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We propose a new encoding of the first-order connection method as a Boolean satisfiability problem. The encoding eschews tree-like presentations of the connection method in favour of matrices, as we show that tree-like calculi have a number of drawbacks in the context of satisfiability solving. The matrix setting permits numerous global refinements of the basic connection calculus. We also show that a suitably-refined calculus is a decision procedure for the Bernays-Sch\"onfinkel class.

Generative modelling aims to accelerate the discovery of novel chemicals by directly proposing structures with desirable properties. Recently, score-based, or diffusion, generative models have significantly outperformed previous approaches. Key to their success is the close relationship between the score and physical force, allowing the use of powerful equivariant neural networks. However, the behaviour of the learnt score is not yet well understood. Here, we analyse the score by training an energy-based diffusion model for molecular generation. We find that during the generation the score resembles a restorative potential initially and a quantum-mechanical force at the end. In between the two endpoints, it exhibits special properties that enable the building of large molecules. Using insights from the trained model, we present Similarity-based Molecular Generation (SiMGen), a new method for zero shot molecular generation. SiMGen combines a time-dependent similarity kernel with descriptors from a pretrained machine learning force field to generate molecules without any further training. Our approach allows full control over the molecular shape through point cloud priors and supports conditional generation. We also release an interactive web tool that allows users to generate structures with SiMGen online (https://zndraw.icp.uni-stuttgart.de).

In this paper we develop a Neumann-Neumann type domain decomposition method for elliptic problems on metric graphs. We describe the iteration in the continuous and discrete setting and rewrite the latter as a preconditioner for the Schur complement system. Then we formulate the discrete iteration as an abstract additive Schwarz iteration and prove that it convergences to the finite element solution with a rate that is independent of the finite element mesh size. We show that the condition number of the Schur complement is also independent of the finite element mesh size. We provide an implementation and test it on various examples of interest and compare it to other preconditioners.

Subsumption resolution is an expensive but highly effective simplifying inference for first-order saturation theorem provers. We present a new SAT-based reasoning technique for subsumption resolution, without requiring radical changes to the underlying saturation algorithm. We implemented our work in the theorem prover Vampire, and show that it is noticeably faster than the state of the art.

K-fold cross-validation is a widely used tool for assessing classifier performance. The reproducibility crisis faced by artificial intelligence partly results from the irreproducibility of reported k-fold cross-validation-based performance scores. Recently, we introduced numerical techniques to test the consistency of claimed performance scores and experimental setups. In a crucial use case, the method relies on the combinatorial enumeration of all k-fold configurations, for which we proposed an algorithm in the binary classification case.

We give an example of automated geometry reasoning for an imaginary classroom project by using the free software package GeoGebra Discovery. The project is motivated by a publicly available toy, a rocking camel, installed at a medical center in Upper Austria. We explain how the process of a false conjecture, experimenting, modeling, a precise mathematical setup, and then a proof by automated reasoning could help extend mathematical knowledge at secondary school level and above., Comment: In Proceedings ADG 2023, arXiv:2401.10725

We address, through the automated reasoning tools in GeoGebra Discovery, a problem from a regional phase of the Austrian Mathematics Olympiad 2023. Trying to solve this problem gives rise to four different kind of feedback: the almost instantaneous, automated solution of the proposed problem; the measure of its complexity, according to some recent proposals; the automated discovery of a generalization of the given assertion, showing that the same statement is true over more general polygons than those mentioned in the problem; and the difficulties associated to the analysis of the surprising and involved high number of degenerate cases that appear when using the LocusEquation command in this problem. In our communication we will describe and reflect on these diverse issues, enhancing its exemplar role for showing some of the advantages, problems, and current fields of development of GeoGebra Discovery., Comment: In Proceedings ADG 2023, arXiv:2401.10725

In our contribution we describe some on-going improvements concerning the Automated Reasoning Tools developed in GeoGebra Discovery, providing different examples of the performance of these new features. We describe the new ShowProof command, that outputs both the sequence of the different steps performed by GeoGebra Discovery to confirm a certain statement, as well as a number intending to grade the difficulty or interest of the assertion. The proposal of this assessment measure, involving the comparison of the expression of the thesis (or conclusion) as a combination of the hypotheses, will be developed., Comment: In Proceedings ADG 2023, arXiv:2401.10725

We consider a so-called quantum graph with standard continuity and Kirchhoff vertex conditions where the Kirchhoff vertex condition is perturbed by Gaussian noise. We show that the quantum graph setting is very different from the classical one dimensional boundary noise setting, where the transition semigroup is known to be strong Feller, by giving examples and counterexamples to the strong Feller property. In particular, when the graph is a tree, and there is noise present in all but one of the terminal vertices, then the transition semigroup associated with the problem is strong Feller at any time $T>0$. This turns out to be also a necessary condition for equilateral star graphs. We also comment on the existence and uniqueness of the invariant measure and the regularity of the solution., Comment: The proof of Theorem 4.4 was not correct. We substantially revised the manuscript and extended our original results to hold in an even more general setting on metric trees

The well known JGEX program became open source a few years ago, but seemingly, further development of the program can only be done without the original authors. In our project, we are looking at whether it is possible to continue such a large project as a newcomer without the involvement of the original authors. Is there a way to internationalize, fix bugs, improve the code base, add new features? In other words, to save a relic found in the attic and polish it into a useful everyday tool., Comment: In Proceedings ADG 2023, arXiv:2401.10725

We give an insight into Java Geometry Expert (JGEX) in use in a school context, focusing on the Austrian school system. JGEX can offer great support in some classroom situations, especially for solving mathematical competition tasks. Also, we discuss some limitations of the program., Comment: In Proceedings ADG 2023, arXiv:2401.10725

In this article, we solve some of the geometry problems of the N\'aboj 2023 competition with the help of a computer, using examples that the software tool GeoGebra Discovery can calculate. In each case, the calculation requires symbolic computations. We analyze the difficulty of feeding the problem into the machine and set further goals to make the problems of this type of contests even more tractable in the future., Comment: In Proceedings ADG 2023, arXiv:2401.10725

ADG is a forum to exchange ideas and views, to present research results and progress, and to demonstrate software tools at the intersection between geometry and automated deduction. The conference is held every two years. The previous editions of ADG were held in Hagenberg in 2021 (online, postponed from 2020 due to COVID-19), Nanning in 2018, Strasbourg in 2016, Coimbra in 2014, Edinburgh in 2012, Munich in 2010, Shanghai in 2008, Pontevedra in 2006, Gainesville in 2004, Hagenberg in 2002, Zurich in 2000, Beijing in 1998, and Toulouse in 1996. The 14th edition, ADG 2023, was held in Belgrade, Serbia, in September 20-22, 2023. This edition of ADG had an additional special focus topic, Deduction in Education. Invited Speakers: Julien Narboux, University of Strasbourg, France "Formalisation, arithmetization and automatisation of geometry"; Filip Mari\'c, University of Belgrade, Serbia, "Automatization, formalization and visualization of hyperbolic geometry"; Zlatan Magajna, University of Ljubljana, Slovenia, "Workshop OK Geometry"

We study the effect of isospin-symmetry breaking in the framework of the extended Linear Sigma Model (eLSM) in vacuum. In this model, several particles mix with each other at tree level, due to the three non-zero scalar condensates (non-strange, strange, isospin). We resolve these mixings with the help of various field transformations. We compute all possible meson mixings and decay widths at tree level and perform a $\chi^2$ fit to PDG data. A very good fit is found if we exclude the (very small $\sim 130$~keV) $\omega\to \pi\pi$ decay. We also investigate the violation of Dashen's theorem., Comment: 32 pages, 1 figure

We present the full Hubble diagram of photometrically-classified Type Ia supernovae (SNe Ia) from the Dark Energy Survey supernova program (DES-SN). DES-SN discovered more than 20,000 SN candidates and obtained spectroscopic redshifts of 7,000 host galaxies. Based on the light-curve quality, we select 1635 photometrically-identified SNe Ia with spectroscopic redshift 0.10$< z <$1.13, which is the largest sample of supernovae from any single survey and increases the number of known $z>0.5$ supernovae by a factor of five. In a companion paper, we present cosmological results of the DES-SN sample combined with 194 spectroscopically-classified SNe Ia at low redshift as an anchor for cosmological fits. Here we present extensive modeling of this combined sample and validate the entire analysis pipeline used to derive distances. We show that the statistical and systematic uncertainties on cosmological parameters are $\sigma_{\Omega_M,{\rm stat+sys}}^{\Lambda{\rm CDM}}=$0.017 in a flat $\Lambda$CDM model, and $(\sigma_{\Omega_M},\sigma_w)_{\rm stat+sys}^{w{\rm CDM}}=$(0.082, 0.152) in a flat $w$CDM model. Combining the DES SN data with the highly complementary CMB measurements by Planck Collaboration (2020) reduces uncertainties on cosmological parameters by a factor of 4. In all cases, statistical uncertainties dominate over systematics. We show that uncertainties due to photometric classification make up less than 10% of the total systematic uncertainty budget. This result sets the stage for the next generation of SN cosmology surveys such as the Vera C. Rubin Observatory's Legacy Survey of Space and Time., Comment: 39 pages, 19 figures; Submitted to ApJ; companion paper Dark Energy Collaboration et al. on consecutive arxiv number 2401.02929

We present cosmological constraints from the sample of Type Ia supernovae (SN Ia) discovered during the full five years of the Dark Energy Survey (DES) Supernova Program. In contrast to most previous cosmological samples, in which SN are classified based on their spectra, we classify the DES SNe using a machine learning algorithm applied to their light curves in four photometric bands. Spectroscopic redshifts are acquired from a dedicated follow-up survey of the host galaxies. After accounting for the likelihood of each SN being a SN Ia, we find 1635 DES SNe in the redshift range $0.100.5$ SNe compared to the previous leading compilation of Pantheon+, and results in the tightest cosmological constraints achieved by any SN data set to date. To derive cosmological constraints we combine the DES supernova data with a high-quality external low-redshift sample consisting of 194 SNe Ia spanning $0.025

Machine-learned force fields have transformed the atomistic modelling of materials by enabling simulations of ab initio quality on unprecedented time and length scales. However, they are currently limited by: (i) the significant computational and human effort that must go into development and validation of potentials for each particular system of interest; and (ii) a general lack of transferability from one chemical system to the next. Here, using the state-of-the-art MACE architecture we introduce a single general-purpose ML model, trained on a public database of 150k inorganic crystals, that is capable of running stable molecular dynamics on molecules and materials. We demonstrate the power of the MACE-MP-0 model - and its qualitative and at times quantitative accuracy - on a diverse set problems in the physical sciences, including the properties of solids, liquids, gases, chemical reactions, interfaces and even the dynamics of a small protein. The model can be applied out of the box and as a starting or "foundation model" for any atomistic system of interest and is thus a step towards democratising the revolution of ML force fields by lowering the barriers to entry., Comment: 119 pages, 63 figures, 37MB PDF

Recent findings show that single, non-neuronal cells are also able to learn signalling responses developing cellular memory. In cellular learning nodes of signalling networks strengthen their interactions e.g. by the conformational memory of intrinsically disordered proteins, protein translocation, miRNAs, lncRNAs, chromatin memory and signalling cascades. This can be described by a generalized, unicellular Hebbian learning process, where those signalling connections, which participate in learning, become stronger. Here we review those scenarios, where cellular signalling is not only repeated in a few times (when learning occurs), but becomes too frequent, too large, or too complex and overloads the cell. This leads to desensitisation of signalling networks by decoupling signalling components, receptor internalization, and consequent downregulation. These molecular processes are examples of anti-Hebbian learning and forgetting of signalling networks. Stress can be perceived as signalling overload inducing the desensitisation of signalling pathways. Aging occurs by the summative effects of cumulative stress downregulating signalling. We propose that cellular learning desensitisation, stress and aging may be placed along the same axis of more and more intensive (prolonged or repeated) signalling. We discuss how cells might discriminate between repeated and unexpected signals, and highlight the Hebbian and anti-Hebbian mechanisms behind the fold-change detection in the NF-\k{appa}B signalling pathway. We list drug design methods using Hebbian learning (such as chemically-induced proximity) and clinical treatment modalities inducing (cancer, drug allergies) desensitisation or avoiding drug-induced desensitisation. A better discrimination between cellular learning, desensitisation and stress may open novel directions in drug design, e.g., helping to overcome drug-resistance., Comment: 19 pages, 4 figures

Classical empirical force fields have dominated biomolecular simulation for over 50 years. Although widely used in drug discovery, crystal structure prediction, and biomolecular dynamics, they generally lack the accuracy and transferability required for predictive modelling. In this paper, we introduce MACE-OFF23, a transferable force field for organic molecules created using state-of-the-art machine learning technology and first-principles reference data computed with a high level of quantum mechanical theory. MACE-OFF23 demonstrates the remarkable capabilities of local, short-range models by accurately predicting a wide variety of gas and condensed phase properties of molecular systems. It produces accurate, easy-to-converge dihedral torsion scans of unseen molecules, as well as reliable descriptions of molecular crystals and liquids, including quantum nuclear effects. We further demonstrate the capabilities of MACE-OFF23 by determining free energy surfaces in explicit solvent, as well as the folding dynamics of peptides. Finally, we simulate a fully solvated small protein, observing accurate secondary structure and vibrational spectrum. These developments enable first-principles simulations of molecular systems for the broader chemistry community at high accuracy and low computational cost.

Decision tree and random forest classification and regression are some of the most widely used in machine learning approaches. Binary decision tree implementations commonly use conditioning in the form 'feature $\leq$ (or $<$) threshold', with the threshold being the midpoint between two observed feature values. In this paper, we investigate the bias introduced by the choice of conditioning operator (an intrinsic property of implementations) in the presence of features with lattice characteristics. We propose techniques to eliminate this bias, requiring an additional prediction with decision trees and incurring no cost for random forests. Using 20 classification and 20 regression datasets, we demonstrate that the bias can lead to statistically significant differences in terms of AUC and $r^2$ scores. The proposed techniques successfully mitigate the bias, compared to the worst-case scenario, statistically significant improvements of up to 0.1-0.2 percentage points of AUC and $r^2$ scores were achieved and the improvement of 1.5 percentage points of $r^2$ score was measured in the most sensitive case of random forest regression. The implementation of the study is available on GitHub at the following repository: \url{https://github.com/gykovacs/conditioning_bias}.

The layered van der Waals material ZrTe$_5$ is known as a candidate topological insulator (TI), however its topological phase and the relation with other properties such as an apparent Dirac semimetallic state is still a subject of debate. We employ a semiclassical multicarrier transport (MCT) model to analyze the magnetotransport of ZrTe$_5$ nanodevices at hydrostatic pressures up to 2 GPa. The temperature dependence of the MCT results between 10 and 300 K is assessed in the context of thermal activation, and we obtain the positions of conduction and valence band edges in the vicinity of the chemical potential. We find evidence of the closing and re-opening of the band gap with increasing pressure, which is consistent with a phase transition from weak to strong TI. This matches expectations from ab initio band structure calculations, as well as previous observations that CVT-grown ZrTe$_5$ is a weak TI in ambient conditions., Comment: Main Text: 11 pages, 5 figures; Supporting Information: 13 pages, 9 figures

The PHENIX experiment has performed a systematic study of identified charged-hadron ($\pi^\pm$, $K^\pm$, $p$, $\bar{p}$) production at midrapidity in $p$$+$Al, $^3$He$+$Au, Cu$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV and U$+$U collisions at $\sqrt{s_{_{NN}}}=193$ GeV. Identified charged-hadron invariant transverse-momentum ($p_T$) and transverse-mass ($m_T$) spectra are presented and interpreted in terms of radially expanding thermalized systems. The particle ratios of $K/\pi$ and $p/\pi$ have been measured in different centrality ranges of large (Cu$+$Au, U$+$U) and small ($p$$+$Al, $^3$He$+$Au) collision systems. The values of $K/\pi$ ratios measured in all considered collision systems were found to be consistent with those measured in $p$$+$$p$ collisions. However the values of $p/\pi$ ratios measured in large collision systems reach the values of $\approx0.6$, which is $\approx2$ times larger than in $p$$+$$p$ collisions. These results can be qualitatively understood in terms of the baryon enhancement expected from hadronization by recombination. Identified charged-hadron nuclear-modification factors ($R_{AB}$) are also presented. Enhancement of proton $R_{AB}$ values over meson $R_{AB}$ values was observed in central $^3$He$+$Au, Cu$+$Au, and U$+$U collisions. The proton $R_{AB}$ values measured in $p$$+$Al collision system were found to be consistent with $R_{AB}$ values of $\phi$, $\pi^\pm$, $K^\pm$, and $\pi^0$ mesons, which may indicate that the size of the system produced in $p$$+$Al collisions is too small for recombination to cause a noticeable increase in proton production., Comment: 480 authors from 78 institutions, 18 pages, 6 tables, 16 figures. v2 is version accepted for publication in Physical Review C. HEPdata tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.html

We solve the long-standing problem concerning the fate of the chiral $U(1)_A$ symmetry in QCD-like theories at high temperature in the chiral limit. We introduce a simple instanton based random matrix model that precisely reproduces the properties of the lowest part of the lattice overlap Dirac spectrum. We show that in the chiral limit the instanton gas splits into a free gas component with a density proportional to $m^{N_f}$ and a gas of instanton-antiinstanton molecules. While the latter do not influence the chiral properties, for any nonzero quark mass the free gas component produces a singular spectral peak at zero that dominates Banks-Casher type spectral sums. By calculating these we show that the difference of the pion and delta susceptibility vanishes only for three or more massless flavors, however, the chiral condensate is zero already for two massless flavors, Comment: 7 pages, 5 figures, Proceedings of the 40th International Symposium on Lattice Field Theory (LATTICE2023), July 31st - August 4th, 2023, Fermi National Accelerator Laboratory

The cross-correlation of cosmic voids with the lensing convergence ($\kappa$) map of the CMB fluctuations offers a powerful tool to refine our understanding of the dark sector in the consensus cosmological model. Our principal aim is to compare the lensing signature of our galaxy data set with simulations based on the concordance model and characterize the results with an $A_{\kappa}$ consistency parameter. In particular, our measurements contribute to the understanding of the "lensing-is-low" tension of the $\Lambda$CDM model. We selected luminous red galaxies from the WISE-Pan-STARSS data set, allowing an extended 14,200 deg$^2$ sky area, that offers a more precise measurement compared to previous studies. We created 2D and 3D void catalogs to cross-correlate their locations with the Planck lensing map and studied their average imprint signal using a stacking methodology. Applying the same procedure, we also generated a mock catalog from the WebSky simulation for comparison. The 2D void analysis revealed good agreement with the standard cosmological model with $A_{\kappa}\approx1.06 \pm 0.08$, i.e. $S/N=13.3$, showing a higher $S/N$ than previous studies using voids detected in the Dark Energy Survey data set. The 3D void analysis exhibited a lower $S/N$ and demonstrated worse agreement with our mock catalog than the 2D voids. These deviations might be attributed to limitations in the mock catalog, such as imperfections in the LRG selection, as well as a potential asymmetry between the North and South patches of the WISE-Pan-STARSS data set in terms of data quality. Overall, we present a significant detection of a CMB lensing signal associated with cosmic voids, largely consistent with the concordance model. Future analyses using even larger data sets also hold great promise of further sharpening these results, given their complementary nature to large-scale structure analyses., Comment: 10 pages, 6 figure, submitted to A&A

We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup stable spaces and symmetric pressure stabilized formulations. We extend the results from Burman and Fern\'andez [\textit{SIAM J. Numer. Anal.}, 47 (2009), pp. 409-439] and provide a unified theoretical analysis of backward difference formulae (BDF methods) of order 1 to 6. The main novelty of our approach lies in the use of Dahlquist's G-stability concept together with multiplier techniques introduced by Nevannlina-Odeh and recently by Akrivis et al. [\textit{SIAM J. Numer. Anal.}, 59 (2021), pp. 2449-2472] to derive optimal stability and error estimates for both the velocity and the pressure. When combined with a method dependent Ritz projection for the initial data, unconditional stability can be shown while for arbitrary interpolation, pressure stability is subordinate to the fulfillment of a mild inverse CFL-type condition between space and time discretizations., Comment: 28 pages, 3 figures

We present methods to constrain fermionic condensates on the level of the path integral, which grant access to the quantum effective potential in the infinite volume limit. In the case of a spontaneously broken symmetry, this potential possesses a manifestly flat region, which is inaccessible to the standard approach on the lattice. However, by constraining the appropriate order parameters such as the chiral condensate, one is then able to probe the flat region. We demonstrate our method of constraining fermionic condensates in the 2-dimensional Gross-Neveu model, which exhibits a spontaneously broken chiral symmetry. We show how the potential flattens for increasing volume and that the flat region is dominated by inhomogeneous field configurations., Comment: 8 pages, 4 figures, contains ancillary files with plot data; talk given at the 40th International Symposium on Lattice Field theory (LATTICE 2023) at Fermilab; July 31 - August 4 2023

Popularity is an approach in mechanism design to find fair structures in a graph, based on the votes of the nodes. Popular matchings are the relaxation of stable matchings: given a graph G=(V,E) with strict preferences on the neighbors of the nodes, a matching M is popular if there is no other matching M' such that the number of nodes preferring M' is more than those preferring M. This paper considers the popularity testing problem, when the task is to decide whether a given matching is popular or not. Previous algorithms applied reductions to maximum weight matchings. We give a new algorithm for testing popularity by reducing the problem to maximum matching testing, thus attaining a linear running time O(|E|). Linear programming-based characterization of popularity is often applied for proving the popularity of a certain matching. As a consequence of our algorithm we derive a more structured dual witness than previous ones. Based on this result we give a combinatorial characterization of fractional popular matchings, which are a special class of popular matchings.

Finite volume effects are studied both with low-momentum cutoff and with momentum discretization in the framework of an (axial)vector meson extended quark-meson model with Polyakov-loop variables. In the momentum cutoff scenario, the CEP moves to lower temperatures and larger quark chemical potentials as the characteristic system size is reduced, however, the treatment of the vacuum term significantly affects its trajectory. The size dependence of the baryon fluctuations is also studied by the kurtosis and the skewness, both of which show moderate dependence on temperature and some dependence on quark chemical potential. The order of the phase transition is also studied near the chiral limit at finite system size and found to be second-order only at vanishing explicit breaking. The implementation of the finite size effect with momentum discretization is more complicated and shows peculiar behavior due to the different modes dropping below the Fermi surface and strong dependence on the type of the boundary condition chosen. We found that both the different boundary conditions and the treatment of the vacuum term cause significant changes in the trajectory of the CEP as the characteristic system size is changed., Comment: 20 pages, 24 figures

Cloud formations often obscure optical satellite-based monitoring of the Earth's surface, thus limiting Earth observation (EO) activities such as land cover mapping, ocean color analysis, and cropland monitoring. The integration of machine learning (ML) methods within the remote sensing domain has significantly improved performance on a wide range of EO tasks, including cloud detection and filtering, but there is still much room for improvement. A key bottleneck is that ML methods typically depend on large amounts of annotated data for training, which is often difficult to come by in EO contexts. This is especially true when it comes to cloud optical thickness (COT) estimation. A reliable estimation of COT enables more fine-grained and application-dependent control compared to using pre-specified cloud categories, as is commonly done in practice. To alleviate the COT data scarcity problem, in this work we propose a novel synthetic dataset for COT estimation, that we subsequently leverage for obtaining reliable and versatile cloud masks on real data. In our dataset, top-of-atmosphere radiances have been simulated for 12 of the spectral bands of the Multispectral Imagery (MSI) sensor onboard Sentinel-2 platforms. These data points have been simulated under consideration of different cloud types, COTs, and ground surface and atmospheric profiles. Extensive experimentation of training several ML models to predict COT from the measured reflectivity of the spectral bands demonstrates the usefulness of our proposed dataset. In particular, by thresholding COT estimates from our ML models, we show on two satellite image datasets (one that is publicly available, and one which we have collected and annotated) that reliable cloud masks can be obtained. The synthetic data, the collected real dataset, code and models have been made publicly available at https://github.com/aleksispi/ml-cloud-opt-thick., Comment: Published in the journal Remote Sensing (2024). Code, data and models available at https://github.com/aleksispi/ml-cloud-opt-thick

Up to now, it seemed that the additional frequencies in the fundamental mode (RRab) and in the overtone mode pulsating (RRc and RRd) RR Lyrae stars have different nature. RRab stars show frequencies associated with periodic doubling, as well as frequencies at the first and second radial overtones, and linear combinations of these. RRc stars show frequencies with specific ratios ($f_1/f_x\sim$0.61, or $\sim$0.63) which are explained by non-radial modes and frequencies with $f_x/f_1\sim0.68$ ratio which have no currently accepted explanation. To search for similarities in spectral content, we compared the Fourier spectra of the recently published TESS and K2 data of RRc stars with the spectra of Kepler RRab stars that do not show the Blazhko effect but contain additional frequencies. The time series data have been analysed using standard Fourier methods, and the possibility of the excitation of the second radial overtone mode in RRab stars has also been tested using numerical hydrodynamical codes. We show that the additional frequencies appear in non-Blazhko RRab stars at the position of the second radial overtone mode, and the pattern they create, is very similar to that caused by the additional frequencies with the period ratio $\sim0.68$ in RRc stars. The former explanation of the additional frequencies of these RRab stars by a second radial overtone is unlikely., Comment: 5 pages, 4 tables, 2 figures, accepted for publication in Astronomy & Astrophysics Letters

Addressing the reproducibility crisis in artificial intelligence through the validation of reported experimental results is a challenging task. It necessitates either the reimplementation of techniques or a meticulous assessment of papers for deviations from the scientific method and best statistical practices. To facilitate the validation of reported results, we have developed numerical techniques capable of identifying inconsistencies between reported performance scores and various experimental setups in machine learning problems, including binary/multiclass classification and regression. These consistency tests are integrated into the open-source package mlscorecheck, which also provides specific test bundles designed to detect systematically recurring flaws in various fields, such as retina image processing and synthetic minority oversampling.

We propose a new way of understanding how chiral symmetry is realized in the high temperature phase of QCD. Based on the finding that a simple free instanton gas precisely describes the details of the lowest part of the spectrum of the lattice overlap Dirac operator, we propose an instanton-based random matrix model of QCD with dynamical quarks. Simulations of this model reveal that even for small quark mass the Dirac spectral density has a singularity at the origin, caused by a dilute gas of free instantons. Even though the interaction, mediated by light dynamical quarks creates small instanton-antiinstanton molecules, those do not influence the singular part of the spectrum, and this singular part is shown to dominate Banks-Casher type sums in the chiral limit. By generalizing the Banks-Casher formula for the singular spectrum, we show that in the chiral limit the chiral condensate vanishes if there are at least two massless flavors. Our model also indicates a possible way of resolving a long-standing debate, as it suggests that for two massless quark flavors the $U(1)_{A}$ symmetry is likely to remain broken up to arbitrarily high finite temperatures., Comment: 6 pages, final published version

We consider the following question by Balister, Gy\H{o}ri and Schelp: given $2^{n-1}$ nonzero vectors in $\mathbb{F}_2^n$ with zero sum, is it always possible to partition the elements of $\mathbb{F}_2^n$ into pairs such that the difference between the two elements of the $i$-th pair is equal to the $i$-th given vector for every $i$? An analogous question in $\mathbb{F}_p$, which is a case of the so-called "seating couples" problem, has been resolved by Preissmann and Mischler in 2009. In this paper, we prove the conjecture in $\mathbb{F}_2^n$ in the case when the number of distinct values among the given difference vectors is at most $n-2\log n-1$, and also in the case when at least a fraction $\frac12+\varepsilon$ of the given vectors are equal (for all $\varepsilon>0$ and $n$ sufficiently large based on $\varepsilon$)., Comment: 19 pages

Binary classification is a fundamental task in machine learning, with applications spanning various scientific domains. Whether scientists are conducting fundamental research or refining practical applications, they typically assess and rank classification techniques based on performance metrics such as accuracy, sensitivity, and specificity. However, reported performance scores may not always serve as a reliable basis for research ranking. This can be attributed to undisclosed or unconventional practices related to cross-validation, typographical errors, and other factors. In a given experimental setup, with a specific number of positive and negative test items, most performance scores can assume specific, interrelated values. In this paper, we introduce numerical techniques to assess the consistency of reported performance scores and the assumed experimental setup. Importantly, the proposed approach does not rely on statistical inference but uses numerical methods to identify inconsistencies with certainty. Through three different applications related to medicine, we demonstrate how the proposed techniques can effectively detect inconsistencies, thereby safeguarding the integrity of research fields. To benefit the scientific community, we have made the consistency tests available in an open-source Python package.

The rapid advancements in Artificial Intelligence (AI), particularly in generative AI and foundational models (FMs), have ushered in transformative changes across various industries. Large language models (LLMs), a type of FM, have demonstrated their prowess in natural language processing tasks and content generation, revolutionizing how we interact with software products and services. This article explores the integration of FMs in the telecommunications industry, shedding light on the concept of AI native telco, where AI is seamlessly woven into the fabric of telecom products. It delves into the engineering considerations and unique challenges associated with implementing FMs into the software life cycle, emphasizing the need for AI native-first approaches. Despite the enormous potential of FMs, ethical, regulatory, and operational challenges require careful consideration, especially in mission-critical telecom contexts. As the telecom industry seeks to harness the power of AI, a comprehensive understanding of these challenges is vital to thrive in a fiercely competitive market., Comment: 5 pages, 1 figure

Context. Binary Cepheids play an important role in investigating the calibration of the classical Cepheid period-luminosity relationship. Therefore a thorough study of individual Cepheids belonging to binary systems is necessary. Aims. Our aim is to determine the orbit of the binary system V1344 Aql using newly observed and earlier published spectroscopic and photometric data. Methods. We collected new radial velocity observations using medium resolution (${R \approx 11000}$ and ${R \lessapprox 20000}$) spectrographs and we updated the pulsation period of the Cepheid based on available photometric observations using $O-C$ diagram. Separating the pulsational and orbital radial velocity variations for each observational season (year), we determined the orbital solution for the system using $\chi^2$ minimisation. Results. The updated pulsation period of the Cepheid estimated for the epoch of HJD 2458955.83 is 7.476826 days. We determined orbital elements for the first time in the literature. The orbital period of the system is about 34.6 years, with an eccentricity e = 0.22., Comment: accepted for publication in A&A

We study a natural complexity measure of Boolean functions known as the (exact) rational degree. For total functions $f$, it is conjectured that $\mathrm{rdeg}(f)$ is polynomially related to $\mathrm{deg}(f)$, where $\mathrm{deg}(f)$ is the Fourier degree. Towards this conjecture, we show that symmetric functions have rational degree at least $\mathrm{deg}(f)/2$ and monotone functions have rational degree at least $\sqrt{\mathrm{deg}(f)}$. We observe that both of these lower bounds are tight. In addition, we show that all read-once depth-$d$ Boolean formulae have rational degree at least $\Omega(\mathrm{deg}(f)^{1/d})$. Furthermore, we show that almost every Boolean function on $n$ variables has rational degree at least $n/2 - O(\sqrt{n})$. In contrast to total functions, we exhibit partial functions that witness unbounded separations between rational and approximate degree, in both directions. As a consequence, we show that for quantum computers, post-selection and bounded-error are incomparable resources in the black-box model., Comment: 17 pages, 3 figures