ShantanuT01/DACTYL-Pretraining huggingface dataset:
We work with non-planar rooted trees which have a label set given by an arbitrary vector space $V$. By equipping $V$ with a complete locally convex topology, we show how a natural topology is induced on the tree algebra over $V$. In this context, we introduce the Grossman-Larson and Connes-Kreimer topological Hopf algebras over $V$, and prove that they form a dual pair in a certain sense. As an application we define the class of branched rough paths over a general Banach space, and propose a new definition of a solution to a rough differential equation (RDE) driven by one of these branched rough paths. We show equivalence of our definition with a Davie-Friz-Victoir-type definition, a version of which is widely used for RDEs with geometric drivers, and we comment on applications to RDEs with manifold-valued solutions.
In this paper we discuss the Mabinogion urn model introduced by D. Williams in Probability with Martingales (1991). Therein he describes an optimal control problem where the objective is to maximize the expected final number of objects of one kind in the Mabinogion urn model. Our main contribution is formulas for the expected time to absorption and its asymptotic behavior in the optimally controlled process. We also present results for the non-controlled Mabinogion urn process and briefly analyze other strategies that become superior if a certain discount factor is included.
We study equilibrium configurations of boson stars in the framework of a class scalar-tensor theories of gravity with massive gravitational scalar (dilaton). In particular we investigate the influence of the mass of the dilaton on the boson star structure. We find that the masses of the boson stars in presence of dilaton are close to those in general relativity and they are sensitive to the ratio of the boson mass to the dilaton mass within a typical few percent. It turns out also that the boson star structure is mainly sensitive to the mass term of the dilaton potential rather to the exact form of the potential.
We derive diffusion equations, which describe spin-charge coupled transport on the helical metal surface of a three-dimensional topological insulator. The main feature of these equations is a large magnitude of the spin-charge coupling, which leads to interesting and observable effects. In particular, we predict a new magnetoresistance effect, which manifests in a nonohmic correction to a voltage drop between a ferromagnetic spin-polarized electrode and a nonmagnetic electrode, placed on top of the helical metal. This correction is proportional to the cross-product of the spin polarization of the ferromagnetic electrode and the charge current between the two electrodes. We also demonstrate tunability of this effect by applying a gate voltage, which makes it possible to operate the proposed device as a transistor.
We report 0.8-4.5 micron SpeX spectroscopy of the narrow-line Seyfert 1 galaxy Mrk1239. The spectrum is outstanding because the nuclear continuum emission in the near-infrared is dominated by a strong bump of emission peaking at 2.2 micron, with a strength not reported before in an AGN. A comparison of the Mrk1239 spectrum to that of Ark564 allowed us to conclude that the continuum is strongly reddened by E(B-V)=0.54. The excess of emission, confirmed by aperture photometry and additional NIR spectroscopy, follows a simple blackbody curve at T=1200 K. This suggest that we may be observing direct evidence of dust heated near to the sublimation temperature, likely produced by the putative torus of the unification model. Although other alternatives are also plausible, the lack of star formation, the strong polarization and low extinction derived for the emission lines support the scenario where the hot dust is located between the narrow line region and the broad line region.
Quantum dots are useful model systems for studying quantum thermoelectric behavior because of their highly energy-dependent electron transport properties, which are tunable by electrostatic gating. As a result of this strong energy dependence, the thermoelectric response of quantum dots is expected to be nonlinear with respect to an applied thermal bias. However, until now this effect has been challenging to observe because, first, it is experimentally difficult to apply a sufficiently large thermal bias at the nanoscale and, second, it is difficult to distinguish thermal bias effects from purely temperature-dependent effects due to overall heating of a device. Here we take advantage of a novel thermal biasing technique and demonstrate a nonlinear thermoelectric response in a quantum dot which is defined in a heterostructured semiconductor nanowire. We also show that a theoretical model based on the Master equations fully explains the observed nonlinear thermoelectric response given the energy-dependent transport properties of the quantum dot.
We prove that multisoliton solutions of the Korteweg--de Vries equation are orbitally stable in $H^{-1}(\mathbb{R})$. We introduce a variational characterization of multisolitons that remains meaningful at such low regularity and show that all optimizing sequences converge to the manifold of multisolitons. The proximity required at the initial time is uniform across the entire manifold of multisolitons; this had not been demonstrated previously, even in $H^1$.
We prove that, for every 6D supergravity theory that has an F-theory description, the property of charge completeness for the connected component of the gauge group (meaning that all charges in the corresponding charge lattice are realized by massive or massless states in the theory) is equivalent to a standard assumption made in F-theory for how geometry encodes the global gauge theory by means of the Mordell-Weil group of the elliptic fibration. This result also holds in 4D F-theory constructions for the parts of the gauge group that come from sections and from 7-branes. We find that in many 6D F-theory models the full charge lattice of the theory is generated by massless charged states; this occurs for each gauge factor where the associated anomaly coefficient satisfies a simple positivity condition. We describe many of the cases where this massless charge sufficiency condition holds, as well as exceptions where the positivity condition fails, and analyze the related global structure of the gauge group and associated Mordell-Weil torsion in explicit F-theory models.
A technique for evaluating the electromagnetic Casimir energy in situations involving spherical or circular boundaries is presented. Zeta function regularization is unambiguously used from the start and the properties of Bessel and related zeta functions are central. Nontrivial results concerning these functions are given. While part of their application agrees with previous knowledge, new results like the zeta-regularized electromagnetic Casimir energy for a circular wire are included.
Several aspects of scalar field dynamics on a brane which differs from corresponding regimes in the standard cosmology are investigated. We consider asymptotic solution near a singularity, condition for inflation and bounces and some detail of chaotic behavior in the brane model. Each results are compared with those known in the standard cosmology.
The moduli spaces of trigonal curves of odd genus $g>4$ are proven to be rational.
The Telescope Array (TA) shows a 20$^{\circ}$ hotspot as well as an excess of UHECRs above 50~EeV when compared with the Auger spectrum. We consider the possibility that both the TA excess and hotspot are due to a dominant source in the Northern sky. We carry out detailed simulations of UHECR propagation in both the intergalactic medium and the Galaxy, using different values for the intergalactic magnetic field. We consider two general classes of sources: transients and steady, adopting a mixed UHECR composition that is consistent with the one found by Auger. The spatial location of the sources is draw randomly. We generate Auger-like and TA-like data sets from which we determine the spectrum, the sky maps and the level of anisotropy. We find that, while steady sources are favored over transients, it is unlikely to account for all the currently available observational data. While we reproduce fairly well the Auger spectrum for the vast majority of the simulated data sets, most of the simulated data sets with a spectrum compatible with that of TA (at most a few percent depending on density model tested) show a much stronger anisotropy than the one observed. We find that the rare cases in which both the spectrum and the anisotropy are consistent require a steady source within $\sim 10$ Mpc, to account for the flux excess, and a strong extragalactic magnetic field $\sim 10$ nG, to reduce the excessive anisotropy.
High-energy photons emitted from gamma-ray bursts (GRBs) are subject to pair-production interactions with lower energy photons, leading to an effective optical depth. In this Letter, we estimate the opacity resulting from photon fields located at various distances from long GRB sites: that of the binary companion to the massive stellar progenitor, that of the star-forming molecular cloud containing the GRB, and the total photon field of the host galaxy. The first two photon fields are found to be transparent for most reasonable sets of assumptions about these systems. In the case of galactic radiation fields, we have performed several numerical simulations to calculate the expected opacities for different line-of-sight geometries through the host galaxy, and include a full accounting of the infrared radiation produced by the absorption and re-radiation of starlight by dust. The optical depth for GeV gamma-rays, due to direct starlight is less than unity for all host galaxies. At higher energies, $>$10 TeV, a spectral cutoff can occur due to the rapidly increasing number of mid- to far-IR intra-galactic photons reradiated by dust. Photons in the extragalactic background light therefore remain the only relevant source of photon-photon opacity for ongoing GRB observations with Fermi LAT, and potential future detections with ground-based gamma-ray telescopes.
We derive the fusion hierarchy of functional equations for critical A-D-E lattice models related to, the sl(2) unitary minimal models, the parafermionic models and the supersymmetric models of conformal field theory, and deduce the related TBA functional equations. The derivation uses fusion projectors and applies in the presence of all known integrable boundary conditions on the torus and cylinder. The resulting TBA functional equations are_universal_ in the sense that they depend only on the Coxeter number of the A-D-E graph and are independent of the particular integrable boundary conditions. We conjecture generally that TBA functional equations are universal for all integrable lattice models associated with rational CFTs and their integrable perturbations.
A new zerofree region of the Riemann Zeta-function $\zeta$ is identified by using Tur\'an's localization criterion linking zeros of $\zeta$ with uniform local suprema of sets of Dirichlet polynomials expanded over the primes. The proof is based on a randomization argument. An estimate for local extrema for some finite families of shifted Dirichlet polynomials, % associated to linearly independent sequences of reals is established by preliminary considering their local increment properties, by means of Montgomery-Vaughan's variant of Hilbert's inequality. A covering argument combined with Tur\'an's localization criterion allows to conclude.
We study the phase diagram and quantum critical region of one of the fundamental models for electronic correlations: the periodic Anderson model. Employing the recently developed dynamical vertex approximation, we find a phase transition between a zero-temperature antiferromagnetic insulator and a Kondo insulator. In the quantum critical region, we determine a critical exponent $\gamma\!=\!2$ for the antiferromagnetic susceptibility. At higher temperatures, we have free spins with $\gamma\!=\!1$ instead, whereas at lower temperatures, there is an even stronger increase and suppression of the susceptibility below and above the quantum critical point, respectively.
We do a generic study of the behavior of a hard disk system under the action of a thermal gradient in presence of an uniform gravity field. We observe the conduction-convection transition and measure the main system observables and fields as the thermal current, global pressure, velocity field, temperature field,... We can highlight two of the main results of this overall work: (1) for large enough thermal gradients and a given gravity, we show that the hydrodynamic fields (density, temperature and velocity) have a natural scaling form with the gradient. And (2) we show that local equilibrium holds if the mechanical pressure and the thermodynamic one are not equal, that is, the Stoke's assumption does not hold in this case. Moreover we observe that the best fit to the data is obtained when the bulk viscosity depends on the mechanical pressure.
We present an optimised galaxy cluster finder, 3D-Matched-Filter (3D-MF), which utilises galaxy cluster radial profiles, luminosity functions and redshift information to detect galaxy clusters in optical surveys. This method is an improvement over other matched-filter methods, most notably through implementing redshift slicing of the data to significantly reduce line-of-sight projections and related false positives. We apply our method to the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) Deep fields, finding ~170 galaxy clusters per square degree in the 0.2 <= z <= 1.0 redshift range. Future surveys such as LSST and JDEM can exploit 3D-MF's automated methodology to produce complete and reliable galaxy cluster catalogues. We determine the reliability and accuracy of the statistical approach of our method through a thorough analysis of mock data from the Millennium Simulation. We detect clusters with 100% completeness for M_200 >= 3.0x10^(14)M_sun, 88% completeness for M_200 >= 1.0x10^(14)M_sun, and 72% completeness well into the 10^(13)M_sun cluster mass range. We show a 36% multiple detection rate for cluster masses >= 1.5x10^(13)M_sun and a 16% false detection rate for galaxy clusters >~ 5x10^(13)M_sun, reporting that for clusters with masses <~ 5x10^(13)M_sun false detections may increase up to ~24%. Utilising these selection functions we conclude that our galaxy cluster catalogue is the most complete CFHTLS Deep cluster catalogue to date.
We study the physical process of gravitational collapse of a perfect fluid with a linear isentropic equation of state $p = k \rho, \ -1/3 < k \leq 1$. We consider a model with ansatz $v'(t,r)/v(t,r) = \xi'(r)$ that give rise to a family of solutions to Einstein equations with equation of state. The solution so obtained lead to homogeneous collapse that evolves from a regular initial data and the positivity of energy conditions. The collapse terminates in the formation of black hole. We show that as the parameter $k \rightarrow 1$, the formation of black hole gets accelerated in time, revealing the significance of equation of state in black hole formation.
We consider a relativistic superalgebra in the picture in which the time and spatial derivative cannot be presented in the operators of the particle. The supersymmetry generators as well as the Hamilton operators for the massive relativistic particles with spin zero and spin-1/2 are expressed in terms of the principal series of the unitary representations of the Lorentz group. We also consider the massless case. New Hamilton operators are conctructed for the massless particles with spin zero and spin 1/2.
We construct explicit examples of one-dimensional driven diffusive systems for two and three species of interacting particles, defined by asymmetric dynamical rules which do not obey detailed balance, but whose nonequilibrium stationary-state measure coincides with a prescribed equilibrium Gibbs measure. For simplicity, the measures considered in this construction only involve nearest-neighbor interactions. For two species, the dynamics thus obtained generically has five free parameters, and does not obey pairwise balance in general. The latter property is satisfied only by the totally asymmetric dynamics and the partially asymmetric dynamics with uniform bias, i.e., the cases originally considered by Katz, Lebowitz, and Spohn. For three species of interacting particles, with nearest-neighbor interactions between particles of the same species, the totally asymmetric dynamics thus obtained has two free parameters, and obeys pairwise balance. These models are put in perspective with other examples of driven diffusive systems. The emerging picture is that asymmetric (nonequilibrium) stochastic dynamics leading to a given stationary-state measure are far more constrained (in terms of numbers of free parameters) than the corresponding symmetric (equilibrium) dynamics.
We report on follow-up observations of candidate X-ray bright, radio-quiet isolated neutron stars (INSs) identified from correlations of the ROSAT All-Sky Survey (RASS) and the Sloan Digital Sky Survey (SDSS) Data Release 4 in Ag\"ueros et al. (2006). We obtained Chandra X-ray Telescope exposures for 13 candidates in order to pinpoint the source of X-ray emission in optically blank RASS error circles. These observations eliminated 12 targets as good INS candidates. We discuss subsequent observations of the remaining candidate with the XMM-Newton X-ray Observatory, the Gemini North Observatory, and the Apache Point Observatory. We identify this object as a likely extragalactic source with an unusually high log(fX/fopt) ~ 2.4. We also use an updated version of the population synthesis models of Popov et al. (2010) to estimate the number of RASS-detected INSs in the SDSS Data Release 7 footprint. We find that these models predict ~3-4 INSs in the 11,000 square deg imaged by SDSS, which is consistent with the number of known INSs that fall within the survey footprint. In addition, our analysis of the four new INS candidates identified by Turner et al. (2010) in the SDSS footprint implies that they are unlikely to be confirmed as INSs; together, these results suggest that new INSs are not likely to be found from further correlations of the RASS and SDSS.
We prove uniqueness of a martingale problem with boundary conditions on a simplex associated to a differential operator with an unbounded drift. We show that the solution of the martingale problem remains absorbed at the boundary once it attains it, and that, after hitting the boundary, it performs a diffusion on a lower dimensional simplex, similar to the original one. We also prove that in the diffusive time scale condensing zero-range processes evolve as this absorbed diffusion.
We study the list chromatic number of Cartesian products of graphs through the Alon-Tarsi number as defined by Jensen and Toft (1995) in their seminal book on graph coloring problems. The Alon-Tarsi number of $G$, $AT(G)$, is the smallest $k$ for which there is an orientation, $D$, of $G$ with max indegree $k\!-\!1$ such that the number of even and odd circulations contained in $D$ are different. It is known that $\chi(G) \leq \chi_\ell(G) \leq \chi_p(G) \leq AT(G)$, where $\chi(G)$ is the chromatic number, $\chi_\ell(G)$ is the list chromatic number, and $\chi_p(G)$ is the paint number of $G$. In this paper we find families of graphs $G$ and $H$ such that $\chi(G \square H) = AT(G \square H)$, reducing this sequence of inequalities to equality. We show that the Alon-Tarsi number of the Cartesian product of an odd cycle and a path is always equal to 3. This result is then extended to show that if $G$ is an odd cycle or a complete graph and $H$ is a graph on at least two vertices containing the Hamilton path $w_1, w_2, \ldots, w_n$ such that for each $i$, $w_i$ has a most $k$ neighbors among $w_1, w_2, \ldots, w_{i-1}$, then $AT(G \square H) \leq \Delta(G)+k$ where $\Delta(G)$ is the maximum degree of $G$. We discuss other extensions for $G \square H$, where $G$ is such that $V(G)$ can be partitioned into odd cycles and complete graphs, and $H$ is a graph containing a Hamiltonian path. We apply these bounds to get chromatic-choosable Cartesian products, in fact we show that these families of graphs have $\chi(G) = AT(G)$, improving previously known bounds.
We investigate the linear stability properties of the plane interface separating two relativistic magnetized flows in relative motion. The two flows are governed by the (special) relativistic equations for a magnetized perfect gas in the infinite conductivity approximation. By adopting the vortex-sheet approximation, the relativistic magnetohydrodynamics equations are linearized around the equilibrium state and the corresponding dispersion relation is derived and discussed. The behavior of the configuration and the regimes of instability are investigated following the effects of four physical parameters, namely: the flow velocity, the relativistic and Alfv\'enic Mach numbers and the inclination of the wave vector on the plane of the interface. From the numerical solution of the dispersion relation, we find in general two separate regions of instability, associated respectively with the slow and fast magnetosonic modes. Modes parallel to the flow velocity are destabilized only for sufficiently low magnetization. For the latter case, stabilization is attained, additionally, at sufficiently large relativistic velocities between the two flows in relative motion. The relevance of these results to the study of the stability of astrophysical jets is briefly commented.
A path $P$ in a graph $G$ is said to be a degree monotone path if the sequence of degrees of the vertices of $P$ in the order in which they appear on $P$ is monotonic. The length of the longest degree monotone path in $G$ is denoted by $mp(G)$. This parameter was first studied in an earlier paper by the authors where bounds in terms of other parameters of $G$ were obtained.   In this paper we concentrate on the study of how $mp(G)$ changes under various operations on $G$. We first consider how $mp(G)$ changes when an edge is deleted, added, contracted or subdivided. We similarly consider the effects of adding or deleting a vertex. We sometimes restrict our attention to particular classes of graphs.   Finally we study $mp(G \times H)$ in terms of $mp(G)$ and $mp(H)$ where $\times$ is either the Cartesian product or the join of two graphs.   In all these cases we give bounds on the parameter $mp$ of the modified graph in terms of the original graph or graphs and we show that all the bounds are sharp.
Rotation of triaxially deformed nucleus has been an interesting subject in the study of nuclear structure. In the present series of work, we investigate wobbling motion and chiral rotation by employing the microscopic framework of angular-momentum projection from cranked triaxially deformed mean-field states. In this first part the wobbling motion is studied in detail. The consequences of the three dimensional cranking are investigated. It is demonstrated that the multiple wobbling rotational bands naturally appear as a result of fully microscopic calculation. They have the characteristic properties, that are expected from the macroscopic triaxial-rotor model or the phenomenological particle-triaxial-rotor model, although quantitative agreement with the existing data is not achieved. It is also found that the excitation spectrum reflects dynamics of the angular-momentum vector in the intrinsic frame of the mean-field (transverse vs. longitudinal wobbling). The results obtained by using the Woods-Saxon potential and the schematic separable interaction are mainly discussed, while some results with the Gogny D1S interaction are also presented.