ShantanuT01/DACTYL-Pretraining huggingface dataset:
Advancements in computing based on qubit networks, and in particular the flux-qubit processor architecture developed by D-Wave System's Inc., have enabled the physical simulation of quantum-dot cellular automata (QCA) networks beyond the limit of classical methods. However, the embedding of QCA networks onto the available processor architecture is a key challenge in preparing such simulations. In this work, two approaches to embedding QCA circuits are characterized: a dense placement algorithm that uses a routing method based on negotiated congestion; and a heuristic method implemented in D-Wave's Solver API package. A set of benchmark QCA networks is used to characterise the algorithms and a stochastic circuit generator is employed to investigate the performance for different processor sizes and active flux-qubit yields.
The miscibility of Au and Li exhibits a potential application as an adhesion layer and electrode material in secondary batteries. Here, to explore alloying properties, we constructed a neural network potential (NNP) of Au-Li binary systems based on density functional theory (DFT) calculations. To accelerate construction of NNPs, we proposed an efficient and inexpensive method of structural dataset generation. The predictions by the constructed NNP on lattice parameters and phonon properties agree well with those obtained by DFT calculations. We also investigated the mixing energy of Au$_{1-x}$Li$_{x}$ with fine composition grids, showing excellent agreement with DFT verifications. We found the existence of various compositions with structures on and slightly above the convex hull, which can explain the lack of consensus on the Au-Li stable phases in previous studies. Moreover, we newly found Au$_{0.469}$Li$_{0.531}$ as a stable phase, which has never been reported elsewhere. Finally, we examined the alloying process starting from the phase separated structure to the complete mixing phase. We found that when multiple adjacent Au atoms dissolved into Li, the alloying of the entire Au/Li interface started from the dissolved region. This paper demonstrates the applicability of NNPs toward miscible phases and provides the understanding of the alloying mechanism.
Lyman Alpha Emitting (LAE) galaxies are thought to be progenitors of present-day L* galaxies. Clustering analyses have suggested that LAEs at z ~ 3 might evolve into LAEs at z ~ 2, but it is unclear whether the physical nature of these galaxies is compatible with this hypothesis. Several groups have investigated the properties of LAEs using spectral energy distribution (SED) fitting, but direct comparison of their results is complicated by inconsistencies in the treatment of the data and in the assumptions made in modeling the stellar populations, which are degenerate with the effects of galaxy evolution. By using the same data analysis pipeline and SED fitting software on two stacked samples of LAEs at z = 3.1 and z = 2.1, and by eliminating several systematic uncertainties that might cause a discrepancy, we determine that the physical properties of these two samples of galaxies are dramatically different. LAEs at z = 3.1 are found to be old (age ~ 1 Gyr) and metal-poor (Z < 0.2 Z_Sun), while LAEs at z = 2.1 appear to be young (age ~ 50 Myr) and metal-rich (Z > Z_Sun). The difference in the observed stellar ages makes it very unlikely that z = 3.1 LAEs evolve directly into z = 2.1 LAEs. Larger samples of galaxies, studies of individual objects and spectroscopic measurements of metallicity at these redshifts are needed to confirm this picture, which is difficult to reconcile with the effects of 1 Gyr of cosmological evolution.
Ensemble inequivalence has been observed in several systems. In particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long-range interactions. We display a connection between such behaviour and a mean-field like structure of the partition function. Since short-range models cannot display this kind of behaviour, this strongly suggests that such systems are necessarily non-mean field in the sense indicated here. We illustrate our results showing an application to the Blume-Emery-Griffiths model. We further show that a broad class of systems with non-integrable interactions are indeed of mean-field type in the sense specified, so that they are expected to display ensemble inequivalence as well as the peculiar behaviour described above in the microcanonical ensemble.
A weak formulation for the so-called "semilinear strongly damped wave equation with constraint" is introduced and a corresponding notion of solution is defined. The main idea in this approach consists in the use of duality techniques in Sobolev-Bochner spaces, aimed at providing a suitable "relaxation" of the constraint term. A global in time existence result is proved under the natural condition that the initial data have finite "physical" energy.
We explore the predictions of the renormalized perturbation theory for an n-channel Anderson model, both with and without Hund's rule coupling, in the regime away from particle-hole symmetry. For the model with n=2 we deduce the renormalized parameters from numerical renormalization group calculations, and plot them as a function of the occupation at the impurity site, nd. From these we deduce the spin, orbital and charge susceptibilities, Wilson ratios and quasiparticle density of states at T=0, in the different parameter regimes, which gives a comprehensive overview of the low energy behavior of the model. We compare the difference in Kondo behaviors at the points where nd=1 and nd=2. One unexpected feature of the results is the suppression of the charge susceptibility in the strong correlation regime over the occupation number range 1 <nd <3.
In this first paper on the results of our Herschel PACS survey of local Ultraluminous Infrared Galaxies (ULIRGs), as part of our SHINING survey of local galaxies, we present far-infrared spectroscopy of Mrk 231, the most luminous of the local ULIRGs, and a type 1 broad absorption line AGN. For the first time in a ULIRG, all observed far-infrared fine-structure lines in the PACS range were detected and all were found to be deficient relative to the far infrared luminosity by 1 - 2 orders of magnitude compared with lower luminosity galaxies. The deficits are similar to those for the mid-infrared lines, with the most deficient lines showing high ionization potentials. Aged starbursts may account for part of the deficits, but partial covering of the highest excitation AGN powered regions may explain the remaining line deficits. A massive molecular outflow, discovered in OH and 18OH, showing outflow velocities out to at least 1400 km/sec, is a unique signature of the clearing out of the molecular disk that formed by dissipative collapse during the merger. The outflow is characterized by extremely high ratios of 18O / 16O suggestive of interstellar medium processing by advanced starbursts.
Let $\pi: X \longrightarrow C$ be a fibration with reduced fibers over a curve $C$ and consider a polarization $H$ on the surface $X$. Let $E$ be a stable vector bundle of rank $2$ on $C$. We prove that the pullback $\pi^*E$ is a $H-$stable bundle over $X$. This result allows us to relate the corresponding moduli spaces of stable bundles $\mathcal{M}_C(2,d)$ and $\mathcal{M}_{X,H}(2,df,0)$ through an injective morphism. We study the induced morphism at the level of Brill-Noether loci to construct examples of Brill-Noether loci on fibered surfaces. Results concerning the emptiness of Brill-Noether loci follow as a consequence of a generalization of Clifford's Theorem for rank two bundles on surfaces.
Recently, video frame interpolation using a combination of frame- and event-based cameras has surpassed traditional image-based methods both in terms of performance and memory efficiency. However, current methods still suffer from (i) brittle image-level fusion of complementary interpolation results, that fails in the presence of artifacts in the fused image, (ii) potentially temporally inconsistent and inefficient motion estimation procedures, that run for every inserted frame and (iii) low contrast regions that do not trigger events, and thus cause events-only motion estimation to generate artifacts. Moreover, previous methods were only tested on datasets consisting of planar and faraway scenes, which do not capture the full complexity of the real world. In this work, we address the above problems by introducing multi-scale feature-level fusion and computing one-shot non-linear inter-frame motion from events and images, which can be efficiently sampled for image warping. We also collect the first large-scale events and frames dataset consisting of more than 100 challenging scenes with depth variations, captured with a new experimental setup based on a beamsplitter. We show that our method improves the reconstruction quality by up to 0.2 dB in terms of PSNR and up to 15% in LPIPS score.
We prove global Lipschitz regularity for a wide class of convex variational integrals among all functions in $W^{1,1}$ with prescribed (sufficiently regular) boundary values, which are not assumed to satisfy any geometrical constraint (as for example bounded slope condition). Furthermore, we do not assume any restrictive assumption on the geometry of the domain and the result is valid for all sufficiently smooth domains. The result is achieved with a suitable approximation of the functional together with a new construction of appropriate barrier functions.
We split the program of explicit descent of elliptic curves into two parts. For $n=3$ and $n=5,$ we first display a model for the universal elliptic curve $E$ with full level $n$ structure and describe the map of rational points of $E$ to the cohomology group $H^1(G, E[n]).$ Second, we find models in $\PP^{n-1}$ of principal homogeneous spaces of $E$ corresponding to all possible elements of $H^1(G, E[n]),$ i.e. for those elements with trivial period-index obstruction. For this we use the relationship established in \cite{me2} between the period-index obstruction and the norm symbol, a generalization of the Hilbert symbol.
The electronic density of states (DOS) of La$_{0.625}$Ca$_{0.375}$MnO$_3$(LCMO) strain free epitaxial thin films with an insulator-metal transition temperature (T$_{IM}$) of 250 K was probed using variable temperature scanning tunneling microscopy and spectroscopy. We find a depression in the DOS with a finite zero bias conductance (ZBC) signifying a pseudogap (PG) in 78-310 K temperature range. With cooling, the ZBC is found to increase indicating an increased DOS near E$_F$. We interpret PG as a signature of Jahn-Teller polarons while ZBC change, in agreement with the bulk insulator-metal transition, optical Drude peak, and photoemission experiments indicates the presence of free carriers at the Fermi energy in the metallic phase. The free carriers are discussed in terms of correlated polaronic states.
We introduce a flexible and tractable infinite-dimensional stochastic volatility model. More specifically, we consider a Hilbert space valued Ornstein-Uhlenbeck-type process, whose instantaneous covariance is given by a pure-jump stochastic process taking values in the cone of positive self-adjoint Hilbert-Schmidt operators. The tractability of our model lies in the fact that the two processes involved are jointly affine, i.e., we show that their characteristic function can be given explicitly in terms of the solutions to a set of generalised Riccati equations. The flexibility lies in the fact that we allow multiple modeling options for the instantaneous covariance process, including state-dependent jump intensity. Infinite dimensional volatility models arise e.g. when considering the dynamics of forward rate functions in the Heath-Jarrow-Morton-Musiela modeling framework using the Filipovi\`c space. In this setting we discuss various examples: an infinite-dimensional version of the Barndorff-Nielsen-Shephard stochastic volatility model, as well as a model involving self-exciting volatility.
The dissipative and decoherence properties of the two-level atom interacting with the squeezed vacuum field reservoir are investigated based on the nonautonomous master equation of the atomic density matrix in the framework of algebraic dynamics. The nonautonomous master equation is converted into a Schr\"{o}dinger-like equations and its dynamical symmetry is found based on the left and right representations of the relevant algebra. The time-dependent solution and the steady solution are obtained analytically. The asymptotic behavior of the solution is examined and the approach to the equilibrium state is proved. Based on the analytic solution the response of the system to the squeezed vacuum field reservoir is studied numerically.
We investigate the effect of uniaxial heterostrain on the interacting phase diagram of magic-angle twisted bilayer graphene. Using both self-consistent Hartree-Fock and density-matrix renormalization group calculations, we find that small strain values ($\epsilon \sim 0.1 - 0.2 \%$) drive a zero-temperature phase transition between the symmetry-broken Kramers intervalley-coherent insulator and a nematic semi-metal. The critical strain lies within the range of experimentally observed strain values, and we therefore predict that strain is at least partly responsible for the sample-dependent experimental observations.
A key task of observational extragalactic astronomy is to determine where -- within galaxies of diverse masses and morphologies -- stellar mass growth occurs, how it depends on galaxy properties and what processes regulate star formation. Using spectroscopic indices derived from the stellar continuum at $\sim 4000$\AA, we determine the spatially resolved star-formation histories of 980000 spaxels in 2404 galaxies in the SDSS-IV MaNGA IFU survey. We examine the spatial distribution of star-forming, quiescent, green valley, starburst and post-starburst spaxels as a function of stellar mass and morphology to see where and in what types of galaxy star formation is occurring. The spatial distribution of star-formation is dependent primarily on stellar mass, with a noticeable change in the distribution at \mstar$>10^{10}$\msun. Galaxies above this mass have an increasing fraction of regions that are forming stars with increasing radius, whereas lower mass galaxies have a constant fraction of star forming regions with radius. Our findings support a picture of inside-out growth and quenching at high masses. We find that morphology (measured via concentration) correlates with the fraction of star-forming spaxels, but not with their radial distribution. We find (post-)starburst regions are more common outside of the galaxy centre, are preferentially found in asymmetric galaxies, and have lower gas-phase metallicity than other regions, consistent with interactions triggering starbursts and driving low metallicity gas into regions at $<1.5R_e$.
Superstring theory on ${\rm AdS}_3\times {\rm S}^3\times \mathbb{T}^4$ with the smallest amount of NS-NS flux (`$k=1$') is shown to be dual to the spacetime CFT given by the large $N$ limit of the free symmetric product orbifold $\mathrm{Sym}^N(\mathbb{T}^4)$. To define the worldsheet theory at $k=1$, we employ the hybrid formalism in which the ${\rm AdS}_3\times {\rm S}^3$ part is described by the $\mathfrak{psu}(1,1|2)_1$ WZW model (which is well defined). Unlike the case for $k\geq2$, it turns out that the string spectrum at $k=1$ does {\it not} exhibit the long string continuum, and perfectly matches with the large $N$ limit of the symmetric product. We also demonstrate that the fusion rules of the symmetric orbifold are reproduced from the worldsheet perspective. Our proposal therefore affords a tractable worldsheet description of a tensionless limit in string theory, for which the dual CFT is also explicitly known.
This article documents my journey down the rabbit hole, chasing what I have come to know as a particularly unyielding problem in Ramsey theory on the integers: the $2$-Large Conjecture. This conjecture states that if $D \subseteq \mathbb{Z}^+$ has the property that every $2$-coloring of $\mathbb{Z}^+$ admits arbitrarily long monochromatic arithmetic progressions with common difference from $D$ then the same property holds for any finite number of colors. We hope to provide a roadmap for future researchers and also provide some new results related to the $2$-Large Conjecture.
The vertices of any graph with $m$ edges can be partitioned into two parts so that each part meets at least $\frac{2m}{3}$ edges. Bollob\'as and Thomason conjectured that the vertices of any $r$-uniform graph may be likewise partitioned into $r$ classes such that each part meets at least $cm$ edges, with $c=\frac{r}{2r-1}$. In this paper, we prove this conjecture for the case $r=3$. In the course of the proof we shall also prove an extension of the graph case which was conjectured by Bollob\'as and Scott.
Detailed knowledge of the variability of classical Cepheids, in particular their modulations and mode composition, provides crucial insight into stellar structure and pulsation. However, tiny modulations of the dominant radial-mode pulsation were recently found to be very frequent, possibly ubiquitous in Cepheids, which makes secondary modes difficult to detect and analyse, since these modulations can easily mask the potentially weak secondary modes. The aim of this study is to re-investigate the secondary mode content in the sample of OGLE-III and -IV single-mode classical Cepheids using kernel regression with adaptive kernel width for pre-whitening, instead of using a constant-parameter model. This leads to a more precise removal of the modulated dominant pulsation, and enables a more complete survey of secondary modes with frequencies outside a narrow range around the primary. Our analysis reveals that significant secondary modes occur more frequently among first overtone Cepheids than previously thought. The mode composition appears significantly different in the Large and Small Magellanic Clouds, suggesting a possible dependence on chemical composition. In addition to the formerly identified non-radial mode at $P_2 \approx 0.6\ldots 0.65 P_1$ (0.62-mode), and a cluster of modes with near-primary frequency, we find two more candidate non-radial modes. One is a numerous group of secondary modes with $P_2 \approx 1.25 P_1$, which may represent the fundamental of the 0.62-mode, supposed to be the first harmonic of an $l \in \{7,8, 9\}$ non-radial mode. The other new mode is at $P_2 \approx 1.46 P_1$, possibly analogous to a similar, rare mode recently discovered among first overtone RR Lyrae stars.
We study the effect of variable jet bulk Lorentz factors, i.e., either jet acceleration or deceleration, on partially synchrotron self-absorbed radio spectra from cores of radio-loud active galactic nuclei and black-hole binaries in the hard state. In about a half of quasars and radio galaxies, their core radio spectra are observed to be soft, i.e., have the spectral index of $\alpha<0$. If they are emitted by jets with constant Lorentz factors, that softness implies deposition of large amounts of energy at large distances from the centre. We show here that such soft spectra can be explained without that energetic requirement by emission of jets with the Doppler factor increasing with the distance. This can happen for either jet acceleration or deceleration, depending on the jet viewing angle. We find our model can explain the quiescent radio to X-ray spectra of the BL Lac objects Mrk 421 and Mrk 501.
We give a geometric interpretation of the group law for Jacobian varieties by extending the geometric construction of chords and tangents on an elliptic curve. For any given algebraic curve $\mathcal X$ and reduced divisors $D_1, D_2 \in \mbox{Jac } \mathcal X$, we define curves $\mathcal X^\prime$ and $\mathcal X^{"}$ such that the intersection $\mathcal X \cap \mathcal X^\prime$ determines precisely the divisor $-(D_1+D_2)$ and the intersection $\mathcal X\cap \mathcal X^{"}$ determines $D_1+D_2$. For superelliptic curves such formulas are made explicit.
For the initial boundary value problem of compressible barotropic Navier-Stokes equations in one-dimensional bounded domains with general density-dependent viscosity and large external force, we prove that there exists a unique global classical solution with large initial data containing vacuum. Furthermore, we show that the density is bounded from above independently of time which in particular yields the large time behavior of the solution as time tends to infinity: the density and the velocity converge to the steady states in $L^p$ and in $W^{1,p}$ ($1\le p<+\infty$) respectively. Moreover, the decay rate in time of the solution is shown to be exponential. Finally, we also prove that the spatial gradient of the density will blow up as time tends to infinity when vacuum states appear initially even at one point.
Optimizing a deep neural network is a fundamental task in computer vision, yet direct training methods often suffer from over-fitting. Teacher-student optimization aims at providing complementary cues from a model trained previously, but these approaches are often considerably slow due to the pipeline of training a few generations in sequence, i.e., time complexity is increased by several times.   This paper presents snapshot distillation (SD), the first framework which enables teacher-student optimization in one generation. The idea of SD is very simple: instead of borrowing supervision signals from previous generations, we extract such information from earlier epochs in the same generation, meanwhile make sure that the difference between teacher and student is sufficiently large so as to prevent under-fitting. To achieve this goal, we implement SD in a cyclic learning rate policy, in which the last snapshot of each cycle is used as the teacher for all iterations in the next cycle, and the teacher signal is smoothed to provide richer information. In standard image classification benchmarks such as CIFAR100 and ILSVRC2012, SD achieves consistent accuracy gain without heavy computational overheads. We also verify that models pre-trained with SD transfers well to object detection and semantic segmentation in the PascalVOC dataset.
We consider multilinear Littlewood polynomials, polynomials in $n$ variables in which a specified set of monomials $U$ have $\pm 1$ coefficients, and all other coefficients are $0$. We provide upper and lower bounds (which are close for $U$ of degree below $\log n$) on the minimum, over polynomials $h$ consistent with $U$, of the maximum of $|h|$ over $\pm 1$ assignments to the variables. (This is a variant of a question posed by Erd\"os regarding the maximum on the unit disk of univariate polynomials of given degree with unit coefficients.) We outline connections to the theory of quasi-random graphs and hypergraphs, and to statistical mechanics models. Our methods rely on the analysis of the Gale-Berlekamp game; on the constructive side of the generic chaining method; on a Khintchine-type inequality for polynomials of degree greater than $1$; and on Bernstein's approximation theory inequality.