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The vast portion of workloads employing LLMs involves answering questions grounded on PDF or scan content. We introduce the Arctic-TILT achieving accuracy on par with models 1000$\times$ its size on these use cases. It can be fine-tuned and deployed on a single 24GB GPU, lowering operational costs while processing Visually Rich Documents with up to 400k tokens. The model establishes state-of-the-art results on seven diverse Document Understanding benchmarks, as well as provides reliable confidence scores and quick inference, which are essential for processing files in large-scale or time-sensitive enterprise environments.

We consider probability measures on infinite sequences over two countable alphabets of a different cardinality. We introduce an invertible mapping between such measures, called the normalized transport, that preserves both stationarity and ergodicity. The normalized transport applies so called self-avoiding codes that generalize comma-separated codes. The normalized transport is also connected to the usual measure transport via underlying asymptotically mean stationary measures. It preserves the ergodic decomposition. The normalized transport arises, for instance, in the problem of successive recurrence times. In particular, we show that successive recurrence times are ergodic for an ergodic measure, which solves an open problem that generalizes a result by Chen Moy from 1959., Comment: 16 pages, no figures

The dynamics of disordered two-dimensional systems is much less understood than the dynamics of disordered chains, mainly due to the lack of appropriate numerical methods. We demonstrate that a single-trajectory version of the fermionic truncated Wigner approximation (fTWA) gives unexpectedly accurate results for the dynamics of one-dimensional (1D) systems with moderate or strong disorder. Additionally, the computational complexity of calculations carried out within this approximation is small enough to enable studies of two-dimensional (2D) systems larger than standard fTWA. Using this method, we analyze the dynamics of interacting spinless fermions propagating on disordered 1D and 2D lattices. We find for both spatial dimensions that the imbalance exhibits a universal dependence on the rescaled time $t/\xi_W$, where in 2D the time-scale $\xi_W$ follows a stretched-exponential dependence on disorder strength., Comment: 11 pages, 8 figures

Understanding the decisions made by image classification networks is a critical area of research in deep learning. This task is traditionally divided into two distinct approaches: post-hoc methods and intrinsic methods. Post-hoc methods, such as GradCam, aim to interpret the decisions of pre-trained models by identifying regions of the image where the network focuses its attention. However, these methods provide only a high-level overview, making it difficult to fully understand the network's decision-making process. Conversely, intrinsic methods, like prototypical parts models, offer a more detailed understanding of network predictions but are constrained by specific architectures, training methods, and datasets. In this paper, we introduce InfoDisent, a hybrid model that combines the advantages of both approaches. By utilizing an information bottleneck, InfoDisent disentangles the information in the final layer of a pre-trained deep network, enabling the breakdown of classification decisions into basic, understandable atomic components. Unlike standard prototypical parts approaches, InfoDisent can interpret the decisions of pre-trained classification networks and be used for making classification decisions, similar to intrinsic models. We validate the effectiveness of InfoDisent on benchmark datasets such as ImageNet, CUB-200-2011, Stanford Cars, and Stanford Dogs for both convolutional and transformer backbones.

Accurate reconstruction of ambient temperature at death scenes is crucial for estimating the postmortem interval (PMI) in forensic science. Typically, this is done by correcting weather station temperatures using measurements from the scene, often through linear regression. While recent attempts to use alternative algorithms like GAM have improved accuracy, they usually require additional variables such as humidity, making them impractical. This study presents two methods for accurate temperature reconstruction using only temperature data. The first, a concurrent regression model, is known in mathematics and is applied here for mid-term reconstructions (several days of measurements). The second, a new method based on Fourier expansion, is designed for short-term reconstructions (only a few hours of measurements). Both models were tested in quasi-indoor conditions, using data from six different environments. The concurrent regression model provided nearly perfect reconstructions for periods longer than six days, while the short-term model achieved similar accuracy after just 4-5 hours of measurements. These findings demonstrate that reliable temperature corrections for PMI estimation can be made with significantly reduced measurement periods, enhancing the practicality of the method in forensic applications., Comment: 12 pages, 7 figures, Original Research Papers, submitted to "Science & Justice"

The discontinuous operations inherent in quantization and sparsification introduce obstacles to backpropagation. This is particularly challenging when training deep neural networks in ultra-low precision and sparse regimes. We propose a novel, robust, and universal solution: a denoising affine transform that stabilizes training under these challenging conditions. By formulating quantization and sparsification as perturbations during training, we derive a perturbation-resilient approach based on ridge regression. Our solution employs a piecewise constant backbone model to ensure a performance lower bound and features an inherent noise reduction mechanism to mitigate perturbation-induced corruption. This formulation allows existing models to be trained at arbitrarily low precision and sparsity levels with off-the-shelf recipes. Furthermore, our method provides a novel perspective on training temporal binary neural networks, contributing to ongoing efforts to narrow the gap between artificial and biological neural networks.

Thermodynamics is based on a coarse-grained approach, from which its fundamental variables emerge, effectively erasing the complicate details of the microscopic dynamics within a macroscopic system. The strength of Thermodynamics lies in the universality provided by this paradigm. In contrast, quantum mechanics focuses on describing the dynamics of microscopic systems, aiming to make predictions about experiments we perform, a goal shared by all fundamental physical theories, which are often framed as gauge theories in modern physics. Recently, a gauge theory for quantum thermodynamics was introduced, defining gauge invariant work and heat, and exploring their connections to quantum phenomena. In this work, we extend that theory in two significant ways. First, we incorporate energy spectrum degeneracies, which were previously overlooked. Additionally, we define gauge-invariant entropy, exploring its properties and connections to other physical and informational quantities. This results in a complete framework for quantum thermodynamics grounded in the principle of gauge invariance. To demonstrate some implications of this theory, we apply it to well-known critical systems.

In this contribution we present a concise introduction to quantum entanglement in multipartite systems. After a brief comparison between bipartite systems and the simplest non-trivial multipartite scenario involving three parties, we review mathematically rigorous definitions of separability and entanglement between several subsystems, as well as their transformations and measures., Comment: Multipartite Entanglement will be a chapter in Encyclopedia of Mathematical Physics 2nd edition

We study the loan contracts offered by decentralised loan protocols (DLPs) through the lens of financial derivatives. DLPs, which effectively are clearinghouses, facilitate transactions between option buyers (i.e. borrowers) and option sellers (i.e. lenders). The loan-to-value at which the contract is initiated determines the option premium borrowers pay for entering the contract, and this can be deduced from the non-arbitrage pricing theory. We show that when there are no market frictions, and there is no spread between lending and borrowing rates, it is optimal to never enter the lending contract. Next, by accounting for the spread between rates and transactional costs, we develop a deep neural network-based algorithm for learning trading strategies on the external markets that allow us to replicate the payoff of the lending contracts that are not necessarily optimally exercised. This allows hedge the risk lenders carry by issuing options sold to the borrowers, which can complement (or even replace) the liquidations mechanism used to protect lenders' capital. Our approach can also be used to exploit (statistical) arbitrage opportunities that may arise when DLP allow users to enter lending contracts with loan-to-value, which is not appropriately calibrated to market conditions or/and when different markets price risk differently. We present thorough simulation experiments using historical data and simulations to validate our approach.

In this chapter, we will cover how stars form from the stellar nurseries that are giant molecular clouds. We will first review the physical processes that compete to regulate star formation. We then review star formation in turbulent, magnetized molecular clouds and the associated statistics giving rise to the star formation rate and the initial mass function of stars. We then present the protostellar stages in detail from an observational perspective. We will primarily discuss low-mass ($<1.5\msun$) stars. Finally, we examine how multiplicity complicates the single-star formation picture. This chapter will focus on star formation at redshift~0, Comment: This is a pre-print of a chapter for the Encyclopedia of Astrophysics (edited by I. Mandel, section editor F.R.N. Schneider) to be published by Elsevier as a Reference Module. 18 pages, 8 Figures

We report the discovery of jets emanating from pre-main-sequence objects exclusively at mid-infrared wavelengths, enabled by the superb sensitivity of JWST's Mid-InfraRed Medium-Resolution Spectrometer (MIRI MRS) instrument. These jets are observed only in lines of [NiII], [FeII], [ArII], and [NeII]. The H$_2$ emission, imaged in eight distinct transitions, has a completely different morphology, exhibiting a wide-angled, biconical shape, symmetrically distributed about the jet axes. Synergistic high-resolution Atacama Large Millimeter/submillimeter Array (ALMA) observations resolve a pair of side-by-side edge-on accretion disks lying at the origin of the twin mid-infrared jets. Assuming coevality of the components of the young multiple system under investigation, the system age is at least (2 $-$ 2.5) $\times$ 10$^6$ yr, despite the discrepantly younger age inferred from the spectral energy distribution of the combined edge-on disk sources. The later system evolutionary stage is corroborated by ALMA observations of CO(2$-$1), $^{13}$CO(2$-1$), and C$^{18}$O(2$-$1), which show no traces of molecular outflows or remnant cavity walls. Consequently, the observed H$_2$ structures must have their origins in wide-angled disk winds, in the absence of any ambient, swept-up gas. In the context of recent studies of protostars, we propose an outflow evolutionary scenario in which the molecular gas component dominates in the youngest sources, whereas the fast, ionized jets dominate in the oldest sources, as is the case for the twin jets discovered in the WL 20 system., Comment: 25 pages, 19 figures; Accepted for publication in ApJ

We analyse the regret arising from learning the price sensitivity parameter $\kappa$ of liquidity takers in the ergodic version of the Avellaneda-Stoikov market making model. We show that a learning algorithm based on a regularised maximum-likelihood estimator for the parameter achieves the regret upper bound of order $\ln^2 T$ in expectation. To obtain the result we need two key ingredients. The first are tight upper bounds on the derivative of the ergodic constant in the Hamilton-Jacobi-Bellman (HJB) equation with respect to $\kappa$. The second is the learning rate of the maximum-likelihood estimator which is obtained from concentration inequalities for Bernoulli signals. Numerical experiment confirms the convergence and the robustness of the proposed algorithm.

Fourier-transform infrared spectroscopy (FTIR) has matured into a versatile technique with relevance for environmental monitoring, pharmaceutical research, and food safety applications. However, compared to other spectroscopic methods, it experiences slower progress in terms of power optimization, miniaturization, and adoption by industry. To overcome this limitation, we developed an ultra-broadband room-temperature FTIR instrument relying on commercially available components that offers a spectral coverage from 1.6 $\mu$m to 31 $\mu$m (9.7-190 THz) without changing optics at a single-Watt-level of electrical power consumption. To demonstrate the capabilities of the instrument, we measured atmospheric species in multiple spectral regions with better than 1.5 cm$^{-1}$ resolution., Comment: 15 pages, 10 figures, 2 tables

As software systems increase in complexity, conventional monitoring methods struggle to provide a comprehensive overview or identify performance issues, often missing unexpected problems. Observability, however, offers a holistic approach, providing methods and tools that gather and analyze detailed telemetry data to uncover hidden issues. Originally developed for cloud-native systems, modern observability is less prevalent in scientific computing, particularly in HPC clusters, due to differences in application architecture, execution environments, and technology stacks. This paper proposes and evaluates an end-to-end observability solution tailored for scientific computing in HPC environments. We address several challenges, including collection of application-level metrics, instrumentation, context propagation, and tracing. We argue that typical dashboards with charts are not sufficient for advanced observability-driven analysis of scientific applications. Consequently, we propose a different approach based on data analysis using DataFrames and a Jupyter environment. The proposed solution is implemented and evaluated on two medical scientific pipelines running on an HPC cluster.

Large language models (LLMs) have revolutionized language processing, delivering outstanding results across multiple applications. However, deploying LLMs on edge devices poses several challenges with respect to memory, energy, and compute costs, limiting their widespread use in devices such as mobile phones. A promising solution is to reduce the number of bits used to represent weights and activations. While existing works have found partial success at quantizing LLMs to lower bitwidths, e.g. 4-bit weights, quantizing activations beyond 16 bits often leads to large computational overheads due to poor on-device quantization support, or a considerable accuracy drop. Yet, 8-bit activations are very attractive for on-device deployment as they would enable LLMs to fully exploit mobile-friendly hardware, e.g. Neural Processing Units (NPUs). In this work, we make a first attempt to facilitate the on-device deployment of LLMs using integer-only quantization. We first investigate the limitations of existing quantization methods for on-device deployment, with a special focus on activation quantization. We then address these limitations by introducing a simple post-training quantization method, named MobileQuant, that extends previous weight equivalent transformation works by jointly optimizing the weight transformation and activation range parameters in an end-to-end manner. MobileQuant demonstrates superior capabilities over existing methods by 1) achieving near-lossless quantization on a wide range of LLM benchmarks, 2) reducing latency and energy consumption by 20\%-50\% compared to current on-device quantization strategies, 3) requiring limited compute budget, 4) being compatible with mobile-friendly compute units, e.g. NPU., Comment: Code and models available: https://github.com/saic-fi/MobileQuant

Magnetic 2D materials enable novel tuning options of magnetism. As an example, the van der Waals material FePS3, a zigzag-type intralayer antiferromagnet, exhibits very strong magnetoelastic coupling due to the different bond lengths along different ferromagnetic and antiferromagnetic coupling directions enabling elastic tuning of magnetic properties. The likely cause of the length change is the intricate competition between direct exchange of the Fe atoms and superexchange via the S and P atoms. To elucidate this interplay, we study the band structure of exfoliated FePS3 by mu m scale ARPES (Angular Resolved Photoelectron Spectroscopy), both, above and, for the first time, below the Neel temperature TN. We find three characteristic changes across TN. They involve S 3p-type bands, Fe 3d-type bands and P 3p-type bands, respectively, as attributed by comparison with density functional theory calculations (DFT+U). This highlights the involvement of all the atoms in the magnetic phase transition providing independent evidence for the intricate exchange paths.

A given self-map $f\colon M\to M$ of a compact manifold determines the sequence $\{L(f^n)\}_{n=1}^\infty$, of the Lefschetz numbers of its iterations. We consider its dual sequence $\{a_n(f)\}_{n=1}^\infty$ given by the M\"obius inversion formula. The set ${\mathcal AP}(f)=\{ n\in \mathbb N\ \colon\ a_n(f)\neq 0\}$ is called the set of algebraic periods. We solve an open problem existing in literature by showing that for every finite subset ${\mathcal A}$ of natural numbers there exist an orientable surface $S_{\rm g}$, as well as a non-orientable surface $N_{\rm g}$, of genus ${\rm g}$, and a Morse$\unicode{x2013}$Smale diffeomorphism $f$ of this surface such that $\mathcal{AP}(f)=\mathcal{A}$. For such a map it implies the existence of points of a minimal period $n$ for each odd $n \in \mathcal{A}$. For the orientation-reversing Morse$\unicode{x2013}$Smale diffeomorphisms of $S_{\rm g}$ we identify strong restrictions on ${\mathcal AP}(f)$. Our method also provides an estimate of the number of homotopy classes of Morse$\unicode{x2013}$Smale diffeomorphisms, which is exponential in ${\rm g}$.

Quantum Convolutional Neural Networks (QCNNs) are widely regarded as a promising model for Quantum Machine Learning (QML). In this work we tie their heuristic success to two facts. First, that when randomly initialized, they can only operate on the information encoded in low-bodyness measurements of their input states. And second, that they are commonly benchmarked on "locally-easy'' datasets whose states are precisely classifiable by the information encoded in these low-bodyness observables subspace. We further show that the QCNN's action on this subspace can be efficiently classically simulated by a classical algorithm equipped with Pauli shadows on the dataset. Indeed, we present a shadow-based simulation of QCNNs on up-to $1024$ qubits for phases of matter classification. Our results can then be understood as highlighting a deeper symptom of QML: Models could only be showing heuristic success because they are benchmarked on simple problems, for which their action can be classically simulated. This insight points to the fact that non-trivial datasets are a truly necessary ingredient for moving forward with QML. To finish, we discuss how our results can be extrapolated to classically simulate other architectures., Comment: 11 + 13 pages , 6 + 3 figures, 1 table

The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these quantities using tools from statistical mechanics or via quantum information-based inequalities. By focusing on the second moment of one-dimensional unitary circuits where nearest neighboring gates act on sets of qudits (with open and closed boundary conditions), we show that one can exactly compute the associated spectral gaps. Indeed, having access to their functional form allows us to prove several important results, such as the fact that the spectral gap for closed boundary condition is exactly the square of the gap for open boundaries, as well as improve on previously known bounds for approximate design convergence. Finally, we verify our theoretical results by numerically computing the spectral gap for systems of up to 70 qubits, as well as comparing them to gaps of random orthogonal and symplectic circuits., Comment: 9 + 6 pages, 3 figures

In this work, we present a GPU-accelerated library for the underlying components of Kolmogorov-Arnold Networks (KANs), along with an algorithm to eliminate bounded grids in KANs. The GPU-accelerated library reduces the computational complexity of Basis Spline (B-spline) evaluation by a factor of $\mathcal{O}$(grid size) compared to existing codes, enabling batch computation for large-scale learning. To overcome the limitations of traditional KANs, we introduce Unbounded KANs (UKANs), which eliminate the need for a bounded grid and a fixed number of B-spline coefficients. To do so, we replace the KAN parameters (B-spline coefficients) with a coefficient generator (CG) model. The inputs to the CG model are designed based on the idea of an infinite symmetric grid extending from negative infinity to positive infinity. The positional encoding of grid group, a sequential collection of B-spline grid indexes, is fed into the CG model, and coefficients are consumed by the efficient implementation (matrix representations) of B-spline functions to generate outputs. We perform several experiments on regression, classification, and generative tasks, which are promising. In particular, UKAN does not require data normalization or a bounded domain for evaluation. Additionally, our benchmarking results indicate the superior memory and computational efficiency of our library compared to existing codes., Comment: 10 pages, 7 figures, 5 tables

Self-supervision has the potential to transform reinforcement learning (RL), paralleling the breakthroughs it has enabled in other areas of machine learning. While self-supervised learning in other domains aims to find patterns in a fixed dataset, self-supervised goal-conditioned reinforcement learning (GCRL) agents discover new behaviors by learning from the goals achieved during unstructured interaction with the environment. However, these methods have failed to see similar success, both due to a lack of data from slow environments as well as a lack of stable algorithms. We take a step toward addressing both of these issues by releasing a high-performance codebase and benchmark JaxGCRL for self-supervised GCRL, enabling researchers to train agents for millions of environment steps in minutes on a single GPU. The key to this performance is a combination of GPU-accelerated environments and a stable, batched version of the contrastive reinforcement learning algorithm, based on an infoNCE objective, that effectively makes use of this increased data throughput. With this approach, we provide a foundation for future research in self-supervised GCRL, enabling researchers to quickly iterate on new ideas and evaluate them in a diverse set of challenging environments. Website + Code: https://github.com/MichalBortkiewicz/JaxGCRL

We improve the lower bound for $V(T)$, the number of sign changes of the error term $\psi(x)-x$ in the Prime Number Theorem in the interval $[1,T]$ for large $T$. We show that \[ \liminf_{T\to\infty}\frac{V(T)}{\log T}\geq\frac{\gamma_{0}}{\pi}+\frac{1}{60} \] where $\gamma_{0}=14.13\ldots$ is the imaginary part of the lowest-lying non-trivial zero of the Riemann zeta-function. The result is based on a new density estimate for zeros of the associated $k$-function, over $4\cdot10^{21}$ times better than previously known estimates of this type.

We present the Learned Ranking Function (LRF), a system that takes short-term user-item behavior predictions as input and outputs a slate of recommendations that directly optimizes for long-term user satisfaction. Most previous work is based on optimizing the hyperparameters of a heuristic function. We propose to model the problem directly as a slate optimization problem with the objective of maximizing long-term user satisfaction. We also develop a novel constraint optimization algorithm that stabilizes objective trade-offs for multi-objective optimization. We evaluate our approach with live experiments and describe its deployment on YouTube., Comment: RecSys 24

We present ultraviolet, optical and near-infrared photometric and optical spectroscopic observations of the luminous, fast blue optical transient (LFBOT), CSS161010:045834-081803 (CSS161010). The transient was found in a low-redshift (z=0.033) dwarf galaxy. The light curves of CSS161010 are characterized by an extremely fast evolution and blue colours. The V-band light curve shows that CSS161010 reaches an absolute peak of M$_{V}^{max}=-20.66\pm0.06$ mag in 3.8 days from the start of the outburst. After maximum, CSS161010 follows a power-law decline $\propto t^{-2.8\pm0.1}$ at all optical bands. These photometric properties are comparable to those of well-observed LFBOTs such as AT 2018cow, AT 2020mrf and AT 2020xnd. However, unlike these objects, the spectra of CSS161010 show a remarkable transformation from a blue and featureless continuum to spectra dominated by very broad, entirely blueshifted hydrogen emission lines of velocities of up to 10% of the speed of light. The persistent blueshifted emission and the lack of any emission at the rest wavelength of CSS161010 are unique features not seen in any transient before CSS161010. The combined observational properties of CSS161010 and its dwarf galaxy host favour the tidal disruption of a star by an intermediate-mass black hole as its origin., Comment: 29 pages (including the appendix); 8 figures in the main text, 4 figures and 8 tables in the appendix. Submitted to ApJ

A leading approach to algorithm design aims to minimize the number of operations in an algorithm's compilation. One intuitively expects that reducing the number of operations may decrease the chance of errors. This paradigm is particularly prevalent in quantum computing, where gates are hard to implement and noise rapidly decreases a quantum computer's potential to outperform classical computers. Here, we find that minimizing the number of operations in a quantum algorithm can be counterproductive, leading to a noise sensitivity that induces errors when running the algorithm in non-ideal conditions. To show this, we develop a framework to characterize the resilience of an algorithm to perturbative noises (including coherent errors, dephasing, and depolarizing noise). Some compilations of an algorithm can be resilient against certain noise sources while being unstable against other noises. We condense these results into a tradeoff relation between an algorithm's number of operations and its noise resilience. We also show how this framework can be leveraged to identify compilations of an algorithm that are better suited to withstand certain noises.

Organic nonlinear optical (NLO) crystals have emerged as efficient room-temperature emitters of broadband THz radiation with high electric field strengths. Although initially confined to high-pulse-energy excitation in the millijoule range with kHz rates, recent efforts have focused on tailoring the physical properties of organic NLO materials for compatibility with popular MHz-rate telecommunication wavelength lasers emitting nanojoule energy pulses. This is motivated by the large potential of such crystals for more portable and user-safe spectroscopic systems, additionally complemented by their room-temperature field-sensitive THz detection capabilities. In this work, we demonstrate the MHz-rate operation of the organic crystal PNPA ((E)-4-((4-nitrobenzylidene)amino)-$N$-phenylaniline), which was recently discovered through data mining algorithms and reported to surpass the conversion efficiency of rivaling NLO crystals at 1 kHz repetition rate. Using a compact 200 mW Er:fiber laser producing 18 fs pulses at 50 MHz repetition rate, we demonstrate the THz field generation and detection capabilities of PNPA via performing gas phase spectroscopy in the 1.3-8.5 THz range. We obtain a dynamic range of 40 dB over 3.6 s and 70 dB over 2 hours. Our work extends the family of organic crystals compatible with telecommunication-wavelength excitation using nJ pulses for spectroscopy beyond 5 THz., Comment: 9 pages, 8 figures

The Reggeized pion is expected to provide the main contribution to the forward cross section in light meson photoproduction reactions with charge exchange at high energies. We discuss the Reggeization of pion exchange in charged pion photoproduction with an emphasis on consistency with current conservation. We show that the gauge-invariant amplitude for the exchange of a particle with generic even spin $J\geq 2$ in the $t$-channel is analytic at $J=0$, and that it can be interpreted in terms of the nucleon electric current. This enables us to reconcile the dynamics in the $s$- and $u$-channel, which involves also nucleon exchanges, with the amplitude expressed in terms of $t$-channel partial waves, as required by Regge theory., Comment: 16 pages, 4 figures

We show how hidden interesting subelections can be discovered in ordinal elections. An interesting subelection consists of a reasonably large set of voters and a reasonably large set of candidates such that the former have a consistent opinion about the latter. Consistency may take various forms but we focus on three: Identity (all selected voters rank all selected candidates the same way), antagonism (half of the selected voters rank candidates in some order and the other half in the reverse order), and clones (all selected voters rank all selected candidates contiguously in the original election). We first study the computation of such hidden subelections. Second, we analyze synthetic and real-life data, and find that identifying hidden consistent subelections allows us to uncover some relevant concepts., Comment: Accepted for publication at AAMAS 2024

We study strategic behavior of project proposers in the context of approval-based participatory budgeting (PB). In our model we assume that the votes are fixed and known and the proposers want to set as high project prices as possible, provided that their projects get selected and the prices are not below the minimum costs of their delivery. We study the existence of pure Nash equilibria (NE) in such games, focusing on the AV/Cost, Phragm\'en, and Method of Equal Shares rules. Furthermore, we report an experimental study of strategic cost selection on real-life PB election data., Comment: 31 pages

Unusual magnetic properties of Van der Waals type antiferromagnetic semiconductors make them highly attractive for spintronics and optoelectronics. A link between the magnetic and optical properties of those materials, required for practical applications, has not been, however, established so far. Here, we report on a combined experimental and theoretical study of magnetic, optical, and structural properties of bulk CrPS$_{4}$ samples. We find that the magnetic-field-dependent circular polarization degree of the photoluminescence is a direct measure of the net magnetization of CrPS$_{4}$. Complementary, Raman scattering measured as a function of magnetic field and temperature enables the determination of the magnetic susceptibility curve of the material. Our experimental results are backed by Our experimental results are supported by density functional theory calculations that take as input the lattice parameters determined from temperature-dependent X-ray diffraction measurements. This allows us to explain the impact of spin ordering on the spectral position of Raman transitions in CrPS$_4$, as well as anomalous temperature shifts of selected of them. The presented method for all-optical determination of the magnetic properties is highly promising for studies of spin ordering and magnetic phase transitions in single- or a few-layer samples of magnetic layered materials, for which a poor signal-to-noise ratio precludes any reliable neutron scattering or magnetometry measurements.

In the development of operational semantics of concurrent systems, a key decision concerns the adoption of a suitable notion of execution model, which basically amounts to choosing a class of partial orders according to which events are arranged along the execution line. Typical kinds of such partial orders are the total, stratified and interval orders. In this paper, we introduce quasi-stratified orders - positioned in-between the stratified and interval orders - which are tailored for transaction-like or hierarchical concurrent executions. Dealing directly with the vast number of executions of concurrent system is far from being practical. It was realised long time ago that it can be much more effective to consider behaviours at a more abstract level of behavioural specifications (often based on intrinsic relationships between events such as those represented by causal partial orders), each such specification - typically, a relational structure - encompassing a (large) number of executions. In this paper, we introduce and investigate suitable specifications for behaviours represented by quasi-stratified orders. The proposed model of quasi-stratified relational structures is based on two relationships between events - the 'before' and 'not later' relationships - which can be used to express and analyse causality, independence, and simultaneity between events., Comment: 18 pages, 6 figures

In the pursuit of understanding the population of stellar remnants within the Milky Way, we analyze the sample of $\sim 950$ microlensing events observed by the Spitzer Space Telescope between 2014 and 2019. In this study we focus on a sub-sample of nine microlensing events, selected based on their long timescales, small microlensing parallaxes and joint observations by the Gaia mission, to increase the probability that the chosen lenses are massive and the mass is measurable. Among the selected events we identify lensing black holes and neutron star candidates, with potential confirmation through forthcoming release of the Gaia time-series astrometry in 2026. Utilizing Bayesian analysis and Galactic models, along with the Gaia Data Release 3 proper motion data, four good candidates for dark remnants were identified: OGLE-2016-BLG-0293, OGLE-2018-BLG-0483, OGLE-2018-BLG-0662, and OGLE-2015-BLG-0149, with lens masses of $2.98^{+1.75}_{-1.28}~M_{\odot}$, $4.65^{+3.12}_{-2.08}~M_{\odot}$, $3.15^{+0.66}_{-0.64}~M_{\odot}$ and $1.4^{+0.75}_{-0.55}~M_{\odot}$, respectively. Notably, the first two candidates are expected to exhibit astrometric microlensing signals detectable by Gaia, offering the prospect of validating the lens masses. The methodologies developed in this work will be applied to the full Spitzer microlensing sample, populating and analyzing the time-scale ($t_{\rm E}$) vs. parallax ($\pi_{\rm E}$) diagram to derive constraints on the population of lenses in general and massive remnants in particular., Comment: submitted to ApJ