ShantanuT01/DACTYL-Pretraining huggingface dataset:
Understanding the evolution of scaling relations between the observable properties of clusters and their total mass is key to realizing their potential as cosmological probes. In this study, we investigate whether the evolution of cluster scaling relations is affected by the spurious evolution of mass caused by the evolving reference density with respect to which halo masses are defined (pseudo-evolution). We use the relation between mass, M, and velocity dispersion, sigma, as a test case, and show that the deviation from the M-sigma relation of cluster-sized halos caused by pseudo-evolution is smaller than 10% for a wide range of mass definitions. The reason for this small impact is a tight relation between the velocity dispersion and mass profiles, sigma(<r) = const * (GM(<r) / r)^1/2, which holds across a wide range of radii. We show that such a relation is generically expected for a variety of density profiles, as long as halos are in approximate Jeans equilibrium. Thus, as the outer "virial" radius used to define the halo mass, R, increases due to pseudo-evolution, halos approximately preserve their M-sigma relation. This result highlights the fact that tight scaling relations are the result of tight equilibrium relations between radial profiles of physical quantities. We find exceptions at very small and very large radii, where the profiles deviate from the relations they exhibit at intermediate radii. We discuss the implications of these results for other cluster scaling relations, and argue that pseudo-evolution should have a small effect on most scaling relations, except for those that involve the stellar masses of galaxies. In particular, we show that the relation between stellar-mass fraction and total mass is affected by pseudo-evolution and is largely shaped by it for halo masses of less than 10^14 solar masses.
We give a criterion which determines when a union of one-dimensional Deligne-Lusztig varieties has a connected closure. We also obtain a new, short proof of the connectedness criterion for Deligne-Lusztig varieties due to Lusztig.
Small-world networks are ubiquitous in real-life systems. Most previous models of small-world networks are stochastic. The randomness makes it more difficult to gain a visual understanding on how do different nodes of networks interact with each other and is not appropriate for communication networks that have fixed interconnections. Here we present a model that generates a small-world network in a simple deterministic way. Our model has a discrete exponential degree distribution. We solve the main characteristics of the model.
Vision-and-Language (VL) pre-training has shown great potential on many related downstream tasks, such as Visual Question Answering (VQA), one of the most popular problems in the VL field. All of these pre-trained models (such as VisualBERT, ViLBERT, LXMERT and UNITER) are built with Transformer, which extends the classical attention mechanism to multiple layers and heads. To investigate why and how these models work on VQA so well, in this paper we explore the roles of individual heads and layers in Transformer models when handling $12$ different types of questions. Specifically, we manually remove (chop) heads (or layers) from a pre-trained VisualBERT model at a time, and test it on different levels of questions to record its performance. As shown in the interesting echelon shape of the result matrices, experiments reveal different heads and layers are responsible for different question types, with higher-level layers activated by higher-level visual reasoning questions. Based on this observation, we design a dynamic chopping module that can automatically remove heads and layers of the VisualBERT at an instance level when dealing with different questions. Our dynamic chopping module can effectively reduce the parameters of the original model by 50%, while only damaging the accuracy by less than 1% on the VQA task.
We conjecture that any graph $G$ with treewidth~$k$ and maximum degree $\Delta(G)\geq k + \sqrt{k}$ satisfies $\chi'(G)=\Delta(G)$. In support of the conjecture we prove its fractional version. We also show that any graph $G$ with treewidth~$k\geq 4$ and maximum degree $2k-1$ satisfies $\chi'(G)=\Delta(G)$, improving an old result of Vizing.
We report the hard X-ray spectrum of the Coma cluster obtained using the PDS data of two independent BeppoSAX observations performed with a time interval of about three years. In both the spectra a non thermal excess with respect to the thermal emission is present at a confidence level of ~ 3.4 sigma. The combined spectrum obtained by adding up the two spectra allows a measurement of the excess at the level of ~ 4.8 sigma at energies above 20 keV. The analysis of the full BeppoSAX data set provides a revised non-thermal X-ray flux which is slightly lower than that previously estimated (Fusco-Femiano et al. 1999) and in agreement with that measured by two RXTE observations. The analysis of the offset fields in our Coma observations provides a possible flux determination of the BL Lac object 1ES 1255+244.
We suggest a mechanism by which four-dimensional Newtonian gravity emerges on a 3-brane in 5D Minkowski space with an infinite size extra dimension. The worldvolume theory gives rise to the correct 4D potential at short distances whereas at large distances the potential is that of a 5D theory. We discuss some phenomenological issues in this framework.
In a previous paper we have calculated the decay $\tau\to\pi\nu_\tau\gamma$. We used a given relative sign between the internal bremsstrahlung and the structure dependent radiation, which has been used by several other authors before. However, we believe that there are good arguments why the opposite sign is the physical one. We briefly discuss these arguments and then investigate how the predictions for the decay $\tau\to\pi\nu_\tau\gamma$ are affected by this sign.
The transient ULX in M83 that went into outburst in or shortly before 2010 is still active. Our new XMM-Newton spectra show that it has a curved spectrum typical of the upper end of the high/soft state or slim-disk state. It appears to be spanning the gap between Galactic stellar-mass black holes and the ultraluminous state, at X-ray luminosities $\approx (1$-$3) \times 10^{39}$ erg s$^{-1}$ (a factor of two lower than in the 2010-2011 Chandra observations). From its broadened disk-like spectral shape at that luminosity, and from the fitted inner-disk radius and temperature, we argue that the accreting object is an ordinary stellar-mass black hole with $M \sim$$10$-$20 M_{\odot}$. We suggest that in the 2010-2011 Chandra observations, the source was seen at a higher accretion rate, resulting in a power-law-dominated spectrum with a soft excess at large radii.
We study the minimal supersymmetric standard model derived from $Z_N \times Z_M$ orbifold models. Moduli dependent threshold corrections of the gauge couplings are investigated to explain the measured values of the coupling constants. Also we study Yukawa couplings of the models. We find that the $Z_2 \times Z_6'$, $Z_2\times Z_6$, $Z_3 \times Z_6$ and $Z_6 \times Z_6$ orbifold models have the possibility to derive Yukawa couplings for the second and third generations as well as the measured gauge coupling constants. Allowed models are shown explicitly by combinations of modular weights for the matter fields.
In this paper we study perpetual integral functionals of diffusions. Our interest is focused on cases where such functionals can be expressed as first hitting times for some other diffusions. In particular, we generalize the result which connects one-sided functionals of Brownian motion with drift with first hitting times of reflecting diffusions.   Interpretating perpetual integral functionals as hitting times allows us to compute numerically their distributions by applying numerical algorithms for hitting times. Hereby, we discuss two approaches: the numerical inversion of the Laplace transform of the first hitting time and the numerical solution of the PDE associated with the distribution function of the first hitting time.   For numerical inversion of Laplace tranforms we have implemented the Euler algorithm developed by Abate and Whitt. However, perpetuities lead often to diffusions for which the explicit forms of the Laplace transforms of first hitting times are not available. In such cases, and also otherwise, algorithms for numerical solutions of PDE's can be evoked. In particular, we analyze the Kolmogorov PDE of some diffusions appearing in our work via the Crank-Nicolson scheme.
Forty years after the discovery of rotation-powered pulsars, we still do not understand many aspects of their pulsed emission. In the last few years there have been some fundamental developments in acceleration and emission models. I will review both the basic physics of the models as well as the latest developments in understanding the high-energy emission of rotation-powered pulsars, with particular emphasis on the polar-cap and slot-gap models. Special and general relativistic effects play important roles in pulsar emission, from inertial frame-dragging near the stellar surface to aberration, time-of-flight and retardation of the magnetic field near the light cylinder. Understanding how these effects determine what we observe at different wavelengths is critical to unraveling the emission physics. I will discuss how current and future X-ray and gamma-ray detectors can test the predictions of these models.
At the 20-th Texas Symposium on Relativistic Astrophysics there was a plenary talk devoted to the recent developments in classical Relativity. In that talk the problems of gravitational collapse, collisions of black holes, and of black holes as celestial bodies were discussed. But probably the problems of the internal structure of black holes are a real great challenge. In my talk I want to outline the recent achievements in our understanding of the nature of the singularity (and beyond!) inside a realistic rotating black hole. This presentation also addresses the following questions: Can we see what happens inside a black hole? Can a falling observer cross the singularity without being crushed? An answer to these questions is probably "yes".
Two particle irreducible effective actions (2PIEAs) are valuable non-perturbative techniques in quantum field theory; however, finite truncations of them violate the Ward identities (WIs) of theories with spontaneously broken symmetries. The symmetry improvement (SI) method of Pilaftsis and Teresi attempts to overcome this by imposing the WIs as constraints on the solution; however the method suffers from the non-existence of solutions in linear response theory and in certain truncations in equilibrium. Motivated by this, we introduce a new method called soft symmetry improvement (SSI) which relaxes the constraint. Violations of WIs are allowed but punished in a least-squares implementation of the symmetry improvement idea. A new parameter $\xi$ controls the strength of the constraint. The method interpolates between the unimproved ($\xi \to \infty$) and SI ($\xi \to 0$) cases and the hope is that practically useful solutions can be found for finite $\xi$. We study the SSI-2PIEA for a scalar O(N) model in the Hartree-Fock approximation. We find that the method is IR sensitive: the system must be formulated in finite volume $V$ and temperature $T=\beta^{-1}$ and the $V\beta \to \infty$ limit taken carefully. Three distinct limits exist. Two are equivalent to the unimproved 2PIEA and SI-2PIEA respectively, and the third is a new limit where the WI is satisfied but the phase transition is strongly first order and solutions can fail to exist depending on $\xi$. Further, these limits are disconnected from each other; there is no smooth way to interpolate from one to another. These results suggest that any potential advantages of SSI methods, and indeed any application of (S)SI methods out of equilibrium, must occur in finite volume.
The dynamics of the approach to equilibrium of the hydrogen atom is investigated numerically through a Monte Carlo procedure. We show that, before approaching ionization, the hydrogen atom may live in a quasi-equilibrium state, characterized by aging, whose duration increases exponentially as the temperatures decreases. By analyzing the quasi-equilibrium state, we compute averages of physical quantities for the hydrogen atom. We have introduced an analytic approach that fits satisfactorily the numerical estimates for low temperatures. Although the present analysis is expected to hold for energies typically up to 6% of the ionization energy, it works well for temperatures as high as 10^{4} K.
This paper investigates the recent stellar merger transient M31LRN 2015 in the Andromeda galaxy. We analyze published optical photometry and spectroscopy along with a Hubble Space Telescope detection of the color and magnitude of the pre-outburst source. The transient outburst is consistent with dynamically driven ejecta at the onset of a common envelope episode, which eventually leads to the complete merger of a binary system. The light curve appears to contain two components: first $\sim10^{-2} M_\odot$ of fast ejecta driven by shocks at the onset of common envelope, and later, $\sim0.3 M_\odot$ of further ejecta as the secondary becomes more deeply engulfed within the primary. Just prior to merger, we find that the primary star is a $3-5.5 M_\odot$ sub-giant branch primary star with radius of $30-40R_\odot$. Its position in the color-magnitude diagram shows that it is growing in radius, consistent with a picture where it engulfs its companion. By matching the properties of the primary star to the transient outburst, we show that the optical transient lasts less than ten orbits of the original binary, which had a pre-merger period of $\sim 10$ days. We consider the possible orbital dynamics leading up to the merger, and argue that if the system merged due to the Darwin tidal instability it implies a lower mass main sequence companion of $0.1-0.6M_\odot$. This analysis represents a promising step toward a more detailed understanding of flows in common envelope episodes through direct observational constraints.
Aims. Forbush decrease (FD) is a transient decrease followed by a gradual recovery in the observed galactic cosmic ray intensity. We seek to understand the relationship between the FDs and near-Earth interplanetary magnetic field (IMF) enhancements associated with solar coronal mass ejections (CMEs). Methods. We use muon data at cutoff rigidities ranging from 14 to 24 GV from the GRAPES-3 tracking muon telescope to identify FD events. We select those FD events that have a reasonably clean profile, and magnitude > 0.25%. We use IMF data from ACE/WIND spacecrafts. We look for correlations between the FD profile and that of the one hour averaged IMF. We ask if the diffusion of high energy protons into the large scale magnetic field is the cause of the lag observed between the FD and the IMF. Results. The enhancement of the IMF associated with FDs occurs mainly in the shock-sheath region, and the turbulence level in the magnetic field is also enhanced in this region. The observed FD profiles look remarkably similar to the IMF enhancement profiles. The FDs typically lag the IMF enhancement by a few hours. The lag corresponds to the time taken by high energy protons to diffuse into the magnetic field enhancement via cross-field diffusion. Conclusions. Our findings show that high rigidity FDs associated with CMEs are caused primarily by the cumulative diffusion of protons across the magnetic field enhancement in the turbulent sheath region between the shock and the CME.
In the same way as the realization of some of the famous gedanken experiments imagined by the founding fathers of quantum mechanics has recently led to the current renewal of the interpretation of quantum physics, it seems that the most recent progresses of observational astrophysics can be interpreted as the realization of some cosmological gedanken experiments such as the removal from the universe of the whole visible matter or the cosmic time travel leading to a new cosmological standard model. This standard model involves two dark components of the universe, dark energy and dark matter. Whereas dark energy is usually associated with the cosmological constant, we propose to explain dark matter as a pure QCD effect, namely a gluonic Bose Einstein condensate, following the transition from the quark gluon plasma phase to the colorless hadronic phase.   Our approach not only allows us to assume a ratio Dark/Visible equal to 11/2 but also provides gluons (and di-gluons, viewed as quasi-particles) with an extra mass of vibrational nature. Such an interpretation would comfort the idea that, apart from the violation of the matter/antimatter symmetry satisfying the Sakharov's conditions, the reconciliation of particle physics and cosmology needs not the recourse to any ad hoc fields, particles or hidden variables.
We propose an efficient method for Monte Carlo simulation of quantum lattice models. Unlike most other quantum Monte Carlo methods, a single run of the proposed method yields the free energy and the entropy with high precision for the whole range of temperature. The method is based on several recent findings in Monte Carlo techniques, such as the loop algorithm and the transition matrix Monte Carlo method. In particular, we derive an exact relation between the DOS and the expectation value of the transition probability for quantum systems, which turns out to be useful in reducing the statistical errors in various estimates.
The purpose of this paper is to establish a Castelnuovo-Mumford regularity bound for threefolds with mild singularities. Let $X$ be a non-degenerate normal projective threefold in $\mathbb{P}^r$ of degree $d$ and codimension $e$. We prove that if $X$ has rational singularities, then $\text{reg}(X) \leq d-e+2$. Our bound is very close to a sharp bound conjectured by Eisenbud-Goto. When $e=2$ and $X$ has Cohen-Macaulay Du Bois singularities, we obtain the conjectured bound $\text{reg}(X) \leq d-1$, and we also classify the extremal cases. To achieve these results, we bound the regularity of fibers of a generic projection of $X$ by using Loewy length, and also bound the dimension of the varieties swept out by secant lines through the singular locus of $X$.
A very nice result of B\'ar\'any and Lehel asserts that every finite subset $X$ or $\mathbb R^d$ can be covered by $f(d)$ $X$-boxes (i.e. each box has two antipodal points in $X$). As shown by Gy\'arf\'as and P\'alv\H{o}lgyi this result would follow from the following conjecture : If a tournament admits a partition of its arc set into $k$ quasi orders, then its domination number is bounded in terms of $k$. This question is in turn implied by the Erd\H{o}s-Sands-Sauer-Woodrow conjecture : If the arcs of a tournament $T$ are colored with $k$ colors, there is a set $X$ of at most $g(k)$ vertices such that for every vertex $v$ of $T$, there is a monochromatic path from $X$ to $v$. We give a short proof of this statement. We moreover show that the general Sands-Sauer-Woodrow conjecture (which as a special case implies the stable marriage theorem) is valid for directed graphs with bounded stability number. This conjecture remains however open.
We consider the family of irreducible crystalline representations of dimension $2$ of ${\rm Gal}(\overline{\bf Q}_p/{\bf Q}_p)$ given by the $V_{k,a_p}$ for a fixed weight integer $k\geq 2$. We study the locus of the parameter $a_p$ where these representations have a given reduction modulo $p$. We give qualitative results on this locus and show that for a fixed $p$ and $k$ it can be computed by determining the reduction modulo $p$ of $V_{k,a_p}$ for a finite number of values of the parameter $a_p$. We also generalize these results to other Galois types.
This paper has been withdrawn by the author(s). Please refer to quant-ph/0311171.
The canonical quantization of dynamical systems with curved phase space introduced by I.A. Batalin, E.S. Fradkin and T.E. Fradkina is applied to the four-dimensional Einstein-Maxwell Dilaton-Axion theory. The spherically symmetric case with radial fields is considered. The Lagrangian density of the theory in the Einstein frame is written as an expression with first order in time derivatives of the fields. The phase space is curved due to the nontrivial interaction of the dilaton with the axion and the electromagnetic fields.
In this contribution we introduce local attachment as an universal network-joining protocol for peer-to-peer networks, social networks, or other kinds of networks. Based on this protocol nodes in a finite-size network dynamically create power-law connectivity distributions. Nodes or peers maintain them in a self-organized statistical way by incorporating local information only. We investigate the structural and macroscopic properties of such local attachment networks by extensive numerical simulations, including correlations and scaling relations between exponents. The emergence of the power-law degree distribution is further investigated by considering preferential attachment with a nonlinear attractiveness function as an approximative model for local attachment. This study suggests the local attachment scheme as a procedure to be included in future peer-to-peer protocols to enable the efficient production of stable network topologies in a continuously changing environment.
We consider the Zakharov system in the energy critical dimension $d=4$ with energy below the ground state. It is known that below the ground state solutions exist globally in time, and scatter in the radial case. Scattering below the ground state in the non-radial case is an open question. We show that if scattering fails, then there exists a minimal energy non-scattering solution below the ground state. Moreover the orbit of this solution is precompact modulo translations. The proof follows by a concentration compactness argument, together with a refined small data theory for energy dispersed solutions.
In this paper, we derive the non-commutative corrections to the maximal acceleration of a massive particle. Using the eight-dimensional kappa-deformed phase-space metric, we obtain the kappa-deformed maximal acceleration, valid up to first order in the deformation parameter. We then derive the kappa-deformed geodesic equation and obtain its Newtonian limit and from this obtain a bound on the deformation parameter. After re-expressing the kappa-deformed Schwarzschild metric in terms of maximal acceleration, we analyse the motion of a particle in this space-time, and also study the modifications to Hawking radiation. We also derive the kappa-deformed corrections to maximal acceleration using kappa-deformed generalised uncertainty principle.