Miracle-dz/UniFAR-FTUs huggingface dataset:
Fast Distributed Brooks' Theorem

We give a randomized $\Delta$-coloring algorithm in the LOCAL model that runs in $\text{poly} \log \log n$ rounds, where $n$ is the number of nodes of the input graph and $\Delta$ is its maximum degree. This means that randomized $\Delta$-coloring is a rare distributed coloring problem with an upper and lower bound in the same ballpark, $\text{poly}\log\log n$, given the known $\Omega(\log_\Delta\log n)$ lower bound [Brandt et al., STOC '16]. Our main technical contribution is a constant time reduction to a constant number of $(\text{deg}+1)$-list coloring instances, for $\Delta = \omega(\log^4 n)$, resulting in a $\text{poly} \log\log n$-round CONGEST algorithm for such graphs. This reduction is of independent interest for other settings, including providing a new proof of Brooks' theorem for high degree graphs, and leading to a constant-round Congested Clique algorithm in such graphs. When $\Delta=\omega(\log^{21} n)$, our algorithm even runs in $O(\log^* n)$ rounds, showing that the base in the $\Omega(\log_\Delta\log n)$ lower bound is unavoidable. Previously, the best LOCAL algorithm for all considered settings used a logarithmic number of rounds. Our result is the first CONGEST algorithm for $\Delta$-coloring non-constant degree graphs.
Interaction effects on Wannier functions for bosons in an optical lattice

We have numerically calculated the single band Wannier functions for interacting Bose gases in optical lattices with a self-consistent approach. We find that the Wannier function is broadened by repulsive atom interaction. The tunneling parameter J and on-site interaction U computed with the broadened Wannier functions are found to change significantly for different atomic number per site. Our theory can explain the nonuniform atomic clock shift observed in [Campbell et al., Science 313, 649 (2006)].
External univalence for second-order generalized algebraic theories

Voevodsky's univalence axiom is often motivated as a realization of the equivalence principle; the idea that equivalent mathematical structures satisfy the same properties. Indeed, in Homotopy Type Theory, properties and structures can be transported over type equivalences. However, we may wish to explain the equivalence principle without relying on the univalence axiom. For example, all type formers preserve equivalences in most type theories; thus it should be possible to transport structures over type equivalences even in non-univalent type theories. We define external univalence, a property of type theories (and more general second-order generalized algebraic theories) that captures the preservation of equivalences (or other homotopy relations). This property is defined syntactically, as the existence of identity types on the (syntactically defined) coclassifying (Sigma,Pi_rep)-CwF (also called generic model or walking model) of the theory. Semantically, it corresponds to the existence of some left semi-model structure on the category of models of the theory. We give syntactic conditions that can be used to check that a theory satisfies external univalence. We prove external univalence for some theories, such as the first-order generalized algebraic theory of categories, and dependent type theory with any standard choice of type formers and axioms, including identity types, Sigma-types, Pi-types, universes \`a la Tarski, the univalence axiom, the Uniqueness of Identity Proofs axiom, etc.
Static and Dynamic Disorder in Formamidinium Lead Bromide Single Crystals

We show that formamidinium-based crystals are distinct from methylammonium-based halide perovskite crystals because their inorganic sublattice exhibits intrinsic local static disorder that coexists with a well-defined average crystal structure. Our study combines terahertz-range Raman scattering with single-crystal X-ray diffraction and first-principles calculations to probe the evolution of inorganic sublattice dynamics with temperature in the range of 10–300 K. The temperature evolution of the Raman spectra shows that low-temperature, local static disorder strongly affects the crystal structural dynamics and phase transitions at higher temperatures.
Layered Control for Cooperative Locomotion of Two Quadrupedal Robots: Centralized and Distributed Approaches

This article presents a layered control approach for real-time trajectory planning and control of robust cooperative locomotion by two holonomically constrained quadrupedal robots. A novel interconnected network of reduced-order models, based on the single rigid body (SRB) dynamics, is developed for trajectory planning purposes. At the higher level of the control architecture, two different model predictive control (MPC) algorithms are proposed to address the optimal control problem of the interconnected SRB dynamics: centralized and distributed MPCs. The distributed MPC assumes two local quadratic programs that share their optimal solutions according to a one-step communication delay and an agreement protocol. At the lower level of the control scheme, distributed nonlinear controllers are developed to impose the full-order dynamics to track the prescribed reduced-order trajectories generated by MPCs. The effectiveness of the control approach is verified with extensive numerical simulations and experiments for the robust and cooperative locomotion of two holonomically constrained A1 robots with different payloads on variable terrains and in the presence of disturbances. It is shown that the distributed MPC has a performance similar to that of the centralized MPC, while the computation time is reduced significantly.
Sampling an Edge in Sublinear Time Exactly and Optimally

Sampling edges from a graph in sublinear time is a fundamental problem and a powerful subroutine for designing sublinear-time algorithms. Suppose we have access to the vertices of the graph and know a constant-factor approximation to the number of edges. An algorithm for pointwise $\varepsilon$-approximate edge sampling with complexity $O(n/\sqrt{\varepsilon m})$ has been given by Eden and Rosenbaum [SOSA 2018]. This has been later improved by T\v{e}tek and Thorup [STOC 2022] to $O(n \log(\varepsilon^{-1})/\sqrt{m})$. At the same time, $\Omega(n/\sqrt{m})$ time is necessary. We close the problem, by giving an algorithm with complexity $O(n/\sqrt{m})$ for the task of sampling an edge exactly uniformly.
Low-cost Unsupervised Outlier Detection by Autoencoders with Robust Estimation

: Recently, an unsupervised outlier detection method based on the reconstruction errors of an autoencoder (AE), which achieves high detection accuracy, was proposed. This method, however, requires a high calculation cost because of its ensemble scheme. Therefore, in this paper, we propose a novel AE-based unsupervised method that can achieve high detection performance at a low calculation cost. Our method introduces the concept of robust estimation to appropriately restrict reconstruction capability and ensure robustness. Experimental results on several public benchmark datasets show that our method outperforms well-known outlier detection methods and at a low calculation cost.
FullPack: Full Vector Utilization for Sub-Byte Quantized Inference on General Purpose CPUs

Although prior art has demonstrated negligible accuracy drop in sub-byte quantization -- where weights and/or activations are represented by less than 8 bits -- popular SIMD instructions of CPUs do not natively support these datatypes. While recent methods, such as ULPPACK, are already using sub-byte quantization on general-purpose CPUs with vector units, they leave out several empty bits between the sub-byte values in memory and in vector registers to avoid overflow to the neighbours during the operations. This results in memory footprint and bandwidth-usage inefficiencies and suboptimal performance. In this paper, we present memory layouts for storing, and mechanisms for processing sub-byte (4-, 2-, or 1-bit) models that utilize all the bits in the memory as well as in the vector registers for the actual data. We provide compute kernels for the proposed layout for the GEMV (GEneral Matrix-Vector multiplication) operations between weights and activations of different datatypes (e.g., 8-bit activations and 4-bit weights). For evaluation, we extended the TFLite package and added our methods to it, then ran the models on the cycle-accurate gem5 simulator to compare detailed memory and CPU cycles of each method. We compare against nine other methods that are actively used in production including GEMLOWP, Ruy, XNNPack, and ULPPACK. Furthermore, we explore the effect of different input and output sizes of deep learning layers on the performance of our proposed method. Experimental results show 0.96-2.1x speedup for small sizes and 1.2-6.7x speedup for mid to large sizes. Applying our proposal to a real-world speech recognition model, Mozilla DeepSpeech, we proved that our method achieves 1.56-2.11x end-to-end speedup compared to the state-of-the-art, depending on the bit-width employed.
Benchmark scenarios for the NMSSM

We discuss constrained and semi--constrained versions of the next--to--minimal supersymmetric extension of the Standard Model (NMSSM) in which a singlet Higgs superfield is added to the two doublet superfields that are present in the minimal extension (MSSM). This leads to a richer Higgs and neutralino spectrum and allows for many interesting phenomena that are not present in the MSSM. In particular, light Higgs particles are still allowed by current constraints and could appear as decay products of the heavier Higgs states, rendering their search rather difficult at the LHC. We propose benchmark scenarios which address the new phenomenological features, consistent with present constraints from colliders and with the dark matter relic density, and with (semi--)universal soft terms at the GUT scale. We present the corresponding spectra for the Higgs particles, their couplings to gauge bosons and fermions and their most important decay branching ratios. A brief survey of the search strategies for these states at the LHC is given.
Quenching across quantum critical points: Role of topological patterns

We introduce a one-dimensional version of the Kitaev model consisting of spins on a two-legged ladder and characterized by Z2 invariants on the plaquettes of the ladder. We map the model to a fermionic system and identify the topological sectors associated with different Z2 patterns in terms of fermion occupation numbers. Within these different sectors, we investigate the effect of a linear quench across a quantum critical point. We study the dominant behavior of the system by employing a Landau-Zener–type analysis of the effective Hamiltonian in the low-energy subspace for which the effective quenching can sometimes be non-linear. We show that the quenching leads to a residual energy which scales as a power of the quenching rate, and that the power depends on the topological sectors and their symmetry properties in a non-trivial way. This behavior is consistent with the general theory of quantum quenching, but with the correlation length exponent ν being different in different sectors.
Star formation activity in the southern Galactic H II region G351.63-1.25

The southern Galactic high-mass star-forming region, G351.63−1.25, is an H ii region–molecular cloud complex with a luminosity of ∼2.0 × 10 5 L ⊙ , located at a distance of 2.4 kpc from the Sun. In this paper, we focus on the investigation of the associated H ii region, embedded cluster and the interstellar medium in the vicinity of G351.63−1.25. We address the identification of exciting source(s) as well as the census of the stellar populations, in an attempt to unfold star formation activity in this region. The ionized gas distribution has been mapped using the Giant Metrewave Radio Telescope, India, at three frequencies: 1280, 610 and 325 MHz. The H ii region shows an elongated morphology and the 1280 MHz map comprises six resolved high-density regions encompassed by diffuse emission spanning 1.4 × 1.0 pc 2 . Based on the measurements of flux densities at multiple radio frequencies, the brightest ultracompact core has electron temperature T e ∼7647 ±153 K and emission measure, EM∼2.0 ± 0.8×10 7 cm −6 pc. The zero-age main-sequence spectral type of the brightest radio core is O7.5. We have carried out near-infrared observations in the JHK s bands using the SIRIUS camera on the 1.4 m Infrared Survey Facility telescope. The near-infrared images reveal the presence of a cluster embedded in nebulous fan-shaped emission. The log-normal slope of the K -band luminosity function of the embedded cluster is found to be ∼0.27 ± 0.03, and the fraction of the near-infrared excess stars is estimated to be 43 per cent. These indicate that the age of the cluster is consistent with ∼1 Myr. Other available data of this region show that the warm (mid-infrared) and cold (millimetre) dust emission peak at different locations indicating progressive stages of star formation process. The champagne flow model from a flat, thin molecular cloud is used to explain the morphology of radio emission with respect to the millimetre cloud and infrared brightness.
Principal eigenvalues of fully nonlinear integro-differential elliptic equations with a drift term

We study existence of principal eigenvalues of a fully nonlinear integro-differential elliptic equations with a drift term via the Krein–Rutman theorem and regularity estimates up to boundary of viscosity solutions. We also show simplicity of eigenfunctions in the viscosity sense by using a nonlocal version of the ABP estimate and a “sweeping lemma”.
ISM composition through X-ray spectroscopy of LMXBs

Context. The diffuse interstellar medium (ISM) is an integral part of the evol uti n of the entire Galaxy. Metals are produced by stars and their abundances are the direct testimony of the history of stellar evolution. However, the interstellar dust compo siti n is not well known and the total abundances are yet to be accurately deter mined. Aims. We probe ISM dust composition, total abundances, and abunda nce gradients through the study of interstellar absorption features in the high-resolution X-ray spectra of Galactic low-mass X -ray binaries (LMXBs). Methods. We use high-quality grating spectra of nine LMXBs taken with XMM-Newton. We measure the column densities of O, Ne, Mg, and Fe with an empirical model and estimate the Galactic a bundance gradients. Results. The column densities of the neutral gas species are in agreem ent with those found in the literature. Solids are a significa nt reservoir of metals like oxygen and iron. Respectively, 15– 25% and 65–90% of the total amount of O i and Fei is found in dust. The dust amount and mixture seem to be consistent along all th e ines-of-sight (LOS). Our estimates of abundance gradien ts a d predictions of local interstellar abundances are in agreem ent with those measured at longer wavelengths. Conclusions. Our work shows that X-ray spectroscopy is a very powerful met hod to probe the ISM. For instance, on a large scale the ISM appears to be chemically homogeneous showing simila r gas ionization ratios and dust mixtures. The agreement bet ween the abundances of the ISM and the stellar objects suggests that t he local Galaxy is also chemically homogeneous.
Supplemental Information File

General NMR, LC-MS and HPLC procedures 1 H and 2D experiments were recorded at a 600MHz using DMSO-d6 in a Varian spectrometer and chemical shifts were recorded based on the corresponding solvent signal (δH 2.50 ppm for DMSO-d6). High resolution ESI-TOF (HRMS) mass spectra were provided by the Scripps Research Institute, La Jolla, CA. Low-resolution LC/ESI-MS data were measured using an Agilent 1200 series LC/MS system-with a reverse-phase C18 column (Phenomenex Luna, 150mm X 4.6 mm, 5 μm) at a flow rate of 0.7 mL/min. Semi-preparative HPLC was performed on an Agilent 1200 series, using a C18 column (Phenomenex Luna, 250 mm X 10.0 mm, 5μm). Collection and phylogenetic analysis of strain SNA-024 The marine-derived bacterium strain SNA-024 was isolated from a sediment sample collected from West Plana Cay, Bahamas. Bacterial spores were collected via a stepwise centrifugation as follows: 2 g of sediment was dried over 24 hr in an incubator at 35ånd the resulting sediment added to 10 mL sH2O containing 0.05% Tween 20. After vigorous vortex for 10 min, the sediment was centrifuged at 18000 rpm for 25 min (4˚C) and the resulting spore pellet collected. The resuspended spore pellet (4 mL sH2O) was plated on an acidified Gause media, giving rise to individual colonies of SNA-024 after 2 weeks. Analysis of the 16S rRNA sequence of SNA-024 revealed 98% identity to Streptomyces coeruleoaurantiacus. Cultivation and Extraction Bacterium SNA-024 was cultured in 15 X 2.8 L Fernbach flasks each containing 1 L of seawater-based medium (10 g starch, 4 g yeast extract, 2 g peptone, 1 g CaCO3, 40 mg Fe2(SO4)3 • 4H2O, 100 mg KBr) and shaken at 200 rpm at 27 °C. After seven days of cultivation, sterilized XAD-7-HP resin (20 g/L) was added to absorb the organic products, and the culture and resin were shaken at 200 rpm for 2 h. The resin was filtered through cheesecloth, washed with deionized water, and eluted with acetone. The acetone-soluble fraction was dried in vacuo to yield 11.4 g of extract. Purification of N6,N6-dimethyladenosine Crude extract (11.4g) was separated into 9 fractions by reverse phase chromatography (C18) using a stepwise gradient, with MeOH /H2O (20%-100%). The biologically active fraction (F5, 91.4mg) was further purified using an automated reversed phase chromatography (ISCO, RediSep Rf Gold® 30 g C18, 35 ml/min) using a gradient solvent system from 10%-100% MeOH:H2O over 25 min and 30 fractions (F5-I1 – F5-I30) were …
Formation and disruption of current filaments in a flow-driven turbulent magnetosphere

Recent observations have established that the magnetosphere is a system of natural complexity. The co-existence of multi-scale structures such as auroral arcs, turbulent convective flows, and scale-free distributions of energy perturbations has lacked a unified explanation, although there is strong reason to believe that they all stem from a common base of physics. In this paper we show that a slow but turbulent convection leads to the formation of multi-scale current filaments reminiscent of auroral arcs. The process involves an interplay between random shuffling of field lines and dissipation of magnetic energy on sub-MHD scales. As the filament system reaches a critical level of complexity, local current disruption can trigger avalanches of energy release of varying sizes, leading to scale-free distributions over energy perturbation, power, and event duration. A long-term memory effect is observed whereby the filament system replicates itself after each avalanche. The results support the view that that the classical and inverse cascades operate simultaneously in the magnetosphere. In the former, the high Reynolds-number plasma flow disintegrate into turbulence through successive breakdowns; in the latter, the interactions of small-scale flow eddies with the magnetic field can self-organize into elongated current filaments and large-scale energy avalanches mimicking the substorm.
Axially deformed relativistic Hartree Bogoliubov theory with a separable pairing force

A separable form of pairing interaction in the 1 S0 channel has been introduced and successfully applied in the description of both static and dynamic properties of superfluid nuclei. By adjusting the parameters to reproduce the pairing properties of the Gogny force in nuclear matter, this separable pairing force is successful in depicting the pairing properties of ground states and vibrational excitations of spherical nuclei on almost the same footing as the original Gogny force. In this article, we extend these investigations for relativistic Hartree-Bogoliubov theory in deformed nuclei with axial symmetry (RHBZ) using the same separable pairing interaction. To preserve translational invariance we construct one- and two-dimensional Talmi-Moshinsky brackets for the cylindrical harmonic oscillator basis. We show that the matrix elements of this force can then be expanded in a series of separable terms. The convergence of this expansion is investigated for various deformations. We observe a relatively fast convergence. This allows for a considerable reduction in computing time as compared to RHBZ calculations with the full Gogny force in the pairing channel. As an example we solve the RHBZ equations with this separable pairing force for the ground states of the chain of Sm isotopes. Good agreement with the experimental data as well as with other theoretical results is achieved.
Spectroscopic orbital elements for the helium-rich subdwarf binary PG 1544+488

PG1544+488 is an exceptional short-period spectroscopic binary containing two subdwarf B stars. It is also exceptional because the surfaces of both components are extremely helium-rich. We present a new analysis of spectroscopy of PG1544+488 obtained with the William Herschel Telescope. We obtain improved orbital parameters and atmospheric parameters for each component. The orbital period $P=0.496\pm0.002$\,d, dynamical mass ratio $M_{\rm B}/M_{\rm A}=0.911\pm0.015$, and spectroscopic radius ratio $R_{\rm B}/R_{\rm A}=0.939\pm0.004$ indicate a binary consisting of nearly identical twins. The data are insufficient to distinguish any difference in surface composition between the components, which are slightly metal-poor (1/3 solar) and carbon-rich (0.3% by number). The latter indicates that the hotter component, at least, has ignited helium. The best theoretical model for the origin of PG1544+488 is by the ejection of a common envelope from a binary system in which both components are giants with helium cores of nearly equal mass. Since precise tuning is necessary to yield two helium cores of similar masses at the same epoch, the mass ratio places very tight constraints on the dimensions of the progenitor system and on the physics of the common-envelope ejection mechanism.
Parameter estimation in memory-assisted noisy quantum interferometry

We demonstrate that memory in an $N$-qubit system subjected to decoherence, is a potential resource for the slow-down of the entanglement decay. We show that this effect can be used to retain the sub shot-noise sensitivity of the parameter estimation in quantum interferometry. We calculate quantum Fisher information, which sets the ultimate bound for the precision of the estimation. We also derive the sensitivity of such a noisy interferometer, when the phase is either estimated from the measurements of the population imbalance or from the one-body density.
Superintegrable and shape invariant systems with position dependent mass

Second order integrals of motion for 3d quantum mechanical systems with position dependent masses (PDM) are classified. Namely, all PDM systems are specified which, in addition to their rotation invariance, admit at least 1 second order integral of motion. All such systems appear to be also shape invariant and exactly solvable. Moreover, some of them possess the property of double shape invariance and can be solved using two different superpotentials. Among them there are systems with double shape invariance which present nice bridges between the Coulomb and isotropic oscillator systems. A simple algorithm for calculating the discrete spectrum and the corresponding state vectors for the considered PDM systems is presented and applied to solve five of the found systems.