ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study an XY-rotor model on regular one dimensional lattices by varying the number of neighbours. The parameter $2\ge\gamma\ge1$ is defined. $\gamma=2$ corresponds to mean field and $\gamma=1$ to nearest neighbours coupling. We find that for $\gamma<1.5$ the system does not exhibit a phase transition, while for $\gamma > 1.5$ the mean field second order transition is recovered. For the critical value $\gamma=\gamma_c=1.5$, the systems can be in a non trivial fluctuating phase for whichthe magnetisation shows important fluctuations in a given temperature range, implying an infinite susceptibility. For all values of $\gamma$ the magnetisation is computed analytically in the low temperatures range and the magnetised versus non-magnetised state which depends on the value of $\gamma$ is recovered, confirming the critical value $\gamma_{c}=1.5$.
We determine the [OIII]$\lambda5007$ equivalent width (EW) distribution of $1.700<\rm{z}<2.274$ rest-frame UV-selected (M$_{\rm{UV}}<-19$) star-forming galaxies in the GOODS North and South fields. We make use of deep HDUV broadband photometry catalogues for selection and 3D-HST WFC3/IR grism spectra for measurement of line properties. The [OIII]$\lambda5007$ EW distribution allows us to measure the abundance of extreme emission line galaxies (EELGs) within this population. We model a log-normal distribution to the [OIII]$\lambda5007$ rest-frame equivalent widths of galaxies in our sample, with location parameter $\mu=4.24\pm0.07$ and variance parameter $\sigma= 1.33\pm0.06$. This EW distribution has a mean [OIII]$\lambda5007$ EW of 168$\pm1\r{A}$. The fractions of $\rm{z}\sim2$ rest-UV-selected galaxies with [OIII]$\lambda5007$ EWs greater than $500, 750$ and $1000\r{A}$ are measured to be $6.8^{+1.0}_{-0.9}\%$, $3.6^{+0.7}_{-0.6}\%$, and $2.2^{+0.5}_{-0.4}\%$ respectively. The EELG fractions do not vary strongly with UV luminosity in the range ($-21.6<M_{\rm{UV}}<-19.0$) considered in this paper, consistent with findings at higher redshifts. We compare our results to $\rm{z}\sim5$ and $\rm{z}\sim7$ studies where candidate EELGs have been discovered through Spitzer/IRAC colours, and we identify rapid evolution with redshift in the fraction of star-forming galaxies observed in an extreme emission line phase (a rise by a factor $\sim10$ between $\rm{z}\sim2$ and $\rm{z}\sim7$). This evolution is consistent with an increased incidence of strong bursts in the galaxy population of the reionisation era. While this population makes a sub-dominant contribution of the ionising emissivity at $\rm{z}\simeq2$, EELGs are likely to dominate the ionising output in the reionisation era.
We examine the four-quark structure of the recently discovered charged $Z_c(3900)$, $Z(4430)$, and $X_b(5568)$ states. We calculate the widths of the strong decays $Z_c^+ \to J/\psi \pi^+$ ($\eta_c\rho^+$, $\bar D^0D^{\ast\,+}$, $\bar D^{\ast\,0}D^+$), $Z(4430)^+ \to J/\psi \pi^+$ ($\psi(2s) \pi^+$), and $X^+_b\to B_s\pi^+$ within a covariant quark model previously developed by us. We find that the tetraquark-type current widely used in the literature for the $Z_c(3900)$ leads to a significant suppression of the $\bar D D^\ast$ and $\bar D^\ast D$ modes. Contrary to this a molecular-type current provides an enhancement by a factor of 6-7 for the $\bar D D^\ast$ modes compared with the $Z_c^+\to J/\psi\pi^+$, $\eta_c\rho^+$ modes in agreement with recent experimental data from the BESIII Collaboration. In case of the $Z(4430)$ state we test a sensitivity of the ratio $R_Z$ of the $Z(4430)^+ \to \psi(2s) \pi^+$ and $Z(4430)^+ \to J/\psi \pi^+$ decay rates to a choice of the size parameter $\Lambda_{Z(4430)}$ of the $Z(4430)$. Using upper constraint for the sum of these two modes deduced from the LHCb Collaboration data we find that $R_Z$ varies from 4.64 to 4.08 when $\Lambda_{Z(4430)}$ changes from 2.2 to 3.2 GeV. Also we make the prediction for the $Z(4430)^+ \to D^{\ast\,+} \bar D^{\ast\,0}$ decay rate.
The conjectured Robin inequality for an integer $n>7!$ is $\sigma(n)<e^\gamma n \log \log n,$ where $\gamma$ denotes Euler constant, and $\sigma(n)=\sum_{d | n} d $. Robin proved that this conjecture is equivalent to Riemann hypothesis (RH). Writing $D(n)=e^\gamma n \log \log n-\sigma(n),$ and $d(n)=\frac{D(n)}{n},$ we prove unconditionally that $\liminf_{n \rightarrow \infty} d(n)=0.$ The main ingredients of the proof are an estimate for Chebyshev summatory function, and an effective version of Mertens third theorem due to Rosser and Schoenfeld. A new criterion for RH depending solely on $\liminf_{n \rightarrow \infty}D(n)$ is derived.
We investigate the possible types of coupling between ferroelectricity and magnetism for the zig-zag spin chain multiferroic LiCu2O2 compound. We construct a multi-order parameter phenomenological model for the material based on a group theoretical analysis. From our calculation we conclude that a coupling involving the inter-chain magnetic structure and ferroelectricity is necessary to understand the experimental results of Park et.al. Our proposed model is able to account for the electric polarization flop in the presence of an externally applied magnetic field. Furthermore, based on our theoretical model we can make specific selection rule predictions about electromagnon excitations present in the LiCu2O2 system. We also predict that the electromagnon peaks measured in an ac-conductivity measurement are field dependent.
We study the phenomenon of weak ergodicity breaking for a class of globally correlated random walk dynamics defined over a finite set of states. The persistence in a given state or the transition to another one depends on the whole previous temporal history of the system. A set of waiting time distributions, associated to each state, set the random times between consecutive steps. Their mean value is finite for all states. The probability density of time-averaged observables is obtained for different memory mechanisms. This statistical object explicitly shows departures between time and ensemble averages. While the mean residence time in each state may result divergent, we demonstrate that this condition is in general not necessary for breaking ergodicity. Hence, global memory effects are an alternative mechanism able to induce this property. Analytical and numerical calculations support these results.
Pedestrian trajectory prediction is an essential and challenging task for a variety of real-life applications such as autonomous driving and robotic motion planning. Besides generating a single future path, predicting multiple plausible future paths is becoming popular in some recent work on trajectory prediction. However, existing methods typically emphasize spatial interactions between pedestrians and surrounding areas but ignore the smoothness and temporal consistency of predictions. Our model aims to forecast multiple paths based on a historical trajectory by modeling multi-scale graph-based spatial transformers combined with a trajectory smoothing algorithm named ``Memory Replay'' utilizing a memory graph. Our method can comprehensively exploit the spatial information as well as correct the temporally inconsistent trajectories (e.g., sharp turns). We also propose a new evaluation metric named ``Percentage of Trajectory Usage'' to evaluate the comprehensiveness of diverse multi-future predictions. Our extensive experiments show that the proposed model achieves state-of-the-art performance on multi-future prediction and competitive results for single-future prediction. Code released at https://github.com/Jacobieee/ST-MR.
The lighter superpartner of the top quark ($\tt_1$) may be considerably lighter than squarks of the first two generations, and hence may be accessible to Tevatron collider searches, even if the other squarks and the gluino are too heavy. For the range of $m_{\tt_1}$ of interest at the Tevatron, the $\tt_1$ decays to a chargino via $\tt_1 \to b\tw_1$ if this is kinematically allowed; otherwise, the flavor-changing loop decay $\tt_1 \to c\tz_1$ dominates. In the latter case, $\tt_1$ production is signalled by jet(s) plus $\eslt$ events. If, instead, the chargino decay is allowed, $1\ell + b$-$jets + \eslt$ and $\ell^+\ell'^- + jet(s) + \eslt$ events from leptonic decays of $\tw_1$ provide the most promising signals. We perform detailed simulations for each of these signals using ISAJET 7.07 and devise cuts to enable the extraction of each of these signals above standard model backgrounds from vector boson or top quark production. With an integrated luminosity of 100 $pb^{-1}$, experiments should be able to probe top squark masses up to $\sim 100$ GeV in each of these channels; the detection of the signal in the single lepton channel, however, requires reasonable capability to tag displaced $b$ decay vertices in the central region.
For a simple normal crossing variety $X$, we introduce the concepts of prelog Chow ring, saturated prelog Chow group, as well as their counterparts for numerical equivalence. Thinking of $X$ as the central fibre in a (strictly) semistable degeneration, these objects can intuitively be thought of as consisting of cycle classes on $X$ for which some initial obstruction to arise as specializations of cycle classes on the generic fibre is absent. Cycle classes in the generic fibre specialize to their prelog counterparts in the central fibre, thus extending to Chow rings the method of studying smooth varieties via strictly semistable degenerations. After proving basic properties for prelog Chow rings and groups, we explain how they can be used in an envisaged further development of the degeneration method by Voisin et al. to prove stable irrationality of very general fibres of certain families of varieties; this extension would allow for much more singular degenerations, such as toric degenerations as occur in the Gross-Siebert programme, to be usable. We illustrate that by looking at the example of degenerations of elliptic curves, which, although simple, shows that our notion of prelog decomposition of the diagonal can also be used as an obstruction in cases where all components in a degeneration and their mutual intersections are rational.   We also compute the saturated prelog Chow group of degenerations of cubic surfaces.
We present precision Monte Carlo data and analytic arguments for an asymmetric exclusion process, involving two species of particles driven in opposite directions on a $2 \times L$ lattice. We propose a scenario which resolves a stark discrepancy between earlier simulation data, suggesting the existence of an ordered phase, and an analytic conjecture according to which the system should revert to a disordered state in the thermodynamic limit. By analyzing the finite size effects in detail, we argue that the presence of a single, seemingly macroscopic, cluster is an intermediate stage of a complex nucleation process: In smaller systems, this cluster is destabilized while larger systems allow the formation of multiple clusters. Both limits lead to exponential cluster size distributions which are, however, controlled by very different length scales.
We have shown in a recent collaboration that the Cauchy problem for the multi-dimensional Burgers equation is well-posed when the initial data u(0) is taken in the Lebesgue space L 1 (R n), and more generally in L p (R n). We investigate here the situation where u(0) is a bounded measure instead, focusing on the case n = 2. This is motivated by the description of the asymptotic behaviour of solutions with integrable data, as t $\rightarrow$ +$\infty$. MSC2010: 35F55, 35L65. Notations. We denote $\times$ p the norm in Lebesgue L p (R n). The space of bounded measure over R m is M (R m) and its norm is denoted $\times$ M. The Dirac mass at X $\in$ R n is $\delta$ X or $\delta$ x=X. If $\nu$ $\in$ M (R m) and $\mu$ $\in$ M (R q), then $\nu$ $\otimes$ $\mu$ is the measure over R m+q uniquely defined by $\nu$ $\otimes$ $\mu$, $\psi$ = $\nu$, f $\mu$, g whenever $\psi$(x, y) $\not\equiv$ f (x)g(y). The closed halves of the real line are denoted R + and R --. * U.M.P.A., UMR CNRS-ENSL \# 5669. 46 all{\'e}e d'Italie,
Low-frequency quasi-periodic oscillations (LFQPOs) are commonly found in black hole X-ray binaries, and their origin is still under debate. The properties of LFQPOs at high energies (above 30 keV) are closely related to the nature of the accretion flow in the innermost regions, and thus play a crucial role in critically testing various theoretical models. The Hard X-ray Modulation Telescope (Insight-HXMT) is capable of detecting emissions above 30 keV, and is therefore an ideal instrument to do so. Here we report the discovery of LFQPOs above 200 keV in the new black hole MAXI J1820+070 in the X-ray hard state, which allows us to understand the behaviours of LFQPOs at hundreds of kiloelectronvolts. The phase lag of the LFQPO is constant around zero below 30 keV, and becomes a soft lag (that is, the high-energy photons arrive first) above 30 keV. The soft lag gradually increases with energy and reaches ~0.9s in the 150-200 keV band. The detection at energies above 200 keV, the large soft lag and the energy-related behaviors of the LFQPO pose a great challenge for most currently existing models, but suggest that the LFQPO probably originates from the precession of a small-scale jet.
With the advent of LEP we discovered jets and at its last years we learned a lot about intermediate vector bosons. All that strongly supports our belief in QCD. Jet physics is briefly described in this talk. Experimental results are compared with QCD predictions. It is shown that the perturbative QCD has been able not only to describe the existing data but also to predict many bright phenomena.
We report a measurement of the quadrupole power spectrum in the two degree field (2dF) QSO redshift (2QZ) survey. The analysis uses an algorithm parallel to that for the estimation of the standard monopole power spectrum without first requiring computation of the correlation function or the anisotropic power spectrum. The error on the quadrupole spectrum is rather large but the best fit value of the bias parameter from the quadrupole spectrum is consistent with that from previous investigations of the 2dF data.
PT symmetric Aubry-Andre model describes an array of N coupled optical waveguides with position dependent gain and loss. We show that the reality of the spectrum depends sensitively on the degree of disorder for small number of lattice sites. We obtain the Hofstadter Butterfly spectrum and discuss the existence of the phase transition from extended to localized states. We show that rapidly changing periodical gain/loss materials almost conserves the total intensity.
We develop a new numerical algorithm to model collisional cascades in debris disks. Because of the large dynamical range in particle masses, we solve the integro-differential equations describing erosive and catastrophic collisions in a particle-in-a-box approach, while treating the orbital dynamics of the particles in an approximate fashion. We employ a new scheme for describing erosive (cratering) collisions that yields a continuous set of outcomes as a function of colliding masses. We demonstrate the stability and convergence characteristics of our algorithm and compare it with other treatments. We show that incorporating the effects of erosive collisions results in a decay of the particle distribution that is significantly faster than with purely catastrophic collisions.
We study extensions to higher dimensions of the classical Bayesian sequential testing and detection problems for Brownian motion. In the main result we show that, for a large class of problem formulations, the cost function is unilaterally concave. This concavity result is then used to deduce structural properties for the continuation and stopping regions in specific examples.
Let $K$ be a set of $q^2+2q+1$ points in $PG(4,q)$. We show that if every 3-space meets $K$ in either one, two or three lines, a line and a non-degenerate conic, or a twisted cubic, then $K$ is a ruled cubic surface. Moreover, $K$ corresponds via the Bruck-Bose representation to a tangent Baer subplane of $PG(2,q^2)$. We use this to prove a characterisation in $PG(2,q^2)$ of a set of points $B$ as a tangent Baer subplane by looking at the intersections of $B$ with Baer-pencils.
We show continuity of the martingale optimal transport optimisation problem as a functional of its marginals. This is achieved via an estimate on the projection in the nested/causal Wasserstein distance of an arbitrary coupling on to the set of martingale couplings with the same marginals. As a corollary we obtain an independent proof of sufficiency of the monotonicity principle established in [Beiglboeck, M., & Juillet, N. (2016). On a problem of optimal transport under marginal martingale constraints. Ann. Probab., 44 (2016), no. 1, 42106] for cost functions of polynomial growth.
The state-of-the-art in semantic segmentation is currently represented by fully convolutional networks (FCNs). However, FCNs use large receptive fields and many pooling layers, both of which cause blurring and low spatial resolution in the deep layers. As a result FCNs tend to produce segmentations that are poorly localized around object boundaries. Prior work has attempted to address this issue in post-processing steps, for example using a color-based CRF on top of the FCN predictions. However, these approaches require additional parameters and low-level features that are difficult to tune and integrate into the original network architecture. Additionally, most CRFs use color-based pixel affinities, which are not well suited for semantic segmentation and lead to spatially disjoint predictions.   To overcome these problems, we introduce a Boundary Neural Field (BNF), which is a global energy model integrating FCN predictions with boundary cues. The boundary information is used to enhance semantic segment coherence and to improve object localization. Specifically, we first show that the convolutional filters of semantic FCNs provide good features for boundary detection. We then employ the predicted boundaries to define pairwise potentials in our energy. Finally, we show that our energy decomposes semantic segmentation into multiple binary problems, which can be relaxed for efficient global optimization. We report extensive experiments demonstrating that minimization of our global boundary-based energy yields results superior to prior globalization methods, both quantitatively as well as qualitatively.
We present a combinatorial criterion on reflexive polytopes of dimension 3 which gives a local-to-global obstruction for the smoothability of the corresponding Fano toric threefolds. As a result, we show examples of singular Gorenstein Fano toric threefolds which have compound Du Val, hence smoothable, singularities but are not smoothable.
In the present work, we extend and generalize our previous work regarding the scale dependence applied to black holes in the presence of non-linear electrodynamics [1]. The starting point for this study is the Einstein-power-Maxwell theory with a vanishing cosmological constant in (3+1) dimensions, assuming a scale dependence of both the gravitational and the electromagnetic coupling. We further examine the corresponding thermodynamic properties and how these quantities experience deviations from their classical counterparts. We solve the effective Einstein's field equations using the "null energy condition" to obtain analytical solutions. The implications of quantum corrections are also briefly discussed. Finally, we analyze our solutions and compare them to related results in the literature.
For every $R>0$, consider the stochastic heat equation $\partial_{t} u_{R}(t\,,x)=\tfrac12 \Delta_{S_{R}^{2}}u_{R}(t\,,x)+\sigma(u_{R}(t\,,x)) \xi_{R}(t\,,x)$ on $S_{R}^{2}$, where $\xi_{R}=\dot{W_{R}}$ are centered Gaussian noises with the covariance structure given by $E [\dot{W_{R}}(t,x)\dot{W_{R}}(s,y)]=h_{R}(x,y)\delta_{0}(t-s)$, where $h_{R}$ is symmetric and semi-positive definite and there exist some fixed constants $-2< C_{h_{up}}< 2$ and $\frac{1}{2}C_{h_{up}}-1 <C_{h_{lo}}\le C_{h_{up}}$ such that for all $R>0$ and $x\,,y \in S_{R}^{2}$, $(\log R)^{C_{h_{lo}}/2}=h_{lo}(R)\leq h_{R}(x,y) \leq h_{up}(R)=(\log R)^{C_{h_{up}}/2}$, $\Delta_{S_{R}^{2}}$ denotes the Laplace-Beltrami operator defined on $S_{R}^{2}$ and $\sigma:R \mapsto R$ is Lipschitz continuous, positive and uniformly bounded away from $0$ and $\infty$. Under the assumption that $u_{R,0}(x)=u_{R}(0\,,x)$ is a nonrandom continuous function on $x \in S_{R}^{2}$ and the initial condition that there exists a finite positive $U$ such that $\sup_{R>0}\sup_{x \in S_{R}^{2}}\vert u_{R,0}(x)\vert \le U$, we prove that for every finite positive $t$, there exist finite positive constants $C_{low}(t)$ and $C_{up}(t)$ which only depend on $t$ such that as $R \to \infty$, $\sup_{x \in S_{R}^{2}}\vert u_{R}(t\,,x)\vert$ is asymptotically bounded below by $C_{low}(t)(\log R)^{1/4+C_{h_{lo}}/4-C_{h_{up}}/8}$ and asymptotically bounded above by $C_{up}(t)(\log R)^{1/2+C_{h_{up}}/4}$ with high probability.
The measurement of the exclusive light hadron decays of the psi'' in e+e- experiments with significant interference between the psi'' and non-resonance continuum amplitudes is discussed. The radiative correction and the Monte Carlo simulation are studied. A possible scheme to verify the destructive interference is proposed for the detectors with energy-momentum resolution of (1-2)%.
We point out that there are two different chiral spin liquid states on the triangular lattice and discuss the conducting states that are expected on doping them. These states labeled CS1 and CS2 are associated with two distinct topological orders with different edge states, although they both spontaneously break time reversal symmetry and exhibit the same quantized spin Hall conductance. While CSL1 is related to the Kalmeyer-Laughlin state, CSL2 is the $\nu =4$ member of Kitaev's 16 fold way classification. Both states are described within the Abrikosov fermion representation of spins, and the effect of doping can be accessed by introducing charged holons. On doping CSL2, condensation of charged holons leads to a topological d+id superconductor. However on doping CSL1 , in sharp contrast , two different scenarios can arise: first, if holons condense, a chiral metal with doubled unit cell and finite Hall conductivity is obtained. However, in a second novel scenario, the internal magnetic flux adjusts with doping and holons form a bosonic integer quantum Hall (BIQH) state. Remarkably, the latter phase is identical to a $d+id$ superconductor. In this case the Mott insulator to superconductor transition is associated with a bosonic variant of the integer quantum Hall plateau transition for the holon. We connect the above two scenarios to two recent numerical studies of doped chiral spin liquids on triangular lattice. Our work clarifies the complex relation between topological superconductors, chiral spin liquids and quantum criticality .