ShantanuT01/DACTYL-Pretraining huggingface dataset:
Global amoebas are a wide and rich family of graphs that emerged from the study of certain Ramsey-Tur\'an problems in $2$-colorings of the edges of the complete graph $K_n$ that deal with the appearance of unavoidable patterns once a certain amount of edges in each color is guaranteed. Indeed, it turns out that, as soon as such coloring constraints are satisfied and if $n$ is sufficiently large, then every global amoeba can be found embedded in $K_n$ such that it has half its edges in each color. Even more surprising, every bipartite global amoeba $G$ is unavoidable in every tonal-variation, meaning that, for any pair of integers $r, b$ such that $r + b $ is the number of edges of $G$, there is a subgraph of $K_n$ isomorphic to $G$ with $r$ edges in the first color and $b$ edges in the second. The feature that makes global amoebas work are one-by-one edge replacements that leave the structure of the graph invariant. By means of a group theoretical approach, the dynamics of this feature can be modeled. As a counterpart to the global amoebas that "live" inside a possibly large complete graph $K_n$, we also consider local amoebas which are spanning subgraphs of $K_n$ with the same feature.   In an effort to highlight their richness and versatility, we present here three different recursive constructions of amoebas, two of them yielding interesting families per se and one of them offering a wide range of possibilities.
We summarize the results on patterns of flavour violation in a Randall-Sundrum model with custodial protection (RSc) and compare them with those identified in the Littlest Higgs Model with T--parity (LHT) and in a number of SUSY Flavour Models. While K decays play in this presentation a prominent role, the inclusion of B physics and lepton flavour violation is crucial in the distinction between these three popular extensions of the Standard Model (SM) by means of flavour physics.
We present Spitzer 16 micron imaging of the Great Observatories Origins Deep Survey (GOODS) fields. We survey 150 square arcminutes in each of the two GOODS fields (North and South), to an average 3 sigma depth of 40 and 65 micro-Jy respectively. We detect about 1300 sources in both fields combined. We validate the photometry using the 3-24 micron spectral energy distribution of stars in the fields compared to Spitzer spectroscopic templates. Comparison with ISOCAM and AKARI observations in the same fields show reasonable agreement, though the uncertainties are large. We provide a catalog of photometry, with sources cross correlated with available Spitzer, Chandra, and HST data. Galaxy number counts show good agreement with previous results from ISOCAM and AKARI, with improved uncertainties. We examine the 16 to 24 micron flux ratio and find that for most sources it lies within the expected locus for starbursts and infrared luminous galaxies. A color cut of S_{16}/S_{24}>1.4 selects mostly sources which lie at 1.1<z<1.6, where the 24 micron passband contains both the redshifted 9.7 micron silicate absorption and the minimum between PAH emission peaks. We measure the integrated galaxy light of 16 micron sources, and find a lower limit on the galaxy contribution to the extragalactic background light at this wavelength to be 2.2\pm 0.2$ nW m^{-2} sr^{-1}.
An experimentally feasible energy-storage concept is formulated based on vorticity (hydro)dynamics within an easy-plane insulating magnet. The free energy, associated with the magnetic winding texture, is built up in a circular easy-plane magnetic structure by injecting a vorticity flow in the radial direction. The latter is accomplished by electrically induced spin-transfer torque, which pumps energy into the magnetic system in proportion to the vortex flux. The resultant magnetic metastable state with a finite winding number can be maintained for a long time because the process of its relaxation via phase slips is exponentially suppressed when the temperature is well below the Curie temperature. We propose to characterize the vorticity-current interaction underlying the energy-loading mechanism through its contribution to the effective electric inductance in the rf response. Our proposal may open an avenue for naturally powering spintronic circuits and nontraditional magnet-based neuromorphic networks.
Perovskite oxides are already widely used in industry and have huge potential for novel device applications thanks to the rich physical behaviour displayed in these materials. The key to the functional electronic properties exhibited by perovskites is often the so-called Jahn-Teller distortion. For applications, an electrical control of the Jahn-Teller distortions, which is so far out of reach, would therefore be highly desirable. Based on universal symmetry arguments, we determine new lattice mode couplings that can provide exactly this paradigm, and exemplify the effect from first-principles calculations. The proposed mechanism is completely general, however for illustrative purposes, we demonstrate the concept on vanadium based perovskites where we reveal an unprecedented orbital ordering and Jahn-Teller induced ferroelectricity. Thanks to the intimate coupling between Jahn-Teller distortions and electronic degrees of freedom, the electric field control of Jahn-Teller distortions is of general relevance and may find broad interest in various functional devices.
This contribution to the proceedings of the 1999 Canadian Conference on General Relativity and Relativistic Astrophysics is a brief exposition of earlier work, with Sumati Surya (hep-th/9805121) Amanda Peet (hep-th/9903213), addressing certain results in higher dimensional supergravity that are related to black hole no-hair theorems. Its purpose is to describe, in language appropriate for an audience of relativists, how these results can be related to the Maldacena conjecture (aka, the AdS/CFT correspondence). The end product may be taken as a new kind of quantitative evidence in support of the Maldacena conjecture.
Here we give a short, concise proof for the following result. There exists a $k$-uniform hypergraph $H$ (for $k\geq 5$) without exponent, i.e., when the Tur\'an function is not polynomial in $n$. More precisely, we have $ex(n,H)=o(n^{k-1})$ but it exceeds $n^{k-1-c}$ for any positive $c$ for $n> n_0(k,c)$.   This is an extension (and simplification) of a result of Frankl and the first author from 1987 where the case $k=5$ was proven. We conjecture that it is true for $k\in \{3, 4\}$ as well.
Preliminary charge balance functions from the STAR Collaboration at the Relativistic Heavy Ion Collider (RHIC) are compared to a model where quarks are produced in two waves. If a chemically equilibrated quark-gluon plasma (QGP) is created the strength and diffusive spread of the first wave should be governed by the chemical composition of the QGP, while the second wave should be determined by the increased number of quarks required to make the observed final-state hadrons. A simple model parameterizes the chemistry of the super-hadronic matter and the two correlation lengths for the two waves. Calculations are compared to preliminary data from the STAR Collaboration. The chemistry of the super-hadronic matter appears to be within 20\% of expectations from lattice gauge theory.
The goal of randomness extraction is to distill (almost) perfect randomness from a weak source of randomness. When the source yields a classical string X, many extractor constructions are known. Yet, when considering a physical randomness source, X is itself ultimately the result of a measurement on an underlying quantum system. When characterizing the power of a source to supply randomness it is hence a natural question to ask, how much classical randomness we can extract from a quantum system. To tackle this question we here take on the study of quantum-to-classical randomness extractors (QC-extractors). We provide constructions of QC-extractors based on measurements in a full set of mutually unbiased bases (MUBs), and certain single qubit measurements. As the first application, we show that any QC-extractor gives rise to entropic uncertainty relations with respect to quantum side information. Such relations were previously only known for two measurements. As the second application, we resolve the central open question in the noisy-storage model [Wehner et al., PRL 100, 220502 (2008)] by linking security to the quantum capacity of the adversary's storage device.
Microstructural analysis of a Mg-Zn alloy deformed at room temperature by high-pressure torsion (HPT) indicates that fine-scale precipitation occurs even without post-deformation heat treatment. Small-angle X-ray scattering detects precipitates with radii between 2.5-20 nm after one rotation, with little increase in particle size or volume fraction after 20 rotations. High resolution electron micrographs identify grain boundary precipitates of monoclinic Mg$_4$Zn$_7$ phase after three rotations and MgZn$_2$ after 20 rotations.
Clustering logs have been the subject of much study in recent literature. They are a class of large logs which arise for non-global jet-shape observables where final-state particles are clustered by a non-cone--like jet algorithm. Their resummation to all orders is highly non--trivial due to the non-trivial role of clustering amongst soft gluons which results in the phase-space being non-factorisable. This may therefore significantly impact the accuracy of analytical estimations of many of such observables. Nonetheless, in this paper we address this very issue for jet shapes defined using the $k_t$ and C/A algorithms, taking the jet mass as our explicit example. We calculate the coefficients of the Abelian $\alpha_s^2 L^2$, $\alpha_s^3 L^3$ and $\alpha_s^4 L^4$ NLL terms in the exponent of the resummed distribution and show that the impact of these logs is small which gives confidence on the perturbative estimate without the neglected higher-order terms. Furthermore we numerically resum the non-global logs of the jet mass distribution in the $k_t$ algorithm in the large-$N_c$ limit.
We discuss the jet kinematics of a complete flux-density-limited sample of 135 radio-loud active galactic nuclei (AGN) resulting from a 13 year program to investigate the structure and evolution of parsec-scale jet phenomena. Our analysis is based on new 2 cm Very Long Baseline Array (VLBA) images obtained between 2002 and 2007, but includes our previously published observations made at the same wavelength, and is supplemented by VLBA archive data. In all, we have used 2424 images spanning the years 1994-2007 to study and determine the motions of 526 separate jet features in 127 jets. The data quality and temporal coverage (a median of 15 epochs per source) of this complete AGN jet sample represents a significant advance over previous kinematics surveys. In all but five AGNs, the jets appear one-sided, most likely the result of differential Doppler boosting. In general the observed motions are directed along the jet ridge line, outward from the optically thick core feature. We directly observe changes in speed and/or direction in one third of the well-sampled jet components in our survey. While there is some spread in the apparent speeds of separate features within an individual jet, the dispersion is about three times smaller than the overall dispersion of speeds among all jets. This supports the idea that there is a characteristic flow that describes each jet, which we have characterized by the fastest observed component speed. The observed maximum speed distribution is peaked at ~10c, with a tail that extends out to ~50c. This requires a distribution of intrinsic Lorentz factors in the parent population that range up to ~50. We also note the presence of some rare low-pattern speeds or even stationary features in otherwise rapidly flowing jets... (abridged)
Let $G$ be a simple graph of order $n$. The domination polynomial of $G$ is the polynomial $D(G, x)=\sum_{i=\gamma(G)}^{n} d(G,i) x^{i}$, where $d(G,i)$ is the number of dominating sets of $G$ of size $i$ and $\gamma(G)$ is the domination number of $G$. In this paper we study the domination polynomials of several classes of $k$-tree related graphs. Also, we present families of these kind of graphs, whose domination polynomial have no nonzero real roots.
We propose an online object-level SLAM system which builds a persistent and accurate 3D graph map of arbitrary reconstructed objects. As an RGB-D camera browses a cluttered indoor scene, Mask-RCNN instance segmentations are used to initialise compact per-object Truncated Signed Distance Function (TSDF) reconstructions with object size-dependent resolutions and a novel 3D foreground mask. Reconstructed objects are stored in an optimisable 6DoF pose graph which is our only persistent map representation. Objects are incrementally refined via depth fusion, and are used for tracking, relocalisation and loop closure detection. Loop closures cause adjustments in the relative pose estimates of object instances, but no intra-object warping. Each object also carries semantic information which is refined over time and an existence probability to account for spurious instance predictions. We demonstrate our approach on a hand-held RGB-D sequence from a cluttered office scene with a large number and variety of object instances, highlighting how the system closes loops and makes good use of existing objects on repeated loops. We quantitatively evaluate the trajectory error of our system against a baseline approach on the RGB-D SLAM benchmark, and qualitatively compare reconstruction quality of discovered objects on the YCB video dataset. Performance evaluation shows our approach is highly memory efficient and runs online at 4-8Hz (excluding relocalisation) despite not being optimised at the software level.
We revisit the duality between ALE singularities in M-theory and 7-branes on a circle in F-theory. We see that a frozen M-theory singularity maps to a circle compactification involving a rotation of the plane transverse to the 7-brane, showing an interesting correspondence between commuting triples in simply-laced groups and Kodaira's classification of singular elliptic fibrations. Our analysis strongly suggests that the O7+ plane is the only completely frozen F-theory singularity.
We define Dedekind sums attached to a totally real number field of class number one. We prove that they satisfy some reciprocity law. Then we relate them to special values of Hecke $L$-functions. We conclude that they are ruled by Stark's conjecture.
We study semileptonic decay B --> eta l nu. The transition form factors for this decays are calculated by using light cone QCD sum rules.
The cobaltates have demonstrated a wide variety complex behavior. The Na rich region of the phase diagram displays various degrees of anomalous behavior, such as Curie-Weiss behavior near a band insulator\cite{Foo:2004}, charge disproportionation\cite{Mukhamedshin:2005}, and non-Fermi-liquid behavior in the resistivity\cite{Foo:2004}. Alternatively, the Na poor region of the phase diagram appears to be a Fermi-liquid. The magnetic susceptibility displays Pauli behavior, the resistivity is roughly quadratic at low temperatures\cite{Foo:2004}, and the system appears to be homogeneous\cite{Mukhamedshin:2005}. Therefore, the Na poor region of the phase diagram seems like a natural starting point to attempt to explain the ARPES experiments and heat capacity measurements from a quantitative standpoint.
This survey is focused on two asymptotic models for internal waves, the Benjamin-Ono (BO) and Intermediate Long Wave (ILW) equations that are integrable by inverse scattering techniques (IST). After recalling briefly their derivations we will review old and recent results on the Cauchy problem, comparing those obtains by IST and PDE techniques and also results more connected to the physical origin of the equations. We will consider mainly the Cauchy problem on the real line with only a few comments on the perodic case. We will also briefly discuss some relevant problems, in particular the higher order extensions and the two-dimensional (KP like) versions of the BO and ILW equations.
Magnetic circular dichroism (MCD) of rutile Ti1-xCoxO2-d is systematically examined with various x and d to reveal a phase diagram for the appearance of ferromagnetism at higher carrier concentration and Co content. The phase diagram exactly matches with that determined from anomalous Hall effect (AHE). The magnetic field dependence of MCD also shows good coincidence with those of the magnetization and AHE. The coincidence of these independent measurements strongly suggests single and intrinsic ferromagnetic origin.
A supersymmetric model which naturally accommodates MeV tau neutrino within the framework of gauge mediated supersymmetry breaking is described. The lepton number violation is originally introduced in the messenger sector of the theory. A large slepton-Higgs mixing mass and a small lepton-higgsino mixing mass are generated at one-loop. Scalar tau neutrino has non-vanishing vacuum expectation value. These result in a non-zero \nu_{\tau} mass which is in the range of (1-10) MeV.
An analysis is made within the quantum formalism of the probabilistic features of the electron spin correlation, with the purpose of clarifying the concepts of contextuality and measurement dependence. The quantum formulas for the spin correlation are then derived on the basis of a probability distribution function and its associated geometric representation, both for a pair of projections of a single-particle spin and for the bipartite system in singlet spin state. This endows the spin correlation with a clear probabilistic meaning and leaves the door open for a possible physical image of the electron spin, as discussed at the end of the paper.
Using numerical modeling and a grid of synthetic spectra, we examine the effects that unresolved binaries have on the determination of various stellar atmospheric parameters for SEGUE targets measured using the SEGUE Stellar Parameter Pipeline (SSPP). To model undetected binaries that may be in the SEGUE sample, we use a variety of mass distributions for the primary and secondary stars in conjunction with empirically determined relationships for orbital parameters to determine the fraction of G-K dwarf stars, as defined by SDSS color cuts, that will be blended with a secondary companion. We focus on the G-K dwarf sample in SEGUE as it records the history of chemical enrichment in our galaxy. To determine the effect of the secondary on the spectroscopic parameters, we synthesize a grid of model spectra from 3275 to 7850 K (~0.1 to 1.0 \msun) and [Fe/H]=-0.5 to -2.5 from MARCS model atmospheres using TurboSpectrum. We analyze both "infinite" signal-to-noise ratio (S/N) models and degraded versions, at median S/N of 50, 25 and 10. By running individual and combined spectra (representing the binaries) through the SSPP, we determine that ~10% of the blended G-K dwarf pairs with S/N>=25 will have their atmospheric parameter determinations, in particular temperature and metallicity, noticeably affected by the presence of an undetected secondary. To account for the additional uncertainty from binary contamination at a S/N~10, uncertainties of ~140 K and ~0.17 dex in [Fe/H] must be added in quadrature to the published uncertainties of the SSPP. (Abridged)
Power corrections both to the strong coupling constant and to the structure function itself are estimated on the basis of the LO, NLO and NNLO QCD analysis of $xF_3$ structure function data. The sign of correction to the coupling constant is found to be negative. The x-shape of a higher twist contribution to the structure function is stable up to NNLO.
We present ground-based optical and near infrared photometric observations and Hubble Space Telescope COS spectroscopic observations of the old nova V842 Cen (Nova Cen 1986). Analysis of the optical light curves reveals a peak at 56.5 +/- 0.3s with an amplitude of 8.9 +/- 4.2 mma, which is consistent with the rotation of a magnetic white dwarf primary in V842 Cen that was detected earlier by Woudt et al., and led to its classification as an intermediate polar.However, our UV lightcurve created from the COS time-tag spectra does not show this periodicity. Our synthetic spectral analysis of an HST COS spectrum rules out a hot white dwarf photosphere as the source of the FUV flux. The best-fitting model to the COS spectrum is a full optically thick accretion disk with no magnetic truncation, a low disk inclination angle, low accretion rate and a distance less than half the published distance that was determined on the basis of interstellar sodium D line strengths.Truncated accretion disks with truncation radii of 3Rwd and 5Rwd yielded unsatisfactory agreement with the COS data. The accretion rate is unexpectedly low for a classical nova only 24 years after the explosion when the accretion rate is expected to be high and the white dwarf should still be very hot, especially if irradiation of the donor star took place. Our low accretion rate is consistent with low accretion rates derived from X-ray and ground-based optical data.
We present Arecibo 21 cm spectroscopy, Keck HIRES Hb spectroscopy, and WIYN R-band images of 11 nearby blue compact galaxies selected to be similar to blue compact star-forming galaxies at intermediate redshifts (0.1<z<1). We detect HI in 10 of 11 sample galaxies, yielding HI masses of 0.3-4x10^9 M_odot, HI linewidths, W_20, of 133-249 km/s, dynamical masses of 0.5-5x10^10 M_odot, gas depletion timescales, tau_gas, of 0.3-7 Gyr, HI mass fractions of 0.01-0.58, and mass-to-light ratios of 0.1-0.8. These values span the range typical of nearby HII galaxies, irregulars and spirals. Despite the restricted morphological selection, our sample is quite heterogeneous in HI content, dynamical mass, and gas depletion timescale. Therefore, these galaxies should look very different from each other in 5 Gyr. Fading of intermediate-z luminous blue compact galaxies into NGC-type spheroidals is a viable evolutionary scenario for the least massive, most gas-poor objects. The most consistent characteristic of our sample is that the ratio, R, of HII linewidth to HI 21 cm linewidth (W_20) are systematically less than unity. The simplest explanation is that the ionized gas is more centrally concentrated than the neutral gas within the gravitational potential. On average R=0.66 +/- 0.16, similar to findings for local HII galaxies. We find R is also a function of linewidth; smaller linewidth galaxies have smaller values of R. Correcting optical linewidths by this factor raises derived masses and places these galaxies on the local luminosity--linewidth (Tully-Fisher) relation. If this ratio applies to intermediate-redshift galaxies, then the proposed luminosity evolution of the Tully-Fisher relation is much smaller and more gradual than suggested by studies using optical emission-linewidth measurements.
The gedanken experiment by Wald to destroy a black hole using a test particle in the equatorial plane is adopted to the case of extremal magnetized black holes. We find the presence of external magnetic fields resulting from the "Ernst magnetization" permits a test particle to have strong enough energy to destroy the black hole. However, the corresponding effective potentials show that such particles would never reach the horizon.
Let $X$ be an ordinary smooth curve defined over an algebraically closed field of characteristic 2. The absolute Frobenius induces a rational map $F$ on the moduli space $M_X$ of rank 2 vector bundles with fixed trivial determinant. If the genus of $X$ is 2, the moduli space $M_X$ is isomorphic to projective space of dimension 3 (as over the complex numbers). In this case we explicitly give the equations of $F$, which enables us to determine, for example, its base locus (one point) and its image (different from $M_X$).