ShantanuT01/DACTYL-Pretraining huggingface dataset:
The main result of this paper is a rigorous proof of criticality and an explicit computation of critical exponents for the decay of avalanches in the Abelian sandpile model (ASM) on a large family of infinite graphs. We begin by introducing the notion of criticality of the ASM for limits of finite graphs in local convergence, which naturally leads to the question about criticality of the ASM in the random weak limit. Our main technical ingredient is a sufficient condition for almost sure criticality of the ASM on sequences of finite cacti (i.e., separable graphs whose blocks are cycles or single edges) under the assumption that the random weak limit is almost surely 1-ended. Examples that allow explicit computations of the critical exponents come from actions of finitely generated groups on regular rooted trees, by automorphisms. Restricting the action to the consecutive levels of the tree defines a sequence of finite graphs whose limits in the local convergence are orbital Schreier graphs for the action of the group on the boundary of the tree. In the case of iterated monodromy groups of complex polynomials, these graphs are cacti, and we show that for 1-ended ones, the critical exponent for the decay of the mass of avalanches depends on the growth of the graph. The well-known Basilica group related to $z^2-1$ gives rise to uncountably many 4-regular one-ended graphs of quadratic growth with the critical exponent for the mass of avalanches equal to 1; as well as uncountably many new non-critical examples of quadratic growth (thus not quasi-isometric to $\mathbb{Z}$). Another iterated monodromy group that we consider provides uncountably many graphs with the critical exponent equal to $2\log 2/\log 3 >1$. Finally, we also exhibit graphs of polynomial growth with arbitrarily small critical exponent.
Previous top-performing methods for 3D instance segmentation often maintain inter-task dependencies and the tendency towards a lack of robustness. Besides, inevitable variations of different datasets make these methods become particularly sensitive to hyper-parameter values and manifest poor generalization capability. In this paper, we address the aforementioned challenges by proposing a novel query-based method, termed as 3D-QueryIS, which is detector-free, semantic segmentation-free, and cluster-free. Specifically, we propose to generate representative points in an implicit manner, and use them together with the initial queries to generate the informative instance queries. Then, the class and binary instance mask predictions can be produced by simply applying MLP layers on top of the instance queries and the extracted point cloud embeddings. Thus, our 3D-QueryIS is free from the accumulated errors caused by the inter-task dependencies. Extensive experiments on multiple benchmark datasets demonstrate the effectiveness and efficiency of our proposed 3D-QueryIS method.
We report the first search for new star clusters performed using the VISTA near-infrared YJKs Magellanic Clouds survey (VMC) data sets. We chose a pilot field of ~ 0.4 deg^2 located in the South-West of the Small Magelllanic Cloud (SMC) bar, where the star field is among the densest and highest reddened region in the galaxy. In order to devise an appropriate automatic procedure we made use of dimensions and stellar densities observed in the VMC data sets of the known clusters in this area. We executed different kernel density estimations over a sample of more than 358000 stars with magnitudes measured in the three YJKs filters. We analysed the new cluster candidates whose colour-magnitude diagrams (CMDs), cleaned from field star contamination, were used to assess the clusters' reality and estimate reddenings and ages of the genuine systems. As a result 38 objects (~ a 55% increase in the known star clusters located in the surveyed field) of 0.15 - 0.40 arcmin (2.6 - 7.0 pc) in radius resulted to have near-infrared CMD features which resemble those of star clusters of young to moderate intermediate age (log(t /yr ) ~ 7.5-9.0). Most of the new star cluster candidates are hardly recognizable in optical images without the help of a sound star field decontaminated CMD analysis. For highly reddened star cluster candidates (E(B - V ) >= 0.6 mag) the VMC data sets were necessary in order to recognize them.
As is well known, pulsars are extremely stable rotators. However, although slowly, they spin down thanks to brake mechanisms, which are in fact still subject of intense investigation in the literature. Since pulsars are usually modelled as highly magnetized neutron stars that emit beams of electromagnetic radiation out of their magnetic poles, it is reasonable to consider that the spindown has to do with a magnetic brake. Although an interesting and simple idea, a pure magnetic brake is not able to adequately account for the spindown rate. Thus, many alternative spindown mechanisms appear in the literature, among them the pulsar wind model, where a wind of particles coming from the pulsar itself can carry part of its rotational kinetic energy. Such a spindown mechanism depends critically on three parameters, namely, the dipole magnetic field $B$, the angle between the magnetic and rotation axes $(\phi)$, and the density of primary particles $(\zeta)$ of the pulsar's magnetosphere. Differently from a series of articles in this subject, we consider for the first time in the literature a statistical modelling which includes a combination of a dipole magnetic and wind brakes. As a result, we are able to constrain the above referred parameters in particular for Crab and Vela pulsars.
We extend the study of supersymmetric tridiagonal Hamiltonians to the case of non-Hermitian Hamiltonians with real or complex conjugate eigenvalues. We find the relation between matrix elements of the non-Hermitian Hamiltonian $H$ and its supersymmetric partner $H^{+}$ in a given basis. Moreover, the orthogonal polynomials in the eigenstate expansion problem attached to $H^{+}$ can be recovered from those polynomials arising from the same problem for $H$ with the help of kernel polynomials. Besides its generality, the developed formalism in this work is a natural home for using the numerically powerful Gauss quadrature techniques in probing the nature of some physical quantities such as the energy spectrum of $\mathcal{PT}$-symmetric complex potentials. Finally, we solve the shifted $\mathcal{PT}$-symmetric Morse oscillator exactly in the tridiagonal representation.
We give potential theoretic estimates for the probability that a set $A$ contains a double point of planar Brownian motion run for unit time. Unlike the probability for $A$ to intersect the range of a Markov process, this cannot be estimated by a capacity of the set $A$. Instead, we introduce the notion of a capacity with respect to two gauge functions simultaneously. We also give a polar decomposition of $A$ into a set that never intersects the set of Brownian double points and a set for which intersection with the set of Brownian double points is the same as intersection with the Brownian path.
A properly colored cycle (path) in an edge-colored graph is a cycle (path) with consecutive edges assigned distinct colors. A monochromatic triangle is a cycle of length $3$ with the edges assigned a same color. It is known that every edge-colored complete graph without containing monochromatic triangles always contains a properly colored Hamilton path. In this paper, we investigate the existence of properly colored cycles in edge-colored complete graphs when monochromatic triangles are forbidden. We obtain a vertex-pancyclic analogous result combined with a characterization of all the exceptions.
Although the Hubbard model is widely investigated, there are surprisingly few attempts to study the behavior of such a model in an external magnetic field. Using the Projector Quantum Monte Carlo technique, we show that the Hubbard model with an easy axis exhibits metamagnetic behavior if an external field is turned on. For the case of intermediate correlations strength $U$, we observe a smooth transition from an antiferromagnetic regime to a paramagnetic phase. While the staggered magnetization will decrease linearly up to a critical field $B_c$, uniform magnetization develops only for fields higher than $B_c$.
Multi-label image recognition is a task that predicts a set of object labels in an image. As the objects co-occur in the physical world, it is desirable to model label dependencies. Previous existing methods resort to either recurrent networks or pre-defined label correlation graphs for this purpose. In this paper, instead of using a pre-defined graph which is inflexible and may be sub-optimal for multi-label classification, we propose the A-GCN, which leverages the popular Graph Convolutional Networks with an Adaptive label correlation graph to model label dependencies. Specifically, we introduce a plug-and-play Label Graph (LG) module to learn label correlations with word embeddings, and then utilize traditional GCN to map this graph into label-dependent object classifiers which are further applied to image features. The basic LG module incorporates two 1x1 convolutional layers and uses the dot product to generate label graphs. In addition, we propose a sparse correlation constraint to enhance the LG module and also explore different LG architectures. We validate our method on two diverse multi-label datasets: MS-COCO and Fashion550K. Experimental results show that our A-GCN significantly improves baseline methods and achieves performance superior or comparable to the state of the art.
We present observations and magnetic field modeling of the large polar crown prominence that erupted on 2010 December 6. Combination of SDO/AIA and STEREO$\_$Behind/EUVI allows us to see the fine structures of this prominence both at the limb and on the disk. We focus on the structures and dynamics of this prominence before the eruption. This prominence contains two parts: an active region part containing mainly horizontal threads, and a quiet Sun part containing mainly vertical threads. On the northern side of the prominence channel, both AIA and EUVI observe bright features which appear to be the lower legs of loops that go above then join in the filament. Filament materials are observed to frequently eject horizontally from the active region part to the quiet Sun part. This ejection results in the formation of a dense-column structure (concentration of dark vertical threads) near the border between the active region and the quiet Sun. Using the flux rope insertion method, we create non-linear force-free field models based on SDO/HMI line-of-sight magnetograms. A key feature of these models is that the flux rope has connections with the surroundings photosphere, so its axial flux varies along the filament path. The height and location of the dips of field lines in our models roughly replicate those of the observed prominence. Comparison between model and observations suggests that the bright features on the northern side of the channel are the lower legs of the field lines that turn into the flux rope. We suggest that plasma may be injected into the prominence along these field lines. Although the models fit the observations quiet well, there are also some interesting differences. For example, the models do not reproduce the observed vertical threads and cannot explain the formation of the dense-column structure.
The special relativistic test theory of Mansouri and Sexl is sketched. Theories based on different clock synchronisations are found to be equivalent to special relativity, as regards experimental results. The conventionality of clock synchronisation is shown not to hold, by means of an example, in a simple accelerated system and through the principle of equivalence in gravitational fields, especially when the metric is not static. Experimental implications on very precise clock synchronisation on earth are discussed.
Approximately forty years ago it was realized that the time development of decaying systems might not be precisely exponential. Rolf Winter (Phys. Rev. {\bf 123}, 1503 (1961)) analyzed the simplest nontrivial system - a particle tunneling out of a well formed by a wall and a delta-function. He calculated the probability current just outside the well and found irregular oscillations on a short time scale followed by an exponential decrease followed by more oscillations and finally by a decrease as a power of the time. We have reanalyzed this system, concentrating on the survival probability of the particle in the well rather than the probability current, and find a different short time behavior.
Let $t$ and $x$ be indeterminates, let $\phi(x)=x^2+t\in\mathbb Q(t)[x]$, and for every positive integer $n$ let $\Phi_n(t,x)$ denote the $n^{\text{th}}$ dynatomic polynomial of $\phi$. Let $G_n$ be the Galois group of $\Phi_n$ over the function field $\mathbb Q(t)$, and for $c\in\mathbb Q$ let $G_{n,c}$ be the Galois group of the specialized polynomial $\Phi_n(c,x)$. It follows from Hilbert's irreducibility theorem that for fixed $n$ we have $G_n\cong G_{n,c}$ for every $c$ outside a thin set $E_n\subset\mathbb Q$. By earlier work of Morton (for $n=3$) and the present author (for $n=4$), it is known that $E_n$ is infinite if $n\le 4$. In contrast, we show here that $E_n$ is finite if $n\in\{5,6,7,9\}$. As an application of this result we show that, for these values of $n$, the following holds with at most finitely many exceptions: for every $c\in\mathbb Q$, more than $81\%$ of prime numbers $p$ have the property that the polynomial $x^2+c$ does not have a point of period $n$ in the $p$-adic field $\mathbb Q_p$.
In this study a rotationally and translationally invariant metric in Finsler space is investigated. We choose to rewrite the metric in Riemanian space by increasing the dimension of space-time and introducing additional coordinates such that for specific values of these coordinates, the geodesics of the four dimensional Finslerian space-time and six dimensional Riemanian space-time are identical. Cosmological solutions described by this metric give rise to an equation of state corresponding to a space dominated by domain walls and an internal space dominated by strings.
In their work on the infinite flag variety, Lam, Lee, and Shimozono (2018) introduced objects called bumpless pipe dreams and used them to give a formula for double Schubert polynomials. We extend this formula to the setting of K-theory, giving an expression for double Grothendieck polynomials as a sum over a larger class of bumpless pipe dreams. Our proof relies on techniques found in an unpublished manuscript of Lascoux (2002). Lascoux showed how to write double Grothendieck polynomials as a sum over alternating sign matrices. We explain how to view the Lam-Lee-Shimozono formula as a disguised special case of Lascoux's alternating sign matrix formula.   Knutson, Miller, and Yong (2009) gave a tableau formula for vexillary Grothendieck polynomials. We recover this formula by showing vexillary marked bumpless pipe dreams and flagged set-valued tableaux are in weight preserving bijection. Finally, we give a bijection between Hecke bumpless pipe dreams and decreasing tableaux. The restriction of this bijection to Edelman-Greene bumpless pipe dreams solves a problem of Lam, Lee, and Shimozono.
One important aspect of the magneto-structural transition in MnCoGe and related materials is the reduction in saturation magnetization from the orthorhombic to the hexagonal phase. Here, by combining an element specific magnetization probe such as x-ray magnetic circular dichroism and band structure calculations, we show that the magnetic moment instability between orthorhombic and hexagonal structures originates from a reduction in the Mn sub-lattice magnetization. The consequences of the moment instability for the magnetocaloric effect are discussed.
Magnetic skyrmions are topological spin textures holding great potential as nanoscale information carriers. Recently, skyrmions have been predicted in antiferromagnets, with key advantages in terms of stability, size, and dynamical properties over their ferromagnetic analogs. However, their experimental demonstration is still lacking. Here, we show the imprint from ferromagnetic skyrmions into a thin film of an IrMn antiferromagnet, at room temperature and zero external magnetic field, using exchange-bias. Using high-spatial-resolution x-ray magnetic circular dichroism photoemission electron microscopy (XMCD-PEEM), we observed the imprinted spin textures within the IrMn from the XMCD signal of the uncompensated Mn spins at the interface with the ferromagnet. This result opens up a path for logic and memory devices based on skyrmion manipulation in antiferromagnets.
Free initial data for general relativity on a pair of intersecting null hypersurfaces are well known, but the lack of a Poisson bracket and concerns about caustics have stymied the development of a constraint free canonical theory. Here it is pointed out how caustics and generator crossings can be neatly avoided and a Poisson bracket on free data is given. On sufficiently regular functions of the solution spacetime geometry this bracket matches the Poisson bracket defined on such functions by the Hilbert action via Peierls' prescription. The symplectic form is also given in terms of free data.
In the paper we consider the partial sum process $\sum_{k=1}^{[nt]}X_k^{(n)}$, where $\{X_k^{(n)}, \ k\in Z\},\ n\ge 1,$ is a series of linear processes with innovations having heavy-tailed tapered distributions with tapering parameter $b_n$ depending on $n$. It is shown that, depending on the properties of a filter of a linear process under consideration and on the parameter $b_n$ defining if the tapering is hard or soft, the limit process for such partial sum process can be fractional Brownian motion or linear fractional stable motion.
Studying the spatial distribution of extragalactic source populations is vital in understanding the matter distribution in the Universe. It also enables understanding the cosmological evolution of dark matter density fields and the relationship between dark matter and luminous matter. Clustering studies are also required for EoR foreground studies since it affects the relevant angular scales. This paper investigates the angular and spatial clustering properties and the bias parameter of radio-selected sources in the Lockman Hole field at 325 MHz. The data probes sources with fluxes $\gtrsim$0.3 mJy within a radius of 1.8$^\circ$ around the phase center of a $6^\circ \times 6^\circ$ mosaic. Based on their radio luminosity, the sources are classified into Active Galactic Nuclei (AGNs) and Star-Forming Galaxies (SFGs). Clustering and bias parameters are determined for the combined populations and the classified sources. The spatial correlation length and the bias of AGNs are greater than SFGs -- indicating that more massive haloes host the former. This study is the first reported estimate of the clustering property of sources at 325 MHz, intermediate between the preexisting studies at high and low-frequency bands. It also probes a well-studied deep field at an unexplored frequency with moderate depth and area. Clustering studies require such observations along different lines of sight, with various fields and data sets across frequencies to avoid cosmic variance and systematics. Thus, an extragalactic deep field has been studied in this work to contribute to this knowledge.
There is a simple formula for the Ehrhart polynomial of a cyclic polytope. The purpose of this paper is to show that the same formula holds for a more general class of polytopes, lattice-face polytopes. We develop a way of decomposing any d-dimensional simplex in general position into d! signed sets, each of which corresponds to a permutation in the symmetric group, and reduce the problem of counting lattice points in a polytope in general position to that of counting lattice points in these special signed sets. Applying this decomposition to a lattice-face simplex, we obtain signed sets with special properties that allow us to count the number of lattice points inside them. We are thus able to conclude the desired formula for the Ehrhart polynomials of lattice-face polytopes.
We prove that a complete bipartite graph can be decomposed into cycles of arbitrary specified lengths provided that the obvious necessary conditions are satisfied, the length of each cycle is at most the size of the smallest part, and the longest cycle is at most three times as long as the second longest. We then use this result to obtain results on incomplete even cycle systems with a hole and on decompositions of complete multipartite graphs into cycles of uniform even length.
Searching for a signal depending on unknown parameters in a noisy background with matched filtering techniques always requires an analysis of the data with several templates in parallel in order to ensure a proper match between the filter and the real waveform. The key feature of such an implementation is the design of the filter bank which must be small to limit the computational cost while keeping the detection efficiency as high as possible. This paper presents a geometrical method which allows one to cover the corresponding physical parameter space by a set of ellipses, each of them being associated to a given template. After the description of the main characteristics of the algorithm, the method is applied in the field of gravitational wave (GW) data analysis, for the search of damped sine signals. Such waveforms are expected to be produced during the de-excitation phase of black holes -- the so-called 'ringdown' signals -- and are also encountered in some numerically computed supernova signals.
We give a new proof of the "weakly admissible implies admissible" theorem of Colmez and Fontaine describing the semi-stable p-adic representations. We study Banach-Colmez spaces, i.e. p-adic Banach spaces with the extra data of a C_p-algebra of analytic functions. The "weakly admissible" theorem is then a result of the existence of dimension and height functions on these objects. Furthermore, we show that the subcategory of Banach-Colmez spaces corresponding to crystalline representations is naturally filtered by the positive rationals.
We consider two different proposals to generate a time series with the same non-Poisson distribution of waiting times, to which we refer to as renewal and modulation. We show that, in spite of the apparent statistical equivalence, the two time series generate different physical effects. Renewal generates aging and anomalous scaling, while modulation yields no aging and either ordinary or anomalous diffusion, according to the prescription used for its generation. We argue, in fact, that the physical realization of modulation involves critical events, responsible for scaling. In conclusion, modulation rather than ruling out the action of critical events, sets the challenge for their identification.
We discuss initial-boundary value problems of arbitrary spatial order subject to arbitrary boundary conditions. We formalise the concept of the conditioning of such a problem and show that it represents a necessary criterion for well-posedness. The other requirement for well-posedness, the convergence of certain series, is also analysed. We illustrate these results with a full classification of 3rd order problems having non-Robin boundary conditions.   Part of this work is devoted to correcting an oversight in the author's earlier work Well-posed two-point initial-boundary value problems with arbitrary boundary conditions in volume 152 of Math. Proc. Camb. Philos. Soc.
Let $S$ be a set of vertices of a connected graph $G$. The Steiner distance of $S$ is the minimum size of a connected subgraph of $G$ containing all the vertices of $S$. The Steiner $k$-Wiener index is the sum of all Steiner distances on sets of $k$ vertices of $G$. Different simple methods for calculating the Steiner $k$-Wiener index of block graphs are presented.