ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we focus on $r$-neighbor bootstrap percolation, which is a process on a graph where initially a set $A_0$ of vertices gets infected. Now subsequently, an uninfected vertex becomes infected if it is adjacent to at least $r$ infected vertices. Call $A_f$ the set of vertices that is infected after the process stops. More formally set $A_t:=A_{t-1}\cup \{v\in V: |N(v)\cap A_{t-1}|\geq r\}$, where $N(v)$ is the neighborhood of $v$. Then $A_f=\bigcup_{t>0} A_t$. We deal with finite graphs only and denote by $n$ the number of vertices. We are mainly interested in the size of the final set $A_f$. We present a theorem for degenerate graphs that bounds the size of the final infected set. More precisely for a $d$-degenerate graph, if $r>d$, we bound the size set $A_f$ from above by $(1+\tfrac{d}{r-d})|A_0|$.
The evolution of the global stellar mass function (MF) of star clusters is studied based on a large set of N-body simulations of clusters with a range of initial masses, initial concentrations, in circular or elliptical orbits in different tidal environments. Models with and without initial mass segregation are included. The depletion of low mass stars in initially Roche-volume (tidal) filling clusters starts typically on a time scale of the order of the core collapse time. In clusters that are initially underfilling their Roche-volume it takes longer because the clusters have to expand to their tidal radii before dynamical mass loss becomes important.   We introduce the concept of the differential mass function (DMF), which describes the changes with respect to the initial mass function (IMF). We show that the evolution of the DMF can be described by a set of very simple analytic expressions that are valid for a wide range of initial cluster parameters and for different IMFs. The agreement between this description and the models is very good, except for initially Roche-volume underfilling clusters that are severely mass segregated.
In this paper we present a simple proof of the strong converse for identification via discrete memoryless quantum channels, based on a novel covering lemma. The new method is a generalization to quantum communication channels of Ahlswede's recently discovered appoach to classical channels. It involves a development of explicit large deviation estimates to the case of random variables taking values in selfadjoint operators on a Hilbert space. This theory is presented separately in an appendix, and we illustrate it by showing its application to quantum generalizations of classical hypergraph covering problems.
We discuss the nonlinear extension of $N=2$ superconformal algebra by generalizing Sugawara construction and coset construction built from $N=2$ currents based on Kazama-Suzuki $N=2$ coset model $\frac{SU(3)}{SU(2) \times U(1)}$ in $N=2$ superspace. For the generic unitary minimal series $c = 6(1-\frac{3}{k+3})$ where $k$ is the level of $SU(3)$ supersymmetric Wess-Zumino-Witten model, this algebra reproduces exactly $N=2$ $W_3$ algebra which has been worked out by Romans in component formalism.
In connection with his counter-example to the fourteenth problem of Hilbert, Nagata formulated a conjecture concerning the postulation of r fat points of the same multiplicity in the projective plane and proved it when r is a square. Iarrobino formulated a similar conjecture in any projective space P^d. We prove Iarrobino's conjecture when r is a d-th power. As a corollary, we obtain new counter-examples modeled on those by Nagata.
High quality factors, strong nonlinearities, and extensive design flexibility make superconducting circuits an ideal platform to investigate synchronization phenomena deep in the quantum regime. Recently~\cite{Loerch-2017}, it was predicted that energy quantization and conservation can block the synchronization of two identical, weakly coupled nonlinear self-oscillators. Here we propose a Josephson junction circuit realization of such a system along with a simple homodyne measurement scheme to observe this effect. We also show that at finite detuning, where phase synchronization takes place, the two oscillators are entangled in the steady state as witnessed by the positivity of the logarithmic negativity.
The volume of phase space may grow super-exponentially ("explosively") with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create new emergent states. Standard ensemble theory can break down as we demonstrate in a simple model reminiscent of complex systems where new collective states emerge. We present an axiomatically defined entropy and argue that it is extensive in the micro-canonical, equal probability, and canonical (max-entropy) ensemble for super-exponentially growing phase spaces. This entropy may be useful in determining probability measures in analogy with how statistical mechanics establishes statistical ensembles by maximising entropy.
To investigate the nature and evolution of TeV pulsar wind nebulae, we examine the firmly identified PWNe in the H.E.S.S. Galactic Plane Survey, along with the few other known detections from the literature, as well as the upper limits extracted from the H.E.S.S survey. These data exhibit a correlation of TeV surface brightness with pulsar spin-down power. It appears to be caused by both an increase of TeV extension and a decrease of TeV luminosity with decreasing spin-down power. We also find that the offsets of pulsars with ages around 10 kyr with respect to the wind nebula centres are frequently larger than can be plausibly explained by pulsar proper motion and could be due to an asymmetric environment. These and other results will be presented and put to context with a basic modelling of TeV pulsar wind nebula evolution.
Constituted with a massive black hole and a stellar mass compact object, Extreme Mass Ratio Inspiral (EMRI) events hold unique opportunity for the study of massive black holes, such as by measuring and checking the relations among the mass, spin and quadrupole moment of a massive black hole, putting the no-hair theorem to test. TianQin is a planned space-based gravitational wave observatory and EMRI is one of its main types of sources. It is important to estimate the capacity of TianQin on testing the no-hair theorem with EMRIs. In this work, we use the analytic kludge waveform with quadrupole moment corrections and study how the quadrupole moment can be constrained with TianQin. We find that TianQin can measure the dimensionless quadrupole moment parameter with accuracy to the level of $10^{-5}$ under suitable scenarios. The choice of the waveform cutoff is found to have significant effect on the result: if the Schwarzschild cutoff is used, the accuracy depends strongly on the mass of the massive black hole, while the spin has negligible impact; if the Kerr cutoff is used, however, the dependence on the spin is more significant. We have also analyzed the cases when TianQin is observing simultaneously with other detectors such as LISA.
We investigate the properties of galaxies as they shut off star formation over the 4 billion years surrounding peak cosmic star formation. To do this we categorize $\sim7000$ galaxies from $1<z<4$ into $90$ groups based on the shape of their spectral energy distributions (SEDs) and build composite SEDs with $R\sim 50$ resolution. These composite SEDs show a variety of spectral shapes and also show trends in parameters such as color, mass, star formation rate, and emission line equivalent width. Using emission line equivalent widths and strength of the 4000\AA\ break, $D(4000)$, we categorize the composite SEDs into five classes: extreme emission line, star-forming, transitioning, post-starburst, and quiescent galaxies. The transitioning population of galaxies show modest H$\alpha$ emission ($EW_{\rm REST}\sim40$\AA) compared to more typical star-forming composite SEDs at $\log_{10}(M/M_\odot)\sim10.5$ ($EW_{\rm REST}\sim80$\AA). Together with their smaller sizes (3 kpc vs. 4 kpc) and higher S\'ersic indices (2.7 vs. 1.5), this indicates that morphological changes initiate before the cessation of star formation. The transitional group shows a strong increase of over one dex in number density from $z\sim3$ to $z\sim1$, similar to the growth in the quiescent population, while post-starburst galaxies become rarer at $z\lesssim1.5$. We calculate average quenching timescales of 1.6 Gyr at $z\sim1.5$ and 0.9 Gyr at $z\sim2.5$ and conclude that a fast quenching mechanism producing post-starbursts dominated the quenching of galaxies at early times, while a slower process has become more common since $z\sim2$.
Planar functions are of great importance in the constructions of DES-like iterated ciphers, error-correcting codes, signal sets and the area of mathematics. They are defined over finite fields of odd characteristic originally and generalized by Y. Zhou \cite{Zhou} in even characteristic. In 2016, L. Qu \cite{Q} proposed a new approach to constructing quadratic planar functions over $\F_{2^n}$. Very recently, D. Bartoli and M. Timpanella \cite{Bartoli} characterized the condition on coefficients $a,b$ such that the function $f_{a,b}(x)=ax^{2^{2m}+1}+bx^{2^m+1} \in\F_{2^{3m}}[x]$ is a planar function over $\F_{2^{3m}}$ by the Hasse-Weil bound.   In this paper, using the Lang-Weil bound, a generalization of the Hasse-Weil bound, and the new approach introduced in \cite{Q}, we completely characterize the necessary and sufficient conditions on coefficients of four classes of planar functions over $\F_{q^k}$, where $q=2^m$ with $m$ sufficiently large (see Theorem \ref{main}). The first and last classes of them are over $\F_{q^2}$ and $\F_{q^4}$ respectively, while the other two classes are over $\F_{q^3}$. One class over $\F_{q^3}$ is an extension of $f_{a,b}(x)$ investigated in \cite{Bartoli}, while our proofs seem to be much simpler. In addition, although the planar binomial over $\F_{q^2}$ of our results is finally a known planar monomial, we also answer the necessity at the same time and solve partially an open problem for the binomial case proposed in \cite{Q}.
We performed a detailed study of the extended cool gas, traced by MgII absorption [$W_r(2796)\geq0.3$~{\AA}], surrounding 14 narrow-line active galactic nuclei (AGNs) at 0.12<z<0.22 using background quasar sight-lines. The background quasars probe the AGNs at projected distances of $60\leq D\leq265$~kpc. We find that, between $100\leq D\leq200$~kpc, AGNs appear to have lower MgII gas covering fractions (0.09$^{+0.18}_{-0.08}$) than quasars (0.47$^{+0.16}_{-0.15}$) and possibly lower than in active field galaxies (0.25$^{+0.11}_{-0.09}$). We do not find a statistically significant azimuthal angle dependence for the MgII covering fraction around AGNs, though the data hint at one. We also study the `down-the-barrel' outflow properties of the AGNs themselves and detect intrinsic NaID absorption in 8/8 systems and intrinsic MgII absorption in 2/2 systems, demonstrating that the AGNs have significant reservoirs of cool gas. We find that 6/8 NaID and 2/2 MgII intrinsic systems contain blueshifted absorption with $\Delta v>50$ km/s, indicating outflowing gas. The 2/2 intrinsic MgII systems have outflow velocities a factor of $\sim4$ higher than the NaID outflow velocities. Our results are consistent with AGN-driven outflows destroying the cool gas within their halos, which dramatically decreases their cool gas covering fraction, while star-burst driven winds are expelling cool gas into their circumgalactic media (CGM). This picture appears contrary to quasar--quasar pair studies which show that the quasar CGM contains significant amounts of cool gas whereas intrinsic gas found `down-the-barrel' of quasars reveals no cool gas. We discuss how these results are complementary and provide support for the AGN unified model.
This paper presents a numerical method to calculate the value function for a general discounted impulse control problem for piecewise deterministic Markov processes. Our approach is based on a quantization technique for the underlying Markov chain defined by the post jump location and inter-arrival time. Convergence results are obtained and more importantly we are able to give a convergence rate of the algorithm. The paper is illustrated by a numerical example.
In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect).
We present new and independent estimates of the distances to the Magellanic Clouds (MCs) using near-infrared (NIR) and optical--NIR period--Wesenheit (PW) relations. The slopes of the PW relations are, within the dispersion, linear over the entire period range and independent of metal content. The absolute zero points were fixed using Galactic Cepheids with distances based on the infrared surface-brightness method. The true distance modulus we found for the Large Magellanic Cloud---$(m-M)_0 = 18.48 \pm 0.01 \pm 0.10$ mag---and the Small Magellanic Cloud---$(m-M)_0 = 18.94 \pm 0.01 \pm 0.10$ mag---agree quite well with similar distance determinations based on robust distance indicators. We also briefly discuss the evolutionary and pulsation properties of MC Cepheids.
We calculate the Hilbert action for the Bondi-Sachs metrics. It yields the Einstein vacuum equations in a closed form. Following the Dirac approach to constrained systems we investigate the related Hamiltonian formulation.
We show that QCD Minkowski observables such as the $e^{+}e^{-}$ R-ratio and the hadronic tau decay $R_{\tau}$ are completely determined by the effective charge (EC) beta-function, $\rho(x)$, corresponding to the Euclidean QCD vacuum polarization Adler D-function, together with the next-to-leading order (NLO) perturbative coefficient of D. An efficient numerical algorithm is given for evaluating R, $R_{\tau}$ from a weighted contour integration of $D(se^{i\theta})$ around a circle in the complex squared energy s-plane, with $\rho(x)$ used to evolve in s around the contour. The EC beta-function can be truncated at next-to-NLO (NNLO) using the known exact perturbative calculation or the uncalculated N^3 LO and higher terms can be approximated by the portion containing the highest power of b, the first QCD beta-function coefficient. The difference between the R, $R_{\tau}$ constructed using the NNLO and "leading-b" resummed versions of $\rho(x)$ provides an estimate of the uncertainty due to the uncalculated higher order corrections. Simple numerical parametrizations are given to facilitate these fits. For $R_{\tau}$ we estimate an uncertainty $\delta\alpha_{s}(m_{\tau}^{2})\simeq0.01$, corresponding to $\delta\alpha_{s}(M_{Z}^{2})\simeq0.002$. This encouragingly small uncertainty is much less than rather pessimistic estimates by other authors based on analogous all-orders resummations, which we demonstrate to be extremely dependent on the chosen renormalization scheme, and hence misleading.
Virial theorem is important for understanding stellar structures. It produces an interesting connection between the magnetic energy and the gravitational one. Using the general form of the virial theorem including the magnetic field (toroidal magnetic field), we may explain the solar dynamo model in related to variations of the magnetic and gravitational energies. We emphasize the role of the gravitational energy in sub-surface layers which has been certainly minored up to now. We also consider two types of solar outer shape (spherical and spheroidal) to study the behavior of magnetic and gravitational energies. The magnetic energy affects the solar shape, while the gravitational energy is not changed by the considered shapes of the Sun.
We introduce a class of Gaussian processes with stationary increments which exhibit long-range dependence. The class includes fractional Brownian motion with Hurst parameter H>1/2 as a typical example. We establish infinite and finite past prediction formulas for the processes in which the predictor coefficients are given explicitly in terms of the MA and AR coefficients.
This paper studies the Seshadri constant of an ample line bundle at a very general point, seeking a very slight improvement on the result of Ein, Kuchle, and Lazarsfeld. The main point is that couting jets more carefully yields a better result. We hope that with some further innovations some type of bound, independent of the dimension, will ultimately be found.
Fundamental relaxation processes in the secular evolution of a collisional star cluster of $N$-'point' stars have been conventionally discussed based on either of collision kinetic theory (for strong two-body encounters) and wave one (for statistical acceleration and gravitational polarization). If combining the both theories together, one must introduce a self-consistent 'truncated' Newtonian mean-field (m.f.) acceleration of star at position $r$ and time $t$ due to a phase-space distribution function $f\left(r', p',t\right)$ for stars $A^{\triangle}(r,t)=-Gm\left(1-\frac{1}{N}\right)\int_{\mid r-r' \mid > \triangle}\frac{r-r'}{\mid r-r' \mid^{3}} f\left(r',p',t\right)\text{d}^{3}{r'}\text{d}^{3}{p'},$ where $G$ is the gravitational constant and $m$ the mass of stars. The lower limit $\triangle$ of the distance between two stars is order of the Landau distance. The truncated m.f. acceleration is a necessary consequence due to the strong encounters and m.f. acceleration being not able to 'coexist' at specific distance between stars.   The present paper aims at initiating a star-cluster convergent kinetic theory to self-consistently derive kinetic equations of star clusters, mathematically non-divergent in distance- and wavenumber- spaces based on the truncated m.f. acceleration, correct at time scales of the secular evolution. This will be achieved by focusing on mathematical formulations of the Kandrup's generalised-Landau equation including the effect of the strong encounters and by extending the Grad's truncated distribution function and Klimontovich's theory of non-ideal systems.
We present thermoelectric power (TEP) studies under pressure and high magnetic field in the antiferromagnet CeRh2Si2 at low temperature. Under magnetic field, large quantum oscillations are observed in the TEP, S(H), in the antiferromagnetic phase. They suddenly disappear when entering in the polarized paramagnetic (PPM) state at Hc pointing out an important reconstruction of the Fermi surface (FS). Under pressure, S/T increases strongly of at low temperature near the critical pressure Pc, where the AF order is suppressed, implying the interplay of a FS change and low energy excitations driven by spin and valence fluctuations. The difference between the TEP signal in the PPM state above Hc and in the paramagnetic state (PM) above Pc can be explained by different FS. Band structure calculations at P = 0 stress that in the AF phase the 4f contribution at the Fermi level (EF) is weak while it is the main contribution in the PM domain. By analogy to previous work on CeRu2Si2, in the PPM phase of CeRh2Si2 the 4f contribution at EF will drop.
We investigate the emergence of a large-scale magnetic field. This field is dynamo-generated by turbulence driven with a helical forcing function. Twisted arcade-like field structures are found to emerge in the exterior above the turbulence zone. Time series of the magnetic field structure show recurrent plasmoid ejections.
To a generically big adelic divisor, we can associate an arithmetic Okounkov body, which is a pair of the geometric Okounkov body and the concave transform of the Green functions. In this paper, we show that the infimum of the concave transform is given by the absolute minimum provided that the divisor is vertically nef. This is a partial generalization of results of Moriwaki (in the curve case) and of Burgos Gil-Moriwaki-Philippon-Sombra (in the toric case).
Humans with an average level of social cognition can infer the beliefs of others based solely on the nonverbal communication signals (e.g. gaze, gesture, pose and contextual information) exhibited during social interactions. This social cognitive ability to predict human beliefs and intentions is more important than ever for ensuring safe human-robot interaction and collaboration. This paper uses the combined knowledge of Theory of Mind (ToM) and Object-Context Relations to investigate methods for enhancing collaboration between humans and autonomous systems in environments where verbal communication is prohibited. We propose a novel and challenging multimodal video dataset for assessing the capability of artificial intelligence (AI) systems in predicting human belief states in an object-context scenario. The proposed dataset consists of precise labelling of human belief state ground-truth and multimodal inputs replicating all nonverbal communication inputs captured by human perception. We further evaluate our dataset with existing deep learning models and provide new insights into the effects of the various input modalities and object-context relations on the performance of the baseline models.
Since it is difficult to collect face images of the same subject over a long range of age span, most existing face aging methods resort to unpaired datasets to learn age mappings. However, the matching ambiguity between young and aged face images inherent to unpaired training data may lead to unnatural changes of facial attributes during the aging process, which could not be solved by only enforcing identity consistency like most existing studies do. In this paper, we propose a attribute-aware face aging model with wavelet-based Generative Adversarial Networks (GANs) to address the above issues. To be specific, we embed facial attribute vectors into both generator and discriminator of the model to encourage each synthesized elderly face image to be faithful to the attribute of its corresponding input. In addition, a wavelet packet transform (WPT) module is incorporated to improve the visual fidelity of generated images by capturing age-related texture details at multiple scales in the frequency space. Qualitative results demonstrate the ability of our model to synthesize visually plausible face images, and extensive quantitative evaluation results show that the proposed method achieves state-of-the-art performance on existing datasets.
Convolution on 3D point clouds that generalized from 2D grid-like domains is widely researched yet far from perfect. The standard convolution characterises feature correspondences indistinguishably among 3D points, presenting an intrinsic limitation of poor distinctive feature learning. In this paper, we propose Adaptive Graph Convolution (AdaptConv) which generates adaptive kernels for points according to their dynamically learned features. Compared with using a fixed/isotropic kernel, AdaptConv improves the flexibility of point cloud convolutions, effectively and precisely capturing the diverse relations between points from different semantic parts. Unlike popular attentional weight schemes, the proposed AdaptConv implements the adaptiveness inside the convolution operation instead of simply assigning different weights to the neighboring points. Extensive qualitative and quantitative evaluations show that our method outperforms state-of-the-art point cloud classification and segmentation approaches on several benchmark datasets. Our code is available at https://github.com/hrzhou2/AdaptConv-master.