ShantanuT01/DACTYL-Pretraining huggingface dataset:
This work looks at the box-counting dimension of sets related to subordinators (non-decreasing L\'evy processes). It was recently shown in [Savov, 2014] that almost surely $\lim_{\delta\to0}U(\delta)N(t,\delta) = t$, where $N(t,\delta)$ is the minimal number of boxes of size at most $\delta$ needed to cover a subordinator's range up to time $t$, and $U(\delta)$ is the subordinator's renewal function. Our main result is a central limit theorem (CLT) for $N(t,\delta)$, complementing and refining work in [Savov, 2014].   Box-counting dimension is defined in terms of $N(t,\delta)$, but for subordinators we prove that it can also be defined using a new process obtained by shortening the original subordinator's jumps of size greater than $\delta$. This new process can be manipulated with remarkable ease in comparison to $N(t,\delta)$, and allows better understanding of the box-counting dimension of a subordinator's range in terms of its L\'evy measure, improving upon [Corollary 1, Savov, 2014]. Further, we shall prove corresponding CLT and almost sure convergence results for the new process.
In this work, we study the 1-bit convolutional neural networks (CNNs), of which both the weights and activations are binary. While being efficient, the classification accuracy of the current 1-bit CNNs is much worse compared to their counterpart real-valued CNN models on the large-scale dataset, like ImageNet. To minimize the performance gap between the 1-bit and real-valued CNN models, we propose a novel model, dubbed Bi-Real net, which connects the real activations (after the 1-bit convolution and/or BatchNorm layer, before the sign function) to activations of the consecutive block, through an identity shortcut. Consequently, compared to the standard 1-bit CNN, the representational capability of the Bi-Real net is significantly enhanced and the additional cost on computation is negligible. Moreover, we develop a specific training algorithm including three technical novelties for 1- bit CNNs. Firstly, we derive a tight approximation to the derivative of the non-differentiable sign function with respect to activation. Secondly, we propose a magnitude-aware gradient with respect to the weight for updating the weight parameters. Thirdly, we pre-train the real-valued CNN model with a clip function, rather than the ReLU function, to better initialize the Bi-Real net. Experiments on ImageNet show that the Bi-Real net with the proposed training algorithm achieves 56.4% and 62.2% top-1 accuracy with 18 layers and 34 layers, respectively. Compared to the state-of-the-arts (e.g., XNOR Net), Bi-Real net achieves up to 10% higher top-1 accuracy with more memory saving and lower computational cost. Keywords: binary neural network, 1-bit CNNs, 1-layer-per-block
We introduce a new slave-boson mean-field theory which allows the investigation of general multi-band Hubbard models. Unlike earlier attempts of such a generalisation, in our approach the quantum-mechanical problem is exactly reformulated in an extended Hilbert space of Fermions and Bosons before a mean-field approximation is applied. Systems with superconducting order parameters are naturally included in our formalism. Our ground-state energy functional agrees with the corresponding quantity derived within the Gutzwiller theory.
It is well known that one-loop free energy of closed strings diverges above the Hagedorn temperature. One explanation for this divergence is that a `winding mode' in the Euclidean time direction becomes tachyonic above the Hagedorn temperature. The Hagedorn transition of closed strings has been proposed as a phase transition via condensation of this winding tachyon. However, we have not known the stable minimum of the potential of this winding tachyon so far. On the other hand, we have previously calculated the finite temperature effective potential of open strings on D-brane--anti-D-brane pairs, and shown that a phase transition occurs near the Hagedorn temperature and D9-brane--anti-D9-brane pairs become stable. In this paper, we present a conjecture that {\it D9-brane--anti-D9-brane pairs are created by the Hagedorn transition of closed strings}, and describe some circumstantial evidences. We compute two types of the cylinder amplitudes of open strings and show that these amplitudes approach to the sphere amplitude of closed strings with two winding tachyon insertion in the closed string vacuum limit together with the Hagedorn temperature limit. We also show that the potential energy at the open string vacuum decreases limitlessly as the temperature approaches to the Hagedorn temperature. It is natural to think that the open string vacuum becomes the global minimum near the Hagedorn temperature.
In this paper we derive an integral (with respect to time) representation of the relative entropy (or Kullback-Leibler Divergence) between measures mu and P on the space of continuous functions from time 0 to T. The underlying measure P is a weak solution to a Martingale Problem with continuous coefficients. Since the relative entropy governs the exponential rate of convergence of the empirical measure (according to Sanov's Theorem), this representation is of use in the numerical and analytical investigation of finite-size effects in systems of interacting diffusions.
We take an analytic approach to the CFT bootstrap, studying the 4-pt correlators of d > 2 dimensional CFTs in an Eikonal-type limit, where the conformal cross ratios satisfy |u| << |v| < 1. We prove that every CFT with a scalar operator \phi must contain infinite sequences of operators O_{\tau,l} with twist approaching \tau -> 2\Delta_\phi + 2n for each integer n as l -> infinity. We show how the rate of approach is controlled by the twist and OPE coefficient of the leading twist operator in the \phi x \phi OPE, and we discuss SCFTs and the 3d Ising Model as examples. Additionally, we show that the OPE coefficients of other large spin operators appearing in the OPE are bounded as l -> infinity. We interpret these results as a statement about superhorizon locality in AdS for general CFTs.
We prove a conjectural formula relating the Bessel period of certain automorphic forms on $\mathrm{GSp}_4$ to a central $L$-value. This formula is proposed by Liu \cite{liu} as the refined Gan-Gross-Prasad conjecture for the groups $(\SO(5), \SO(2))$. The conjecture has been previously proved for certain automorphic forms on $\mathrm{GSp_4}$ from lifts. In this paper, we extend the formula to Siegel modular forms of $\Sp_4(\bZ)$.
Stellar photometry of about one million stars in the system of the interacting galaxies M51 (NGC5194/NGC5195) has been carried out on the basis of the ACS/WFC images of the Hubble Space telescope. The distance to the system has been determined by TRGB method and metallicity of red supergiants along the NGC5194 radius has been measured. A comparison of the spacial distribution of stars in the main galaxy NGC5194 with our empirical model of spiral galaxies showed their similarity, in spite of interaction in system M51. It has been discovered that the "feathers", arising as a result of the interaction of galaxies, mainly consist of stars of intermediate age.
Magnetic cylindrical nanowires are very fascinating objects where the curved geometry allows many novel magnetic effects and a variety of non-trivial magnetic structures. Micromagnetic modelling plays an important role in revealing the magnetization distribution in magnetic nanowires, often not accessible by imaging methods with sufficient details. Here we review the magnetic properties of the shape anisotropy-dominated nanowires and the nanowires with competing shape and magnetocrystalline anisotropies, as revealed by micromagnetic modelling. We discuss the variety of magnetic walls and magnetic domains reported by micromagnetic simulations in cylindrical nanowires. The most known domain walls types are the transverse and vortex (Bloch point) domain walls and the transition between them is materials and nanowire diameter dependent. Importantly, the field or current-driven domain walls in cylindrical nanowires can achieve very high velocities. In recent simulations of nanowires with larger diameter the skyrmion tubes are also reported. In nanowires with large saturation magnetization the core of these tubes may form a helicoidal ('corkscrew') structure. The topology of the skyrmion tubes play an important role in the pinning mechanism, discussed here on the example of FeCo modulated nanowires. Other discussed examples include the influence of antinotches ('bamboo' nanowires) on the remanent magnetization configurations for hcp Co and FeCo nanowires and Co-Ni multisegmented nanowires.
The Dirichlet characters of reduced residue systems modulo m are tabulated for moduli m <= 195. The associated L-series are tabulated for m <= 14 and small positive integer argument s accurate to 10^(-50), their first derivatives for m <= 6. Restricted summation over primes only defines Dirichlet Prime L-functions which lead to Euler products (Prime Zeta Modulo functions). Both are materialized over similar ranges of moduli and arguments. Formulas and numerical techniques are well known; the aim is to provide direct access to reference values.
In this study, we performed powder neutron diffraction and inelastic scattering measurements of frustrated pyrochlore Nd$_2$Ir$_2$O$_7$, which exhibits a metal-insulator transition at a temperature $T_{\rm MI}$ of 33 K. The diffraction measurements revealed that the pyrochlore has an antiferromagnetic long-range structure with propagation vector $\vec{q}_{0}$ of (0,0,0) and that it grows with decreasing temperature below 15 K. This structure was analyzed to be of the all-in all-out type, consisting of highly anisotropic Nd$^{3+}$ magnetic moments of magnitude $2.3\pm0.4$$\mu_{\rm B}$, where $\mu_{\rm B}$ is the Bohr magneton. The inelastic scattering measurements revealed that the Kramers ground doublet of Nd$^{3+}$ splits below $T_{\rm MI}$. This suggests the appearance of a static internal magnetic field at the Nd sites, which probably originates from a magnetic order consisting of Ir$^{4+}$ magnetic moments. Here, we discuss a magnetic structure model for the Ir order and the relation of the order to the metal-insulator transition in terms of frustration.
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and combinatorics of symmetric groups and their representations is explained. Applications of the results to constructing efficient computations in problems related to models of quantum field theories are given.
Full Coupled Channels Calculations were performed for the $^{16}O(d,n)^{17}F$ and $^{16}O(d,p)^{17}O$ transfer reactions at several deuteron incident energies from $E_{lab}=2.29$ MeV up to 3.27 MeV. A strong polarization effect between the entrance channel and the transfer channels $^{16}O(d,n)^{17}F(1/2^{+},0.495)$ and $^{16}O(d,p)^{17}O(1/2^{+},0.87)$ was observed. This polarization effect had to be taken into account in order to obtain realistic spectroscopic factors from these reactions.
The insulator/metal transition induced by hole-doping due to neodymium vacancies of the Mott- Hubbard antiferromagnetic insulator, Nd1-xTiO3, is studied over the composition range 0.010(6) < x < 0.243(10). Insulating p-types conduction is found for x < 0.071(10). Anderson localization in the presence of a Mott-Hubbard gap, is the dominant localization mechanism for the range of 0.074(10) < x < 0.089(1) samples. For x < 0.089(1), n-type conduction is observed and the activation energy extrapolates to zero by x < 0.1. The 0.095(8) < x < 0.203(10) samples are Fermi-liquid metals and the effects of strong electronic correlations are evident near the metal-to-insulator boundaries in features such as large Fermi liquid T2 coefficients. For 0.074(9) < x < 0.112(4), a weak negative magnetoresistance is found below ~ 15 K and it is attributed to the interaction of conduction electrons with Nd3+ magnetic moments. Combining information from our companion study of the magnetic properties of Nd1-xTiO3 solid solution, a phase diagram is proposed. The main conclusions are that long range antiferromagnetic order disappears before the onset of metallic behavior and that the Anderson-Mott transition occurs over a finite range of doping levels. Our results differ from conclusions drawn from a similar study on the hole doped Nd1-xCaxTiO3 system which found the co-existence of antiferromagnetic order and metallic behavior and that the Mott transition occurs at a discrete doping level.
Bounds and other relations involving variables connected with Carmichael numbers are reviewed and extended. Families of numbers or individual numbers attaining or approaching these bounds are given. A new algorithm for finding three-prime Carmichael numbers is described, with its implementation up to $10^{24}$. Statistics relevant to the distribution of three-prime Carmichael numbers are given, with particular reference to the conjecture of Granville and Pomerance in [A.Granville and C.Pomerance, Two contradictory conjectures concerning Carmichael numbers, Math. Comp. 71 (2001), 883-908].
We present a novel visual attention tracking technique based on Shared Attention modeling. Our proposed method models the viewer as a participant in the activity occurring in the scene. We go beyond image salience and instead of only computing the power of an image region to pull attention to it, we also consider the strength with which other regions of the image push attention to the region in question. We use the term Attentional Push to refer to the power of image regions to direct and manipulate the attention allocation of the viewer. An attention model is presented that incorporates the Attentional Push cues with standard image salience-based attention modeling algorithms to improve the ability to predict where viewers will fixate. Experimental evaluation validates significant improvements in predicting viewers' fixations using the proposed methodology in both static and dynamic imagery.
I present several scenarios developed in Zagreb, in which TeV-scale particles belonging to non-trivial weak-isospin multiplets give rise to neutrino-mass mechanisms different from conventional type I, II and III seesaw models. Two dim 9 tree-level mechanisms, presented first, provide an appealing testability of their exotic TeV-scale particles at the LHC. These models are not genuine, since their particles also provide competing dim 5 loop contributions. The loop-models presented next are genuine, without competing tree-level contributions. Among them, the three-loop model involves high-order weak multiplets leading to Landau poles. The one-loop model with scalar triplet as the largest multiplet, in addition to good UV properties, provides the particle set promising for gauge coupling unification. Therefore, it served us as a starting point for a study of SU(5) embedding of additional particles leading to viable unification scenarios. To distinguish among them begs for additional principle which reigns over particle completion and eventual dark matter considerations.
Combinatorial $t$-designs have been an interesting topic in combinatorics for decades. It is a basic fact that the codewords of a fixed weight in a code may hold a $t$-design. Till now only a small amount of work on constructing $t$-designs from codes has been done. In this paper, we determine the weight distributions of two classes of cyclic codes: one related to the triple-error correcting binary BCH codes, and the other related to the cyclic codes with parameters satisfying the generalized Kasami case, respectively. We then obtain infinite families of $2$-designs from these codes by proving that they are both affine-invariant codes, and explicitly determine their parameters. In particular, the codes derived from the dual of binary BCH codes hold five $3$-designs when $m=4$.
Deep in the ultrastrong light-matter coupling regime, it has been predicted that the ground state of a two-level atom interacting with a cavity mode takes the form of a "virtual" Schr\"odinger cat entangled state between light and matter. We propose a method to convert this Schr\"odinger cat state from virtual to real, and back again, by driving the atom with optimally chosen pulses. Our system consists of a four-level atom, with two of these levels ultrastrongly coupled to a cavity mode. We show that the Schr\"odinger cat state can be converted between virtual and real by making use of either an ideal ultrafast pulse or a multi-tone {\pi}-pulse. In addition to allowing us to observe these unusual virtual states this method could also be used to generate entangled cat states on demand for quantum information processing.
The chemical evolution of the Universe is governed by the chemical yields from stars, which in turn is determined primarily by the initial stellar mass. Even stars as low as 0.9Msun can, at low metallicity, contribute to the chemical evolution of elements. Stars less massive than about 10Msun experience recurrent mixing events that can significantly change the surface composition of the envelope, with observed enrichments in carbon, nitrogen, fluorine, and heavy elements synthesized by the slow neutron capture process (the s-process). Low and intermediate mass stars release their nucleosynthesis products through stellar outflows or winds, in contrast to massive stars that explode as core-collapse supernovae. Here we review the stellar evolution and nucleosynthesis for single stars up to ~10Msun from the main sequence through to the tip of the asymptotic giant branch (AGB). We include a discussion of the main uncertainties that affect theoretical calculations and review the latest observational data, which are used to constrain uncertain details of the stellar models. We finish with a review of the stellar yields available for stars less massive than about 10Msun and discuss efforts by various groups to address these issues and provide homogeneous yields for low and intermediate-mass stars covering a broad range of metallicities.
We show that density functions of a $(\alpha,1,\beta)$-superprocesses are almost sure multifractal for $\alpha>\beta+1$, $\beta\in(0,1)$ and calculate the corresponding spectrum of singularities.
The mass and size distributions are the key characteristics of any astrophysical objects, including the densest clumps comprising the cold phase of multiphase environments. In our recent papers, we showed how individual clouds of various sizes form and evolve in AGN. In particular, we showed that large clouds undergo damped oscillations as a response to their formation process. Here we followup this investigation, addressing how different size clouds interact. We find that smaller clouds become trapped in the advective flows generated by larger clouds. The explanation for this behavior leads to a rather remarkable conclusion: even in the absence of gravity, complexes of clouds are dynamically unstable. In an idealized environment (e.g., one free of turbulence and magnetic fields) a perfectly symmetric arrangement of static clouds will remain static, but any small spatial perturbation will lead to all clouds coalescing into a single, large cloud, given enough time. Using numerical simulations, we investigate the main factors that determine the rate of coalescence. Besides the cloud separation distance, we find that the transient response of clouds to a disturbance is the primary factor. Turbulent motions in the flow can easily suppress this tendency for spatially well-separated clouds to coalesce, so it is as yet unclear if this phenomenon can occur in nature. Nevertheless, this work casts strong doubts on a recent hypothesis that large clouds are prone to fragmentation.
Recent years have brought an explosion of activities in the research of topological aspects of condensed-matter systems. Topologically non-trivial phases of matter are typically accompanied by protected surface states or exotic degenerate excitations such as Majorana end states or Haldane's localized spinons. Topologically protected degeneracies can, however, also appear in the bulk. An intriguing example is provided by Weyl semimetals, where topologically protected electronic band degeneracies and exotic surface states emerge even in the absence of interactions. Here we demonstrate experimentally and theoretically that Weyl degeneracies appear naturally in an interacting quantum dot system, for specific values of the external magnetic field. These magnetic Weyl points are robust against spin-orbit coupling unavoidably present in most quantum dot devices. Our transport experiments through an InAs double dot device placed in magnetic field reveal the presence of a pair of Weyl points, exhibiting a robust ground state degeneracy and a corresponding protected Kondo effect.
We briefly discuss the present status of models of neutrino mixing. Among the existing viable options we review the virtues of Bimaximal Mixing (that could be implemented by an $S_4$ discrete symmetry), corrected by terms arising from the charged lepton mass diagonalization. In particular in a GUT formulation the property of quark lepton "weak" complementarity can be naturally realized. We discuss in some detail two new versions of particular GUT models, one based on $SU(5)$ and one on $SO(10)$ and the associated phenomenology. We compare these approaches based on symmetry to models based on chance, like Anarchy or $U(1)_{FN}$.
A well-known diffuse interface model for incompressible isothermal mixtures of two immiscible fluids consists of the Navier-Stokes system coupled with a convective Cahn-Hilliard equation. In some recent contributions the standard Cahn-Hilliard equation has been replaced by its nonlocal version. The corresponding system is physically more relevant and mathematically more challenging. Indeed, the only known results are essentially the existence of a global weak solution and the existence of a suitable notion of global attractor for the corresponding dynamical system defined without uniqueness. In fact, even in the two-dimensional case, uniqueness of weak solutions is still an open problem. Here we take a step forward in the case of regular potentials. First we prove the existence of a (unique) strong solution in two dimensions. Then we show that any weak solution regularizes in finite time uniformly with respect to bounded sets of initial data. This result allows us to deduce that the global attractor is the union of all the bounded complete trajectories which are strong solutions. We also demonstrate that each trajectory converges to a single equilibrium, provided that the potential is real analytic and the external forces vanish.
Nuclei are prototypes of many-body open quantum systems. Complex aggregates of protons and neutrons that interact through forces arising from quantum chromo-dynamics, nuclei exhibit both bound and unbound states, which can be strongly coupled. In this respect, one of the major challenges for computational nuclear physics, is to provide a unified description of structural and reaction properties of nuclei that is based on the fundamental underlying physics: the constituent nucleons and the realistic interactions among them. This requires a combination of innovative theoretical approaches and high-performance computing. In this contribution, we present one of such promising techniques, the ab initio no-core shell model/resonating-group method, and discuss applications to light nuclei scattering and fusion reactions that power stars and Earth-base fusion facilities.