ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance of the number of (possibly overlapping) ordered labeled subgraphs of a labeled graph as a function of its randomness deficiency (how far it falls short of the maximum possible Kolmogorov complexity) and (ii) a new elementary proof for the number of unlabeled graphs.
We consider the corner avoiding property of $s$-dimensional $\boldsymbol \beta$-adic Halton sequences. After extending this class of point sequences in an intuitive way, we show that the hyperbolic distance between each element of the sequence and the closest corner of $[0,1)^s$ is $\mathcal{O}\left(\frac{1}{N^{s/2+\epsilon}}\right)$, where $N$ denotes the index of the element. In our proof we use tools from Diophantine analysis, more precisely, we apply Schmidt's Subspace Theorem.
We report CCD photometry and analysis of the first observed superoutburst of the SU UMa-type dwarf nova KP Cassiopeiae during 2008 October. We observed a distinct shortening of the superhump period at superhump cycle 15. Before that point Psh was 0.08556(3) d and afterwards it evolved from 0.08517(2) d to 0.08544(3) d with a rate of period change dPsh/dt = 3.2(2) * 10-5. We measured the likely orbital period as 0.0814(4) d placing KP Cas just below the period gap. The superhump period excess is 0.048(5) and, empirically, the mass ratio q is 0.20(2). The superoutburst lasted between 8 and 12 days, peaked close to magnitude 13 with an amplitude above quiescence of 5 magnitudes, and faded for 4 days at a rate of 0.14 mag/d. Close monitoring following the end of the superoutburst detected a single normal outburst 60 days later which reached magnitude 14.7 and lasted less than 3 days.
The multi-wavelength electromagnetic afterglow from the binary neutron star merger GW170817/GRB170817A has displayed long-term power-law brightening, and presented challenges to post-merger models of the non-thermal emission. The most recent radio observations up to 200 days post-merger suggest that the afterglow has finally peaked and may now be fading, but fading has not been confirmed in the X-rays. We present new, deep Chandra observations of GW170817/GRB170817A at 260 days post-merger that reveal an X-ray flux of F{0.3-8keV} = 1.1 x 10^-14 erg/s/cm^2, and confirm that the X-ray light curve is now also fading. Through rigorous comparisons to previous Chandra observations of GW170817/GRB170817A, X-ray fading is detected between 160 and 260 days post-merger at a 4.4 sigma significance, based on the X-ray data alone. We further constrain the X-ray photon index to steepen by <0.5 at 3.1 sigma significance during this period, which disfavors the passing of the synchrotron cooling frequency through the X-ray band as the cause of the observed fading. These observations remain consistent with optically thin synchrotron afterglow emission. If this afterglow emission arises from a quasi-spherical mildly relativistic outflow, the X-ray fading suggests that the outflow is now decelerating. Alternatively, if this afterglow arises from a successful off-axis structured jet, the X-ray fading suggests that emission from the jet core has already entered the line of sight.
Germanene has emerged as a novel two-dimensional material with various interesting properties and applications. Here we report the possibility of superconductivity in a stable potassium intercalated germanene compound, KGe$_2$, with a transition temperature $T_c \sim 11$ K, and an electron-phonon coupling of 1.9. Applying a 5\% tensile strain, which reduces the buckling height by 4.5\%, leads to the reduction of the electron-phonon coupling by 11\% and a slight increase in $T_c \sim 12$ K. That is, strong electron-phonon coupling results from the buckled structure of the germanene layers. Despite being an intercalated van der Waals material similar to intercalated graphite superconductors, it does not possess an occupied interlayer state.
A non-singular exact black hole solution in General Relativity is presented. The source is a non-linear electromagnetic field, which reduces to the Maxwell theory for weak field. The solution corresponds to a charged black hole with |q| \leq 2s_c m \approx 0.6 m, having metric, curvature invariants, and electric field bounded everywhere.
In this paper, we prove that temperature patch solutions to the subcritical Boussinesq-Navier-Stokes System with no diffusion preserve the H\"older regularity of their boundary for all time, which generalises the previously known result by F. Gancedo and E. Garc\'ia-Ju\'arez [Annals of PDE, 3(2):14, 2017] to the full range of subcritical viscosity.
In order to incorporate the finite range effect into effective interactions, a modification of the Skyrme force by introducing a cut-off factor for high momentum transfers is proposed. The parameters of the cut-off factor are determined by fitting the microscopic in-medium cross-sections of Li and Machleidt over a wide range of energy and nuclear density. Results for the SkM* and SLy4 forces are presented.
We compute rigorously the ground and equilibrium states for Kitaev's model in 2D, both the finite and infinite version, using an analogy with the 1D Ising ferromagnet. Next, we investigate the structure of the reduced dynamics in the presence of thermal baths in the Markovian regime. Special attention is paid to the dynamics of the topological freedoms which have been proposed for storing quantum information.
We prove that in the Hartle-Hawking approach to quantum cosmology the existence of an inflationary phase is a general property of minisuperspace models given by a closed Friedmann-Robertson-Walker universe containing a massless scalar field with a $\lambda\phi^{n}$ self-interaction. The evolution in time of the cosmic scale factor and of the scalar field in the very early universe is derived, together with the conditions to be satisfied in order to solve the horizon and flatness problems.
Quantum Darwinism explains the emergence of a classical description of objects in terms of the creation of many redundant registers in an environment containing their classical information. This amplification phenomenon, where only classical information reaches the macroscopic observer and through which different observers can agree on the objective existence of such object, has been revived lately for several types of situations, successfully explaining classicality. We explore quantum Darwinism in the setting of an environment made of two level systems which are initially prepared in the ground state of the XX model, which exhibits different phases; we find that the different phases have different ability to redundantly acquire classical information about the system, being the "ferromagnetic phase" the only one able to complete quantum Darwinism. At the same time we relate this ability to how non-Markovian the system dynamics is, based on the interpretation that non-Markovian dynamics is associated to back flow of information from environment to system, thus spoiling the information transfer needed for Darwinism. Finally, we explore mixing of bath registers by allowing a small interaction among them, finding that this spoils the stored information as previously found in the literature.
We correct an unfortunate error in an earlier work of the author, and show that in center-vortex QCD (gauge group SU(3)) the baryonic area law is the so-called $Y$ law, described by a minimal area with three surfaces spanning the three quark world lines and meeting at a central Steiner line joining the two common meeting points of the world lines. (The earlier claim was that this area law was a so-called $\Delta$ law, involving three extremal areas spanning the three pairs of quark world lines.) We give a preliminary discussion of the extension of these results to $SU(N), N>3$. These results are based on the (correct) baryonic Stokes' theorem given in the earlier work claiming a $\Delta$ law. The $Y$-form area law for SU(3) is in agreement with the most recent lattice calculations.
We classify Harish-Chandra modules generated by the pullback to the metaplectic group of harmonic weak Maa{\ss} forms with exponential growth allowed at the cusps. This extends work by Schulze-Pillot and parallels recent work by Bringmann-Kudla, who investigated the case of integral weights. We realize each of our cases via a regularized theta lift of an integral weight harmonic weak Maa{\ss} form. Harish-Chandra modules in both integral and half-integral weight that occur need not be irreducible. Therefore, our display of the role that the theta lifting takes in this picture, we hope, contributes to an initial understanding of a theta correspondence for extensions of Harish-Chandra modules.
We report on how a straightforward (albeit technically involved) analytic study of the 1-loop effective potential in the Minimal Supersymmetric Standard Model, modifies the usual electroweak symmetry breaking conditions involving $\tan \beta$ and the other free parameters of the model. The study implies new constraints which (in contrast with the existing ones like $1 \leq \tan \beta \leq m_t/m_b$) are fully model-independent and exclude more restrictively a region around $\tan \beta \sim 1$. Further results of this study will be only touched upon here.
We consider the membrane model on a box $V_N\subset \mathbb{Z}^n$ of size $(2N+1)^n$ with zero boundary condition in the subcritical dimensions $n=2$ and $n=3$. We show optimal estimates for the probability that the field is positive in a subset $D_N$ of $V_N$. In particular we obtain for $D_N=V_N$ that the probability to be positive on the entire domain is exponentially small and the rate is of the order of the surface area $N^{n-1}$.
We report on the observation of microwave-induced resistance oscillations associated with the fractional ratio n/m of the microwave irradiation frequency to the cyclotron frequency for m up to 8 in a two-dimensional electron system with high electron density. The features are quenched at high microwave frequencies independent of the fractional order m. We analyze temperature, power, and frequency dependencies of the magnetoresistance oscillations and discuss them in connection with existing theories.
The feasibility of using data from the NASA STEREO mission for variable star and asteroseismology studies has been examined. A data analysis pipeline has been developed that is able to apply selected algorithms to the entire database of nearly a million stars to search for signs of variability. An analysis limited to stars of magnitude 10.5 has been carried out, which has resulted in the extraction of 263 eclipsing binaries (EBs), of which 122 are not recorded as such in the SIMBAD online database. The characteristics of the STEREO observations are shown to be extremely well-suited to variable star studies with the ability to provide continuous phase coverage for extended periods as well as repeated visits that allow both short and long term variability to be observed. This will greatly inform studies of particular stars, such as the pre-cataclysmic variable V471 Tau, as well as entire classes of stars, including many forms of rotational variability. The high-precision photometry has also revealed a potentially substellar companion to a bright (R = 7.5 mag) nearby star (HD 213597), detected with 5-sigma significance. This would provide a significant contribution to exoplanet research if follow-up observations ascertain the mass to be within the planetary domain. Some particularly unusual EBs from the recovered sample are discussed, including a possible reclassification of a well-known star as an EB rather than a rotational variable (HR 7355) and several particularly eccentric systems, including very long-period EBs.
In the present work we suggest new and more generalized parameterizations for the Equation of State, EoS, of dark energy, maintaining the basic structure of two-parameters CPL-model, but covering both the past and the future of the cosmic history, without divergences and consistently with the current observational data. We propose two generalizations, starting from the extended MZp-model by Ma and Zhang, 2011, the $\xi$MZp-model and the DFp-model. The potential advantages of using these new formulations is their extended range of validity, mainly in the future, to determine possible future scenarios of the cosmic evolution.
We study the evolution of a perfect--fluid sphere coupled to a scalar radiation field. By ensuring a Ricci invariant regularity as a conformally flat spacetime at the central world line we find that the fluid coupled to the scalar field satisfies the equation of state $\rho_c+3p_c=$ constant at the center of the sphere, where the energy $\rho_c$ density and the pressure $p_c$ do not necessarily contain the scalar field contribution. The fluid can be interpreted as anisotropic and radiant because of the scalar field, but it becomes perfect and non radiative at the center of the sphere. These results are being currently considered to build up a numerical relativistic hydrodynamic solver.
Context: Periodicity in 6.7 GHz methanol maser sources is a rare phenomenon that was discovered during long-term monitoring programmes. Understanding the underlying processes that lead to periodic variability might provide insights into the physical processes in high-mass star-forming regions. Aims: We aim to identify and describe new periodic methanol masers. Methods: The observations were obtained with the Torun 32m antenna. Time series analysis was conducted using well-proven statistical methods. Additionally, NEOWISE data were used to search for a correlation between infrared and maser fluxes. Results: We found two new periodic sources, G45.804-0.356 and G49.043-1.079, with periods of 416.9 and 469.3 days, respectively. For G49.043-1.079, infrared variability is simultaneous with methanol flares. Conclusions: A most likely cause of the periodicity in G49.043-1.079 is modulated accretion. For G45.804-0.356, the periodicity cannot be explained with the available data, and further research is needed.
Properties of the population of millisecond extragalactic radio bursts discovered by Thornton et al. (2013) are in good correspondence with the hypothesis that such events are related to hyperflares of magnetars, as was proposed by us after the first observation of an extragalactic millisecond radio burst by Lorimer et al. (2007). We also point that some of multiple millisecond radio bursts from M31 discovered by Rubio-Herrera et al. (2013) also can be related to weaker magnetar bursts.
Our main goal in this article is to establish a quantitative version of the positivity properties of twisted relative pluricanonical bundles and their direct images. The notion of "singular Hermitian metric" on vector bundles (together with an appropriate definition of positivity of the associated curvature) plays a major role here, and its properties are studied via a version of Ohsawa-Takegoshi extension theorem. Part of this article is based on the joint work of the first named author with Bo Berndtsson, and it can be seen as an expanded and updated version of it.
It is shown, for the self-consistent system of scalar, electro-magnetic and gravitational fields in general relativity, that the equations of motion admit a special kind of solutions with spherical or cylindrical symmetry. For these solutions, the physical fields vanish and the space-time is flat outside of the critical sphere or cylinder. Therefore, the mass and the electric charge of these configurations are zero. The principal difference between droplet-like solutions with spherical symmetry and those with cylindrical one has been established. In the first case there exists a possibility of continuous transformation of droplet-like configuration into the solitonian one, when for the second case there is no such a possibility.
We use the Fundamental Plane (FP) to measure the redshift evolution of the dynamical mass-to-light ratio ($M_{\mathrm{dyn}}/L$) and the dynamical-to-stellar mass ratio ($M_{\mathrm{dyn}}/M_*$). Although conventionally used to study the properties of early-type galaxies, we here obtain stellar kinematic measurements from the Large Early Galaxy Astrophysics Census (LEGA-C) Survey for a sample of $\sim1400$ massive ($\log( M_*/M_\odot) >10.5$) galaxies at $0.6<z<1.0$ that span a wide range in star formation activity. In line with previous studies, we find a strong evolution in $M_{\mathrm{dyn}}/L_g$ with redshift. In contrast, we find only a weak dependence of the mean value of $M_{\mathrm{dyn}}/M_*$ on the specific star formation rate, and a redshift evolution that likely is explained by systematics. Therefore, we demonstrate that star-forming and quiescent galaxies lie on the same, stable mass FP across $0<z<1$, and that the decrease in $M_{\mathrm{dyn}}/L_g$ toward high redshift can be attributed entirely to evolution of the stellar populations. Moreover, we show that the growth of galaxies in size and mass is constrained to occur within the mass FP. Our results imply either minimal structural evolution in massive galaxies since $z\sim1$, or a tight coupling in the evolution of their morphological and dynamical properties, and establish the mass FP as a tool for studying galaxy evolution with low impact from progenitor bias.
We explore the eikonal approximation to graviton exchange in AdS_5 space, as relevant to scattering in gauge theories. We restrict ourselves to the regime where conformal invariance of the dual gauge theory holds, and to large 't Hooft coupling where the computation involves pure gravity. We give a heuristic argument, a direct loop computation, and a shock wave derivation. The scalar propagator in AdS_3 plays a key role, indicating that even at strong coupling, two-dimensional conformal invariance controls high-energy four-dimensional gauge-theory scattering.
We present two novel schemes to generate photon polarization entanglement via single electron spins confined in charged quantum dots inside microcavities. One scheme is via entangled remote electron spins followed by negatively-charged exciton emissions, and another scheme is via a single electron spin followed by the spin state measurement. Both schemes are based on giant circular birefringence and giant Faraday rotation induced by a single electron spin in a microcavity. Our schemes are deterministic and can generate an arbitrary amount of multi-photon entanglement. Following similar procedures, a scheme for a photon-spin quantum interface is proposed.
We present the analysis result of a gravitational binary-lensing event OGLE-2005-BLG-018. The light curve of the event is characterized by 2 adjacent strong features and a single weak feature separated from the strong features. The light curve exhibits noticeable deviations from the best-fit model based on standard binary parameters. To explain the deviation, we test models including various higher-order effects of the motions of the observer, source, and lens. From this, we find that it is necessary to account for the orbital motion of the lens in describing the light curve. From modeling of the light curve considering the parallax effect and Keplerian orbital motion, we are able to measure not only the physical parameters but also a complete orbital solution of the lens system. It is found that the event was produced by a binary lens located in the Galactic bulge with a distance $6.7\pm 0.3$ kpc from the Earth. The individual lens components with masses $0.9\pm 0.3\ M_\odot$ and $0.5\pm 0.1\ M_\odot$ are separated with a semi-major axis of $a=2.5 \pm 1.0$ AU and orbiting each other with a period $P=3.1 \pm 1.3$ yr. The event demonstrates that it is possible to extract detailed information about binary lens systems from well-resolved lensing light curves.
The possibility to extract relevant information on spectroscopic factors from (e,e$'$p) reactions at high $Q^2$ is studied. Recent ${}^{16}$O(e,e$'$p) data at $Q^2 = 0.8$ (GeV/$c)^2$ are compared to a theoretical approach which includes an eikonal description of the final-state interaction of the proton, a microscopic nuclear matter calculation of the damping of this proton, and high-quality quasihole wave functions for $p$-shell nucleons in ${}^{16}{\rm O}$. Good agreement with the $Q^2 = 0.8$ (GeV/$c)^2$ data is obtained when spectroscopic factors are employed which are identical to those required to describe earlier low $Q^2$ experiments.
The volume coefficient $K$(=incompressibility of the nuclear matter), the Coulomb coefficient $K_c$, and the volume-symmetry coefficient $K_{vs}$ of the nucleus incompressibility are studied in the framework of the relativistic mean field theory, with aid of the scaling model. It is found that $K= 300\pm 50$MeV is necessary to account for the empirical values of $K_v$, $K_c$, and $K_{vs}$, simultaneously. The result is independent on the detail descriptions of the potential of the $\sigma$-meson self-interaction and is almost independent of the strength of the $\omega$-meson self-interaction.
In this paper we characterize global regularity in the sense of Shubin of twisted partial differential operators of second order in dimension $2$. These operators form a class containing the twisted Laplacian, and in bi-unique correspondence with second order ordinary differential operators with polynomial coefficients and symbol of degree $2$. This correspondence is established by a transformation of Wigner type. In this way the global regularity of twisted partial differential operators turns out to be equivalent to global regularity and injectivity of the corresponding ordinary differential operators, which can be completely characterized in terms of the asymptotic behavior of the Weyl symbol. In conclusion we observe that we have obtained a new class of globally regular partial differential operators which is disjoint from the class of hypo-elliptic operators in the sense of Shubin.
Oscillations of coronal loops in the Sun have been reported in both imaging and spectral observations at the onset of flares. Images reveal transverse oscillations, whereas spectra detect line-of-sight velocity or Doppler-shift oscillations. The Doppler-shift oscillations are commonly interpreted as longitudinal modes. Our aim is to investigate the relationship between loop dynamics and flows seen in TRACE 195\AA images and Doppler shifts observed by SUMER in Si III 1113.2\AA and Fe XIX 1118.1\AA at the time of a C.8-class limb flare and an associated CME. We carefully co-aligned the sequence of TRACE 195 \AA images to structures seen in the SUMER Si III, Ca X,and Fe XIX emission lines. Additionally, H-alpha observations of a lifting prominence associated with the flare and the coronal mass ejection (CME) are available in three bands around 6563.3 \AA . They give constraints on the timing and geometry. Large-scale Doppler-shift oscillations in Fe XIX and transverse oscillations in intensity images were observed over a large region of the corona after the passage of a wide bright extreme-ultraviolet (EUV) disturbance, which suggests ionization, heating, and acceleration of hot plasma in the wake of a blast wave.
We construct a connected, irreducible component of the moduli space of minimal surfaces of general type with $p_g=q=2$ and $K^2=5$, which contains both examples given by Chen-Hacon and the first author. This component is generically smooth of dimension 4, and all its points parametrize surfaces whose Albanese map is a generically finite triple cover.
We discuss the question of finding conditions on a derived equivalence between two smooth projective varieties $X$ and $Y$ that imply that $X$ and $Y$ are birational. The types of conditions we consider are in the spirit of finding categorical analogous of classical Torelli theorems. We study, in particular, a notion of strongly filtered derived equivalence and study cases where strongly filtered derived equivalence implies birationality. We also consider an open variant of our main question.