ShantanuT01/DACTYL-Pretraining huggingface dataset:
Phase transitions (PTs) are generally classified into second-order and first-order transitions, each exhibiting different intrinsic properties. For instance, a first-order transition exhibits latent heat and hysteresis when a control parameter is increased and then decreased across a transition point, whereas a second-order transition does not. Recently, hybrid percolation transitions (HPTs) are issued in diverse complex systems, in which the features of first-order and second-order PTs occur at the same transition point. Thus, the question whether hysteresis appears in an HPT arises. Herein, we investigate this fundamental question with a so-called restricted Erd\H{o}s--R\'enyi random network model, in which a cluster fragmentation process is additionally proposed. The hysteresis curve of the order parameter was obtained. Depending on when the reverse process is initiated, the shapes of hysteresis curves change, and the critical behavior of the HPT is conserved throughout the forward and reverse processes.
In a previous work, we introduced the notion of uniform generators of the Brauer group and proved that general diagonal cubic surfaces do not have such generators. In this paper, we prove that a similar non-existence result holds for affine diagonal quadrics.
We present a comprehensive study of accretion activity in the most underdense environments in the universe, the voids, based on the SDSS DR2 data. Based on investigations of multiple void regions, we show that AGN's occurrence rate and properties differ from those in walls. AGN are more common in voids than in walls, but only among moderately luminous and massive galaxies (M_r < -20, log M_*/M_sun < 10.5), and this enhancement is more pronounced for the weakly accreting systems (i.e., L_[O III] < 10^39 erg/s). Void AGN hosted by moderately massive and luminous galaxies are accreting at equal or lower rates than their wall counterparts, show less obscuration than in walls, and similarly aged stellar populations. The very few void AGN in massive bright hosts accrete more strongly, are more obscured, and are associated with younger stellar emission than wall AGN. Thus, accretion strength is probably connected to the availability of fuel supply, and accretion and star-formation co-evolve and rely on the same source of fuel. Nearest neighbor statistics indicate that the weak accretion activity (LINER-like) is not influenced by the local environment. However, H IIs, Seyferts, and Transition objects prefer more grouped small scale structures, indicating that the rate at which galaxies interact with each other affects their activity. These trends support a potential H II -> Seyfert/Transition Object -> LINER evolutionary sequence that we show is apparent in many properties of actively line-emitting galaxies, in both voids and walls. The subtle differences between void and wall AGN might be explained by a longer, less disturbed duty cycle of these systems in voids.
Although the Tomonaga-Luttinger liquid exhibits spin-charge separation and the electron is not an elementary excitation of the system, nevertheless an effective electronic dispersion may be defined by the frequency-dependent peak in the momentum distribution curve (MDC). The MDC is defined by considering the single hole spectral function $A^<(\vec{k},\omega)$ as a function of $\vec{k}$ at a fixed frequency $\omega$. We show the existence of a \emph{kink} in this dispersion for the spin-rotationally invariant Tomonaga-Luttinger liquid at finite temperature. In the repulsive regime where the charge velocity $v_{c}$ is greater than the spin velocity $v_{s}$, the low frequency effective electronic dispersion is linear in $\vec{k}$ and follows a velocity $v_l$ between the spin and charge velocities, $v_s < v_l < v_c$. The high frequency part (which is also linear in $\vec{k}$) disperses with the charge velocity $v_c$. The energy scale of the crossover between the two velocities defines a kink, $E_{\rm kink}$. In addition, the high energy dispersion extrapolates to the Fermi energy at a wavevector $k_{ex} \ne k_F$ which is shifted from the Fermi wavevector. The presence of such a kink is measurable with, {\em e.g.}, angle-resolved photoemission experiments, and may be used to test for the presence of Luttinger liquid behavior in systems in which the separate contributions from spin and charge to the MDC are not discernible due to strong interactions or low experimental resolution.
We study vectors formed by entries on the diagonal of standard Young tableaux of shifted shapes. Such vectors are in bijection with integer lattice points of certain integral polytopes, which are Minkowski sums of simplices. We also describe vertices of these polytopes, and construct corresponding shifted Young tableaux.
Generative adversarial networks (GANs) while being very versatile in realistic image synthesis, still are sensitive to the input distribution. Given a set of data that has an imbalance in the distribution, the networks are susceptible to missing modes and not capturing the data distribution. While various methods have been tried to improve training of GANs, these have not addressed the challenges of covering the full data distribution. Specifically, a generator is not penalized for missing a mode. We show that these are therefore still susceptible to not capturing the full data distribution.   In this paper, we propose a simple approach that combines an encoder based objective with novel loss functions for generator and discriminator that improves the solution in terms of capturing missing modes. We validate that the proposed method results in substantial improvements through its detailed analysis on toy and real datasets. The quantitative and qualitative results demonstrate that the proposed method improves the solution for the problem of missing modes and improves training of GANs.
Optical (BVRI) photometry of the first three weeks of the 2016 outburst of the recurrent Nova LMC 1968 is presented and discussed. The 2016 I-band light-curve is an exact replica, even in the most minute details, of that for the 2010 eruption. The maximum is inferred to have occurred on 2016 Jan 21.2 at I=11.5 mag, corresponding to an absolute magnitude M(I)=-7.15. A ~1 day plateau is present in all bands about six days past optical maximum, simultaneous with the emergence of super-soft X-ray emission in Swift observations, signalling the widespread ionization of the ejecta. The nova entered a much longer plateau about 9 days past maximum, governed by the brightness of the white dwarf, now directly visible and still nuclearly burning on its surface. An outburst recurrence mean period of ~955 days (2.6 yrs) would fit both the OGLE inter-season gaps and the observed intervals between previous outburts.
Determining the heating mechanism (or mechanisms) that causes the outer atmosphere of the Sun, and many other stars, to reach temperatures orders of magnitude higher than their surface temperatures has long been a key problem. For decades the problem has been known as the coronal heating problem, but it is now clear that `coronal heating' cannot be treated or explained in isolation and that the heating of the whole solar atmosphere must be studied as a highly coupled system. The magnetic field of the star is known to play a key role, but, despite significant advancements in solar telescopes, computing power and much greater understanding of theoretical mechanisms, the question of which mechanism or mechanisms are the dominant supplier of energy to the chromosphere and corona is still open. Following substantial recent progress, we consider the most likely contenders and discuss the key factors that have made, and still make, determining the actual (coronal) heating mechanism (or mechanisms) so difficult.
The Chandra HETGS spectra of the Seyfert 1 galaxy MCG--6-30-15 show numerous narrow, unresolved (FWHM < 200 km/s) absorption lines from a wide range of ionization states of N, O, Mg, Ne, Si, S, Ar, and Fe. The initial analysis of these data, presented in Lee et al. (2001), shows that a dusty warm absorber model adequately explains the spectral features > 0.48 keV (< 26 A). We attribute previous reports of an apparently highly redshifted O VII edge to the neutral Fe L absorption complex and the O VII resonance series (by transitions higher than He $\gamma$; He $\alpha,\beta,\gamma$ are also seen at lower energies). The implied dust column density needed to explain the FeI L edge feature agrees with that obtained from earlier reddening studies, which had already concluded that the dust should be associated with the ionized absorber (given the relatively lower observed X-ray absorption by cold gas). Our findings contradict the interpretation of Branduardi-Raymont et al. (2001), based on XMM-Newton RGS spectra, that this spectral region is dominated by highly relativistic soft X-ray line emission originating near the central black hole. Here we review these issues pertaining to the soft X-ray spectral features as addressed by Lee et al., (2001). (Details found in Lee et al., 2001, ApJ., 554, L13)
We present the results of a study of the type II Cepheid ($P_{puls} = 4.974 d$) in the eclipsing binary system OGLE-LMC-T2CEP-098 ($P_{orb} = 397.2 d$). The Cepheid belongs to the peculiar W Vir group, for which the evolutionary status is virtually unknown. It is the first single-lined system with a pulsating component analyzed using the method developed by Pilecki et al. (2013). We show that the presence of a pulsator makes it possible to derive accurate physical parameters of the stars even if radial velocities can be measured for only one of the components. We have used four different methods to limit and estimate the physical parameters, eventually obtaining precise results by combining pulsation theory with the spectroscopic and photometric solutions. The Cepheid radius, mass and temperature are $25.3 \pm 0.2 R_\odot$, $1.51 \pm 0.09 M_\odot$ and $5300 \pm 100 K$, respectively, while its companion has similar size ($26.3 R_\odot$), but is more massive ($6.8 M_\odot$) and hotter ($9500 K$). Our best estimate for the p-factor of the Cepheid is $1.30 \pm 0.03$. The mass, position on the period-luminosity diagram, and pulsation amplitude indicate that the pulsating component is very similar to the Anomalous Cepheids, although it has a much longer period and is redder in color. The very unusual combination of the components suggest that the system has passed through a mass transfer phase in its evolution. More complicated internal structure would then explain its peculiarity.
Let F be the imaginary quadratic field of discriminant -3 and OF its ring of integers. Let Gamma be the arithmetic group GL_3 (OF), and for any ideal n subset OF let Gamma_0 (n) be the congruence subgroup of level n consisting of matrices with bottom row (0,0,*) bmod n. In this paper we compute the cohomology spaces H^{nu - 1} (Gamma_0 (n); C) as a Hecke module for various levels n, where nu is the virtual cohomological dimension of Gamma. This represents the first attempt at such computations for GL_3 over an imaginary quadratic field, and complements work of Grunewald--Helling--Mennicke and Cremona, who computed the cohomology of GL_2 over imaginary quadratic fields. In our results we observe a variety of phenomena, including cohomology classes that apparently correspond to nonselfdual cuspforms on GL_3/F.
In this paper, we show the global well-posedness for periodic gKdV equations in the space $H^s(\mathbb{T})$, $s\ge \frac12$ for quartic case, and $s> \frac59$ for quintic case. These improve the previous results of I-team in 2004. In particular, the result is sharp for quintic case. The main approaches are the I-method combining with the resonance decomposition developed by Miao et al in 2010, and a bilinear Strichartz estimate in periodic setting.
Bilayer graphene under a magnetic field has an octet of quasidegenerate levels due to spin, valley, and orbital degeneracies. This zero-energy Landau level is resolved into several incompressible states whose nature is still elusive. We use a Hartree-Fock treatment of a realistic tight-binding four-band model to understand the quantum ferromagnetism phenomena expected for integer fillings of the octet levels. We include the exchange interaction with filled Landau levels below the octet states. This Lamb-shift-like effect contributes to the orbital splitting of the octet. We give phase diagrams as a function of applied bias and magnetic field. Some of our findings are in agreement with experiments. We discuss the possible appearance of phases with orbital coherence.
Segmenting object instances is a key task in machine perception, with safety-critical applications in robotics and autonomous driving. We introduce a novel approach to instance segmentation that jointly leverages measurements from multiple sensor modalities, such as cameras and LiDAR. Our method learns to predict embeddings for each pixel or point that give rise to a dense segmentation of the scene. Specifically, our technique applies contrastive learning to points in the scene both across sensor modalities and the temporal domain. We demonstrate that this formulation encourages the models to learn embeddings that are invariant to viewpoint variations and consistent across sensor modalities. We further demonstrate that the embeddings are stable over time as objects move around the scene. This not only provides stable instance masks, but can also provide valuable signals to downstream tasks, such as object tracking. We evaluate our method on the Cityscapes and KITTI-360 datasets. We further conduct a number of ablation studies, demonstrating benefits when applying additional inputs for the contrastive loss.
We construct D0-branes in SO(32)$\times$SO(32) open type 0 string theory using the same method as the one used to construct non-BPS D0-brane in type I string theory. It has been proposed that this theory is S-dual to bosonic string theory compactified on SO(32) lattice, which has SO(32)$\times$SO(32) spinor states as excited states of fundamental string. One of these states seems to correspond to the D0-brane, and by the requirement that other states which do not have corresponding states must be removed, we can determine the way of truncation of the spectrum. This result supports the conjecture.
A detailed analysis of the magnetic properties of a vanthoffite type mineral Na6Mn(SO4)4 basedon dc magnetization, low temperature neutron powder diffraction and theoretical calculations is reported. The mineral crystallizes in a monoclinic system with space group P21/c, where MnO6 octahedra are linked via SO4 tetrahedra. This gives rise to super-exchange interaction between two Mn2+ ions mediated by two nonmagnetic bridging anions and leads to an antiferromagnetic ordering below 3 K. The magnetic structure derived from neutron powder diffraction at 1.7 K depicts an antiferromagnetic spin arrangement in the bc plane of the crystal. The magnetic properties are modelled by numerical calculations using exact diagonalization technique, which fits the experimental results and provides antiferromagnetic ground state of Na6Mn(SO4)4.
The 2D TI edge states are considered within the Volkov-Pankratov (VP) Hamiltonian. A smooth transition between TI and OI is assumed. The edge states are formed in the total gap of homogeneous 2D material. A pair of these states are of linear dispersion, others have gapped Dirac spectra. The optical selection rules are found. The optical transitions between the neighboring edge states appear in the global 2D gap for the in-plane light electric field directed across the edge.   The electrons in linear edge states have no backscattering, that is indicative of the fact of topological protection. However, when linear edge states get to the energy domain of Dirac edge states, the backscattering becomes permitted. The elastic backscattering rate is found. The Drude-like conductivity is found when the Fermi level gets into the energy domain of the coexistence of linear and Dirac edge states. The localization edge conductance of a finite sample at zero temperature is determined.
Generative models using neural network have opened a door to large-scale studies for various application domains, especially for studies that suffer from lack of real samples to obtain statistically robust inference. Typically, these generative models would train on existing data to learn the underlying distribution of the measurements (e.g., images) in latent spaces conditioned on covariates (e.g., image labels), and generate independent samples that are identically distributed in the latent space. Such models may work for cross-sectional studies, however, they are not suitable to generate data for longitudinal studies that focus on "progressive" behavior in a sequence of data. In practice, this is a quite common case in various neuroimaging studies whose goal is to characterize a trajectory of pathologies of a specific disease even from early stages. This may be too ambitious especially when the sample size is small (e.g., up to a few hundreds). Motivated from the setup above, we seek to develop a conditional generative model for longitudinal data generation by designing an invertable neural network. Inspired by recurrent nature of longitudinal data, we propose a novel neural network that incorporates recurrent subnetwork and context gating to include smooth transition in a sequence of generated data. Our model is validated on a video sequence dataset and a longitudinal AD dataset with various experimental settings for qualitative and quantitative evaluations of the generated samples. The results with the AD dataset captures AD specific group differences with sufficiently generated longitudinal samples that are consistent with existing literature, which implies a great potential to be applicable to other disease studies.
When the standard model is extended with right-handed neutrinos the symmetries of the resulting Lagrangian are enlarged with a new global U(1)R Abelian factor. In the context of minimal seesaw models we analyze the implications of a slightly broken U(1)R symmetry on charged lepton flavor violating decays. We find, depending on the R-charge assignments, models where charged lepton flavor violating rates can be within measurable ranges. In particular, we show that in the resulting models due to the structure of the light neutrino mass matrix muon flavor violating decays are entirely determined by neutrino data (up to a normalization factor) and can be sizable in a wide right-handed neutrino mass range.
Parton Reggeization approach is the scheme of kT-factorization for multiscale hard processes, which is based on the Lipatov's gauge invariant effective field theory (EFT) for high energy processes in QCD. The new type of rapidity divergences, associated with the log 1/x-corrections, appears in the loop corrections in this formalism. The covariant procedure of regularization of rapidity divergences, preserving the gauge invariance of effective action is described. As an example application, the one-loop correction to the propagator of Reggeized quark and gamma Q q -scattering vertex are computed. Obtained results are used to construct the Regge limit of one-loop gamma+gamma -> q + barq amplitude. The cancelation of rapidity divergences and consistency of the EFT prediction with the full QCD result is demonstrated. The rapidity renormalization group within the EFT is discussed.
Models issued from ecology, chemical reactions and several other application fields lead to semi-linear parabolic equations with super-linear growth. Even if, in general, blow-up can occur, these models share the property that mass control is essential. In many circumstances, it is known that this $L^1$ control is enough to prove the global existence of weak solutions. The theory is based on basic estimates initiated by M. Pierre and collaborators, who have introduced methods to prove $L^2$ a priori estimates for the solution. Here, we establish such a key estimate with initial data in $L^1$ while the usual theory uses $L^2$. This allows us to greatly simplify the proof of some results. We also establish new existence results of semilinearity which are super-quadratic as they occur in complex chemical reactions. Our method can be extended to semi-linear porous medium equations.
We use deep Hubble Space Telescope Wide Field Camera 3 near-infrared imaging obtained of the GOODS-South field as part of the CANDELS survey to investigate a stellar mass-limited sample of quiescent galaxies at 1.5 < z < 2.5. We measure surface brightness profiles for these galaxies using a method that properly measures low surface brightness flux at large radii. We find that quiescent galaxies at z ~ 2 very closely follow Sersic profiles, with n_{median} = 3.7, and have no excess flux at large radii. Their effective radii are a factor ~ 4 smaller than those of low-redshift quiescent galaxies of similar mass. However, there is significant spread in sizes (sigma_{log r_e} = 0.24), with the largest z ~ 2 galaxies lying close to the z = 0 mass-size relation. We compare the stellar mass surface density profiles with those of massive elliptical galaxies in the Virgo cluster and confirm that most of the mass-growth which occurs between z ~ 2 and z = 0 must be due to accretion of material onto the outer regions of the galaxies. Additionally, we investigate the evolution in the size distribution of massive quiescent galaxies. We find that the minimum size growth required for z ~ 2 quiescent galaxies to fall within the z = 0 size distribution is a factor ~ 2 smaller than the total median size growth between z ~ 2 and z = 0.
The ultraviolet divergences of amplitude diagrams in maximal supergravity are investigated using the pure spinor superfield formalism in maximal supergravity, with maximally supersymmetric Yang-Mills theory for reference. We comment on the effects of the loop regularisation in relation to the actual absence of high powers (within the degrees of freedom) of the non-minimal variable r. The absence affects previous results of the field theory description, which is examined more closely (with a new b-ghost) with respect to the limit on the dimension for finiteness of the theory, dependent on the number of loops present. The results imply a cut-off of the loop dependence at six loops for the 4-point amplitude, and at seven loops otherwise.
We study a one-dimensional particles system, in the overdamped limit, where nearest particles attract with a force inversely proportional to a power of their distance and coalesce upon encounter. The detailed shape of the distribution function for the gap between neighbouring particles serves to discriminate between different laws of attraction. We develop an exact Fokker-Planck approach for the infinite hierarchy of distribution functions for multiple adjacent gaps and solve it exactly, at the mean-field level, where correlations are ignored. The crucial role of correlations and their effect on the gap distribution function is explored both numerically and analytically. Finally, we analyse a random input of particles, which results in a stationary state where the effect of correlations is largely diminished.
A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. We use comparison relationships between networks of this class with i.i.d. driving sequences and the $GI /GI /1/1$ queue to obtain the tail asymptotics of the stationary maximal dater under light-tailed assumptions for service times. The exponential rate of decay is given as a function of a logarithmic moment generating function. We exemplify an explicit computation of this rate for the case of queues in tandem under various stochastic assumptions.