arXiv subjects

Adam Brown

Publications and source records attributed to Adam Brown.

At least 19 recordsLinked to original sources

arXiv2025

Measurement of the $^{35}Cl(n, p)^{35}S$ cross-section at the CERN n\_TOF facility from subthermal energy to 120 keV

Background: The $^{35}Cl(n, p)^{35}S$ reaction is of special interest in three different applications. First, in Boron Neutron Capture Therapy due to the presence of $^{35}Cl$ in brain and skin tissue. Second, it is involved in the creation of $^{36}S$, whose astrophysical origin remains unresolved. Third, in the designing of fast nuclear reactors of new generation based on molten salts. Purpose: To measure the $^{35}Cl(n, p)^{35}S$ cross-section from thermal energy to 120 keV, determine the resonance parameters in this range and Maxwellian Averaged Cross-Section (MACS). Method: We made use of the Time-of-Flight technique with microMEGAS detectors at Experimental Area 2 (EAR-2) of n\_TOF facility at CERN. The $^{10}B(n, \alpha)^{7}Li$ and $^{235}U(n, f)$ reactions were used as references. Rutherford Back-scattering Spectrometry technique was performed at Centro Nacional de Aceleradores (CNA) in Sevilla, in order to accurately determine the masses of the irradiated samples. Results: We obtain a thermal cross-section of $0.470 \pm 0.009$ barns. The $1/v$ energy dependence of the cross-section is observed up to the first resonance at 0.398 keV, the resonances up to 120 keV are analyzed and MACS calculated for $k_{B} T$ from 1 to 100 keV. Conclusions: The $^{35}Cl(n, p)^{35}S$ cross-section has been obtained over a wide energy range for the first time, with high accuracy across the aforementioned range. The thermal cross-section and first two resonances are in agreement with latest evaluation in ENDF/B-VIII.1, while lower resonance strength was found for high energy resonances. These data are used to calculate the MACS for different $k_{B} T$.

nucl-ex↗

arXiv2025

Normalizations of factorizations over convex cones and their effects on extension complexity

Factorizations over cones and their duals play central roles for many areas of mathematics and computer science. One of the reasons behind this is the ability to find a representation for various objects using a well-structured family of cones, where the representation is captured by the factorizations over these cones. Several major questions about factorizations over cones remain open even for such well-structured families of cones as non-negative orthants and positive semidefinite cones. Having said that, we possess a far better understanding of factorizations over non-negative orthants and positive semidefinite cones than over other families of cones. One of the key properties that led to this better understanding is the ability to normalize factorizations, i.e., to guarantee that the norms of the vectors involved in the factorizations are bounded in terms of an input and in terms of a constant dependent on the given cone. Our work aims at understanding which cones guarantee that factorizations over them can be normalized, and how this effects extension complexity of polytopes over such cones.

math.OC↗

arXiv2024

Morse theory for chromatic Delaunay triangulations

The chromatic alpha filtration is a generalization of the alpha filtration that can encode spatial relationships among classes of labelled point cloud data, and has applications in topological data analysis of multi-species data. In this paper we introduce the chromatic Delaunay-\v{C}ech and chromatic Delaunay-Rips filtrations, which are computationally favourable alternatives to the chromatic alpha filtration. We use generalized discrete Morse theory to show that the \v{C}ech, chromatic Delaunay-\v{C}ech, and chromatic alpha filtrations are related by simplicial collapses. Our result generalizes a result of Bauer and Edelsbrunner from the non-chromatic to the chromatic setting. We also show that the chromatic Delaunay-Rips filtration is locally stable to perturbations of the underlying point cloud. Our results provide theoretical justification for the use of chromatic Delaunay-\v{C}ech and chromatic Delaunay-Rips filtrations in applications, and we demonstrate their computational advantage with numerical experiments.

math.AT↗

arXiv2024

Proportional scintillation in liquid xenon: demonstration in a single-phase liquid-only time projection chamber

The largest direct dark matter search experiments to date employ dual-phase time projection chambers (TPCs) with liquid noble gas targets. These detect both the primary photons generated by particle interactions in the liquid target, as well as proportional secondary scintillation light created by the ionization electrons in a strong electric field in the gas phase between the liquid-gas interface and the anode. In this work, we describe the detection of charge signals in a small-scale single-phase liquid-xenon-only TPC, that features the well-established TPC geometry with light readout above and below a cylindrical target. In the single-phase TPC, the proportional scintillation light (S2) is generated in liquid xenon in close proximity to 10 {\mu}m diameter anode wires. The detector was characterized and the proportional scintillation process was studied using the 32.1 keV and 9.4 keV signals from 83mKr decays. A charge gain factor g2 of up to (1.9 $\pm$ 0.3) PE/electron was reached at an anode voltage 4.4 kV higher than the gate electrode 5 mm below it, corresponding to (29 $\pm$ 6) photons emitted per ionization electron. The duration of S2 signals is dominated by electron diffusion and approaches the xenon de-excitation timescale for very short electron drift times. The electron drift velocity and the longitudinal diffusion constant were measured at a drift field of 470 V/cm. The results agree with the literature and demonstrate that a single-phase TPC can be operated successfully.

physics.ins-det↗

arXiv2024

Maximizing the Minimum Eigenvalue in Constant Dimension

In an instance of the minimum eigenvalue problem, we are given a collection of $n$ vectors $v_1,\ldots, v_n \subset {\mathbb{R}^d}$, and the goal is to pick a subset $B\subseteq [n]$ of given vectors to maximize the minimum eigenvalue of the matrix $\sum_{i\in B} v_i v_i^{\top} $. Often, additional combinatorial constraints such as cardinality constraint $\left(|B|\leq k\right)$ or matroid constraint ($B$ is a basis of a matroid defined on $[n]$) must be satisfied by the chosen set of vectors. The minimum eigenvalue problem with matroid constraints models a wide variety of problems including the Santa Clause problem, the E-design problem, and the constructive Kadison-Singer problem. In this paper, we give a randomized algorithm that finds a set $B\subseteq [n]$ subject to any matroid constraint whose minimum eigenvalue is at least $(1-\epsilon)$ times the optimum, with high probability. The running time of the algorithm is $O\left( n^{O(d\log(d)/\epsilon^2)}\right)$. In particular, our results give a polynomial time asymptotic scheme when the dimension of the vectors is constant. Our algorithm uses a convex programming relaxation of the problem after guessing a rescaling which allows us to apply pipage rounding and matrix Chernoff inequalities to round to a good solution. The key new component is a structural lemma which enables us to "guess'' the appropriate rescaling, which could be of independent interest. Our approach generalizes the approximation guarantee to monotone, homogeneous functions and as such we can maximize $\det(\sum_{i\in B} v_i v_i^\top)^{1/d}$, or minimize any norm of the eigenvalues of the matrix $\left(\sum_{i\in B} v_i v_i^\top\right)^{-1} $, with the same running time under some mild assumptions. As a byproduct, we also get a simple algorithm for an algorithmic version of Kadison-Singer problem.

cs.DS↗

arXiv2024

Approximation Algorithms for the Weighted Nash Social Welfare via Convex and Non-Convex Programs

In an instance of the weighted Nash Social Welfare problem, we are given a set of $m$ indivisible items, $\mathscr{G}$, and $n$ agents, $\mathscr{A}$, where each agent $i \in \mathscr{A}$ has a valuation $v_{ij}\geq 0$ for each item $j\in \mathscr{G}$. In addition, every agent $i$ has a non-negative weight $w_i$ such that the weights collectively sum up to $1$. The goal is to find an assignment $\sigma:\mathscr{G}\rightarrow \mathscr{A}$ that maximizes $\prod_{i\in \mathscr{A}} \left(\sum_{j\in \sigma^{-1}(i)} v_{ij}\right)^{w_i}$, the product of the weighted valuations of the players. When all the weights equal $\frac1n$, the problem reduces to the classical Nash Social Welfare problem, which has recently received much attention. In this work, we present a $5\cdot\exp\left(2\cdot D_{\text{KL}}(\mathbf{w}\, ||\, \frac{\vec{\mathbf{1}}}{n})\right) = 5\cdot\exp\left(2\log{n} + 2\sum_{i=1}^n w_i \log{w_i}\right)$-approximation algorithm for the weighted Nash Social Welfare problem, where $D_{\text{KL}}(\mathbf{w}\, ||\, \frac{\vec{\mathbf{1}}}{n})$ denotes the KL-divergence between the distribution induced by $\mathbf{w}$ and the uniform distribution on $[n]$. We show a novel connection between the convex programming relaxations for the unweighted variant of Nash Social Welfare presented in \cite{cole2017convex, anari2017nash}, and generalize the programs to two different mathematical programs for the weighted case. The first program is convex and is necessary for computational efficiency, while the second program is a non-convex relaxation that can be rounded efficiently. The approximation factor derives from the difference in the objective values of the convex and non-convex relaxation.

cs.DS↗

arXiv2023

PANCAKE: a large-diameter cryogenic test platform with a flat floor for next generation multi-tonne liquid xenon detectors

The PANCAKE facility is the world's largest liquid xenon test platform. Inside its cryostat with an internal diameter of 2.75 m, components for the next generation of liquid xenon experiments, such as DARWIN or XLZD, will be tested at their full scale. This is essential to ensure their successful operation. This work describes the facility, including its cryostat, cooling systems, xenon handling infrastructure, and its monitoring and instrumentation. The inner vessel has a flat floor, which allows the full diameter to be used with a modest amount of xenon. This is a novel approach for such a large cryostat and is of interest for future large-scale experiments, where a standard torispherical head would require tonnes of additional xenon. Our current xenon inventory of 400 kg allows a liquid depth of about 2 cm in the inner cryostat vessel. We also describe the commissioning of the facility, which is now ready for component testing.

physics.ins-det↗

arXiv2023

Using Logs Data to Identify When Software Engineers Experience Flow or Focused Work

Beyond self-report data, we lack reliable and non-intrusive methods for identifying flow. However, taking a step back and acknowledging that flow occurs during periods of focus gives us the opportunity to make progress towards measuring flow by isolating focused work. Here, we take a mixed-methods approach to design a logs-based metric that leverages machine learning and a comprehensive collection of logs data to identify periods of related actions (indicating focus), and validate this metric against self-reported time in focus or flow using diary data and quarterly survey data. Our results indicate that we can determine when software engineers at a large technology company experience focused work which includes instances of flow. This metric speaks to engineering work, but can be leveraged in other domains to non-disruptively measure when people experience focus. Future research can build upon this work to identify signals associated with other facets of flow.

cs.HC↗

arXiv2022

Efficient Determinant Maximization for All Matroids

Determinant maximization provides an elegant generalization of problems in many areas, including convex geometry, statistics, machine learning, fair allocation of goods, and network design. In an instance of the determinant maximization problem, we are given a collection of vectors $v_1,\ldots, v_n \in \mathbb{R}^d$, and the goal is to pick a subset $S\subseteq [n]$ of given vectors to maximize the determinant of the matrix $\sum_{i \in S} v_iv_i^\top$, where the picked set of vectors $S$ must satisfy some combinatorial constraint such as cardinality constraint ($|S| \leq k$) or matroid constraint ($S$ is a basis of a matroid defined on $[n]$). In this work, we give a combinatorial algorithm for the determinant maximization problem under a matroid constraint that achieves $O(d^{O(d)})$-approximation for any matroid of rank $r\geq d$. This complements the recent result of~\cite{BrownLPST22} that achieves a similar bound for matroids of rank $r\leq d$, relying on a geometric interpretation of the determinant. Our result matches the best-known estimation algorithms~\cite{madan2020maximizing} for the problem, which could estimate the objective value but could not give an approximate solution with a similar guarantee. Our work follows the framework developed by~\cite{BrownLPST22} of using matroid intersection based algorithms for determinant maximization. To overcome the lack of a simple geometric interpretation of the objective when $r \geq d$, our approach combines ideas from combinatorial optimization with algebraic properties of the determinant. We also critically use the properties of a convex programming relaxation of the problem introduced by~\cite{madan2020maximizing}.

cs.DS↗

arXiv2022

Discrete Microlocal Morse Theory

We establish several results combining discrete Morse theory and microlocal sheaf theory in the setting of finite posets and simplicial complexes. Our primary tool is a computationally tractable description of the bounded derived category of sheaves on a poset with the Alexandrov topology. We prove that each bounded complex of sheaves on a finite poset admits a unique (up to isomorphism of complexes) minimal injective resolution, and we provide algorithms for computing minimal injective resolution of an injective complex, as well as several useful functors between derived categories of sheaves. For the constant sheaf on a simplicial complex, we give asymptotically tight bounds on the complexity of computing the minimal injective resolution using those algorithms. Our main result is a novel definition of the discrete microsupport of a bounded complex of sheaves on a finite poset. We detail several foundational properties of the discrete microsupport, as well as a microlocal generalization of the discrete homological Morse theorem and Morse inequalities.

math.GN↗

arXiv2022

Reduction of $^{222}$Rn-induced Backgrounds in a Hermetic Dual-Phase Xenon Time Projection Chamber

The continuous emanation of $^{222}$Rn from detector surfaces causes the dominant background in current liquid xenon time projection chambers (TPCs) searching for dark matter. A significant reduction is required for the next generation of detectors which are aiming to reach the neutrino floor, such as DARWIN. $^{222}$Rn-induced back\-grounds can be reduced using a hermetic TPC, in which the sensitive target volume is mechanically separated from the rest of the detector containing the majority of Rn-emanating surfaces. We present a hermetic TPC that mainly follows the well-established design of leading xenon TPCs and has been operated successfully over a period of several weeks. By scaling up the results achieved to the DARWIN-scale, we show that the hermetic TPC concept can reduce the $^{222}$Rn concentration to the required level, even with imperfect separation of the volumes.

physics.ins-det↗

arXiv2022

The XeBRA platform for liquid xenon time projection chamber development

XeBRA is a flexible cryogenic platform designed to perform research and development for liquid xenon detectors searching for rare events. Its extra-large outer cryostat makes it possible to install a wide variety of detector designs. We present the system, including its cryogenic, gas handling, data acquisition and slow control subsystems. Two dual phase time projection chambers with sensitive masses at the 1 kg scale have so far been operated in XeBRA. Using data from these, we determine the field-dependence of the electron drift velocity in liquid xenon. We also measure the relative charge and light yields for 41.5 keV energy deposits from Kr-83m with electric drift fields between 50 V/cm and 677 V/cm.

physics.ins-det↗

arXiv2022

Determinant Maximization via Matroid Intersection Algorithms

Determinant maximization problem gives a general framework that models problems arising in as diverse fields as statistics \cite{pukelsheim2006optimal}, convex geometry \cite{Khachiyan1996}, fair allocations\linebreak \cite{anari2016nash}, combinatorics \cite{AnariGV18}, spectral graph theory \cite{nikolov2019proportional}, network design, and random processes \cite{kulesza2012determinantal}. In an instance of a determinant maximization problem, we are given a collection of vectors $U=\{v_1,\ldots, v_n\} \subset \RR^d$, and a goal is to pick a subset $S\subseteq U$ of given vectors to maximize the determinant of the matrix $\sum_{i\in S} v_i v_i^\top $. Often, the set $S$ of picked vectors must satisfy additional combinatorial constraints such as cardinality constraint $\left(|S|\leq k\right)$ or matroid constraint ($S$ is a basis of a matroid defined on the vectors). In this paper, we give a polynomial-time deterministic algorithm that returns a $r^{O(r)}$-approximation for any matroid of rank $r\leq d$. This improves previous results that give $e^{O(r^2)}$-approximation algorithms relying on $e^{O(r)}$-approximate \emph{estimation} algorithms \cite{NikolovS16,anari2017generalization,AnariGV18,madan2020maximizing} for any $r\leq d$. All previous results use convex relaxations and their relationship to stable polynomials and strongly log-concave polynomials. In contrast, our algorithm builds on combinatorial algorithms for matroid intersection, which iteratively improve any solution by finding an \emph{alternating negative cycle} in the \emph{exchange graph} defined by the matroids. While the $\det(.)$ function is not linear, we show that taking appropriate linear approximations at each iteration suffice to give the improved approximation algorithm.

cs.DS↗

arXiv2021

Computing Minimal Injective Resolutions of Sheaves on Finite Posets

In this paper we introduce two new methods for constructing injective resolutions of sheaves of finite-dimensional vector spaces on finite posets. Our main result is the existence and uniqueness of a minimal injective resolution of a given sheaf and an algorithm for its construction. For the constant sheaf on a simplicial complex, we give a topological interpretation of the multiplicities of indecomposable injective sheaves in the minimal injective resolution, and give asymptotically tight bounds on the complexity of computing the minimal injective resolution with our algorithm.

math.AT↗

arXiv2021

Contravariant pairings between standard Whittaker modules and Verma modules

We classify contravariant pairings between standard Whittaker modules and Verma modules over a complex semisimple Lie algebra. These contravariant pairings are useful in extending several classical techniques for category $\mathcal{O}$ to the Mili\v{c}i\'{c}--Soergel category $\mathcal{N}$. We introduce a class of costandard modules which generalize dual Verma modules, and describe canonical maps from standard to costandard modules in terms of contravariant pairings. We show that costandard modules have unique irreducible submodules and share the same composition factors as the corresponding standard Whittaker modules. We show that costandard modules give an algebraic characterization of the global sections of costandard twisted Harish-Chandra sheaves on the associated flag variety, which are defined using holonomic duality of $\mathcal{D}$-modules. We prove that with these costandard modules, blocks of category $\mathcal{N}$ have the structure of highest weight categories and we establish a BGG reciprocity theorem for $\mathcal{N}$.

math.RT↗

arXiv2019

Contravariant forms on Whittaker modules

Let $\mathfrak{g}$ be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker $\mathfrak{g}$-modules $Y(\chi, \eta)$ introduced by Kostant. We prove that the set of all contravariant forms on $Y(\chi, \eta)$ forms a vector space whose dimension is given by the cardinality of the Weyl group of $\mathfrak{g}$. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules $M(\chi, \eta)$ introduced by McDowell.

math.RT↗

arXiv2019

Probabilistic Convergence and Stability of Random Mapper Graphs

We study the probabilistic convergence between the mapper graph and the Reeb graph of a topological space $\mathbb{X}$ equipped with a continuous function $f: \mathbb{X} \rightarrow \mathbb{R}$. We first give a categorification of the mapper graph and the Reeb graph by interpreting them in terms of cosheaves and stratified covers of the real line $\mathbb{R}$. We then introduce a variant of the classic mapper graph of Singh et al.~(2007), referred to as the enhanced mapper graph, and demonstrate that such a construction approximates the Reeb graph of $(\mathbb{X}, f)$ when it is applied to points randomly sampled from a probability density function concentrated on $(\mathbb{X}, f)$. Our techniques are based on the interleaving distance of constructible cosheaves and topological estimation via kernel density estimates. Following Munch and Wang (2018), we first show that the mapper graph of $(\mathbb{X}, f)$, a constructible $\mathbb{R}$-space (with a fixed open cover), approximates the Reeb graph of the same space. We then construct an isomorphism between the mapper of $(\mathbb{X},f)$ to the mapper of a super-level set of a probability density function concentrated on $(\mathbb{X}, f)$. Finally, building on the approach of Bobrowski et al.~(2017), we show that, with high probability, we can recover the mapper of the super-level set given a sufficiently large sample. Our work is the first to consider the mapper construction using the theory of cosheaves in a probabilistic setting. It is part of an ongoing effort to combine sheaf theory, probability, and statistics, to support topological data analysis with random data.

math.AT↗

arXiv2018

Arakawa-Suzuki functors for Whittaker modules

In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type $A_n$ to the category of finite-dimensional modules of the graded affine Hecke algebra of type $A_\ell$. Using results of Backelin and of Arakawa-Suzuki, we prove that these functors map standard modules to standard modules (or zero) and simple modules to simple modules (or zero). Moreover, we show that each simple module of the graded affine Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker category contains the BGG category $\mathcal{O}$ as a full subcategory, our results generalize results of Arakawa-Suzuki, which in turn generalize Schur-Weyl duality between finite-dimensional representations of $SL_n(\mathbb{C})$ and representations of the symmetric group $S_n$.

math.RT↗