ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we define tropical analogues of real Hurwitz numbers, i.e. numbers of covers of surfaces with compatible involutions satisfying prescribed ramification properties. We prove a correspondence theorem stating the equality of the tropical numbers with their real counterparts. We apply this theorem to the case of double Hurwitz numbers (which generalizes our result from arXiv:1409.8095).
We investigate the origin of the ubiquitous existence of flat bands in the network superstructures of atomic chains, where one-dimensional(1D) atomic chains array periodically. While there can be many ways to connect those chains, we consider two representative ways of linking them, the dot-type and triangle-type links. Then, we construct a variety of superstructures, such as the square, rectangular, and honeycomb network superstructures with dot-type links and the honeycomb superstructure with triangle-type links. These links provide the wavefunctions with an opportunity to have destructive interference, which stabilizes the compact localized state(CLS). The CLS is a localized eigenstate whose amplitudes are finite only inside a finite region and guarantees the existence of a flat band. In the network superstructures, there exist multiple flat bands proportional to the number of atoms of each chain, and the corresponding eigenenergies can be found from the stability condition of the compact localized state. Finally, we demonstrate that the finite bandwidth of the nearly flat bands of the network superstructures arising from the next-nearest-neighbor hopping processes can be suppressed by increasing the length of the chains consisting of the superstructures.
Andreatta-Iovita-Pilloni constructed eigenvarieties for cuspidal Hilbert modular forms. The eigenvariety has a natural map to the weight space, called the weight map. At a classical point, we compute a lower bound of the dimension of the tangent space of the fiber of the weight map using Galois deformation theory. Along with the classicality theorem due to Tian-Xiao, this enables us to characterize the classical points of the eigenvariety which are ramified over the weight space, in terms of the local splitting behavior of the associated Galois representation.
Solar flares presumably have an impact on the deepest layers of the solar atmosphere and yet the observational evidence for such an impact is scarce. Using ten years of measurements of the Na D$_{1}$ and Na D$_2$ Fraunhofer lines, measured by GOLF onboard SOHO, we show that this photospheric line is indeed affected by flares. The effect of individual flares is hidden by solar oscillations, but a statistical analysis based on conditional averaging reveals a clear signature. Although GOLF can only probe one single wavelength at a time, we show that both wings of the Na line can nevertheless be compared. The varying line asymmetry can be interpreted as an upward plasma motion from the lower solar atmosphere during the peak of the flare, followed by a downward motion.
Metalization of carbon fiber reinforced polymers (CFRPs) composites by the surface modification method to enhance their electrical conductivity, thermal conductivity, electromagnetic shielding, erosion, and radiation protection, has a significant meaning in the aerospace field. In this study, Sn coating was successfully fabricated on the CFRP composite substrate via low-pressure cold spray under four gas temperatures (473K, 523K, 573K, and 623K). Their bonding mechanism was explored via the surface observation after peel-off adhesion strength, accompanying with surface temperature distribution investigation. The results indicates that we cannot obtain coating at 623 K, the epoxy matrix of the CFRP substrate was gradually eroded during deposition over 523 K. Meanwhile, Sn particles melt under 623 K condition. Three kinds of interfaces: Sn/epoxy, Sn/CF, and Sn/CF/epoxy are revealed as characteristics with respect to different gas temperatures to explore the bonding mechanisms.
Weakly-supervised object localization methods tend to fail for object classes that consistently co-occur with the same background elements, e.g. trains on tracks. We propose a method to overcome these failures by adding a very small amount of model-specific additional annotation. The main idea is to cluster a deep network's mid-level representations and assign object or distractor labels to each cluster. Experiments show substantially improved localization results on the challenging ILSVC2014 dataset for bounding box detection and the PASCAL VOC2012 dataset for semantic segmentation.
We worked out the Batalin-Fradkin-Tyutin (BFT) conversion program of second class constraints to first class constraints in the GS superstring using light cone coordinates. By applying this systematic procedure we were able to obtain a gauge system that is equivalent to the recent model proposed by Berkovits and Marchioro to relate the GS superstring to the pure spinor formalism.
We investigate the existence, uniqueness, and $L^1$-contractivity of weak solutions to a porous medium equation with fractional diffusion on an evolving hypersurface. To settle the existence, we reformulate the equation as a local problem on a semi-infinite cylinder, regularise the porous medium nonlinearity and truncate the cylinder. Then we pass to the limit first in the truncation parameter and then in the nonlinearity, and the identification of limits is done using the theory of subdifferentials of convex functionals.   In order to facilitate all of this, we begin by studying (in the setting of closed Riemannian manifolds and Sobolev spaces) the fractional Laplace--Beltrami operator which can be seen as the Dirichlet-to-Neumann map of a harmonic extension problem. A truncated harmonic extension problem will also be examined and convergence results to the solution of the harmonic extension will be given. For a technical reason, we will also consider some related extension problems on evolving hypersurfaces which will provide us with the minimal time regularity required on the harmonic extensions in order to properly formulate the moving domain problem. This functional analytic theory is of course independent of the fractional porous medium equation and will be of use generally in the analysis of fractional elliptic and parabolic problems on manifolds.
We present a new drift condition which implies rates of convergence to the stationary distribution of the iterates of a \psi-irreducible aperiodic and positive recurrent transition kernel. This condition, extending a condition introduced by Jarner and Roberts [Ann. Appl. Probab. 12 (2002) 224-247] for polynomial convergence rates, turns out to be very convenient to prove subgeometric rates of convergence. Several applications are presented including nonlinear autoregressive models, stochastic unit root models and multidimensional random walk Hastings-Metropolis algorithms.
Atom optics, a field which takes much inspiration from traditional optics, has advanced to the point that some of the fundamental experiments of quantum optics, involving photon correlations, have found atomic analogs. We discuss some recent experiments on atom bunching and anti-bunching as well as some prospects for extending them to the field of many body physics.
WY Cancri is a short-period ($P$=0.829 d) eclipsing RS Canum Venaticorum stars, and both components are late-type stars. Recently, observations provided by photometric observations and light time minima show that the orbital period of WY Cancri is experiencing a secular decrease at a rate of ${\rm d} P/{\rm d}t=-1.2\times10^{-7}\rm d yr^{-1}$. In this Letter, we attempt to investigate if the period change of WY Cancri can originate from the angular momentum loss. In calculation, we assume that this source has a high wind loss rate of $\sim10^{-10} \rm M_{\odot} yr^{-1}$. To account for the observation, magnetic braking demands a strong surface magnetic field of $\gtrsim 10000$ G like Ap/Bp stars. Furthermore, if this source may be surrounded by a circumbinary disk, and 6% of the wind loss feeds the disk, tidal torque between the disk and the binary can offer the observed angular momentum loss rate. Such a strong magnetic field or an extremely high wind input fraction seem to be highly unlikely.
A global analysis of the world data on differential cross sections and polarization asymmetries of backward pion-nucleon scattering for invariant collision energies above 3 GeV is performed in a Regge model. Including the $N_\alpha$, $N_\gamma$, $\Delta_\delta$ and $\Delta_\beta$ trajectories, we reproduce both angular distributions and polarization data for small values of the Mandelstam variable $u$, in contrast to previous analyses. The model amplitude is used to obtain evidence for baryon resonances with mass below 3 GeV. Our analysis suggests a $G_{39}$ resonance with a mass of 2.83 GeV as member of the $\Delta_{\beta}$ trajectory from the corresponding Chew-Frautschi plot.
In this paper we study the effects of letting the dark matter and the gas in the Universe couple to the scalar field of the symmetron model, a modified gravity theory, with varying coupling strength. We also search for a way to distinguish between universal and non-universal couplings in observations. The research is performed utilising a series of hydrodynamic, cosmological N-Body simulations, studying the resulting power spectra and galaxy halo properties, such as the density and temperature profiles. Results show that in the cases of universal couplings, the deviations in the baryon fraction from $\Lambda$CDM are smaller than in the cases of non-universal couplings throughout the halos. The same is apparent in the power spectrum baryon bias, defined as the ratio of gas to dark matter power spectrum. Deviations of the density profiles and power spectra from the $\Lambda$CDM reference values can differ significantly between dark matter and gas because the dark matter deviations are mostly larger than the deviations in the gas.
Rapporteur talk at the Lepton-Photon Conference, Rome, July 2001: reviewing the evidence and strategies for understanding scalar mesons, glueballs and hybrids, the gluonic Pomeron and the interplay of heavy flavours and light hadron dynamics. Dedicated to the memory of Nathan Isgur, long-time collaborator and friend, whose original ideas in hadron spectroscopy formed the basis for much of the talk.
Let $C$ be a smooth complex projective curve of genus $g \,\geq\, 2$ and $C_d$ its $d$-fold symmetric product. In this paper, we study the question of semi-orthogonal decomposition of the derived category of $C_d$. This entails investigations of the canonical system on $C_d$, in particular its base locus.
We examine diffusive shock acceleration (DSA) of the pre-exisiting as well as freshly injected populations of nonthermal, cosmic-ray (CR) particles at weak cosmological shocks. Assuming simple models for thermal leakage injection and Alfv\'enic drift, we derive analytic, time-dependent solutions for the two populations of CRs accelerated in the test-particle regime. We then compare them with the results from kinetic DSA simulations for shock waves that are expected to form in intracluster media and cluster outskirts in the course of large-scale structure formation. We show that the test-particle solutions provide a good approximation for the pressure and spectrum of CRs accelerated at these weak shocks. Since the injection is extremely inefficient at weak shocks, the pre-existing CR population dominates over the injected population. If the pressure due to pre-existing CR protons is about 5 % of the gas thermal pressure in the upstream flow, the downstream CR pressure can absorb typically a few to 10 % of the shock ram pressure at shocks with the Mach number $M \la 3$. Yet, the re-acceleration of CR electrons can result in a substantial synchrotron emission behind the shock. The enhancement in synchrotron radiation across the shock is estimated to be about a few to several for $M \sim 1.5$ and $10^2-10^3$ for $M \sim 3$, depending on the detail model parameters. The implication of our findings for observed bright radio relics is discussed.
In this note, we investigate the behaviour of suprema for band-limited spherical random fields. We prove upper and lower bound for the expected values of these suprema, by means of metric entropy arguments and discrete approximations; we then exploit the Borell-TIS inequality to establish almost sure upper and lower bounds for their fluctuations. Band limited functions can be viewed as restrictions on the sphere of random polynomials with increasing degrees, and our results show that fluctuations scale as the square root of the logarithm of these degrees.
The increased amount of high precision seismic data for solar-like stars calls for the existence of tools that can extract information from such data. In the case of the study of acoustic glitches there are no publicly available tools and most existing ones require a deep knowledge of their implementation. In this work a tool is presented that aims to both simplify the interaction with the user and also be capable of working automatically to determine properties of acoustic glitches from seismic data of solar-like stars. This tool is shown to work with both the Sun and other solar analogs but also shows that are still severe limitations to the methods used, when considering smaller datasets.
We report the electronic transport properties of a new photo-addressable molecular switch. The switching process relies on a new concept based on linear {\pi}-conjugated dynamic systems, in which the geometry and hence the electronic properties of an oligothiophene chain can be reversibly modified by the photochemical trans-cis isomerization of an azobenzene unit fixed in a lateral loop. Electron transport measurements through self-assembled monolayers on gold, contacted with eGaIn top contact, show switching with a conductance ratio up to 1E3. Ab initio calculations have been used to identify the most energetically stable conformations of the molecular switch, the corresponding calculated conductances qualitatively explain the trend observed in the photo-switching experiments.
In this paper we study various aspects of classical solutions to the affine Toda equations on a half-line with integrable boundary conditions. We begin by finding conditions that the theory has a stable vacuum by finding a Bogomolny bound on the energy, and analysing the possible singularities of the field at the boundary. Using these constraints and extensive numerical investigations we classify the vacuum configurations and reflection factors for A_r^(1) Toda theories up to r=5.
We present prelimiary results from a coordinated spectroscopic campaign in 2011, centered on the \delta Sco periastron passage in July. Data have mostly been obtained with the FEROS/2.2 m at La Silla and ESPaDOnS/CFHT at Mauna Kea echelle instruments. Main results include the absence of tidally induced disturbance to the main \beta Cephei pulsation mode and the absence of tidally triggered mass-ejection at time of periastron proper. The observed (as far as yet analyzed) variations are compatible with the picture of a disk that is disturbed on its outer radius, with the disturbance propagating inwards after the periastron.
We use distant Blue Horizontal Branch stars with Galactocentric distances 16 < r/kpc < 48 as kinematic tracers of the Milky Way dark halo. We model the tracer density as an oblate, power-law embedded within a spherical power-law potential. Using a distribution function method, we estimate the overall power-law potential and the velocity anisotropy of the halo tracers. We measure the slope of the potential to be gamma ~ 0.4 and the overall mass within 50 kpc is ~ 4 x 10^11 M_sol. The tracer velocity anisotropy is radially biased with beta ~ 0.5, which is in good agreement with local solar neighbourhood studies. Our results provide an accurate outer circular velocity profile for the Milky Way and suggest a relatively high concentration dark matter halo (c_vir ~ 20).
We introduce and study a minimum two-orbital Hubbard model on a triangular lattice, which captures the key features of both the trilayer ABC-stacked graphene-boron nitride heterostructure and twisted transition metal dichalcogenides in a broad parameter range. Our model comprises first- and second-nearest neighbor hoppings with valley-contrasting flux that accounts for trigonal warping in the band structure. For the strong-coupling regime with one electron per site, we derive a spin-orbital exchange Hamiltonian and find the semiclassical ground state to be a spin-valley density wave. We show that a relatively small second-neighbor exchange interaction is sufficient to stabilize the ordered state against quantum fluctuations. Effects of spin- and valley Zeeman fields as well as thermal fluctuations are also examined.
The observation of ultrahigh energy (UHE) neutrinos has become a priority in experimental astroparticle physics. UHE neutrinos can be detected with a variety of techniques. In particular, neutrinos can interact in the atmosphere (downward-going neutrinos) or in the Earth crust (Earth-skimming neutrinos), producing air showers that can be observed with arrays of detectors at the ground. With the Surface Detector Array of the Pierre Auger Observatory we can detect these types of cascades. The distinguishing signature for neutrino events is the presence of very inclined showers produced close to the ground (i.e. after having traversed a large amount of atmosphere). In this work we review the procedure and criteria established to search for UHE neutrinos in the data collected with the ground array of the Pierre Auger Observatory. This includes Earth-skimming as well as downward-going neutrinos. No neutrino candidates have been found, which allows us to place competitive limits to the diffuse flux of UHE neutrinos in the EeV range and above.
A maniplex of rank $n$ is a combinatorial object that generalises the notion of a rank $n$ abstract polytope. A maniplex with the highest possible degree of symmetry is called reflexible. In this paper we prove that there is a rank $4$ reflexible maniplex with automorphism group $\textrm{PSL}_2(q)$ for infinitely many prime powers $q$, and that no reflexible maniplex of rank $n > 4$ exists that has $\textrm{PSL}_2(q)$ as its full automorphism group.
We compare the mass functions of young star clusters (ages $\leq 10$ Myr) and giant molecular clouds (GMCs) in six galaxies that cover a large range in mass, metallicity, and star formation rate (LMC, M83, M51, NGC 3627, the Antennae, and NGC 3256). We perform maximum-likelihood fits of the Schechter function, $\psi(M) = dN/dM \propto M^{\beta} \exp(-M/M_*)$, to both populations. We find that most of the GMC and cluster mass functions in our sample are consistent with a pure power-law distribution ($M_* \rightarrow \infty$). M51 is the only galaxy that shows some evidence for an upper cutoff ($M_*$) in both populations. Therefore, physical upper mass cutoffs in populations of both GMCs and clusters may be the exception rather than the rule. When we perform power-law fits, we find a range of indices $\beta_{\rm PL}=-2.3\pm0.3$ for our GMC sample and $\beta_{\rm PL}=-2.0\pm0.3$ for the cluster sample. This result, that $\beta_{\rm Clusters} \approx \beta_{\rm GMC} \approx -2$, is consistent with theoretical predictions for cluster formation and suggests that the star-formation efficiency is largely independent of mass in the GMCs.
We summarize recent developments in modeling of mass outflows from accretion disks in AGN. We illustrate how the hydrodynamical and magnetohydrodynamical wind structures revealed in numerical simulations relate to observations. Important results from the numerical simulations include: no shielding from X-rays is needed to radiatively launch a wind from the inner disk; shielding is needed to accelerate the wind to high velocities. Disk winds launched magnetically seem to be too dense to be accelerated by line driving. It appears that we have an all or nothing situation for radiation-driving: radiation driving has to be responsible for both launching and accelerating the wind or a wind launched by some other mechanism must have a very finely tuned density in order to be accelerated by radiation driving to velocities as high as measured in BAL QSOs.
We explore the prospects of observing leptonic CP violation in a neutrino factory in the context of a scenario with three strongly oscillating neutrinos able to account for the solar, the atmospheric and the LSND results. We address also the problems related with the fake asymmetries induced by the experimental device and by the presence of matter.
Gas-rich galaxies in dense environments such as galaxy clusters and massive groups are affected by a number of possible types of interactions with the cluster environment, which make their evolution radically different than that of field galaxies. The dIrr galaxy NGC 1427A, presently infalling towards the core of the Fornax galaxy cluster, offers a unique opportunity to study those processes in a level of detail not possible to achieve for galaxies at higher redshifts. Using HST/ACS and auxiliary VLT/FORS ground-based observations, we study the properties of the most recent episodes of star formation in this gas-rich galaxy, the only one of its type near the core of the Fornax cluster. We study the structural and photometric properties of young star cluster complexes in NGC 1427A, identifying 12 bright such complexes with exceptionally blue colors. The comparison of our broadband near-UV/optical photometry with simple stellar population models yields ages below ~4x10^6 yr and stellar masses from a few thousand up to ~3x10^4 Msun, slightly dependent on the assumption of cluster metallicity and IMF. Their grouping is consistent with hierarchical and fractal star cluster formation. We use deep Ha imaging data to determine the current Star Formation Rate (SFR) in NGC 1427A and estimate the ratio, Gamma, of star formation occurring in these star cluster complexes to that in the entire galaxy. We find Gamma to be among the largest such values available in the literature, consistent with starburst galaxies. Thus a large fraction of the current star formation in NGC 1427A is occurring in star clusters, with the peculiar spatial arrangement of such complexes strongly hinting at the possibility that the starburst is being triggered by the passage of the galaxy through the cluster environment.
In 2006, in a paper published in Compositio, titled "Bounds on canonical Green's functions", J. Jorgenson and J. Kramer proved a certain key identity which relates the two natural metrics, namely the hyperbolic metric and the canonical metric defined on a compact hyperbolic Riemann surface. In this article, we extend this identity to product of noncompact hyperbolic Riemann orbisurfaces of finite volume, which can be realized as a quotient space of the action of a Fuchsian subgroup of first kind on the hyperbolic upper half plane.
We consider the production of $\gamma^*, W$ and $Z$ vector bosons in hadron-hadron collisions in perturbative QCD. We present results from a new numerical program which gives a full description of the production of the vector bosons and of their decay products. At small $\qt$ the calculation includes resummation of large logarithms and non-perturbative effects. The resummation is matched with the full $O(\alpha_S)$ calculation. In addition, the program correctly reproduces the known $O(\alpha_S)$ cross section when integrated over $\qt$. Besides presenting results for $W$ and $Z$ production at the Tevatron, we also review constraints on the non-perturbative functions using fixed target data on lepton pair production, and make several observations on this topic.