ShantanuT01/DACTYL-Pretraining huggingface dataset:
We have performed magnetization measurements at high magnetic fields of up to 53 T on single crystals of a uranium heavy-fermion compound U$_2$Zn$_{17}$ grown by the Bridgman method. In the antiferromagnetic state below the N\'{e}el temperature $T_{\rm N}$ = 9.7 K, a metamagnetic transition is found at $H_c$ $\simeq$ 32 T for the field along the [11$\bar{2}$0] direction ($a$-axis). The magnetic phase diagram for the field along the [11$\bar{2}$0] direction is given. The magnetization curve shows a nonlinear increase at $H_m$ $\simeq$ 35 T in the paramagnetic state above $T_{\rm N}$ up to a characteristic temperature $T_{{\chi}{\rm max}}$ where the magnetic susceptibility or electrical resistivity shows a maximum value. This metamagnetic behavior of the magnetization at $H_m$ is discussed in comparison with the metamagnetic magnetism of the heavy-fermion superconductors UPt$_3$, URu$_2$Si$_2$, and UPd$_2$Al$_3$. We have also carried out high-pressure resistivity measurement on U$_2$Zn$_{17}$ using a diamond anvil cell up to 8.7 GPa. Noble gas argon was used as a pressure-transmitting medium to ensure a good hydrostatic environment. The N\'{e}el temperature $T_{\rm N}$ is almost pressure-independent up to 4.7 GPa and starts to increase in the higher-pressure region. The pressure dependences of the coefficient of the $T^2$ term in the electrical resistivity $A$, the antiferromagnetic gap $\Delta$, and the characteristic temperature $T_{{\rho}{\rm max}}$ are discussed. It is found that the effect of pressure on the electronic states in U$_2$Zn$_{17}$ is weak compared with those in the other heavy fermion compounds.
The semistable minimal model program is a special case of the minimal model program concerning 3-folds fibred over a curve and birational morphisms preserving this structure. We classify semistable divisorial contractions which contract the exceptional divisor to a normal point of a fibre. Our results can be applied to describe compact moduli spaces of surfaces.
We find a conserved monodromy matrix differential operator T in the quantum Self-Dual Yang-Mills (SDYM) system and show that it satisfies the exchange algebra RTT=TTR. From its two infinitesimal forms, we obtain the infinite conserved quantum nonlocal-charge algebras and the infinite conserved Yangian algebras. It is remarkable that such conserved algebras exist in a four-dimensional nontrivial quantum field theory with interactions.
We study the dimension of the higher secant varieties $X^s$ of ${\Bbb X} = {\Bbb P}^{n_1}\times ...\times {\Bbb P}^{n_t}$ embedded the morphism given by ${\cal O}_{\Bbb X}({a_1,...,a_t})$. We call it a {\it Segre-Veronese variety} and the embedding a {\it Segre-Veronese embedding}. In several cases (e.g. for 3 factors {\Bbb P}^{1}, or when $s$ is small) we show that $X^s$ has the expected dimension except for a few cases. A list of examples of defective $X^s$'s is given.
Van der Waals (vdW) and Casimir interactions depend crucially on material properties and geometry, especially at molecular scales, and temperature can produce noticeable relative shifts in interaction characteristics. Despite this, common treatments of these interactions ignore electromagnetic retardation, atomism, or contributions of collective mechanical vibrations (phonons) to the infrared response, which can interplay with temperature in nontrivial ways. We present a theoretical framework for computing electromagnetic interactions among molecular structures, accounting for their geometry, electronic delocalization, short-range interatomic correlations, dissipation, and phonons at atomic scales, along with long-range electromagnetic interactions among themselves or in the vicinity of continuous macroscopic bodies. We find that in carbon allotropes, particularly fullerenes, carbyne wires, and graphene sheets, phonons can couple strongly with long-range electromagnetic fields, especially at mesoscopic scales (nanometers), to create delocalized phonon polaritons that significantly modify the infrared molecular response. These polaritons especially depend on the molecular dimensionality and dissipation, and in turn affect the vdW interaction free energies of these bodies above a macroscopic gold surface, producing nonmonotonic power laws and nontrivial temperature variations at nanometer separations that are within the reach of current Casimir force experiments.
This paper introduces a new asymptotic regime for simplifying stochastic models having non-stationary effects, such as those that arise in the presence of time-of-day effects. This regime describes an operating environment within which the arrival process to a service system has an arrival intensity that is fluctuating rapidly. We show that such a service system is well approximated by the corresponding model in which the arrival process is Poisson with a constant arrival rate. In addition to the basic weak convergence theorem, we also establish a first order correction for the distribution of the cumulative number of arrivals over $[0,t]$, as well as the number-in-system process for an infinite-server queue fed by an arrival process having a rapidly changing arrival rate. This new asymptotic regime provides a second regime within which non-stationary stochastic models can be reasonably approximated by a process with stationary dynamics, thereby complementing the previously studied setting within which rates vary slowly in time.
Let $P \in \mathbb{Z} [X, Y]$ be a given square-free polynomial of total degree $d$ with integer coefficients of bitsize less than $\tau$, and let $V_{\mathbb{R}}   (P) := \{ (x,y) \in \mathbb{R}^2, P (x,y) = 0 \}$ be the real planar algebraic curve implicitly defined as the vanishing set of $P$. We give a deterministic and certified algorithm to compute the topology of $V_{\mathbb{R}} (P)$ in terms of a straight-line planar graph $\mathcal{G}$ that is isotopic to $V_{\mathbb{R}} (P)$. Our analysis yields the upper bound $\tilde O (d^5 \tau + d^6)$ on the bit complexity of our algorithm, which matches the current record bound for the problem of computing the topology of a planar algebraic curve However, compared to existing algorithms with comparable complexity, our method does not consider any change of coordinates, and the returned graph $\mathcal{G}$ yields the cylindrical algebraic decomposition information of the curve.   Our result is based on two main ingredients: First, we derive amortized quantitative bounds on the the roots of polynomials with algebraic coefficients as well as adaptive methods for computing the roots of such polynomials that actually exploit this amortization. Our second ingredient is a novel approach for the computation of the local topology of the curve in a neighborhood of all critical points.
Rectification of microwave oscillations of magnetization in a permalloy film is realized using planar Hall effect. Two different rectified signals are obtained: a signal from the linearly excited uniform magnetization precession at the frequency of the external pumping and a signal from the pairs of contra-propagating short-wavelength spin waves parametrically generated at a half of the pumping frequency. The second, most unusual, rectified signal is caused by the uniform component of the dynamic magnetization created due to the interference of the phase correlated pairs of parametric spin waves.
Superconducting circuits are well established as a strong candidate platform for the development of quantum computing. In order to advance to a practically useful level, architectures are needed which combine arrays of many qubits with selective qubit control and readout, without compromising on coherence. Here we present a coaxial circuit QED architecture in which qubit and resonator are fabricated on opposing sides of a single chip, and control and readout wiring are provided by coaxial wiring running perpendicular to the chip plane. We present characterisation measurements of a fabricated device in good agreement with simulated parameters and demonstrating energy relaxation and dephasing times of $T_1 = 4.1\,\mu$s and $T_2 = 5.7\,\mu$s respectively. The architecture allows for scaling to large arrays of selectively controlled and measured qubits with the advantage of all wiring being out of the plane.
The main topic of these notes are Markov loops, studied in the context of continuous time Markov chains on discrete state spaces. We refer to [1] and [2] for the short "history" of the subject. In contrast with these references, symmetry is not assumed, and more attention is given to the infinite case. All results are presented in terms of the semigroup generator. In comparison with [1], some delicate proofs are given in more details or with a better method. We focus mostly on properties of the (multi)occupation field but also included some results about loop clusters (see [3] in the symmetric context) and spanning trees.   [1] Markov paths, loops and fields, by Yves Le Jan, Lecture Notes in Mathematics, vol. 2026, Springer, Heidelberg, 2011 [2] Topics in occupation times and Gaussian free fields, by Alain-Sol Sznitman, Zurich Lectures in Advanced Mathematics, European Mathematical Society (EMS), Z\"urich, 2012 [3] Markovian loop clusters on graphs, by Yves Le Jan and Sophie Lemaire, Preprint, arxiv:1211.0300 [math.PR], 2012
This is the first paper in a series devoted to review the main properties of galaxies designated S0 in the Hubble classification system. Our aim is to gather abundant and, above all, robust information on the most relevant physical parameters of this poorly-understood morphological type and their possible dependence on the environment that could later be used to assess their possible formation channel(s). The adopted approach combines the characterisation of the fundamental features of the optical spectra of $68{,}043$ S0 with heliocentric $z\lesssim 0.1$ with the exploration of a comprehensive set of their global attributes. A principal component analysis is used to reduce the huge number of dimensions of the spectral data to a low-dimensional space facilitating a bias-free machine-learning-based classification of the galaxies. This procedure has revealed that objects bearing the S0 designation consist, despite their similar morphology, of two separate sub-populations with statistically inconsistent physical properties. Compared to the absorption-dominated S0, those with significant nebular emission are, on average, somewhat less massive, more luminous with less concentrated light profiles, have a younger, bluer and metal-poorer stellar component, and avoid high-galaxy-density regions. Noteworthy is the fact that the majority of members of this latter class, which accounts for at least a quarter of the local S0 population, show star formation rates and spectral characteristics entirely similar to those seen in late spirals. Our findings suggest that star-forming S0 might be less rare than hitherto believed and raise the interesting possibility of identifying them with plausible progenitors of their quiescent counterparts.
We study quantum dissipative dynamics of entanglement in the spin-boson model, described by the generalized master equation. We consider the two opposite limits of pure-dephasing and relaxation models, measuring the degree of entanglement with the concurrence. When the Markovian approximation is employed, entanglement is shown to decay exponentially in both cases. On the other hand, non-Markovian contributions alter the analytic structure of the master equation, resulting in logarithmic decay in the pure dephasing model.
There are two critical sensors for 3D perception in autonomous driving, the camera and the LiDAR. The camera provides rich semantic information such as color, texture, and the LiDAR reflects the 3D shape and locations of surrounding objects. People discover that fusing these two modalities can significantly boost the performance of 3D perception models as each modality has complementary information to the other. However, we observe that current datasets are captured from expensive vehicles that are explicitly designed for data collection purposes, and cannot truly reflect the realistic data distribution due to various reasons. To this end, we collect a series of real-world cases with noisy data distribution, and systematically formulate a robustness benchmark toolkit, that simulates these cases on any clean autonomous driving datasets. We showcase the effectiveness of our toolkit by establishing the robustness benchmark on two widely-adopted autonomous driving datasets, nuScenes and Waymo, then, to the best of our knowledge, holistically benchmark the state-of-the-art fusion methods for the first time. We observe that: i) most fusion methods, when solely developed on these data, tend to fail inevitably when there is a disruption to the LiDAR input; ii) the improvement of the camera input is significantly inferior to the LiDAR one. We further propose an efficient robust training strategy to improve the robustness of the current fusion method. The benchmark and code are available at https://github.com/kcyu2014/lidar-camera-robust-benchmark
Monolayers of group VA elements have attracted great attention with the rising of black phosphorus. Here, we derive a simple tight-binding model for monolayer grey arsenic, referred as arsenene (ML-As), based on the first-principles calculations within the partially self-consistent GW0 approach. The resulting band structure derived from the six p-like orbitals coincides with the quasi-particle energy from GW0 calculations with a high accuracy. In the presence of a perpendicular magnetic field, ML-As exhibits two sets of Landau levels linear with respect to the magnetic field and level index. Our numerical calculation of the optical conductivity reveals that the obtained optical gap is very close to the GW0 value and can be effectively tuned by external magnetic field. Thus, our proposed TB model can be used for further large-scale simulations of the electronic, optical and transport properties of ML-As.
The s=3/2 Ising spin chain with uniform nearest-neighbor coupling, quadratic single-site potential, and magnetic field is shown to be equivalent to a system of 17 species of particles with internal structure. The same set of particles (with different energies) is shown to generate the spectrum of the s=1/2 Ising chain with dimerized nearest-neighbor coupling. The particles are free of interaction energies even at high densities. The mutual exclusion statistics of particles from all species is determined by their internal structure and encoded in a generalized Pauli principle. The exact statistical mechanical analysis can be performed for thermodynamically open or closed systems and with arbitrary energies assigned to all particle species. Special circumstances make it possible to merge two or more species into a single species. All traits that distinguish the original species become ignorable. The particles from the merged species are effectively indistinguishable and obey modified exclusion statistics. Different mergers may yield the same endproduct, implying that the inverse process (splitting any species into subspecies) is not unique. In a macroscopic system of two merged species at thermal equilibrium, the concentrations of the original species satisfy a functional relation governed by their mutual statistical interaction. That relation is derivable from an extremum principle. In the Ising context the system is open and the particle energies depend on the Hamiltonian parameters. Simple models of polymerization and solitonic paramagnetism each represent a closed system of two species that can transform into each other. Here they represent distinguishable traits with different energies of the same physical particle.
Asymptotic expansion of the distribution of a perturbation $Z_n$ of a Skorohod integral jointly with a reference variable $X_n$ is derived. We introduce a second-order interpolation formula in frequency domain to expand a characteristic functional and combine it with the scheme developed in the martingale expansion. The second-order interpolation and Fourier inversion give asymptotic expansion of the expectation $E[f(Z_n,X_n)]$ for differentiable functions $f$ and also measurable functions $f$. In the latter case, the interpolation method connects the two non-degeneracies of variables for finite $n$ and $\infty$. Random symbols are used for expressing the asymptotic expansion formula. Quasi tangent, quasi torsion and modified quasi torsion are introduced in this paper. We identify these random symbols for a certain quadratic form of a fractional Brownian motion and for a quadratic from of a fractional Brownian motion with random weights. For a quadratic form of a Brownian motion with random weights, we observe that our formula reproduces the formula originally obtained by the martingale expansion.
The network of Barabasi and Albert, a preferential growth model where a new node is linked to the old ones with a probability proportional to their connectivity, is applied to Brazilian election results. The application of the Sznajd rule, that only agreeing pairs of people can convince their neighbours, gives a vote distribution in good agreement with reality.
For unsupervised data-dependent hashing, the two most important requirements are to preserve similarity in the low-dimensional feature space and to minimize the binary quantization loss. A well-established hashing approach is Iterative Quantization (ITQ), which addresses these two requirements in separate steps. In this paper, we revisit the ITQ approach and propose novel formulations and algorithms to the problem. Specifically, we propose a novel approach, named Simultaneous Compression and Quantization (SCQ), to jointly learn to compress (reduce dimensionality) and binarize input data in a single formulation under strict orthogonal constraint. With this approach, we introduce a loss function and its relaxed version, termed Orthonormal Encoder (OnE) and Orthogonal Encoder (OgE) respectively, which involve challenging binary and orthogonal constraints. We propose to attack the optimization using novel algorithms based on recent advances in cyclic coordinate descent approach. Comprehensive experiments on unsupervised image retrieval demonstrate that our proposed methods consistently outperform other state-of-the-art hashing methods. Notably, our proposed methods outperform recent deep neural networks and GAN based hashing in accuracy, while being very computationally-efficient.
A graph is strongly perfect if every induced subgraph H has a stable set that meets every maximal clique of H. A graph is claw-free if no vertex has three pairwise non-adjacent neighbors. The characterization of claw-free graphs that are strongly perfect by a set of forbidden induced subgraphs was conjectured by Ravindra in 1990 and was proved by Wang in 2006. Here we give a shorter proof of this characterization.
A coloring of the ground set of a matroid is proper if elements of the same color form an independent set. For a loopless matroid $M$, its chromatic number $\chi (M)$ is the minimum number of colors in a proper coloring. In this note we study a game-theoretic variant of this parameter. Suppose that Alice and Bob alternately properly color the ground set of a matroid $M$ using a fixed set of colors. The game ends when the whole matroid has been colored, or if they arrive to a partial coloring that cannot be further properly extended. Alice wins in the first case, while Bob in the second. The game chromatic number of $M$, denoted by $\chi_{g}(M)$, is the minimum size of the set of colors for which Alice has a winning strategy. Clearly, $\chi_{g}(M)\geq\chi (M)$. We prove an upper bound $\chi_{g}(M)\leq 2\chi (M)$ for every matroid $M$. This improves and extends a result of Bartnicki, Grytczuk and Kierstead, who showed that $\chi_{g}(M)\leq 3\chi (M)$ holds for graphic matroids. Our bound is almost tight, as we construct a family of matroids $M_k$ (for $k\geq 3$) satisfying $\chi (M_k)=k$ and $\chi_{g}(M_k)=2k-1$.
We study two kinds of weighted networks, weighted small-world (WSW) and weighted scale-free (WSF). The weight $w_{ij}$ of a link between nodes $i$ and $j$ in the network is defined as the product of endpoint node degrees; that is $w_{ij}=(k_{i}k_{j})^{\theta}$. In contrast to adding weights to links during networks being constructed, we only consider weights depending on the `` popularity\rq\rq of the nodes represented by their connectivity. It was found that the both weighted networks have broad distributions on characterization the link weight, vertex strength, and average shortest path length. Furthermore, as a survey of the model, the epidemic spreading process in both weighted networks was studied based on the standard \emph{susceptible-infected} (SI) model. The spreading velocity reaches a peak very quickly after the infection outbreaks and an exponential decay was found in the long time propagation.
We examine the kinematic morphology of early-type galaxies (ETGs) in eight galaxy clusters in the Sydney-AAO Multi-object Integral field spectrograph (SAMI) Galaxy Survey. The clusters cover a mass range of 14.2<log(M_200/M_odot)<15.2 and we measure spatially-resolved stellar kinematics for 315 member galaxies with stellar masses 10.0<log(M_*/M_odot)<11.7 within 1R_200 of the cluster centers. We calculate the spin parameter, lambda_R and use that to classify the kinematic morphology of the galaxies as fast or slow rotators. The total fraction of slow rotators in the early-type galaxy population, F_SR=0.14+/-0.02 and does not depend on host cluster mass. Across the eight clusters, the fraction of slow rotators increases with increasing local overdensity. We also find that the slow-rotator fraction increases at small clustercentric radii (R_cl<0.3R_200), and note that there is also an increase in slow-rotator fraction at R_cl~0.6R_200. The slow rotators at these larger radii reside in cluster substructure. We find the strongest increase in slow-rotator fraction occurs with increasing stellar mass. After accounting for the strong correlation with stellar mass, we find no significant relationship between spin parameter and local overdensity in the cluster environment. We conclude that the primary driver for the kinematic morphology--density relationship in galaxy clusters is the changing distribution of galaxy stellar mass with local environment. The presence of slow rotators in substructure suggests that the cluster kinematic morphology--density relationship is a result of mass segregation of slow-rotating galaxies forming in groups that later merge with clusters and sink to the cluster center via dynamical friction.
In this paper, we prove transportation inequalities on the space of continuous paths with respect to the uniform metric, for the law of solution to a stochastic heat equation defined on $[0,T]\times [0,1]^d$. This equation is driven by the Gaussian noise, white in time and colored in space. The proof is based on a new moment inequality under the uniform metric for the stochastic convolution with respect to the time-white and space-colored noise, which is of independent interest.
We review our recent work on the simulation, description and prediction of spin-excitations in adatoms and dimers deposited on metallic surfaces. This work done together with Douglas L. Mills, is an extension of his seminal contribution (with Pascal Lederer) published 50 years ago on the spin-dynamics of transition metal impurities embedded in transition metal hosts [P. Lederer, D.L. Mills, Phys. Rev. {\bf 160}, 590 (1967)]. The main predictions of his model were verified experimentally with state of the art inelastic scanning tunneling spectroscopy on adatoms. Our formalism, presented in this review, is based on time-dependent density functional theory, combined with the Korringa-Kohn-Rostoker Green function method. Comparison to experiments is shown and discussed in detail. Our scheme enables the description and prediction of the main characteristics of these excitations, \emph{i.e.} their resonance frequency, their lifetime and their behavior upon application of external perturbations such as a magnetic field.