ShantanuT01/DACTYL-Pretraining huggingface dataset:
The superspace ring $\Omega_n$ is a rank $n$ polynomial ring tensor a rank $n$ exterior algebra. Using an extension of the Vandermonde determinant to $\Omega_n$, the authors previously defined a family of doubly graded quotients $\mathbb{W}_{n,k}$ of $\Omega_n$ which carry an action of the symmetric group $\mathfrak{S}_n$ and satisfy a bigraded version of Poincar\'e Duality. In this paper, we examine the duality modules $\mathbb{W}_{n,k}$ in greater detail. We describe a monomial basis of $\mathbb{W}_{n,k}$ and give combinatorial formulas for its bigraded Hilbert and Frobenius series. These formulas involve new combinatorial objects called {\em ordered superpartitions}. These are ordered set partitions $(B_1 \mid \cdots \mid B_k)$ of $\{1,\dots,n\}$ in which the non-minimal elements of any block $B_i$ may be barred or unbarred.
We consider the effect that a change in the magnetic induction B has in causing an orbitally quantized field-induced spin- or charge density wave (FISDW or FICDW) state to depart from thermodynamic equilibrium. The competition between elastic forces of the density wave (DW) and pinning leads to the realization of a critical state that is in many ways analogous to that realized within the vortex state of type II superconductors. Such a critical state has been verified experimentally in charge-transfer salts of the composition alpha-(BEDT-TTF)MHg(SCN)4, but should be a generic property of all orbitally quantized DW phases. The metastable state consists of a balance between the DW pinning force and the Lorentz force on extended currents associated with drifting cyclotron orbits, resulting in the establishment of persistent currents throughout the bulk and to the possibly of a three-dimensional `chiral metal' that extends deep into the interior of a crystal.
In this paper, we give some effective bounds for the $j$-invariant of integral points on arbitrary modular curves over arbitrary number fields assuming that the number of cusps is not less than 3.
Multi-channel spin-orbit quantum wires, when subjected to a magnetic field and proximity coupled to s-wave superconductor, may support Majorana states. We study what happens to these systems in the presence of disorder. Inspired by the widely established theoretical methods of mesoscopic superconductivity, we develop a la Eilenberger a quasiclassical approach to topological nanowires valid in the limit of strong spin-orbit coupling. We find that the "Majorana number", distinguishing between the state with Majorana fermion (symmetry class B) and no Majorana (class D), is given by the product of two Pfaffians of gapped quasiclassical Green's functions fixed by right and left terminals connected to the wire. A numerical solution of the Eilenberger equations reveals that the class D disordered quantum wires are prone to the formation of the zero-energy anomaly (class D impurity spectral peak) in the local density of states which shares the key features of the Majorana peak. In this way we confirm the robustness of our previous conclusions [Phys. Rev. Lett. 109, 227005 (2012)] on a more restrictive system setup. Generally speaking, we find that the quasiclassical approach provides a highly efficient means to address disordered class D superconductors both in the presence and absence of topological structures.
In this paper we propose a semi-supervised variational autoencoder for classification of overall survival groups from tumor segmentation masks. The model can use the output of any tumor segmentation algorithm, removing all assumptions on the scanning platform and the specific type of pulse sequences used, thereby increasing its generalization properties. Due to its semi-supervised nature, the method can learn to classify survival time by using a relatively small number of labeled subjects. We validate our model on the publicly available dataset from the Multimodal Brain Tumor Segmentation Challenge (BraTS) 2019.
In Ehrhart theory, the $h^*$-vector of a rational polytope often provide insights into properties of the polytope that may be otherwise obscured. As an example, the Birkhoff polytope, also known as the polytope of real doubly-stochastic matrices, has a unimodal $h^*$-vector, but when even small modifications are made to the polytope, the same property can be very difficult to prove. In this paper, we examine the $h^*$-vectors of a class of polytopes containing real doubly-stochastic symmetric matrices.
We examine the behaviour of charged particles in homogeneous, constant and/or oscillating magnetic fields in the non-relativistic approximation. A special role of the geometric center of the particle trajectory is elucidated. In quantum case it becomes a 'fuzzy point' with non-commuting coordinates, an element of non-commutative geometry which enters into the traditional control problems. We show that its application extends beyond the usually considered time independent magnetic fields of the quantum Hall effect. Some simple cases of magnetic control by oscillating fields lead to the stability maps differing from the traditional Strutt diagram.
We construct a quasi-sure version (in the sense of Malliavin) of geometric rough paths associated with a Gaussian process with long-time memory. As an application we establish a large deviation principle (LDP) for capacities for such Gaussian rough paths. Together with Lyons' universal limit theorem, our results yield immediately the corresponding results for pathwise solutions to stochastic differential equations driven by such Gaussian process in the sense of rough paths. Moreover, our LDP result implies the result of Yoshida on the LDP for capacities over the abstract Wiener space associated with such Gaussian process.
The Brackett decrement in the Class I source HH100 IR has been observed and analyzed to set constraints on the origin of the IR HI emission in this young object. We have used both low resolution (R ~ 800) observations of the Brackett lines from Brg, to Br24, and medium resolution (R~9000) spectra of the Brg, Br12 and Br13 lines. The dereddened fluxes indicates that the lines remain moderately thick up to high quantum numbers. Moreover, the profiles of the three lines observed in medium resolution are all broad and nearly symmetric, with a trend for the lines at high n-number to be narrower than the Brg, line. With the assumption that the three lines have different optical depths and consequently trace zones at different physical depths, we interprete the observed profiles as evidence that the ionized gas velocity in the HI emitting region is increasing as we move outwards, as expected in an accelerating wind more than in an infalling gas. We have modelled the observed line ratios and velocities with a simplified model for the HI excitation in an expanding circumstellar gas. Such a comparison indicates that the observations are consistent with the emission coming from a very compact region of 4-6 solar radii, where the gas has been already accelerated to velocities of the order of 200 \kms, with an associated mass flow rate of the ionized component of the order of 10^{-7} solar masses per year. This implies that the observed lines should originate either from a stellar wind or from the inner part of a disk wind, providing that the disk inner truncation radius is close to the stellar surface.
We present exact tree-order amplitudes for $H^* \to n~H$, for final states containing one or two particles with non-zero three-momentum, for various interaction potentials. We show that there are potentials leading to tree amplitudes that satisfy unitarity, not only at threshold but also in the above kinematical configurations and probably beyond. As a by-product, we also calculate $2\to n$ tree amplitudes at threshold and show that for the unbroken $\phi^4$ theory they vanish for $n>4~$, for the Standard Model Higgs they vanish for $n\ge 3~$ and for a model potential, respecting tree-order unitarity, for $n$ even and $n>4~$. Finally, we calculate the imaginary part of the one-loop $1\to n$ amplitude in both symmetric and spontaneously broken $\phi^4$ theory.
The "golden" channel, in which the newly-discovered Higgs boson decays to four leptons by means of intermediate vector bosons, is important for determining the properties of the Higgs boson and for searching for subtle new physics effects. Different approaches exist for parametrizing the relevant Higgs couplings in this channel; here we relate the use of pseudo-observables to methods based on specifying the most general amplitude or Lagrangian terms for the $HVV$ interactions. We also provide projections for sensitivity in this channel in several novel scenarios, illustrating the use of pseudo-observables, and analyze the role of kinematic distributions and (ratios of) rates in such $H\to4\ell$ studies.
We study the possibility of charge order at quarter filling and antiferromagnetism at half-filling in a tight-binding model of magic angle twisted bilayer graphene. We build on the model proposed by Kang and Vafek [Physical Review X 8(3), 031088 (2018)], relevant to a twist angle of $1.30^\circ$, and add on-site and extended density-density interactions. Applying the variational cluster approximation with an exact-diagonalization impurity solver, we find that the system is indeed a correlated (Mott) insulator at fillings $\frac14$, $\frac12$ and $\frac34$. At quarter filling, we check that the most probable charge orders do not arise, for all values of the interaction tested. At half-filling, antiferromagnetism only arises if the local repulsion $U$ is sufficiently large compared to the extended interactions, beyond what is expected from the simplest model of extended interactions.
We develop an intensive embedding for visualizing the space of all predictions for probabalistic models, using replica theory. Our embedding is isometric (preserves the distinguishability between models) and faithful (yields low-dimensional visualizations of models with simple emergent behavior). We apply our intensive embedding to the Ising model of statistical mechanics and the $\Lambda$CDM model applied to cosmic microwave background radiation. It provides an intuitive, quantitative visualization applicable to renormalization-group calculations and optimal experimental design.
We investigate models where structure formation is initiated by scaling seeds: We consider rapidly expanding relativistic shells of energy and show that they can fit current CMB and large scale structure data if they expand with super-luminal velocities. These acausally expanding shells provide a viable alternative to inflation for cosmological structure formation with the same minimal number of parameters to characterize the initial fluctuations. Causally expanding shells alone cannot fit present data. Hybrid models where causal shells and inflation are mixed also provide good fits.
We constructed the cumulative luminosity distributions of most supergiant fast X-ray transients (SFXTs) and the classical supergiant X-ray binary (SgXB) IGR J18027-2016 by taking advantage of the long term monitoring of these sources carried out with Swift/XRT (0.3-10 keV). Classical SgXBs are characterized by cumulative distributions with a single knee around $\sim$10$^{36}$-10$^{37}$ erg/s, while all SFXTs are found to be significantly sub-luminous and the main knee in their distributions is shifted at lower luminosities ($<$10$^{35}$ erg/s). As the latter are below the sensitivity limit of large field of view instruments operating in the hard X-ray domain ($>$15 keV), we show that a soft X-ray monitoring is required to reconstruct the entire profile of the SFXT cumulative luminosity distributions. The difference between the cumulative luminosity distributions of classical SgXBs and SFXTs is interpreted in terms of different wind accretion modes.
We provide some examples which give evidence to the conjectures contained in my paper "Finiteness of $p$-Divisible Sets of Multiple Harmonic Sums" (math.NT/0303043). All the main theoretical results can be found in that paper.
Complementary diffuse and inelastic synchrotron X-ray scattering measurements of lead zirconate-titanate single crystals with composition near the morphotropic phase boundary (x=0.475) are reported. In the temperature range 293 K < T < 400 K a highly anisotropic quasielastic diffuse scattering is observed. Above 400 K this scattering disappears. Its main features can be reproduced by model of inhomogeneous lattice deformations caused by inclusions of a tetragonal phase into a rhombohedral or monoclinic phase. This observation supports the idea that PZT at its morphotropic phase boundary is essentially structurally inhomogeneous.
In this paper, we study configurations of three rational points on the Hermitian curve over $\mathbb{F}_{q^2}$ and classify them according to their Weierstrass semigroups. For $q>3$, we show that the number of distinct semigroups of this form is equal to the number of positive divisors of $q+1$ and give an explicit description of the Weierstrass semigroup for each triple of points studied. To do so, we make use of two-point discrepancies and derive a criterion which applies to arbitrary curves over a finite field.
A spatially-independent model that can be used to calculate the temporal evolution of the electron/ positron spectrum in a spherically expanding pulsar wind nebula is presented. The model is applied to the young nebula G21.5-0.9, as well as to the unidentified TeV sources HESS J1427-608 and HESS J1507-622. The parameters derived from the model strengthens the idea that the unidentified sources can be identified as evolved pulsar wind nebulae.
Context: The discovery of new massive star clusters and massive stellar populations in previously known clusters in our Galaxy by means of infrared studies has changed our view of the Milky Way from an inactive to an active star-forming machine. Within this scenario, we present a near-infrared spectrophotometric study of the stellar content of the compact H II region Sh2-152.   Aims: We aim to determine the distance, extinction, age, and mass of Sh2-152, using for the first time near-infrared stellar classification for several sources in the region.   Methods: Using our near-infrared (J, H, and Ks) photometry and the colour-magnitude diagram for the cluster field, we selected 13 bright stars, candidate members of the reddened cluster's main sequence, for H- and K- spectroscopy and spectral classification. This near-infrared information was complemented with an optical spectrum of the ionizing central star to confirm its spectral nature.   Results: From the 13 spectroscopically observed stars, 5 were classified as B-type, 3 as G-type, 2 were young stellar objects (YSOs), and 3 remained unclassified (because of the poor data quality). The cluster's extinction varies from A_{Ks}=0.5 to 2.6 magnitudes (A_V=4.5 to 24 magnitudes) and the distance is estimated to be 3.21\pm0.21 kpc. The age of the cluster is younger than 9.4 Myr and the lower limit to the total mass of the cluster is (2.45\pm0.79)\cdot10^3 M_{Sun}. We compare the number of ionizing photons emitted from the OB-type stars with the Lyman continuum photons derived from the radio observations and conclude that both quantities are consistent for the central region of Sh2-152. In contrast, the main ionizing source of the lower region remains unidentified.
We reconsider the problem of determining the semiclassical 3-point function in the Euclidean AdS_3 model. Exploiting the affine symmetry of the model we use solutions of the classical Knizhnik-Zamolodchikov (KZ) equation to compute the saddle point of the action in the presence of three vertex operators. This alternative derivation reproduces the "heavy charge" classical limit of the quantum 3-point correlator. It is different from the recently proposed expression obtained by generalised Pohlmeyer reduction in AdS_2
We present a search for the synchrotron emission from the synchrotron cosmic web by cross correlating 180MHz radio images from the Murchison Widefield Array with tracers of large scale structure (LSS). We use two versions of the radio image covering $21.76\times 21.76$ degrees with point sources brighter than 0.05 Jy subtracted, with and without filtering of Galactic emission. As tracers of the LSS we use the Two-Micron-All-Sky-Survey (2MASS) and the Widefield InfraRed Explorer (WISE) redshift catalogues to produce galaxy number density maps. The cross correlation functions all show peak amplitudes at zero degrees, decreasing with varying slopes towards zero correlation over a range of one degree. The cross correlation signals include components from point source, Galactic, and extragalactic diffuse emission. We use models of the diffuse emission from smoothing the density maps with Gaussians of sizes 1-4 Mpc to find limits on the cosmic web components. From these models we find surface brightness 99.7 per cent upper limits in the range of 0.09-2.20 mJy beam$^{-1}$ (average beam size of 2.6 arcmin), corresponding to 0.01-0.30 mJy arcmin$^{-2}$. Assuming equipartition between energy densities of cosmic rays and the magnetic field, the flux density limits translate to magnetic field strength limits of 0.03-1.98 $\mu$G, depending heavily on the spectral index. We conclude that for a 3$\sigma$ detection of 0.1 $\mu$G magnetic field strengths via cross correlations, image depths of sub-mJy to sub-$\mu$Jy are necessary. We include discussion on the treatment and effect of extragalactic point sources and Galactic emission, and next steps for building on this work.
We present the calculation of the density matrix response function of the two-dimensional electron gas with Rashba spin-orbit interaction, which is applicable in a wide range of parameters covering the diffusive and non-diffusive, the dirty and the clean limits. A description of the crossover between the different regimes is thus provided as well. On the basis of the derived microscopic expressions we study the propagating charge and spin-polarization modes in the clean, non-diffusive regime, which is accessible in the modern experiments.
We show that a general prime Fano threefold X of genus 8 can be reconstructed from the pair $(\Gamma,L)$, where $\Gamma$ is its Fano curve of lines and $L=O_{\Gamma}(1)$ is the theta-characteristic which gives a natural embedding $\Gamma \subset \matbb{P}^5$.
We have examined how a Standard Model or Supersymmetric Higgs boson h might be detected at possible hadron colliders. The channels W(to ell nu)h(to b b~), Z(to ell ell~)h(to b b~) and W/Z(to jets)h(to tau+ tau-) are most useful. The results imply that h with mass M_h can be detected or excluded for M_h between about 80--130 GeV at any hadron collider with energy greater or similar to 2 TeV and an integrated luminosity greater or similar to 10 fb^{-1}; high luminosity is the essential requirement. We comment on measuring $h$ couplings and branching ratios.
We present new HST/WFC3 imaging data of RCSGA 032727-132609, a bright lensed galaxy at z=1.7 that is magnified and stretched by the lensing cluster RCS2 032727-132623. Using this new high-resolution imaging, we modify our previous lens model (which was based on ground-based data) to fully understand the lensing geometry, and use it to reconstruct the lensed galaxy in the source plane. This giant arc represents a unique opportunity to peer into 100-pc scale structures in a high-redshift galaxy. This new source reconstruction will be crucial for a future analysis of the spatially-resolved rest-UV and rest-optical spectra of the brightest parts of the arc.
The zCOSMOS-bright 10k spectroscopic sample reveals a strong environmental dependence of close kinematic galaxy pair fractions in the redshift range 0.2 < z < 1. The fraction of close pairs is three times higher in the top density quartile than in the lowest one. This environmental variation in pair fractions will translate into merger fractions since merger timescales are shown, based on Millennium simulation catalogs, to be largely independent of environment. While galactic properties of close kinematic pairs (morphologies and star formation rates) may seem to be non-representative of an underlying galaxy population, they can be explained by taking into account well-known effects of environment, and changes caused by interactions. The latter is responsible for an increase of irregular galaxies in pairs by a factor of 50-75%, with a disproportionate increase in the number of irregular-irregular pairs (4-8 times), due to disturbance of about 15% of the disk galaxies in pairs. Another sign of interaction is an observed boost in specific star formation rate (factor 2-4) for the closest pairs. While significant for paired galaxies, this triggered star-formation due to interactions represents only about 5% of the integrated star-formation activity in our volume-limited sample. Although majority of close kinematic pairs are in dense environments, the effects of interactions appear to be strongest in the lower density environments. This may introduce strong biases into observational studies of mergers, especially those based on morphological criteria. Relative excess of post-starburst galaxies observed in paired galaxies (factor \sim2) as well as excess of AGNs (factor of over 2), linked with environmental dependence of the pair fractions could indicate that early phases of interactions and merging are plausible candidates for environmental quenching, observed in the global galaxy populations.
We report the results of our study of lightcurve modulation in a sample of 493 RR1 variables from the OGLE-III survey of galactic bulge fields. Each object in this list has 1500 or more I-band observations. We compare our findings with earlier studies regarding lightcurve modulation in LMC and galactic field RR1 stars. We also report the discovery of the modulated-Blazhko RR1 star OGLE-BLG-RRLYR-03825 which has a Blazhko period of 16.469 d which itself is modulated with a period of 339.2 d.
We consider shifts of a set $A\subseteq\mathbb{N}$ by elements from another set $B\subseteq\mathbb{N}$, and prove intersection properties according to the relative asymptotic size of $A$ and $B$. A consequence of our main theorem is the following: If $A=\{a_n\}$ is such that $a_n=o(n^{k/k-1})$, then the $k$-recurrence set $R_k(A)=\{x\mid |A\cap(A+x)|\ge k\}$ contains the distance sets of arbitrarily large finite sets.
A perturbed lattice is a point process $\Pi=\{x+Y_x:x\in \mathbb{Z}^d\}$ where the lattice points in $\mathbb{Z}^d$ are perturbed by i.i.d.\ random variables $\{Y_x\}_{x\in \mathbb{Z}^d}$. A random point process $\Pi$ is said to be rigid if $|\Pi\cap B_0(1)|$, the number of points in a ball, can be exactly determined given $\Pi \setminus B_0(1)$, the points outside the ball. The process $\Pi$ is called deletion tolerant if removing one point of $\Pi$ yields a process with distribution indistinguishable from that of $\Pi$. Suppose that $Y_x\sim N_d(0,\sigma^2 I)$ are Gaussian vectors with with $d$ independent components of variance $\sigma^2$. Holroyd and Soo showed that in dimensions $d=1,2$ the resulting Gaussian perturbed lattice $\Pi$ is rigid and deletion intolerant. We show that in dimension $d\geq 3$ there exists a critical parameter $\sigma_r(d)$ such that $\Pi$ is rigid if $\sigma<\sigma_r$ and deletion tolerant (hence non-rigid) if $\sigma>\sigma_r$.
Electron spin relaxation induced by phonon-mediated s-d exchange interaction in a II-VI diluted magnetic semiconductor quantum dot is investigated theoretically. The electron-acoustic phonon interaction due to piezoelectric coupling and deformation potential is included. The resulting spin lifetime is typically on the order of microseconds. The effectiveness of the phonon-mediated spin-flip mechanism increases with increasing Mn concentration, electron spin splitting, vertical confining strength and lateral diameter, while it shows non-monotonic dependence on the magnetic field and temperature. An interesting finding is that the spin relaxation in a small quantum dot is suppressed for strong magnetic field and low Mn concentration at low temperature.