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Commit messages are crucial in software development, supporting maintenance tasks and communication among developers. While Large Language Models (LLMs) have advanced Commit Message Generation (CMG) using various software contexts, some contexts developers consider are often missed by CMG techniques and can't be easily retrieved or even retrieved at all by automated tools. To address this, we propose Commit Message Optimization (CMO), which enhances human-written messages by leveraging LLMs and search-based optimization. CMO starts with human-written messages and iteratively improves them by integrating key contexts and feedback from external evaluators. Our extensive evaluation shows CMO generates commit messages that are significantly more Rational, Comprehensive, and Expressive while outperforming state-of-the-art CMG methods and human messages 88.2%-95.4% of the time.

This is a critical discussion of theoretical and descriptive deficiencies of the recently used "flat Odderon" model., Comment: 5 pages

Considering quasisymmetric mappings between b-metric spaces we have found a new estimation for the ratio of diameters of two subsets which are images of two bounded subsets. This result generalizes the well-known Tukia-V\"{a}is\"{a}l\"{a} inequality. The condition under which the image of a b-metric space under quasisymmetry is also a b-metric space is established. Moreover, the latter question is investigated for additive metric spaces., Comment: 12 pages. arXiv admin note: text overlap with arXiv:2501.02834, arXiv:2412.20526, arXiv:2501.00393

In 1980 P. Tukia and J. V\"{a}is\"{a}l\"{a} in seminal paper [P. Tukia and J. V\"ais\"al\"a, Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn., Ser. A I, Math. 5, 97--114 (1980)] extended a concept of quasisymmetric mapping known from the theory of quasiconformal mappings to the case of general metric spaces. They also found an estimation for the ratio of diameters of two subsets which are images of two bounded subsets of a metric space under a quasisymmetric mapping. We improve this estimation for the case of ultrametric spaces. It was also shown that the image of an ultrametric space under an $\eta$-quasisymmetric mapping with $\eta(1)=1$ is again an ultrametric space. In the case of finite ultrametric spaces it is proved that such mappings are ball-preserving., Comment: 12 pages. arXiv admin note: text overlap with arXiv:2412.17421

Contemporary real-time RFI mitigation is carried out at different stages primarily using regulatory and technical approaches. Regulatory approaches include spectrum management, radio quiet zones, and ensuring protection from self-generated RFI. The technical approaches include mitigation RFI in the analog and RF frontend systems, digital signal processing systems, and offline systems. As is known, the signal received by a radio telescope is a combination of the contributions from the astronomical signal and a combination of system and sky background noise. RFI has an additive effect on the signal received by the radio telescope. The key distinguishing properties of RFI are that it is generally stronger than the signal and non-Gaussian. The capability of signal processing receiver systems has grown manifold with the advent of high-speed signal processing platforms like Field Programmable Gate Arrays (FPGA)and Graphics Processing Unit (GPU). This has enabled the development of different signal-processing techniques for real-time RFI mitigation algorithms. This document provides an overview of contemporary techniques while focusing on the implementation of the same in specific radio telescopes.

Large-scale pre-trained language models have demonstrated high performance on standard datasets for natural language inference (NLI) tasks. Unfortunately, these evaluations can be misleading, as although the models can perform well on in-distribution data, they perform poorly on out-of-distribution test sets, such as contrast sets. Contrast sets consist of perturbed instances of data that have very minor, but meaningful, changes to the input that alter the gold label, revealing how models can learn superficial patterns in the training data rather than learning more sophisticated language nuances. As an example, the ELECTRA-small language model achieves nearly 90% accuracy on an SNLI dataset but drops to 75% when tested on an out-of-distribution contrast set. The research carried out in this study explores how the robustness of a language model can be improved by exposing it to small amounts of more complex contrast sets during training to help it better learn language patterns. With this approach, the model recovers performance and achieves nearly 90% accuracy on contrast sets, highlighting the importance of diverse and challenging training data.

In the present paper, we prove generalizations of Banach, Kannan, Chatterjea, \'Ciri\'c-Reich-Rus fixed point theorems, as well as of the fixed point theorem for mappings contracting perimeters of triangles. We consider corresponding mappings in semimetric spaces with triangle functions introduced by M. Bessenyei and Z. P\'ales. Such an approach allows us to derive corollaries for various types of semimetric spaces including metric spaces, ultrametric spaces, b-metric spaces etc. The significance of these generalized theorems extends across multiple disciplines, including optimization, mathematical modeling, and computer science. They may serve to establish stability conditions, demonstrate the existence of optimal solutions, and improve algorithm design., Comment: 17 pages, This is the submitted version. The published version is available at https://doi.org/10.3389/fams.2024.1392560. arXiv admin note: substantial text overlap with arXiv:2501.00392

The problem of continuation of a partially defined metric can be efficiently studied using graph theory. Let $G=G(V,E)$ be an undirected graph with the set of vertices $V$ and the set of edges $E$. A necessary and sufficient condition under which the weight $w\colon E\to\mathbb R^+$ on the graph $G$ has a unique continuation to a metric $d\colon V\times V\to\mathbb R^+$ is found., Comment: 7 pages, This is the submitted version. The published version is available at https://doi.org/10.20429/tag.2022.100101

The class of quasisymmetric mappings on the real axis was first introduced by A. Beurling and L. V. Ahlfors in 1956. In 1980 P. Tukia and J. V\"{a}is\"{a}l\"{a} considered these mappings between general metric spaces. In our paper we generalize the concept of quasisymmetric mappings to the case of general semimetric spaces and study some properties of these mappings. In particular, conditions under which quasisymmetric mappings preserve triangle functions, Ptolemy's inequality and the relation ``to lie between'' are found. Considering quasisymmetric mappings between semimetric spaces with different triangle functions we have found a new estimation for the ratio of diameters of two subsets, which are images of two bounded subsets. This result generalizes the well-known Tukia-V\"{a}is\"{a}l\"{a} inequality. Moreover, we study connections between quasisymmetric mappings and weak similarities which are a special class of mappings between semimetric spaces., Comment: 28 pages, 1 figure

This paper advances a line of research in fixed point theory initiated by M. Bessenyei and Z. P\'ales, building on their introduction of the triangle function concept in [J. Nonlinear Convex Anal, Vol 18 (3), 515-524 (2017)]. By applying this concept, the study revises several well-known fixed point theorems in metric spaces, extending their applicability to semimetric spaces with triangle functions. The paper focuses on general theorems involving weak, partial, Bianchini and Chatterjea-Bianchini contractions, deriving corollaries relevant to metric spaces, $b$-metric spaces, ultrametric spaces, and distance spaces with power triangle functions. Notably, several new and interesting findings emerge in the context of weak and partial contractions., Comment: 19 pages

Many analyses of two-body non-leptonic decays of $D$-mesons rely on flavor SU(3) symmetry relations and fits of experimental data of decays rates to extract the universal transition amplitudes. Such fits assume that the final state mesons are well-defined asymptotic states of QCD. We develop a technique to take into account the finite width effects of the final state mesons and study their effects on the extracted values of transition amplitudes., Comment: 15 Pages, 3 figures

We investigate positivity and probabilistic properties arising from the Young-Fibonacci lattice $\mathbb{YF}$, a 1-differential poset on binary words composed of 1's and 2's (known as Fibonacci words). Building on Okada's theory of clone Schur functions (Trans. Amer. Math. Soc. 346 (1994), 549-568), we introduce clone coherent measures on $\mathbb{YF}$ which give rise to random Fibonacci words of increasing length. Unlike coherent systems associated to classical Schur functions on the Young lattice of integer partitions, clone coherent measures are generally not extremal on $\mathbb{YF}$. Our first main result is a complete characterization of Fibonacci positive specializations - parameter sequences which yield positive clone Schur functions on $\mathbb{YF}$. We connect Fibonacci positivity with total positivity of tridiagonal matrices, Stieltjes moment sequences, and orthogonal polynomials in one variable from the ($q$-)Askey scheme. Our second family of results concerns the asymptotic behavior of random Fibonacci words derived from various Fibonacci positive specializations. We analyze several limiting regimes for specific examples, revealing stick-breaking-like processes (connected to GEM distributions), dependent stick-breaking processes of a new type, or discrete limits tied to the Martin boundary of the Young-Fibonacci lattice. Our stick-breaking-like scaling limits significantly extend the result of Gnedin-Kerov (Math. Proc. Camb. Philos. Soc. 129 (2000), no. 3, 433-446) on asymptotics of the Plancherel measure on $\mathbb{YF}$. We also establish Cauchy-like identities for clone Schur functions (with the right-hand side given by a quadridiagonal determinant), and construct and analyze models of random permutations and involutions based on Fibonacci positive specializations and a version of the Robinson-Schensted correspondence for $\mathbb{YF}$., Comment: 71 pages, 12 figures

Weak similarities form a special class of mappings between semimetric spaces. Two semimetric spaces $X$ and $Y$ are weakly similar if there exists a weak similarity $\Phi\colon X\to Y$. We find a structural characteristic of finite ultrametric spaces for which the isomorphism of its representing trees implies a weak similarity of the spaces. We also find conditions under which the Hasse diagrams of balleans of finite semimetric spaces are isomorphic., Comment: 14 pages, 2 figures. arXiv admin note: text overlap with arXiv:2412.17421

The problems of continuation of a partially defined metric and a partially defined ultrametric were considered in (O. Dovgoshey, O. Martio and M. Vuorinen, Metrization of weighted graphs, Ann. Comb., 17:455--476, 2013) and (A. A. Dovgoshey and E. A. Petrov, Subdominant pseudoultrametric on graphs, Sb. Math., 204:1131--1151, 2013), respectively. Using the language of graph theory we generalize the criteria of existence of continuation obtained in these papers. For these purposes we use the concept of a triangle function introduced by M. Bessenyei and Z. P\'ales in (M. Bessenyei and Z. P\'ales, A contraction principle in semimetric spaces, J. Nonlinear Convex Anal., 18:515--524, 2017), which gives a generalization of the triangle inequality in metric spaces. The obtained result allows us to get criteria of the existence of continuation for a wide class of semimetrics including not only metrics and ultrametrics, but also multiplicative metrics and semimetrics with power triangle inequality. Moreover, the explicit formula for the maximal continuations is also obtained., Comment: 11 pages

In 2017 M. Bessenyei and Z. P\'ales introduced a definition of a triangle function which generates a concept of a generalized triangle inequality in semimetric spaces. Inspired by this concept we discuss already known inequalities in metric spaces that relate the six distances determined by four points and introduce a definition of a generalized four-point inequality in semimetric spaces. Conditions under which quasisymmetric mappings and quasim\"{o}bius mappings between semimetric spaces preserve such inequality are obtained., Comment: 19 pages

We introduce a metric on the set of permutations of given order, which is a weighted generalization of Kendall's $\tau$ rank distance and study its properties. Using the edge graph of a permutohedron, we give a criterion which guarantees that a permutation lies metrically between another two fixed permutations. In addition, the conditions under which four points from the resulting metric space form a pseudolinear quadruple were found., Comment: 17 pages, 3 figures

A characterization of finite homogeneous ultrametric spaces and finite ultrametric spaces generated by unrooted labeled trees is found in terms of representing trees. A characterization of finite ultrametric spaces having perfect strictly $n$-ary trees is found in terms of special graphs connected with the space. Further, we give a detailed survey of some special classes of finite ultrametric spaces, which were considered in the last ten years, and study their hereditary properties. More precisely, we are interested in the following question. Let $X$ be an arbitrary finite ultrametric space from some given class. Does every subspace of $X$ also belong to this class?, Comment: 25 pages, 4 figures. arXiv admin note: text overlap with arXiv:1610.08282

It is shown that a minimum weight spanning tree of a finite ultrametric space can be always found in the form of path. As a canonical representing tree such path uniquely defines the whole space and, moreover, it has much more simple structure. Thus, minimum spanning paths are a convenient tool for studying finite ultrametric spaces. To demonstrate this we use them for characterization of some known classes of ultrametric spaces. The explicit formula for Hausdorff distance in finite ultrametric spaces is also found. Moreover, the possibility of using minimum spanning paths for finding this distance is shown., Comment: 18 pages, 4 figures

Ordinal data analysis is an interesting direction in machine learning. It mainly deals with data for which only the relationships `$<$', `$=$', `$>$' between pairs of points are known. We do an attempt of formalizing structures behind ordinal data analysis by introducing the notion of ordinal spaces on the base of a strict axiomatic approach. For these spaces we study general properties as isomorphism conditions, connections with metric spaces, embeddability in Euclidean spaces, topological properties etc., Comment: 28 pages, 3 figures

By using the Bogoliubov perturbation theory we describe the self-bound ground state and excited breathing states of $N$ two-dimensional bosons with zero-range attractive interactions. Our results for the ground state energy $B_N$ and size $R_N$ improve previously known large-$N$ asymptotes and we better understand the crossover to the few-body regime. The oscillatory breathing motion results from the quantum-mechanical breaking of the mean-field scaling symmetry. The breathing-mode frequency scales as $\Omega\propto |B_N|/\sqrt{N}$ at large $N$.

We introduce the concept of resonant optical torque that allows enhancing substantially a transfer of optical angular momentum (AM) of light to a subwavelength particle. We consider high-index cylindrical dielectric nanoparticles supporting Mie resonances, and explore a transfer of AM and how it is affected by absorption and particle shape. We analyse a simple trapping geometry of standing wave patterns created by opposite helical light waves. We uncover stable rotation of particles in both nodes and anti-nodes, and also study how specific particle properties influence the resonant optical torque. We demonstrate that adjusting particle losses can maximize spinning torque, and we predict "super-torque" originating from the superabsorption effect at resonances. Our study offers a deeper understanding of the physics of resonant optical torque and its importance in manipulating AM transfer in optical systems, with promising implications for various fields and inspiring further research in resonant light-matter interactions., Comment: 11 pages, 6 figures

Solid-state synthesis is widely used in exploratory research to study various structural modifications that affect the properties (critical temperature, critical current density, irreversibility field, etc.) of superconductors. The popularity of this method is due to its relative simplicity and availability of the necessary equipment. Combining solid-state synthesis and top-seeded melt growth allows us to increase the grain size in a Tm- and Nd-based 1-2-3 superconductor. Samples with a grain size up to 0.1 mm have been obtained. X-ray diffraction, scanning electron microscopy and magnetization measurements have been used for investigating this superconducting material. The magnetization width {\Delta}M has increased significantly in the synthesized samples. However the temperature dependence of the intragrain critical current density and the pinning force scaling give evidences that the pinning mechanism in the obtained superconductor is essentially the same as in polycrystalline superconductors synthesized by standard solid-state technology. The increase in grain size in the synthesized samples is the main reason for the high values of {\Delta}M., Comment: 12 pages, 7 figures

In 1975, Stein made a wide generalisation of the Ryser-Brualdi-Stein conjecture on transversals in Latin squares, conjecturing that every equi-$n$-square (an $n\times n$ array filled with $n$ symbols where each symbol appears exactly $n$ times) has a transversal of size $n-1$. That is, it should have a collection of $n-1$ entries that share no row, column, or symbol. In 2017, Aharoni, Berger, Kotlar, and Ziv showed that equi-$n$-squares always have a transversal with size at least $2n/3$. In 2019, Pokrovskiy and Sudakov disproved Stein's conjecture by constructing equi-$n$-squares without a transversal of size $n-\frac{\log n}{42}$, but asked whether Stein's conjecture is approximately true. I.e., does an equi-$n$-square always have a transversal with size $(1-o(1))n$? We answer this question in the positive. More specifically, we improve both known bounds, showing that there exist equi-$n$-squares with no transversal of size $n-\Omega(\sqrt{n})$ and that every equi-$n$-square contains $n-n^{1-\Omega(1)}$ disjoint transversals of size $n-n^{1-\Omega(1)}$., Comment: 16 pages, 2 figures

We investigate the $\mathcal{N} = 2$ supersymmetric generalization of the dual equivalence between the Maxwell-Chern-Simons model and two massive self-dual models. One of the self-dual models is described by a real scalar superfield, while the other is described by a chiral spinor superfield. The equivalence is analyzed in the presence of dynamical matter chiral superfields. Initially, we establish the duality by demonstrating the existence of master actions that interpolate between the models. We then show that the field equations are identical when the proper identifications are made. Finally, we confirm the dual equivalence by defining a master generating functional, which, after changing the variables, provides the generating functionals of the Maxwell-Chern-Simons model and the two massive self-dual models coupled to matter., Comment: 19 pages

We present a theoretical study of the exchange interaction in a system of spatially disordered magnetic moments. A typical example of such a system is an impurity semiconductor, whose magnetic properties are associated with the exchange interaction of the impurity atoms. In this study, we consider the case of antiferromagnetic exchange interaction, which we describe by the Heisenberg Hamiltonian. To calculate the magnetic properties of the disordered system, we employ the density of states method. Our calculations demonstrate a good quantitative agreement with the dependence of the Si:P magnetic susceptibility on temperature in a wide range of impurity concentrations and temperatures.

Modeling 3D human-object interaction (HOI) is a problem of great interest for computer vision and a key enabler for virtual and mixed-reality applications. Existing methods work in a one-way direction: some recover plausible human interactions conditioned on a 3D object; others recover the object pose conditioned on a human pose. Instead, we provide the first unified model - TriDi which works in any direction. Concretely, we generate Human, Object, and Interaction modalities simultaneously with a new three-way diffusion process, allowing to model seven distributions with one network. We implement TriDi as a transformer attending to the various modalities' tokens, thereby discovering conditional relations between them. The user can control the interaction either as a text description of HOI or a contact map. We embed these two representations into a shared latent space, combining the practicality of text descriptions with the expressiveness of contact maps. Using a single network, TriDi unifies all the special cases of prior work and extends to new ones, modeling a family of seven distributions. Remarkably, despite using a single model, TriDi generated samples surpass one-way specialized baselines on GRAB and BEHAVE in terms of both qualitative and quantitative metrics, and demonstrating better diversity. We show the applicability of TriDi to scene population, generating objects for human-contact datasets, and generalization to unseen object geometry. The project page is available at: https://virtualhumans.mpi-inf.mpg.de/tridi.

This paper establishes a lower bound on the number of states necessary in the worst case to simulate an $n$-state two-way nondeterministic finite automaton (2NFA) by a one-way unambiguous finite automaton (UFA). It is proved that for every $n$, there is a language recognized by an $n$-state 2NFA that requires a UFA with at least $\sum_{k=1}^{n} (k - 1)! \cdot k! \cdot \mathrm{stirling2}(n, k) \cdot \mathrm{stirling2}(n+1, k)$ = $\Omega \big( n^{2n+2} / e^{2n} \big)$ states, where $\mathrm{stirling2}(n, k)$ denotes Stirling's numbers of the second kind. This result is proved by estimating the rank of a certain matrix, which is constructed for the universal language for $n$-state 2NFAs, and describes every possible behaviour of these automata during their computation., Comment: 31 pages, 7 figures

Thermoelectric effects in $p-n$ junctions are widely used for energy generation with thermal gradients, creation of compact Peltier refrigerators and, most recently, for sensitive detection of infrared and terahertz radiation. It is conventionally assumed that electrons and holes creating thermoelectric current are in equilibrium and share the common quasi-Fermi level. We show that lack of interband equilibrium results in an anomalous sign and magnitude of thermoelectric voltage developed across the $p-n$ junction. The anomalies appear provided the diffusion length of minority carriers exceeds the size of hot spot at the junction. Normal magnitude of thermoelectric voltage is partly restored if interband tunneling at the junction is allowed. The predicted effects can be relevant to the cryogenically cooled photodetectors based on bilayer graphene and mercury cadmium telluride quantum wells., Comment: 5 pages, 3 figures

The kinetic stability of collisionless, sloshing beam-ion (45{\deg} pitch angle) plasma is studied in a 3D simple magnetic mirror, mimicking the Wisconsin High-temperature superconductor Axisymmetric Mirror (WHAM) experiment. The collisional Fokker-Planck code CQL3D-m provides a slowing-down beam-ion distribution to initialize the kinetic-ion/fluid-electron code Hybrid-VPIC, which then simulates free plasma decay without external heating or fueling. Over 1-10 $\mu$s, drift-cyclotron loss-cone (DCLC) modes grow and saturate in amplitude. DCLC scatters ions to a marginally-stable distribution with gas-dynamic rather than classical-mirror confinement. Sloshing ions can trap cool (low-energy) ions in an electrostatic potential well to stabilize DCLC, but DCLC itself does not scatter sloshing beam-ions into said well. Instead, cool ions must come from external sources such as charge-exchange collisions with a low-density neutral population. Manually adding cool ~1 keV ions improves beam-ion confinement ~2-5x in Hybrid-VPIC simulations, which qualitatively corroborates measurements from real mirror devices with sloshing ions., Comment: Submitted; 35 pages, 14 figures

Shaping the structure of light with flat optical devices has driven significant advancements in our fundamental understanding of light and light-matter interactions, and enabled a broad range of applications, from image processing and microscopy to optical communication, quantum information processing, and the manipulation of microparticles. Yet, pushing the boundaries of structured light beyond the linear optical regime remains an open challenge. Nonlinear optical interactions, such as wave mixing in nonlinear flat optics, offer a powerful platform to unlock new degrees of freedom and functionalities for generating and detecting structured light. In this study, we experimentally demonstrate the non-trivial structuring of third-harmonic light enabled by the addition of total angular momentum projection in a nonlinear, isotropic flat optics element -- a single thin film of amorphous silicon. We identify the total angular momentum projection and helicity as the most critical properties for analyzing the experimental results. The theoretical model we propose, supported by numerical simulations, offers quantitative predictions for light structuring through nonlinear wave mixing under various pumping conditions, including vectorial and non-paraxial pump light. Notably, we reveal that the shape of third-harmonic light is highly sensitive to the polarization state of the pump. Our findings demonstrate that harnessing the addition of total angular momentum projection in nonlinear wave mixing can be a powerful strategy for generating and detecting precisely controlled structured light.

We saturate a high-school-level hacking benchmark with plain LLM agent design. Concretely, we obtain 95% performance on InterCode-CTF, a popular offensive security benchmark, using prompting, tool use, and multiple attempts. This beats prior work by Phuong et al. 2024 (29%) and Abramovich et al. 2024 (72%). Our results suggest that current LLMs have surpassed the high school level in offensive cybersecurity. Their hacking capabilities remain underelicited: our ReAct&Plan prompting strategy solves many challenges in 1-2 turns without complex engineering or advanced harnessing.

We introduce ShapeWords, an approach for synthesizing images based on 3D shape guidance and text prompts. ShapeWords incorporates target 3D shape information within specialized tokens embedded together with the input text, effectively blending 3D shape awareness with textual context to guide the image synthesis process. Unlike conventional shape guidance methods that rely on depth maps restricted to fixed viewpoints and often overlook full 3D structure or textual context, ShapeWords generates diverse yet consistent images that reflect both the target shape's geometry and the textual description. Experimental results show that ShapeWords produces images that are more text-compliant, aesthetically plausible, while also maintaining 3D shape awareness., Comment: Project webpage: https://lodurality.github.io/shapewords/

Ultrafast excitation of non-equilibrium carriers under intense pulses offer unique opportunities for controlling optical properties of semiconductor materials. In this work, we propose a scheme for ultrafast generation of surface plasmon polaritons (SPPs) via a transient metagrating formed under two interfering optical pump pulses in the semiconductor GaAs thin film. The grating can be formed due to modulation of the refractive index associated with the non-equilibrium carriers generation. The formed temporal grating structure enables generation of SPP waves at GaAs/Ag interface via weak probe pulse excitation. We propose a theoretical model describing non-equilibrium carriers formation and diffusion and their contribution to permittivity modulation via Drude and band-filling mechanisms. We predict that by tuning the parameters of the pump and probe one can reach critical coupling regime and achieve efficient generation of SPP at the times scales of 0.1-1 ps.

In this work, we study the acoustic forces acting on particles due to sound scattering at the interface with an elastic substrate. Utilizing the Green's function formalism, we predict that excitation of leaking Rayleigh wave results in strong modification of the acoustic pressure force acting on a monopole scatterer and changes the equilibrium position of particles above the substrate surface. We also showed that the presence of a substrate changes the configuration of the acoustical binding of two particles due to multiple rescattering of acoustic wave from the interface. The reported results propose the method of acoustic manipulation via surface waves excitation and demonstrate the effect from elastic media in acoustical trapping of microobjects.

We give a new, short proof of the formula for the first potentially non-zero differential of the Hochschild--Serre spectral sequence for semiabelian varieties over non-closed fields. We show that this differential is non-zero for the Jacobian of a curve when the image of the torsor of theta-characteristics under the Bockstein map is non-zero. An explicit example is a curve of genus 2 whose Albanese torsor is not divisible by 2. When the Albanese torsor is trivial, we show that the Hochschild--Serre spectral sequence for the Jacobian degenerates at the second page. We give a formula for the differential of the Hochschild--Serre spectral sequence for a torus which computes its Brauer group. Finally, we describe the differentials of the Hochschild--Serre spectral sequence for a smooth projective curve, generalising a lemma of Suslin., Comment: 34 pages

Pulsar timing array observations have found evidence for an isotropic gravitational wave background with the Hellings-Downs angular correlations, expected from general relativity. This interpretation hinges on the measured shape of the angular correlations, which is predominately quadrupolar under general relativity. Here we explore a more flexible parameterization: we expand the angular correlations into a sum of Legendre polynomials and use a Bayesian analysis to constrain their coefficients with the 15-year pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). When including Legendre polynomials with multipoles $\ell \geq 2$, we only find a significant signal in the quadrupole with an amplitude consistent with general relativity and non-zero at the $\sim 95\%$ confidence level and a Bayes factor of 200. When we include multipoles $\ell \leq 1$, the Bayes factor evidence for quadrupole correlations decreases by more than an order of magnitude due to evidence for a monopolar signal at approximately 4 nHz which has also been noted in previous analyses of the NANOGrav 15-year data. Further work needs to be done in order to better characterize the properties of this monopolar signal and its effect on the evidence for quadrupolar angular correlations., Comment: 15 pages, 6 figures

Assessing forecasting proficiency is a time-intensive activity, often requiring us to wait months or years before we know whether or not the reported forecasts were good. In this study, we develop adaptive cognitive tests that predict forecasting proficiency without the need to wait for forecast outcomes. Our procedures provide information about which cognitive tests to administer to each individual, as well as how many cognitive tests to administer. Using item response models, we identify and tailor cognitive tests to assess forecasters of different skill levels, aiming to optimize accuracy and efficiency. We show how the procedures can select highly-informative cognitive tests from a larger battery of tests, reducing the time taken to administer the tests. We use a second, independent dataset to show that the selected tests yield scores that are highly related to forecasting proficiency. This approach enables real-time, adaptive testing, providing immediate insights into forecasting talent in practical contexts.

This paper presents the Hammir tandem mirror design based on Realta Fusion's first-of-a-kind model for axisymmetric magnetic mirror fusion performance. This model uses an integrated end plug simulation model including, heating, equilibrium, and transport combined with a new formulation of the plasma operation contours (POPCONs) technique for the tandem mirror central cell. Using this model, it is shown that an end plug utilizing high temperature superconducting magnets and modern neutral beams enables a classical tandem mirror pilot plant producing a fusion gain Q > 5. The approach here represents an important advance in tandem mirror design. The high fidelity end plug model enables calculations of heating and transport in the highly non-Maxwellian end plug to be made more accurately and the central cell POPCON technique allows consideration of a wide range of parameters in the relatively simple near-Maxwellian central cell, facilitating the selection of more optimal central cell plasmas. These advances make it possible to find more conservative classical tandem mirror fusion pilot plant operating points with lower $\beta$, temperatures, neutral beam energies, and end plug performance than designs in the literature. Despite being more conservative, it is shown that these operating points can still form the basis of a viable fusion pilot plant.

The study of differential forms that are closed but not exact reveals important information about the global topology of a manifold, encoded in the de Rham cohomology groups $H^k(M)$, named after Georges de Rham (1903-1990). This expository paper provides an explanation and exploration of de Rham cohomology and its equivalence to singular cohomology. We present an intuitive introduction to de Rham cohomology and discuss four associated computational tools: the Mayer-Vietoris theorem, homotopy invariance, Poincar\'e duality, and the K\"unneth formula. We conclude with a statement and proof of de Rham's theorem, which asserts that de Rham cohomology is equivalent to singular cohomology., Comment: Expository article, 25 pages, 7 figures

The detection of a stochastic gravitational wave background by pulsar timing arrays suggests the presence of a supermassive black hole binary population. Although the observed spectrum generally aligns with predictions from orbital evolution driven by gravitational wave emission in circular orbits, there is a discernible preference for a turnover at the lowest observed frequencies. This turnover could indicate a significant hardening phase, transitioning from early environmental influences to later stages predominantly influenced by gravitational wave emission. In the vicinity of these binaries, the ejection of stars or dark matter particles through gravitational three-body slingshots efficiently extracts orbital energy, leading to a low-frequency turnover in the spectrum. By analyzing the NANOGrav 15-year data, we assess how the gravitational wave spectrum depends on the initial inner galactic profile prior to disruption by binary ejections, accounting for a range of initial binary eccentricities. Our findings suggest a parsec-scale galactic center density around $10^6\,M_\odot/\textrm{pc}^3$ across most of the parameter space, offering insights into the environmental effects on black hole evolution and combined matter density near galaxy centers., Comment: 15 pages, 5 figures

In this work, we start by examining a spherically symmetric black hole within the framework of non-commutative geometry and apply a modified Newman-Janis method to obtain a new rotating solution. We then investigate its consequences, focusing on the horizon structure, ergospheres, and the black hole's angular velocity. Following this, a detailed thermodynamic analysis is performed, covering surface gravity, Hawking temperature, entropy, and heat capacity. We also study geodesic motion, with particular emphasis on null geodesics and their associated radial accelerations. Additionally, the photon sphere and the resulting black hole shadows are explored. Finally, we compute the quasinormal modes for scalar perturbations using the 6th-order WKB approximation., Comment: 37 pages, 16 figures and 2 tables

In the present paper, a new type of mappings called perimetric contractions on $k$-polygons is introduced. These contractions can be viewed as a generalization of mappings that contracts perimeters of triangles. A fixed point theorem for this type of mappings in a complete metric space is established. Achieving a fixed point necessitates the avoidance of periodic points of prime period $2,3,\cdots, k-1$. The class of contraction mappings is encompassed by perimeter-based mappings, leading to the recovery of Banach's fixed point theorem as a direct outcome from our main result. A sufficient condition to guarantee the uniqueness of the fixed point is also provided. Moreover, we introduce the Kannan type perimetric contractions on $k$-polygons, establishing a fixed point theorem and a sufficient uniqueness condition. The relationship between these contractions, generalized Kannan type mappings, and mappings contracting the perimeters on $k$-polygons is investigated. Several examples are illustrated to support the validity of our main results., Comment: 15 pages

GPT-4o is an autoregressive omni model that accepts as input any combination of text, audio, image, and video, and generates any combination of text, audio, and image outputs. It's trained end-to-end across text, vision, and audio, meaning all inputs and outputs are processed by the same neural network. GPT-4o can respond to audio inputs in as little as 232 milliseconds, with an average of 320 milliseconds, which is similar to human response time in conversation. It matches GPT-4 Turbo performance on text in English and code, with significant improvement on text in non-English languages, while also being much faster and 50\% cheaper in the API. GPT-4o is especially better at vision and audio understanding compared to existing models. In line with our commitment to building AI safely and consistent with our voluntary commitments to the White House, we are sharing the GPT-4o System Card, which includes our Preparedness Framework evaluations. In this System Card, we provide a detailed look at GPT-4o's capabilities, limitations, and safety evaluations across multiple categories, focusing on speech-to-speech while also evaluating text and image capabilities, and measures we've implemented to ensure the model is safe and aligned. We also include third-party assessments on dangerous capabilities, as well as discussion of potential societal impacts of GPT-4o's text and vision capabilities.

A number of popular transfer learning methods rely on grid search to select regularization hyperparameters that control over-fitting. This grid search requirement has several key disadvantages: the search is computationally expensive, requires carving out a validation set that reduces the size of available data for model training, and requires practitioners to specify candidate values. In this paper, we propose an alternative to grid search: directly learning regularization hyperparameters on the full training set via model selection techniques based on the evidence lower bound ("ELBo") objective from variational methods. For deep neural networks with millions of parameters, we specifically recommend a modified ELBo that upweights the influence of the data likelihood relative to the prior while remaining a valid bound on the evidence for Bayesian model selection. Our proposed technique overcomes all three disadvantages of grid search. We demonstrate effectiveness on image classification tasks on several datasets, yielding heldout accuracy comparable to existing approaches with far less compute time.

The spontaneous conversion of muonium to antimuonium is one of the interesting charged lepton flavor violation phenomena, offering a sensitive probe of potential new physics and serving as a tool to constrain the parameter space beyond the Standard Model. Utilizing a high-intensity muon beam, a Michel electron magnetic spectrometer and a positron transport solenoid together with a positron detection system, MACE aims to discover or constrain this rare process at the conversion probability beyond the level of $10^{-13}$. This report provides an overview of the theoretical framework and detailed experimental design in the search for the muonium-to-antimuonium conversion., Comment: 115 pages, 59 figures

With the rapid growth of the volume of research fields like computer vision and computer graphics, researchers require effective and user-friendly rendering tools to visualize results. While advanced tools like Blender offer powerful capabilities, they also require a significant effort to master. This technical report introduces Blendify, a lightweight Python-based framework that seamlessly integrates with Blender, providing a high-level API for scene creation and rendering. Blendify reduces the complexity of working with Blender's native API by automating object creation, handling the colors and material linking, and implementing features such as shadow-catcher objects while maintaining support for high-quality ray-tracing rendering output. With a focus on usability Blendify enables efficient and flexible rendering workflow for rendering in common computer vision and computer graphics use cases. The code is available at https://github.com/ptrvilya/blendify, Comment: Project page: https://virtualhumans.mpi-inf.mpg.de/blendify/

Co-crystallization is an accessible way to control physicochemical characteristics of organic crystals, which finds many biomedical applications. In this work, we present Generative Method for Co-crystal Design (GEMCODE), a novel pipeline for automated co-crystal screening based on the hybridization of deep generative models and evolutionary optimization for broader exploration of the target chemical space. GEMCODE enables fast de novo co-crystal design with target tabletability profiles, which is crucial for the development of pharmaceuticals. With a series of experimental studies highlighting validation and discovery cases, we show that GEMCODE is effective even under realistic computational constraints. Furthermore, we explore the potential of language models in generating co-crystals. Finally, we present numerous previously unknown co-crystals predicted by GEMCODE and discuss its potential in accelerating drug development., Comment: Accepted at 38th Conference on Neural Information Processing Systems (NeurIPS)

We propose a simple method of measuring the autocorrelation function of a spin noise based on multiplication and averaging two digitized signal traces, with one of them being a time-reversed copy of the other. This procedure allows one to obtain, with lower computational expenses, all the information usually derived in the Fourier transform spin-noise spectroscopy, retaining all the merits of the latter. We successfully applied this method to the measurements of spin noise in cesium vapors by using a digital oscilloscope in the capacity of the analog-to-digital converter. Specific opportunities of this experimental approach as applied to a more general problem of studying the nature of light-intensity noise are discussed., Comment: 5 pages, 3 figures