Search

Benchmarks are important tools for tracking the rapid advancements in large language model (LLM) capabilities. However, benchmarks are not keeping pace in difficulty: LLMs now achieve over 90\% accuracy on popular benchmarks like MMLU, limiting informed measurement of state-of-the-art LLM capabilities. In response, we introduce Humanity's Last Exam (HLE), a multi-modal benchmark at the frontier of human knowledge, designed to be the final closed-ended academic benchmark of its kind with broad subject coverage. HLE consists of 2,700 questions across dozens of subjects, including mathematics, humanities, and the natural sciences. HLE is developed globally by subject-matter experts and consists of multiple-choice and short-answer questions suitable for automated grading. Each question has a known solution that is unambiguous and easily verifiable, but cannot be quickly answered via internet retrieval. State-of-the-art LLMs demonstrate low accuracy and calibration on HLE, highlighting a significant gap between current LLM capabilities and the expert human frontier on closed-ended academic questions. To inform research and policymaking upon a clear understanding of model capabilities, we publicly release HLE at https://lastexam.ai., Comment: 27 pages, 6 figures

We describe the testing of a prototype SiPM-on-tile iron-scintillator calorimeter at the Relativistic Heavy Ion Collider (RHIC) during its 200 GeV $pp$ run in 2024. The prototype, measuring $20 \times 20 \, \text{cm}^{2}$ and 24 radiation lengths in depth, was positioned in the STAR experimental hall, approximately 8 m from the interaction point and 65 cm from the beam line, covering a pseudorapidity range of about $3.1<\eta<3.4$. By using the dark current of a reference SiPM as a radiation monitor, we estimate that the prototype was exposed to a fluence of about $10^{10}$ 1-MeV $n_{\mathrm{eq}}$/cm$^2$. Channel-by-channel calibration was performed in a data-driven way with the signature from minimum-ionizing particles during beam-on conditions. A Geant4 detector simulation, with inputs from the Pythia8 event generator, describes measurements of energy spectra and hit multiplicities reasonably well. These results mark the first deployment, commissioning, calibration, and long-term operation of a SiPM-on-tile calorimeter in a collider environment. This experimental campaign will guide detector designs and operational strategies for the ePIC detector at the future EIC, as well as other applications.

In this short note, we give examples of binding sums of contact 3-manifolds that do not preserve properties such as tightness or symplectic fillability. We also prove vanishing of the Heegaard Floer contact invariant for an infinite family of binding sums where the summands are Stein fillable. This recovers a result of Wendl and Latschev-Wendl. Along the way, we rectify a subtle computational error in a paper of Juhasz-Kang concerning the spectral order of a neighbourhood of a Giroux torsion domain., Comment: 16 pages, 12 figures. Comments welcome!

We show that closures of homogeneous braids are visually prime, addressing a question of Cromwell. The key technical tool for the proof is the following criterion concerning primeness of open books, which we consider to be of independent interest. For open books of 3-manifolds the property of having no fixed essential arcs is preserved under essential Murasugi sums with a strictly right-veering open book, if the plumbing region of the original open book veers to the left. We also provide examples of open books in S^3 demonstrating that primeness is not necessarily preserved under essential Murasugi sum, in fact not even under stabilizations a.k.a. Hopf plumbings. Furthermore, we find that trefoil plumbings need not preserve primeness. In contrast, we establish that figure-eight knot plumbings do preserve primeness., Comment: 25 pages, 14 figures. Comments welcome!

We develop an approach analogous to classical Frobenius theory for the analysis of singularities of ODEs in the case of discrete dynamical systems. Our methodology is based on the Roman-Rota theory of finite operators and relies crucially on the idea of preserving the Leibniz rule on a lattice of points by means of the notion of Rota algebras. The relevant cases of the Bessel, Hermite and Airy equations are discussed., Comment: 19 pages, 1 figure

We consider various classes of bounded operators on the Fock space $F^2$ of Gaussian square integrable entire functions over the complex plane. These include Toeplitz (type) operators, weighted composition operators, singular integral operators, Volterra-type operators and Hausdorff operators and range from classical objects in harmonic analysis to more recently introduced classes. As a leading problem and closely linked to well-known compactness characterizations we pursue the question of when these operators are contained in the Toeplitz algebra. This paper combines a (certainly in-complete) survey of the classical and more recent literature including new ideas for proofs from the perspective of quantum harmonic analysis (QHA). Moreover, we have added a number of new theorems and links between known results., Comment: 36 pages; comments are welcome

Monolithic 3YTZP and 3YTZP containing 2.5 vol.% of single-walled carbon nanotubes (SWCNT) were fabricated by Spark Plasma Sintering (SPS) at 1250 C. Microstructural characterization of the as-fabricated 3YTZP/SWCNTs composite shows a homogeneous CNTs dispersion throughout of ceramic matrix. The specimens have been crept at temperatures between 1100 and 1200 C in order to investigate the influence of the SWCNTs addition on high temperature deformation mechanisms in zirconia. Slightly higher stress exponent values are found for 3YTZP/SWCNTs nanocomposites (n~2.5) compared to monolithic 3YTZP (n~2.0). However, the activation energy in 3YTZP (Q = 715 +- 60 kJ/mol) experiences a reduction of about 25% by the addition of 2.5 vol.% of SWCNTs (Q = 540 +- 40 kJ/mol). Scanning electron microscopy studies indicate that there is no microstructural evolution in crept specimens, and Raman spectroscopy measurements show that SWCNTs preserved their integrity during the creep tests. All these results seem to indicate that the high temperature deformation mechanism is grain boundary sliding (GBS) accommodated by grain-boundary diffusion, which is influenced by yttrium segregation and the presence of SWCNTs at the grain boundary.

Effects on mechanical properties of the presence of either single-walled carbon nanotubes (SWCNTs) or multi-walled carbon nanotubes (MWCNTs) in a 3YTZP matrix have been investigated in this work. Thus, monolithic 3YTZP and 3YTZP containing 2.5 vol% either SWCNTs or MWCNTs were fabricated by Spark Plasma Sintering (SPS) at 1250 C. Samples were crept at temperatures between 1100 and 1200 C and stresses between 5 and 230 MPa. Raman spectroscopy measurements indicate the absence of severe damages in the CNTs structure after sintering and testing. Scanning electron microscopy studies show that microstructures do not evolve during creep tests. Mechanical results point out that monolithic 3YTZP exhibits a higher creep resistance than composites since CNTs facilitate grain boundary sliding during high-temperature deformation. SWCNTs and MWCNTs have a similar effect on the high temperature mechanical behavior in 3YTZP where the bundle length and the level of dispersion of CNTs play a crucial role., Comment: arXiv admin note: text overlap with arXiv:2402.06651

Samples of $\alpha$-SiC have been sintered with liquid phase (LPS) to 1950 $^\circ$C, in atmosphere of argon and processing times between 1 and 7 hours. Using scanning electron microscopy (SEM) the microstructure of the samples has been characterized, being obtained average grain size that grows with the processing time from 0.64 to 1.61 $\mu$m. These samples have been deformed in compression under constant load, to temperatures between 1450 and 1625 C, stresses between 25 and 450 MPa and strain rate between $4.2\times 10^{-8}$ and $1.5\times 10^{-6}$ s$^{-1}$. The creep parameters have been determined, obtaining for n values between 2.4 0.1 and 4.5 0.2 and Q=680 35 kJ.mol$^{-1}$ in samples sintered during 1 hour and n between 1.2 0.1 and 2.4 0.1 and Q=710 90 kJ.mol$^{-1}$ for samples sintered during 7 hours. These results have been correlated with the microstructure, being the grain boundary sliding (GBS) accommodated by lattice diffusion and the movement of dislocations the possible deformation mechanisms, operating both in a simultaneous way., Comment: in Spanish language (Microestructura y propiedades mec\'anicas a altas temperaturas del $\alpha$-SiC sinterizado con fase l\'iquida de Y$_2$O$_3$-Al$_2$O$_3$)

The plastic deformation of Cr3+ -doped a-Al2 O3 (ruby) with four distinct Cr concentrations has been studied at temperatures between 900 and 1500 $^\circ$C. The mechanical tests indicate that the processes of dislocation multiplication and the adjustments of the slip velocity of these dislocations to the imposed strain rate in undoped a-Al2 O3 are not significantly affected by the Cr concentra%on. The yield stress increment is approximately constant with temperature and the hardening increases with the Cr concentration. The critical resolved shear stress (CRSS) is fixed to a model based on dislocation glide controlled by the nucleation and propagation of kink pairs, modified to include the hardening due to Cr. Satisfactory fits are achieved with adjustable parameters close to those employed for undoped a-Al2 O3 .

The influence that the atmosphere (N_2 or Ar) and sintering time have on microstructure evolution in liquid-phase-sintered alpha-sic and on its mechanical properties at high temperature was investigated. The microstructure of the samples sintered in N2 was equiaxed with a grain size of 0.70 {\mu}m and a density of 98% of the theoretical value regardless of the sintering time. In contrast, samples sintered in Ar had an elongated-grain microstructure with a density decreasing from 99% to 95% and a grain size increasing from 0.64 to 1.61 {\mu}m as the sintering time increased from 1 to 7 hours. The mechanical behaviour at 1450 {\deg}C showed the samples sintered in nitrogen to be brittle and fail at very low strains, with a fracture stress increasing from 400 to 800 MPa as the sintering time increased. In contrast, the samples sintered in Ar were quasi-ductile with increasing strain to failure as the sintering time increased, and a fracture stress strongly linked to the form and size of the grains. These differences in the mechanical properties of the two materials are discussed in the text. During mechanical tests, a loss of intergranular phase takes place in a region, between 50 and 150 {\mu}m thick, close to the surface of the samples--the effect being more important in the samples sintered in Ar, Comment: 27 pages, 8 figures

A model based on dislocation glide controlled by the nucleation and propagation of kink pairs in a high Peierls stress crystal is revisited and modified to account for changes in dislocation densities and segment lengths with temperature and stress. It is applied to the critical resolved shear stress (CRSS) for basal and prism plane slip in sapphire (alpha-Al2O3). According to agreed-upon knowledge on dislocations in sapphire, basal slip and prism plane slip are modelled with undissociated and dissociated dislocations, respectively. In the latter case, partial dislocations move independently. Amongst a number of sets of fitting parameters, good fits between experimental and modelled CRSS9s are obtained in the long segment limit over the whole range of temperatures by making use of physically sound parameters, including a stress dependence of the dislocation density.

A result of Honda, Kazez, and Mati\'{c} states that a contact structure is tight if and only if all its supporting open books are right-veering. We show a combinatorial way of detecting the left-veering arcs in open books, implying the existence of an algorithm that detects the right-veering property for compact surfaces with boundary., Comment: Comments are welcome

In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange functions when the orders of the singularities of the radial function's Fourier transforms at zero do not match the parity of the dimension of the space, and therefore new expansions and coefficients are needed to overcome this problem. We develop explicit constructions of infinite Fourier expansions that provide these coefficients and make an extensive comparison of the approximation qualities and - with a particular focus - polynomial precision and uniform approximation order of the various formulae. One of the interesting observations concerns the link between algebraic conditions of expansion coefficients and analytic properties of localness and convergence.

We recently proposed a high-granularity calorimeter insert for the Electron-Ion Collider (EIC) that uses plastic scintillator tiles read out by SiPMs. Among its innovative features are an ASIC-away-of-SiPM strategy for reducing cooling requirements and minimizing space use, along with employing 3D-printed frames to reduce optical crosstalk and dead areas. To evaluate these features, we built a 40-channel prototype and tested it using a 4 GeV positron beam at Jefferson Laboratory. The measured energy spectra and 3D shower shapes are well described by simulations, confirming the effectiveness of the design, construction techniques, and calibration strategy. This constitutes the first use of SiPM-on-tile technology in EIC detector designs.

We discuss the notion of spectral synthesis for the setting of Quantum Harmonic Analysis. Using these concepts, we study subalgebras of the full Toeplitz algebra with certain invariant symbols and their commutators. In particular, we find a new class of commutative Toeplitz C$^\ast$ algebras on the Fock space. In the end, we investigate the Gelfand theory of those commutative C$^\ast$ algebras., Comment: Final version, to appear in the Journal of Operator Theory

In a recent paper we have classified scalar Ito equations which admits a standard symmetry; these are also directly integrable by the Kozlov substitution. In the present work, we consider the diffusion (Fokker-Planck) equations associated to such symmetric Ito equations., Comment: 24 pages, no figures

Determining if an (1+1)-differential-difference equation is integrable or not (in the sense of possessing an infinite number of symmetries) can be reduced to the study of the dependence of the equation on the lattice points, according to Yamilov's theorem. We shall apply this result to a class of differential-difference equations obtained as partial continuous limits of 3-points difference equations in the plane and conclude that they cannot be integrable.

Finding new ways to tune the behavior of thermoresponsive microgels in bulk and confined at 2D liquid interfaces is key to achieve a deeper understanding and control of these smart materials. We studied the interaction of positively charged pNIPAM microgels with the Keggin-type polyoxometalate $Na_{3}PW_{12}O_{40}$ (POM). In bulk, we observed charge inversions below and above the volume phase transition temperature (VPTT) at significantly low POM concentrations as $5\cdot10^{-5}$ M. In the presence of POM, the microgels exhibited a deswelling-swelling-deswelling behaviour below the VPTT, and a two-step further deswelling above the VPTT. When microgels were confined at 2D water/air interfaces, adding $10^{-5}$ M of POM below the VPTT was equivalent to heat above the VPTT and compress the monolayer from $5$ to $20\,\text{mN m$^{-1}$}$. Above the VPTT, the diameter at the interface did not change while the portion immersed in the subphase further deswelled, in agreement with the behavior in bulk. Adding more POM did not change the diameter at the interface nor the height of the microgels, showing a saturation effect in 2D. The restructuring of the pNIPAM polymeric network by the POM was characterized by EDS mapping and XPS. The microgel monolayers with POM improved their resistance to plasma etching, which could be useful for soft colloidal lithography.

Microgels are soft microparticles that often exhibit thermoresponsiveness and feature a transformation at a critical temperature, referred to as the volume phase transition temperature. The question of whether this transformation occurs as a smooth or as a discontinuous one is still a matter of debate. This question can be addressed by studying individual microgels trapped in optical tweezers. For this aim, composite particles were obtained by decorating pNIPAM microgels with iron oxide nanocubes. These composites become self-heating when illuminated by the infrared trapping laser, featuring Hot Brownian Motion within the trap. Above a certain laser power, a single decorated microgel features a volume phase transition that is discontinuous, while the usual continuous sigmoidal-like dependence is recovered after averaging over different microgels. The collective sigmoidal behavior enables the application of a power-to-temperature calibration and provides the effective drag coefficient of the self-heating microgels, thus establishing these composite particles as potential micro-thermometers and micro-heaters. Moreover, the self-heating microgels also exhibit an unexpected and intriguing bistability behavior above the critical temperature, probably due to partial collapses of the microgel. These results set the stage for further studies and the development of applications based on the Hot Brownian Motion of soft particles.

We recently proposed a high-granularity calorimeter insert for the Electron-Ion Collider (EIC) that is based on plastic scintillator tiles readout with silicon photomultipliers. In this work, we concretize its design by characterizing its building blocks with measurements of light yield, optical crosstalk, and timing resolutions using cosmic-rays, an LED, and a beta source. We also compared two approaches for the optical isolation of cells: ``megatiles'' with grooved boundaries between cells, and a 3D-printed plastic frame hosting individual cells. We found that the latter suppresses optical crosstalk to negligible levels while providing an easier assembly method. Overall, these performance studies can help inform calorimeter design and realistic simulations of 5D showers (time, energy, position) for the EIC and other experiments., Comment: added journal reference, and updated text

The classification of scalar Ito equations with a single noise source which admit a so called standard symmetry and hence are -- by the Kozlov construction -- integrable is by now complete. In this paper we study the situation, occurring in physical as well as biological applications, where there are two independent noise sources. We determine all such autonomous Ito equations admitting a standard symmetry; we then integrate them by means of the Kozlov construction. We also consider the case of three or more independent noises, showing no standard symmetry is present., Comment: 32 pages, no figures. V3 is the published version

We introduce a family of $n$-dimensional Hamiltonian systems which, contain, as special reductions, several superintegrable systems as the Tremblay-Turbiner-Winternitz system, a generalized Kepler potential and the anisotropic harmonic oscillator with Rosochatius terms. We conjecture that there exist special values in the space of parameters, apart from those leading to known cases, for which this new Hamiltonian family is superintegrable., Comment: 9 pages, no figures

Responding to the current urgent need for low carbon emissions and high efficiency in manufacturing processes, the relationships between three different machining factors (depth of cut, feed rate, and spindle rate) on power consumption and surface finish (roughness) were analysed by applying a Bayesian seemingly unrelated regressions (SUR) model. For the analysis, an optimization criterion was established and minimized by using an optimization algorithm that combines evolutionary algorithm methods with a derivative-based (quasi-Newton) method to find the optimal conditions for energy consumption that obtains a good surface finish quality. A Bayesian ANOVA was also performed to identify the most important factors in terms of variance explanation of the observed outcomes. The data were obtained from a factorial experimental design performed in two computerized numerical control (CNC) vertical machining centers (Haas UMC-750 and Leadwell V-40iT). Some results from this study show that the feed rate is the most influential factor in power consumption, and the depth of cut is the factor with the stronger influence on roughness values. An optimal operational point is found for the three factors with a predictive error of less than 0.01% and 0.03% for the Leadwell V-40iT machine and the Haas UMC-750 machine, respectively.

It is known that knowledge of a symmetry of a scalar Ito stochastic differential equations leads, thanks to the Kozlov substitution, to its integration. In the present paper we provide a classification of scalar autonomous Ito stochastic differential equations with simple noise possessing symmetries; here "simple noise" means the noise coefficient is of the form $\s (x,t) = s x^k$, with $s$ and $k$ real constants. Such equations can be taken to a standard form via a well known transformation; for such standard forms we also provide the integration of the symmetric equations. Our work extends previous classifications in that it also consider recently introduced types of symmetries, in particular standard random symmetries, not considered in those., Comment: published version; 49 pages in OCNMP format

We present and study commutative Banach algebras generated by Toeplitz operators with generalized quasi-radial pseudo-homogeneous symbols acting on the Bergman space over the unit ball. We develop the Gelfand theory of these algebras and give some structural information about them. In particular, we provide a description of the radical of these algebras. This paper generalizes and completes the results from previous works related to Toeplitz operators with quasi-radial quasi-homogeneous symbols.