitions which is separable. Various generic properties of these processes will be given. For example: 1. The generic partition defines a process that is not Rosenblatt mixing. 2. If T is a K-automorphism that is not Bernoulli then the generic partition is also K but not Bernoulli. Extensions to the relative setting and to actions of amenable groups will also be discussed.

math.DS↗

arXiv2025

Measurable entire functions II

Let $\mathcal{E}$ denote the space of entire functions with the topology of uniform convergence on compact sets. The action of $\mathbb C$ by translations on $\mathcal E$ is defined by $T_zf(w) = f(w+z)$. Let $\mathcal{U}$ denote the set of entire functions whose orbit under $T$ is dense. Birkhoff showed, in [B], that $\mathcal{U}$ is not empty. One of the problems in the collection by T-C Dinh and N. Sibony [DS] asks whether there exists an invariant probability measure on $\mathcal{E}$ whose support is contained in $\mathcal U$. We will show how an old construction of the second author can be modified to provide a positive answer to their question. Furthermore, we modify the construction to produce a wealth of ergodic measures on the space of entire functions of several complex variables.

math.DS↗

arXiv2025

The isomorphism problem for group actions

We discuss the isomorphism problem for ergodic actions of locally compact groups. In particular we show that the conjugacy relation is not Borel for ergodic measure preserving actions of indicable groups.

math.DS↗

arXiv2025

Universality of G-subshifts with specification

Let $G$ be an infinite countable amenable group and let $(X,G)$ be a $G$-subshift with specification, containing a free element. We prove that $(X,G)$ is universal, i.e., has positive topological entropy and for any free ergodic $G$-action on a standard probability space, $(Y,\nu,G)$, with $h(\nu)<h_{top}(X)$, there exists a shift-invariant measure $\mu$ on $X$ such that the systems $(Y,\nu,G)$ and $(X,\mu,G)$ are isomorphic. In particular, any $K$-shift (consisting of the indicator functions of all maximal $K$-separated sets) containing a free element is universal.

math.DS↗

arXiv2025

The abc conjecture implies infinitely many non-Wieferich places for fixed bases in number fields

Silverman showed that, assuming the $abc$ conjecture, there are $\gg \log x$ non-Wieferich primes base $a$ less than $x$ \cite{silverman}, for all non-zero $a$. This inspired Graves and Murty \cite{Graves}, Chen and Ding \cite{Chen1} \cite{Chen2}, and then Ding \cite{Ding} to find growth results, assuming the $abc$ conjecture, for non-Wieferich primes $p$ base $a$, where $p \equiv 1 \pmod{k}$ for integers $k \geq 2$. In light of Murty, Srinivas, and Subramani's recent work on `the Wieferich primes conjecture' and Euclidean algorithms in number fields \cite{murty}, number theorists need results on non-Wieferich places in number fields. We prove analogues of the results of Graves \& Murty and Ding, and show Ding's result holds for all bases $a$ in all imaginary quadratic fields' rings of integers, with $31$ explicitly listed exceptions. Along the way, we generalize useful results on rational integers to algebraic integers.

math.NT↗

arXiv2025

On the Jewett-Krieger theorem for amenable groups

Up to now there has been no proof in the literature of the often quoted fact that the Jewett-Krieger theorem is valid for all countable amenable groups. In this brief note I will close this gap by applying a recent result of B. Frej and D. Huczek [FH].

math.GR↗

arXiv2024

Poisson genericity in numeration systems with exponentially mixing probabilities

We define Poisson genericity for infinite sequences in any finite or countable alphabet with an invariant exponentially-mixing probability measure. A sequence is Poisson generic if the number of occurrences of blocks of symbols asymptotically follows a Poisson law as the block length increases. We prove that almost all sequences are Poisson generic. Our result generalizes Peres and Weiss' theorem about Poisson genericity of integral bases numeration systems. In particular, we obtain that their continued fraction expansions for almost all real numbers are Poisson generic.

math.PR↗

arXiv2024

Kac's Lemma and countable generators for actions of countable groups

Kac's lemma determines the expected return time to a set of positive measure under iterations of an ergodic probability preserving transformations. We introduce the notion of an \emph{allocation} for a probability preserving action of a countable group. Using this notion, we formulate and prove generalization of Kac's lemma for an action of a general countable group, and another generalization that applies to probability preserving equivalence relations. As an application, we provide a short proof for the existence of countable generating partitions for any ergodic action of a countable group.

math.DS↗

arXiv2024

On the class of systems which are disjoint from every ergodic system

In this note we give a fairly direct proof of a recent theorem of Gorska, Lemanczyk and de la Rue which characterises the class of measure preserving transformations that are disjoint from every ergodic measure preserving transformation. Our proof works just as well for any countable acting group.

math.DS↗

arXiv2024

Monotonicity, Topology, and Convexity of Recurrence in Random Walks

We consider non-homogeneous random walks on the two-dimensional positive quadrant $\mathbb{N}^2$ and the one-dimensional slab $\{0,1,\dots,k\}\times\mathbb{N}$. In the 1960's the following question was asked for $\mathbb{N}^2$: is it true if such a random walk $X$ is recurrent and $Y$ is another random walk that at every point is more likely to go down and more likely to go left than $Y$, then $Y$ is also recurrent? We provide an example showing that the answer is negative. We also show, via a coupling argument, that if either the random walk $X$ or $Y$ is sufficiently homogeneous then the answer is in fact positive. In addition, we show using the Rayleigh monotonicity principle that the analogous question for random walks on trees is positive. These results show that the subset of parameter space that yields recurrent random walks possesses some geometric properties, in this case the structure of an order ideal. Motivated by this perspective, we consider the more symmetric setting of homogeneous random walks on finitely generated abelian groups, and ask when this subset possesses other geometric properties, namely various topological properties and convexity. We answer some of these questions: in particular, we show that this subset is closed, and under a symmetric support condition, show it is path-connected and additionally show it is convex if and only if its effective dimension is at most 2. We also show its complement is in some sense typically path-connected but not convex. We finally propose some related open problems.

math.PR↗

arXiv2023

On intermediate factors of a product of disjoint systems

We consider an intermediate factor situation in two categories: probability measure preserving ergodic theory and compact topological dynamics. In the first we prove a master-key theorem and examine a wide range of applications. In the second we treat the case when one of the systems is distal and then provide some counterexamples.

math.DS↗

arXiv2023

Lifting generic points

Let $(X,T)$ and $(Y,S)$ be two topological dynamical systems, where $(X,T)$ has the weak specification property. Let $\xi$ be an invariant measure on the product system $(X\times Y, T\times S)$ with marginals $\mu$ on $X$ and $\nu$ on $Y$, with $\mu$ ergodic. Let $y\in Y$ be quasi-generic for $\nu$. Then there exists a point $x\in X$ generic for $\mu$ such that the pair $(x,y)$ is quasi-generic for $\xi$. This is a generalization of a similar theorem by T.\ Kamae, in which $(X,T)$ and $(Y,S)$ are full shifts on finite alphabets.

math.DS↗

arXiv2022

Rigid topologies on groups

Our main result is to show that every infinite, countable, residually finite group $G$ admits a Hausdorff group topology which is neither discrete nor precompact.

math.GR↗