ShantanuT01/DACTYL-Pretraining huggingface dataset:
We introduce several classes of polytopes contained in $[0,1]^n$ and cut out by inequalities involving sums of consecutive coordinates. We show that the normalized volumes of these polytopes enumerate circular extensions of certain partial cyclic orders. Among other things this gives a new point of view on a question popularized by Stanley. We also provide a combinatorial interpretation of the Ehrhart $h^*$-polynomials of some of these polytopes in terms of descents of total cyclic orders. The Euler numbers, the Eulerian numbers and the Narayana numbers appear as special cases.
We present ground-based SpectroCam-10 mid-infrared, MMT optical, and Spitzer Space Telescope IRS mid-infrared spectra taken 7.62, 18.75, and 19.38 years respectively after the outburst of the old classical nova QU Vulpeculae (Nova Vul 1984 #2). The spectra of the ejecta are dominated by forbidden line emission from neon and oxygen. Our analysis shows that neon was, at the first and last epochs respectively, more than 76 and 168 times overabundant by number with respect to hydrogen compared to the solar value. These high lower limits to the neon abundance confirm that QU Vul involved a thermonuclear runaway on an ONeMg white dwarf and approach the yields predicted by models of the nucleosynthesis in such events.
We describe a simple method for unsupervised domain adaptation, whereby the discrepancy between the source and target distributions is reduced by swapping the low-frequency spectrum of one with the other. We illustrate the method in semantic segmentation, where densely annotated images are aplenty in one domain (synthetic data), but difficult to obtain in another (real images). Current state-of-the-art methods are complex, some requiring adversarial optimization to render the backbone of a neural network invariant to the discrete domain selection variable. Our method does not require any training to perform the domain alignment, just a simple Fourier Transform and its inverse. Despite its simplicity, it achieves state-of-the-art performance in the current benchmarks, when integrated into a relatively standard semantic segmentation model. Our results indicate that even simple procedures can discount nuisance variability in the data that more sophisticated methods struggle to learn away.
The Imaging Magnetograph eXperiment (IMaX) is a spectropolarimeter built by four institutions in Spain that flew on board the Sunrise balloon-borne telesocope in June 2009 for almost six days over the Arctic Circle. As a polarimeter IMaX uses fast polarization modulation (based on the use of two liquid crystal retarders), real-time image accumulation, and dual beam polarimetry to reach polarization sensitivities of 0.1%. As a spectrograph, the instrument uses a LiNbO3 etalon in double pass and a narrow band pre-filter to achieve a spectral resolution of 85 mAA. IMaX uses the high Zeeman sensitive line of Fe I at 5250.2 AA and observes all four Stokes parameters at various points inside the spectral line. This allows vector magnetograms, Dopplergrams, and intensity frames to be produced that, after reconstruction, reach spatial resolutions in the 0.15-0.18 arcsec range over a 50x50 arcsec FOV. Time cadences vary between ten and 33 seconds, although the shortest one only includes longitudinal polarimetry. The spectral line is sampled in various ways depending on the applied observing mode, from just two points inside the line to 11 of them. All observing modes include one extra wavelength point in the nearby continuum. Gauss equivalent sensitivities are four Gauss for longitudinal fields and 80 Gauss for transverse fields per wavelength sample. The LOS velocities are estimated with statistical errors of the order of 5-40 m/s. The design, calibration and integration phases of the instrument, together with the implemented data reduction scheme are described in some detail.
K. Kato has recently defined and studied heights of mixed motives and proposed some interesting questions. In this paper, we relate the study of heights to the study of Tamagawa numbers of motives. We also partially answer one of Kato's questions about the number of mixed motives of bounded heights in the case of mixed Tate motives with two graded quotients. Finally, we provide a concrete computation with the number of mixed Tate motives with three graded quotients.
Using the semiclassical theory of dense matter proposed by P.Savic and R.Kasanin,the mean molecular masses of the Galilean satellites of Jupiter are determined.The calculated values are fitted by plausible combinations of chemical elements,and the results are in good agreement with the observations by "Galileo".Possible cosmogonical explanations are briefly discussed.
Existing classification-based face recognition methods have achieved remarkable progress, introducing large margin into hypersphere manifold to learn discriminative facial representations. However, the feature distribution is ignored. Poor feature distribution will wipe out the performance improvement brought about by margin scheme. Recent studies focus on the unbalanced inter-class distribution and form a equidistributed feature representations by penalizing the angle between identity and its nearest neighbor. But the problem is more than that, we also found the anisotropy of intra-class distribution. In this paper, we propose the `gradient-enhancing term' that concentrates on the distribution characteristics within the class. This method, named IntraLoss, explicitly performs gradient enhancement in the anisotropic region so that the intra-class distribution continues to shrink, resulting in isotropic and more compact intra-class distribution and further margin between identities. The experimental results on LFW, YTF and CFP-FP show that our outperforms state-of-the-art methods by gradient enhancement, demonstrating the superiority of our method. In addition, our method has intuitive geometric interpretation and can be easily combined with existing methods to solve the previously ignored problems.
We prove that the helicity is preserved in the scattering of photons in the Born-Infeld theory (in 4d) on the tree level.
Since the thermal conduction equation has form invariance under coordinate transformation, one can design thermal metamaterials with novel functions by tailoring materials' thermal conductivities. In this work, we establish a different transformation theory, and propose a layered device with anisotropic thermal conductivities. The device is able to convert heat flux from parallel patterns into non-parallel patterns and vice versa. In the mean time, the heat flux pattern outside the device keeps undisturbed as if this device is absent. We perform finite-element simulations to confirm the converting behavior. This work paves a different way to manipulate the flow of heat at will.
On 2010 October 13, the X-ray astronomical satellite Rossi XTE, during the observation of the newly discovered accretion powered X-ray pulsar IGR J17480--2446, detected a lunar occultation of the source. From knowledge of lunar topography and Earth, Moon, and spacecraft ephemeris at the epoch of the event, we determined the source position with an accuracy of 40 mas (1{\sigma} c.l.), which is interesting, given the very poor imaging capabilities of RXTE (\sim 1\circ). For the first time, using a non-imaging X-ray observatory, the position of an X-ray source with a subarcsecond accuracy is derived, demonstrating the neat capabilities of a technique that can be fruitfully applied to current and future X-ray missions.
We show that the permanent of a matrix is a linear combination of determinants of block diagonal matrices which are simple functions of the original matrix. To prove this, we first show a more general identity involving \alpha-permanents: for arbitrary complex numbers \alpha and \beta, we show that the \alpha-permanent of any matrix can be expressed as a linear combination of \beta-permanents of related matrices. Some other identities for the \alpha-permanent of sums and products of matrices are shown, as well as a relationship between the \alpha-permanent and general immanants. We conclude with a discussion of the computational complexity of the \alpha-permanent and provide some numerical illustrations.
Semileptonic $B$($B_s, B_c$) decays are investigated systematically in the light-cone QCD sum rules. Special emphasis is put on the LCSR calculation on weak form factors with an adequate chiral current correlator, which turns out to be particularly effective to control the pollution by higher twist components of spectator mesons. The result for each channel depends on the distribution amplitude of the the producing meson. The leading twist distribution amplitudes of the related heavy mesons and charmonium are worked out by a model approach in the reasonable way. A practical scenario is suggested to understand the behavior of weak form factors in the whole kinematically accessible ranges. The decay widths and branching ratios are estimated for several $B$($B_c$) decay modes of current interest.
The methods by which one characterizes the distribution of matter in cosmological simulations is intrinsically different from how one performs the same task observationally. In this paper, we make substantial steps towards comparing simulations and observations of the intergalactic medium (IGM) in a more sensible way. We present a pipeline that generates and fits synthetic QSO absorption spectra using sight lines cast through a cosmological simulation, and simultaneously identifies structure by directly analyzing the variations in HI and OVI number density. We compare synthetic absorption spectra with a less observationally motivated, but more straightforward density threshold-based method for finding absorbers. Our efforts focus on HI and OVI to better characterize the warm/hot intergalactic medium, a subset of the IGM that is challenging to conclusively identify observationally. We find that the two methods trace roughly the same quantities of HI and OVI above observable column density limits, but the synthetic spectra typically identify more substructure in absorbers. We use both methods to characterize HI and OVI absorber properties. We find that both integrated and differential column density distributions from both methods generally agree with observations. The distribution of Doppler parameters between the two methods are similar for Lya and compare reasonably with observational results, but while the two methods agree with each other with OVI systems, they both are systematically different from observations. We find a strong correlation between OVI baryon fraction and OVI column density. We also discuss a possible bimodality in the temperature distribution of the gas traced by OVI.
Galaxy counts and recent measurements of the luminosity density in the near-infrared (NIR) have indicated the possibility that the local universe may be under-dense on scales of several hundred megaparsecs. The presence of a large-scale under-density in the local universe could introduce significant biases into the interpretation of cosmological observables, and, in particular, into the inferred effects of dark energy on the expansion rate. Here we measure the K-band luminosity density as a function of redshift to test for such a local under-density. In this effort, we combine photometry from UKIDSS and 2MASS with redshifts from the SDSS, 2DFGRS, 6DFGRS, 2MR, and GAMA surveys. We find that the overall shape of the z=0 rest-frame K-band luminosity function (M* = -22.15 +/- 0.04 and alpha = -1.02 +/- 0.03) appears to be relatively constant as a function of environment and redshift out to z ~0.2. We find a local (z < 0.07) luminosity density that is in good agreement with previous studies. Beyond z ~ 0.07 we detect a rising luminosity density that reaches a value ~1.5 times higher than that measured locally at z>0.1. This suggests that the stellar mass density as a function of redshift follows a similar trend. Assuming that luminous matter traces the underlying dark matter distribution, this implies that the local mass density of the universe may be lower than the global value on a scale and amplitude sufficient to introduce significant biases into the determination of basic cosmological observables, such as the expansion rate. An under-density of roughly this scale and amplitude would be sufficient to resolve the apparent tension between direct measurements of the Hubble constant and those inferred by Planck.
Penta-graphene is the name given to a novel puckered monolayer of carbon atoms tightly packed into an inerratic pentagonal network, theoretically, which exhibits excellent thermal and mechanical stability and can be rolled into penta-graphene nanotubes (PGNTs). Herein, we perform the first simulation study of mechanical properties of PGNTs under uniaxial tension. In addition to comparable mechanical properties with that of carbon nanotubes (CNT), it is found that PGNTs possess promising extensibility with typical plastic behavior due to the irreversible pentagon-to-polygon structural transformation and the hexagon carbon ring becomes the dominating structural motif after the transformation. The plastic characteristic of PGNTs is inherent with strain-rate and tube-diameter independences. Moreover, within ultimate temperature (T<1100 K), tensile deformed PGNTs manifest similar phase transition with an approximate transition ratio from pentagon to hexagon. The intrinsic insight provides a fundamental understanding of mechanic properties of PGNTs, which should open up a novel perspective for the design of plastic carbon-based nanomaterials.
This thesis gives an extension for the Density Matrix Renormalisation Group (DMRG) to two dimensions and described a newly developed combination of the DMRG and a Green Function Monte Carlo simulation (GFMC).   The first two chapters focus on the DMRG method. The properties are reviewed and it is shown that good quality results can be obtained for two-dimensional systems through finite-size scaling.   In the third and fourth chapter the properties of the two-dimensional frustrated Heisenberg model are analysed using a similar combination of DMRG and finite-size scaling.   The final chapter presents the combination of the DMRG and GFMC with Stochastic Reconfiguration (Sorella, Capriotti cond-mat/9902211) We find an intermediate phase between Neel and collinear long-range order. This phase shows spatial inhomogeneities with a tendency towards plaquette formation.
The contribution of rescattering to final state interactions in the (e,e'p) cross section is studied using a semiclassical model. This approach considers a two-step process with the propagation of an intermediate nucleon and uses Glauber theory to account for the reduction of the experimental yield due to N--N scattering. This calculation has relevance for the analysis of data at high missing energies and in particular at the kinematics of the E97-006 experiment done at JLab. It is found that rescattering is strongly reduced in parallel kinematics and that the excitation of nucleon resonances is likely to give important contributions to the final state interactions in the correlated region. For heavy nuclei, further enhancement to the rescattering is expected to be generated from the strength in the mean field region.
It is now established that, contrary to common belief, (electro-)vacuum Brans-Dicke gravity does not reduce to general relativity for large values of the Brans-Dicke coupling $\omega$. Since the essence of experimental tests of scalar-tensor gravity consists of providing stringent lower bounds on $\omega$, the PPN formalism on which these tests are based could be in jeopardy. We show that, in the linearized approximation used by the PPN formalism, the anomaly in the limit to general relativity disappears. However, it survives to second (and higher) order and in strong gravity. This fact is relevant for experiments aiming to test second order light deflection and Shapiro time delay.
We propose a scalable method for implementing linear optics quantum computation using the ``linked-state'' approach. Our method avoids the two-dimensional spread of errors occurring in the preparation of the linked-state. Consequently, a proof is given for the scalability of this modified linked-state model, and an exact expression for the efficiency of the method is obtained. Moreover, a considerable improvement in the efficiency, relative to the original linked-state method, is achieved. The proposed method is applicable to Nielsen's optical ``cluster-state'' approach as well.
The elemental Nb is mainly investigated for its eminent superconducting properties. In contrary, we report of a relatively unexplored property, namely, its superior optoelectronic property in reduced dimension. We demonstrate here that nanostructured Nb thin films (NNFs), under optical illumination, behave as room temperature photo-switches and exhibit bolometric features below its superconducting critical temperature. Both photo-switch and superconducting bolometric behavior are monitored by its resistance change with light in visible and near infrared (NIR) wavelength range. Unlike the conventional photodetectors, the NNF devices switch to higher resistive states with light and the corresponding resistivity change is studied with thickness and grain size variations. At low temperature in its superconducting state, the light exposure shifts the superconducting transition towards lower temperature. The room temperature photon sensing nature of the NNF is explained by the photon assisted electron-phonon scattering mechanism while the low temperature light response is mainly related to the heat generation which essentially changes the effective temperature for the device and the device is capable of sensing a temperature difference of few tens of milli-kelvins. The observed photo-response on the transport properties of NNFs can be very important for future superconducting photon detectors, bolometers and phase slip based device applications.
We study the strong coupling behaviour of fixed length single trace operators in the scalar SU(2) sector of ${\cal N} = 4$ SYM. We assume the recently proposed connection with a twisted half-filled Hubbard model. By explicit direct diagonalization of operators with length $L=4, 6, 8$ we study the full {\em perturbative multiplet} of those lattice states which have a clear correspondence with gauge theory composite operators. For this multiplet, we follow the weak-strong coupling flow to free fermion states and identify in particular the precise asymptotic fermion configuration. Next, we analyze the Lieb-Wu equations of the twisted Hubbard model. For the antiferromagnetic state we derive its strong coupling expansion working at $L$ up to 32. We also study the lightest state in the perturbative multiplet. This state is non trivial since involves complex solutions of the Lieb-Wu equations. It is particularly interesting for $AdS_5\times S^5$ duality since it is dual to the folded string semiclassical solution in the thermodynamical limit. We are able to perform the full analysis and compute the next-to-next-to leading terms in the strong coupling expansion for the non trivial lengths L=12 and L=20. A general formula is proposed for the NLO expansion for any $L=4(2k+1)$, $k\in\mathbb{N}$.
We have investigated the electron spin resonance (ESR) on single crystals of BaCu$\_2$Ge$\_2$O$\_7$ at temperatures between 300 and 2 K and in a large frequency band, 9.6 -134 GHz, in order to test the predictions of a recent theory, proposed by Oshikawa and Affleck (OA), which describes the ESR in a $S$=1/2 Heisenberg chain with the Dzyaloshinskii-Moriya interaction. We find, in particular, that the ESR linewidth, $\Delta H$, displays a rich temperature behavior. As the temperature decreases from $T\_{max}/2\approx $ 170 K to 50 K, $\Delta H$ shows a rapid and linear decrease, $\Delta H \sim T$. At low temperatures, below 50 K, $\Delta H$ acquires a strong dependence on the magnetic field orientation and for $H \| c$ it shows a $(h/T)^2$ behavior which is due to an induced staggered field $h$, according to OA's prediction.
The high temperature behaviour of graphene is studied by atomistic simulations based on an accurate interatomic potential for carbon. We find that clustering of Stone-Wales defects and formation of octagons are the first steps in the process of melting which proceeds via the formation of carbon chains. The molten state forms a three-dimensional network of entangled chains rather than a simple liquid. The melting temperature estimated from the two-dimensional Lindemann criterion and from extrapolation of our simulation for different heating rates is about 4900 K.
This note is about the Hilbert square $X=S^{[2]}$, where $S$ is a general $K3$ surface of degree $10$, and the anti-symplectic birational involution $\iota$ of $X$ constructed by O'Grady. The main result is that the action of $\iota$ on certain pieces of the Chow groups of $X$ is as expected by Bloch's conjecture. Since $X$ is birational to a double EPW sextic $X^\prime$, this has consequences for the Chow ring of the EPW sextic $Y\subset{\mathbb{P}}^5$ associated to $X^\prime$.
Let X be a supersingular K3 surface in characteristic 5 with Artin invariant 1. Then X has a polarization that realizes X as the Fermat sextic double plane. We present a list of polarizations of X with degree 2 whose intersection number with this Fermat sextic polarization is less than or equal to 5, and give the defining equations of the corresponding projective models. We also present a method to describe birational morphisms between these projective models explicitly. As a by-product, a non-projective automorphism of the Fermat sextic double plane is obtained.
Compact string expressions are found for non-intersecting Wilson loops in SU(N) Yang-Mills theory on any surface (orientable or nonorientable) as a weighted sum over covers of the surface. All terms from the coupled chiral sectors of the 1/N expansion of the Wilson loop expectation values are included.
Renormalization-group theory stands, since over 40 years, as one of the pillars of modern physics. As such, there should be no remaining doubt regarding its validity. However, finite-size scaling, which derives from it, has long been poorly understood above the upper critical dimension $d_c$ in models with free boundary conditions. Besides its fundamental significance for scaling theories, the issue is important at a practical level because finite-size, statistical-physics systems, with free boundaries above $d_c$, are experimentally accessible with long-range interactions. Here we address the roles played by Fourier modes for such systems and show that the current phenomenological picture is not supported for all thermodynamic observables either with free or periodic boundaries. Instead, the correct picture emerges from a sector of the renormalization group hitherto considered unphysical.
We compare the measurement of the gravitational mass of 38 high-redshift galaxy clusters observed by Chandra using Modified Newtonian Dynamics (MOND) and standard Newtonian gravity. Our analysis confirms earlier findings that MOND cannot explain the difference between the baryonic mass and the total mass inferred from the assumption of hydrostatic equilibrium. We also find that the baryon fraction at $r_{2500}$ using MOND is consistent with the Wilkinson Microwave Anisotropy Probe (WMAP) value of $\Omega_{B}/\Omega_{M}$