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Balance functions have been regarded in the past as a method of investigating the late-stage hadronization found in the presence of a strongly-coupled medium. They are also used to constrain mechanisms of particle production in large and small collision systems. Measurements of charge balance functions for inclusive and identified particle pairs are reported as a function of charged particle multiplicity in proton--proton collisions simulated with the PYTHIA8 and the EPOS4 models. The charge balance functions of inclusive, pion, kaon, and proton pairs exhibit amplitudes and shapes that depend on particle species and differ significantly in the two models due to the different particle production mechanisms implemented in PYTHIA and EPOS. The shapes and amplitudes also evolve with multiplicity in both models. In addition, the evolution of the longitudinal rms width and that of balance functions integrals with multiplicity (and average transverse momentum) feature significant differences in the two models.

Mass measurements with the ISOLTRAP mass spectrometer at CERN-ISOLDE improve mass uncertainties of neutron-deficient tin isotopes towards doubly-magic $^{100}$Sn. The mass uncertainty of $^{103}$Sn was reduced by a factor of 4, and the new value for the mass excess of -67104(18) keV is compared with nuclear \textit{ab initio} and density functional theory calculations. Based on these results and local trends in the mass surface, the masses of $^{101,103}$Sn, as determined through their $Q_{\textrm{EC}}$ values, were found to be inconsistent with the new results. From our measurement for $^{103}$Sn, we extrapolate the mass excess of $^{101}$Sn to -60005(300) keV, which is significantly more bound than previously suggested. By correcting the mass values for $^{101,103}$Sn, we also adjust the values of $^{104}$Sb, $^{105,107}$Te, $^{108}$I, $^{109,111}$Xe, and $^{112}$Cs near the proton drip line which are connected through their $\alpha$- and proton $Q$-values. The results show an overall smoothening of the mass surface, suggesting the absence of deformation energy above the ${N=50}$ shell closure., Comment: 13 pages, 6 figures, published in Phys. Rev. C 111, 014315 - 9 January, 2025

Analog Content Addressable Memories (aCAMs) have proven useful for associative in-memory computing applications like Decision Trees, Finite State Machines, and Hyper-dimensional Computing. While non-volatile implementations using FeFETs and ReRAM devices offer speed, power, and area advantages, they suffer from slow write speeds and limited write cycles, making them less suitable for computations involving fully dynamic data patterns. To address these limitations, in this work, we propose a capacitor gain cell-based aCAM designed for dynamic processing, where frequent memory updates are required. Our system compares analog input voltages to boundaries stored in capacitors, enabling efficient dynamic tasks. We demonstrate the application of aCAM within transformer attention mechanisms by replacing the softmax-scaled dot-product similarity with aCAM similarity, achieving competitive results. Circuit simulations on a TSMC 28 nm node show promising performance in terms of energy efficiency, precision, and latency, making it well-suited for fast, dynamic AI applications.

In this paper, we study a series of algorithmic problems related to the subsequences occurring in the strings of a given language, under the assumption that this language is succinctly represented by a grammar generating it, or an automaton accepting it. In particular, we focus on the following problems: Given a string $w$ and a language $L$, does there exist a word of $L$ which has $w$ as subsequence? Do all words of $L$ have $w$ as a subsequence? Given an integer $k$ alongside $L$, does there exist a word of $L$ which has all strings of length $k$, over the alphabet of $L$, as subsequences? Do all words of $L$ have all strings of length $k$ as subsequences? For the last two problems, efficient algorithms were already presented in [Adamson et al., ISAAC 2023] for the case when $L$ is a regular language, and efficient solutions can be easily obtained for the first two problems. We extend that work as follows: we give sufficient conditions on the class of input-languages, under which these problems are decidable; we provide efficient algorithms for all these problems in the case when the input language is context-free; we show that all problems are undecidable for context-sensitive languages. Finally, we provide a series of initial results related to a class of languages that strictly includes the regular languages and is strictly included in the class of context-sensitive languages, but is incomparable to the of class context-free languages; these results deviate significantly from those reported for language-classes from the Chomsky hierarchy., Comment: Abstract to be published in the proceedings of ISAAC 2024

The existence of high-$\alpha$ stars with inferred ages < 6 Gyr has been confirmed recently with large spectroscopic and photometric surveys. However, stellar mergers or binary interactions can induce properties associated with young ages, such as high mass, rapid rotation, or high activity, even in old populations. Literature studies have confirmed that at least some of these apparently young stars are old merger products. However, none have ruled out the possibility of genuinely young high-$\alpha$ stars. Because cool GKM dwarfs spin down, rapid rotation can be used to indicate youth. In this paper, we provide strong evidence that truly young high-$\alpha$ stars exist by studying high-$\alpha$ rotators in the Kepler and K2 field with abundance measurements from GALAH and APOGEE. After excluding close binaries using radial velocity (RV) measurements from Gaia DR3 and multi-epoch RVs from APOGEE, we find a total of 70 high-$\alpha$ rapid rotators with periods ~10-30 days, 29 of which have lithium measurements from GALAH, indicating that they have not gone through past mass transfer or stellar merger events. We identify 10 young high-$\alpha$ candidates with no signs of merger-induced mixing or close companions. One clear example is a G dwarf with a measurable rotation and an age of 1.98$^{+0.12}_{-0.28}$ Gyr that is likely a single star with multiple RV measurements from APOGEE, has significant lithium detection from GALAH (A(Li) = 1.79), and has no signs of planet engulfment., Comment: 21 pages, 13 figures, submitted to AJ

Transformer networks, driven by self-attention, are central to Large Language Models. In generative Transformers, self-attention uses cache memory to store token projections, avoiding recomputation at each time step. However, GPU-stored projections must be loaded into SRAM for each new generation step, causing latency and energy bottlenecks. We present a custom self-attention in-memory computing architecture based on emerging charge-based memories called gain cells, which can be efficiently written to store new tokens during sequence generation and enable parallel analog dot-product computation required for self-attention. However, the analog gain cell circuits introduce non-idealities and constraints preventing the direct mapping of pre-trained models. To circumvent this problem, we design an initialization algorithm achieving text processing performance comparable to GPT-2 without training from scratch. Our architecture respectively reduces attention latency and energy consumption by up to two and five orders of magnitude compared to GPUs, marking a significant step toward ultra-fast, low-power generative Transformers., Comment: 25 pages, 6 figures, 1 table

Information extraction from textual data, where the query is represented by a finite transducer and the task is to enumerate all results without repetition, and its extension to the weighted case, where each output element has a weight and the output elements are to be enumerated sorted by their weights, are important and well studied problems in database theory. On the one hand, the first framework already covers the well-known case of regular document spanners, while the latter setting covers several practically relevant tasks that cannot be described in the unweighted setting. It is known that in the unweighted case this problem can be solved with linear time preprocessing $O(|D|)$ and output-linear delay $O(|s|)$ in data complexity, where $D$ is the input data and $s$ is the current output element. For the weighted case, Bourhis, Grez, Jachiet, and Riveros [ICDT 2021] recently designed an algorithm with linear time preprocessing, but the delay of $O(|s| \cdot \log|\mathsf{D}|)$ depends on the size of the data. We first show how to leverage the existing results on enumerating shortest paths to obtain a simple alternative algorithm with linear preprocessing and a delay of $O(|s_i| + \min\{ \log i, \log|\mathsf{D}|\})$ for the $i^{\text{th}}$ output element $s_i$ (in data complexity); thus, substantially improving the previous algorithm. Next, we develop a technically involved rounding technique that allows us to devise an algorithm with linear time preprocessing and output-linear delay $O(|s|)$ with high probability. To this end, we combine tools from algebra, high-dimensional geometry, and linear programming.

Using the language of homotopy type theory (HoTT), we 1) prove a synthetic version of the classification theorem for covering spaces, and 2) explore the existence of canonical change-of-basepoint isomorphisms between homotopy groups. There is some freedom in choosing how to translate concepts from classical algebraic topology into HoTT. The final translations we ended up with are easier to work with than the ones we started with. We discuss some earlier attempts to shed light on this translation process. The proofs are mechanized using the Coq proof assistant and closely follow classical treatments like those by Hatcher., Comment: 23 pages

The Fourteenth International Workshop on Non-Classical Models of Automata and Applications (NCMA 2024) was held in G\"ottingen, Germany, on August 12 and 13, 2024, at the historic Georg-Augustus-Universit\"at, organized by the Theoretical Computer Science research group of the respective university. The NCMA workshop series was established in 2009 as an annual event for researchers working on non-classical and classical models of automata, grammars or related devices. Such models are investigated both as theoretical models and as formal models for applications from various points of view. The goal of the NCMA workshop series is to exchange and develop novel ideas in order to gain deeper and interdisciplinary coverage of this particular area that may foster new insights and substantial progress.

The main motivation behind this paper stems from a notable gap in the existing literature: the absence of a discrete counterpart to the Laplace-Beltrami operator on Riemannian manifolds, which can be effectively used to solve PDEs. We consider that the natural approach to pioneer this field is to first explore one of the simplest non-trivial (i.e., non-Euclidean) scenario, specifically focusing on the $2$-dimensional hyperbolic space $\mathbb{H}^2$. To this end, we present two variants of discrete finite-difference operator tailored to this constant negatively curved space, both serving as approximations to the (continuous) Laplace-Beltrami operator within the $\mathrm{L}^2$ framework. Moreover, we prove that the discrete heat equation associated to both aforesaid operators exhibits stability and converges towards the continuous heat-Beltrami Cauchy problem on $\mathbb{H}^2$. Eventually, we illustrate that a discrete Laplacian specifically designed for the geometry of the hyperbolic space yields a more precise approximation and offers advantages from both theoretical and computational perspectives.

For two strings u, v over some alphabet A, we investigate the problem of embedding u into w as a subsequence under the presence of generalised gap constraints. A generalised gap constraint is a triple (i, j, C_{i, j}), where 1 <= i < j <= |u| and C_{i, j} is a subset of A^*. Embedding u as a subsequence into v such that (i, j, C_{i, j}) is satisfied means that if u[i] and u[j] are mapped to v[k] and v[l], respectively, then the induced gap v[k + 1..l - 1] must be a string from C_{i, j}. This generalises the setting recently investigated in [Day et al., ISAAC 2022], where only gap constraints of the form C_{i, i + 1} are considered, as well as the setting from [Kosche et al., RP 2022], where only gap constraints of the form C_{1, |u|} are considered. We show that subsequence matching under generalised gap constraints is NP-hard, and we complement this general lower bound with a thorough (parameterised) complexity analysis. Moreover, we identify several efficiently solvable subclasses that result from restricting the interval structure induced by the generalised gap constraints.

In this paper, we analyze the preservation of asymptotic properties of partially dissipative hyperbolic systems when switching to a discrete setting. We prove that one of the simplest consistent and unconditionally stable numerical methods - the central finite difference scheme - preserves both the asymptotic behaviour and the parabolic relaxation limit of one-dimensional partially dissipative hyperbolic systems which satisfy the Kalman rank condition. The large time asymptotic-preserving property is achieved by conceiving time-weighted perturbed energy functionals in the spirit of the hypocoercivity theory. For the relaxation-preserving property, drawing inspiration from the observation that solutions in the continuous case exhibit distinct behaviours in low and high frequencies, we introduce a novel discrete Littlewood-Paley theory tailored to the central finite difference scheme. This allows us to prove Bernstein-type estimates for discrete differential operators and leads to a new relaxation result: the strong convergence of the discrete linearized compressible Euler system with damping towards the discrete heat equation, uniformly with respect to the mesh parameter.

Mixed species charge and baryon balance functions are computed based on proton--proton (pp) collisions simulated with the PYTHIA8 model. Simulations are performed with selected values of the collision energy $\sqrt{s}$ and the Monash tune and the Ropes and Shoving modes of PYTHIA8 to explore whether such measurements provide useful new information and constraints on mechanisms of particle production in pp collisions. Charge balance functions are studied based on mixed pairs of pions, kaons, and protons, whereas baryon balance functions are computed for mixed low mass strange and non-strange baryons. Both charge and baryon balance functions of mixed particle pairs feature shapes and amplitudes that sensitively depend on the particle considered owing largely to the particle production mechanisms implemented in PYTHIA. The evolution of balance functions integrals with the longitudinal width of the acceptance are presented and one finds that sums of such integrals for a given reference particle obey expected sum rules for both charge and baryon balance functions. Additionally, both types of balance functions are found to evolve in shape and amplitude with increasing collision energy $\sqrt{s}$ and the PYTHIA tunes considered., Comment: 5 figures, 12 pages

Modern SMT solvers, such as Z3, offer user-controllable strategies, enabling users to tailor solving strategies for their unique set of instances, thus dramatically enhancing solver performance for their use case. However, this approach of strategy customization presents a significant challenge: handcrafting an optimized strategy for a class of SMT instances remains a complex and demanding task for both solver developers and users alike. In this paper, we address this problem of automatic SMT strategy synthesis via a novel Monte Carlo Tree Search (MCTS) based method. Our method treats strategy synthesis as a sequential decision-making process, whose search tree corresponds to the strategy space, and employs MCTS to navigate this vast search space. The key innovations that enable our method to identify effective strategies, while keeping costs low, are the ideas of layered and staged MCTS search. These novel heuristics allow for a deeper and more efficient exploration of the strategy space, enabling us to synthesize more effective strategies than the default ones in state-of-the-art (SOTA) SMT solvers. We implement our method, dubbed Z3alpha, as part of the Z3 SMT solver. Through extensive evaluations across six important SMT logics, Z3alpha demonstrates superior performance compared to the SOTA synthesis tool FastSMT, the default Z3 solver, and the CVC5 solver on most benchmarks. Remarkably, on a challenging QF_BV benchmark set, Z3alpha solves 42.7% more instances than the default strategy in the Z3 SMT solver., Comment: Accepted at IJCAI 2024

Urban road transport is a major civilisational and economic challenge, affecting the quality of life and economic activity. Addressing these challenges requires a multidisciplinary approach and sustainable urban planning strategies to mitigate the negative effects of traffic in cities. In this paper, we introduce an extension of one of the most popular macroscopic traffic simulation models, the Payne-Whitham model. We investigate how this model, originally designed to model highway traffic on straight road segments, can be adapted to more realistic conditions with arbitrary road network graphs and multiple intersections with traffic signals. Furthermore, we showcase the practical application of this extension in experiments aimed at optimising traffic signal settings. For computational reasons, these experiments involve the adoption of surrogate models for approximating our extended Payne-Whitham model, and subsequently, we utilise the Differential Evolution optimization algorithm, resulting in the identification of traffic signal settings that enhance the average speed of cars and decrease the total length of queues, thereby facilitating smoother traffic flow.

In this paper, we provide a novel enumeration algorithm for the set of all walks of a given length within a directed graph. Our algorithm has worst-case constant delay between outputting succinct representations of such walks, after a preprocessing step requiring linear time relative to the size of the graph. We apply these results to the problem of enumerating succinct representations of the strings of a given length from a prefix-closed regular language (languages accepted by a finite automaton which has final states only).

A subsequence of a word $w$ is a word $u$ such that $u = w[i_1] w[i_2] \dots w[i_{k}]$, for some set of indices $1 \leq i_1 < i_2 < \dots < i_k \leq \lvert w\rvert$. A word $w$ is $k$-subsequence universal over an alphabet $\Sigma$ if every word in $\Sigma^k$ appears in $w$ as a subsequence. In this paper, we study the intersection between the set of $k$-subsequence universal words over some alphabet $\Sigma$ and regular languages over $\Sigma$. We call a regular language $L$ \emph{$k$-$\exists$-subsequence universal} if there exists a $k$-subsequence universal word in $L$, and \emph{$k$-$\forall$-subsequence universal} if every word of $L$ is $k$-subsequence universal. We give algorithms solving the problems of deciding if a given regular language, represented by a finite automaton recognising it, is \emph{$k$-$\exists$-subsequence universal} and, respectively, if it is \emph{$k$-$\forall$-subsequence universal}, for a given $k$. The algorithms are FPT w.r.t.~the size of the input alphabet, and their run-time does not depend on $k$; they run in polynomial time in the number $n$ of states of the input automaton when the size of the input alphabet is $O(\log n)$. Moreover, we show that the problem of deciding if a given regular language is \emph{$k$-$\exists$-subsequence universal} is NP-complete, when the language is over a large alphabet. Further, we provide algorithms for counting the number of $k$-subsequence universal words (paths) accepted by a given deterministic (respectively, nondeterministic) finite automaton, and ranking an input word (path) within the set of $k$-subsequence universal words accepted by a given finite automaton.

The observed chemical diversity of Milky Way stars places important constraints on Galactic chemical evolution and the mixing processes that operate within the interstellar medium. Recent works have found that the chemical diversity of disk stars is low. For example, the APOGEE "chemical doppelganger rate," or the rate at which random pairs of field stars appear as chemically similar as stars born together, is high, and the chemical distributions of APOGEE stars in some Galactic populations are well-described by two-dimensional models. However, limited attention has been paid to the heavy elements (Z > 30) in this context. In this work, we probe the potential for neutron-capture elements to enhance the chemical diversity of stars by determining their effect on the chemical doppelganger rate. We measure the doppelganger rate in GALAH DR3, with abundances rederived using The Cannon, and find that considering the neutron-capture elements decreases the doppelganger rate from 2.2% to 0.4%, nearly a factor of 6, for stars with -0.1 < [Fe/H] < 0.1. While chemical similarity correlates with similarity in age and dynamics, including neutron-capture elements does not appear to select stars that are more similar in these characteristics. Our results highlight that the neutron-capture elements contain information that is distinct from that of the lighter elements and thus add at least one dimension to Milky Way abundance space. This work illustrates the importance of considering the neutron-capture elements when chemically characterizing stars and motivates ongoing work to improve their atomic data and measurements in spectroscopic surveys., Comment: 23 pages, 16 figures, 1 table. Submitted to AAS Journals, comments welcome. Associated catalog of high precision, Cannon-rederived abundances for GALAH giants to be made publicly available upon acceptance and available now upon request. See Walsen et al. 2023 for a complementary, high precision, Cannon-rederived abundance catalog for GALAH solar twins

AF Lep A+b is a remarkable planetary system hosting a gas-giant planet that has the lowest dynamical mass among directly imaged exoplanets. We present an in-depth analysis of the atmospheric composition of the star and planet to probe the planet's formation pathway. Based on new high-resolution spectroscopy of AF Lep A, we measure a uniform set of stellar parameters and elemental abundances (e.g., [Fe/H] = $-0.27 \pm 0.31$ dex). The planet's dynamical mass ($2.8^{+0.6}_{-0.5}$ M$_{\rm Jup}$) and orbit are also refined using published radial velocities, relative astrometry, and absolute astrometry. We use petitRADTRANS to perform chemically-consistent atmospheric retrievals for AF Lep b. The radiative-convective equilibrium temperature profiles are incorporated as parameterized priors on the planet's thermal structure, leading to a robust characterization for cloudy self-luminous atmospheres. This novel approach is enabled by constraining the temperature-pressure profiles via the temperature gradient $(d\ln{T}/d\ln{P})$, a departure from previous studies that solely modeled the temperature. Through multiple retrievals performed on different portions of the $0.9-4.2$ $\mu$m spectrophotometry, along with different priors on the planet's mass and radius, we infer that AF Lep b likely possesses a metal-enriched atmosphere ([Fe/H] $> 1.0$ dex). AF Lep b's potential metal enrichment may be due to planetesimal accretion, giant impacts, and/or core erosion. The first process coincides with the debris disk in the system, which could be dynamically excited by AF Lep b and lead to planetesimal bombardment. Our analysis also determines $T_{\rm eff} \approx 800$ K, $\log{(g)} \approx 3.7$ dex, and the presence of silicate clouds and dis-equilibrium chemistry in the atmosphere. Straddling the L/T transition, AF Lep b is thus far the coldest exoplanet with suggested evidence of silicate clouds., Comment: AJ, in press. Main text: Pages 1-32, Figures 1-15, Tables 1-6. All figures and tables after References belong to the Appendix (Pages 32-58, Figures 16-20, Table 7). For supplementary materials, please refer to the Zenodo repository https://doi.org/10.5281/zenodo.8267466

The significant features identified in a representative subset of the dataset during the learning process of an artificial intelligence model are referred to as a 'global' explanation. 3D global explanations are crucial in neuroimaging, where a complex representational space demands more than basic 2D interpretations. However, current studies in the literature often lack the accuracy, comprehensibility, and 3D global explanations needed in neuroimaging and beyond. To address this gap, we developed an explainable artificial intelligence (XAI) 3D-Framework capable of providing accurate, low-complexity global explanations. We evaluated the framework using various 3D deep learning models trained on a well-annotated cohort of 596 structural MRIs. The binary classification task focused on detecting the presence or absence of the paracingulate sulcus, a highly variable brain structure associated with psychosis. Our framework integrates statistical features (Shape) and XAI methods (GradCam and SHAP) with dimensionality reduction, ensuring that explanations reflect both model learning and cohort-specific variability. By combining Shape, GradCam, and SHAP, our framework reduces inter-method variability, enhancing the faithfulness and reliability of global explanations. These robust explanations facilitated the identification of critical sub-regions, including the posterior temporal and internal parietal regions, as well as the cingulate region and thalamus, suggesting potential genetic or developmental influences. Our XAI 3D-Framework leverages global explanations to uncover the broader developmental context of specific cortical features. This approach advances the fields of deep learning and neuroscience by offering insights into normative brain development and atypical trajectories linked to mental illness, paving the way for more reliable and interpretable AI applications in neuroimaging.

We introduce and investigate a series of matching problems for patterns with variables under Simon's congruence. Our results provide a thorough picture of these problems' computational complexity.