ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $G=(V,E)$ be a locally finite connected weighted graph, $\Delta$ be the usual graph Laplacian. In this paper, we study the blow-up problems for the nonlinear parabolic equation $u_t=\Delta u + f(u)$ on $G$. The blow-up phenomenons of the equation are discussed in terms of two cases: (i) an initial condition is given; (ii) a Dirichlet boundary condition is given. We prove that if $f$ satisfies appropriate conditions, then the solution of the equation blows up in a finite time.
In the first part of this talk I discuss two somewhat different supergravity approaches to calculating correlation functions in strongly coupled Yang-Mills theory. The older approach relates two-point functions to cross-sections for absorption of certain incident quanta by threebranes. In this approach the normalization of operators corresponding to the incident particles is fixed unambiguously by the D3-brane DBI action. By calculating absorption cross-sections of all partial waves of the dilaton we find corresponding two-point functions at strong `t Hooft coupling and show that they are identical to the weak coupling results. The newer approach to correlation functions relates them to boundary conditions in AdS space. Using this method we show that for a certain range of negative mass-squared there are two possible operator dimensions corresponding to a given scalar field in AdS, and indicate how to calculate correlation functions for either of these choices. In the second part of the talk I discuss an example of AdS/CFT duality which arises in the context of type 0 string theory. The CFT on N coincident electric and magnetic D3-branes is argued to be stable for sufficiently weak `t Hooft coupling. It is suggested that its transition to instability at a critical coupling is related to singularity of planar diagrams.
Modern cosmological analyses constrain physical parameters using Markov Chain Monte Carlo (MCMC) or similar sampling techniques. Oftentimes, these techniques are computationally expensive to run and require up to thousands of CPU hours to complete. Here we present a method for reconstructing the log-probability distributions of completed experiments from an existing MCMC chain (or any set of posterior samples). The reconstruction is performed using Gaussian process regression for interpolating the log-probability. This allows for easy resampling, importance sampling, marginalization, testing different samplers, investigating chain convergence, and other operations. As an example use-case, we reconstruct the posterior distribution of the most recent Planck 2018 analysis. We then resample the posterior, and generate a new MCMC chain with forty times as many points in only thirty minutes. Our likelihood reconstruction tool can be found online at https://github.com/tmcclintock/AReconstructionTool.
A phenomenological model with active and sterile neutrinos is used for calculations of neutrino oscillation characteristics at the normal mass hierarchy of active neutrinos. Taking into account the contributions of sterile neutrinos, appearance and survival probabilities for active neutrinos are calculated. Modified graphical dependencies for the probability of appearance of electron neutrinos/antineutrinos in muon neutrino/antineutrino beams as a function of the ratio of the distance to the neutrino energy and other model parameters are obtained. It is shown that in the case of a certain type mixing between active and sterile neutrinos it is possible to clarify some features of the anomalies of neutrino data at short distances. A new parametrization for a particular type mixing matrix of active and sterile neutrinos that takes into account the additional sources of CP violation is used. The comparison with the existing experimental data is performed and, with using this knowledge, the estimates of some model parameters are found. The theoretical results obtained for mixing of active and sterile neutrinos can be applied for interpretation and prediction of results of ground-based experiments on search of sterile neutrinos as well as for analyses of some astrophysical data.
We derive a singular version of the Sphere Covering Inequality which was recently introduced in [42], suitable for treating singular Liouville-type problems with superharmonic weights. As an application we deduce new uniqueness results for solutions of the singular mean field equation both on spheres and on bounded domains, as well as new self-contained proofs of previously known results, such as the uniqueness of spherical convex polytopes first established in [56]. Furthermore, we derive new symmetry results for the spherical Onsager vortex equation.
Single photons emerging from q-plates (or Pancharatnam-Berry phase optical element) exhibit entanglement in the degrees of freedom of spin and orbital angular momentum. We put forward an experimental scheme for probing the spin-orbit correlations of single photons. It is found that the Clauser-Horne-Shimony-Holt (CHSH) parameter S for the single-photon spin-orbit entangled state could be up to 2.828, evidently violating the Bell-like inequality and thus invalidating the noncontextual hidden variable (NCHV) theories.
ATR points were introduced by Darmon as a conjectural construction of algebraic points on certain elliptic curves for which in general the Heegner point method is not available. So far the only numerical evidence, provided by Darmon--Logan and G\"artner, concerned curves arising as quotients of Shimura curves. In those special cases the ATR points can be obtained from the already existing Heegner points, thanks to results of Zhang and Darmon--Rotger--Zhao.   In this paper we compute for the first time an algebraic ATR point on a curve which is not uniformizable by any Shimura curve, thus providing the first piece of numerical evidence that Darmon's construction works beyond geometric modularity. To this purpose we improve the method proposed by Darmon and Logan by removing the requirement that the real quadratic field be norm-euclidean, and accelerating the numerical integration of Hilbert modular forms.
We study F-saturation games, first introduced by F\"uredi, Reimer and Seress in 1991, and named as such by West. The main question is to determine the length of the game whilst avoiding various classes of graph, playing on a large complete graph. We show lower bounds on the length of path-avoiding games, and more precise results for short paths. We show sharp results for the tree avoiding game and the star avoiding game.
We show that there exist linear-time algorithms that compute the strong chromatic index and a maximum induced matching of tree-cographs when the decomposition tree is a part of the input. We also show that there exist efficient algorithms for the strong chromatic index of (bipartite) permutation graphs and of chordal bipartite graphs.
In the whole space $\mathbb R^d$, linear estimates for heat semi-group in Besov spaces are well established, which are estimates of $L^p$-$L^q$ type, maximal regularity, e.t.c. This paper is concerned with such estimates for semi-group generated by the Dirichlet Laplacian of fractional order in terms of the Besov spaces on an arbitrary open set of $\mathbb R^d$.
In this paper we study standing waves for pseudo-relativistic nonlinear Schr\"odinger equations. In the first part we find ground state solutions. We also prove that they have one sign and are radially symmetric. The second part is devoted to take nonrelativistic limit of the ground state solutions in $H^1 (\mathbb{R}^n)$ space.
It is generally expected that quantum gravity affects the structure of space-time by introducing stochastic fluctuations in the geometry, and, ultimately, in the measurements of four-distances and four-momenta.These fluctuations may induce observable consequences on the propagation of ultra high energy particles, mainly in the range of energies of interest for cosmic ray physics, over large distances, leading to their detection or constraining the underlying quantum gravitational structure. We argue that the detectable effects of fluctuations may extend to energies much lower than the threshold for proton photopion production (the so-called GZK cut-off), so that lower energy observations may provide strong constraints on the role of a fluctuating space-time structure.
In this article, we prove an explicit bound for $N(\sigma,T)$, the number of zeros of the Riemann zeta function satisfying $\sigma < \Re s <1 $ and $0 < \Im s < T$. This result provides a significant improvement over Rosser's bound for $N(T)$ when used for estimating prime counting functions. For instance this is applied to obtain new bounds for $\psi(x)$ (arXiv:1310.6374).
It is shown that if a complete set of mutually commuting operators is formed by constants of motion, then, up to a factor that only depends on the time, each common eigenfunction of such operators is a solution of the Schr\"odinger equation. In particular, the operators representing the initial values of the Cartesian coordinates of a particle are constants of motion that commute with each other and from their common eigenfunction one readily obtains the Green function.
We present a perturbative approach to the problem of computation of mixed-state fidelity susceptibility (MFS) for thermal states. The mathematical techniques used provides an analytical expression for the MFS as a formal expansion in terms of the thermodynamic mean values of successively higher commutators of the Hamiltonian with the operator involved through the control parameter. That expression is naturally divided into two parts: the usual isothermal susceptibility and a constituent in the form of an infinite series of thermodynamic mean values which encodes the noncommutativity in the problem. If the symmetry properties of the Hamiltonian are given in terms of the generators of some (finite dimensional) algebra, the obtained expansion may be evaluated in a closed form. This issue is tested on several popular models, for which it is shown that the calculations are much simpler if they are based on the properties from the representation theory of the Heisenberg or SU(1, 1) Lie algebra.
In this symposium the Fermi-LAT collaboration released the results of its measurement of the $e^-$ and $e^+$ separate spectra, obtained using the Earth magnetic field. Those results confirm PAMELA finding of an increasing positron fraction above 10 GeV and allow, for the first time independently on the electron spectrum, to reject cosmic ray spallation onto the ISM as the dominant positron production mechanism above that energy. We show, for two different propagation setups, that double component models which were developed to provide a consistent interpretation of PAMELA positron fraction and Fermi-LAT $e^+ + e^-$ data, naturally reproduce also the Fermi-LAT $e^-$ and $e^+$ separate spectra.
We report the clearest detection to date of dusty torus signatures in a Weak-Line Radio Galaxy (WLRG). The deep Spitzer InfraRed Spectrograph (IRS) rest-frame mid-infrared (MIR) spectrum of the WLRG PKS 0043-42 (z=0.116) shows a clear spectral turnover at wavelengths longer than ~20 micron suggestive of warm dust, as well as a 9.7 micron silicate absorption feature. In addition, the hard X-ray results, based on Chandra data, strongly support a picture in which PKS 0043-42 has a torus and accretion disc more typical of Strong-Line Radio Galaxies (SLRGs). The MIR and X-ray spectra are markedly different from those of other WLRGs at similar redshifts, and here we show that the former can be successfully fitted with clumpy torus models with parameters characteristic of Type-2 AGN tori: close to edge-on (i=74 deg) and relatively broad (torus angular width=60 deg), with an outer radius of 2 pc, hydrogen column density ~1.6x10^(23) cm^(-2), and AGN bolometric luminosity ~1.6x10^(44) erg s^(-1). The presence of a compact torus in PKS 0043-42 provides evidence that this WLRG is fuelled by cold, rather than hot, gas accretion. We suggest that WLRGs are a diverse population, and PKS 0043-42 may represent a type of radio galaxy in which the AGN activity has been recently re-triggered as a consequence of intermittent gas supply, or in which the covering factor of the Narrow-Line Region (NLR) clouds is relatively low.
The appearance of a convex dip in the microcanonical entropy of finite systems usually signals a first order transition. However, a convex dip also shows up in some systems with a continuous transition as for example in the Baxter-Wu model and in the four-state Potts model in two dimensions. We demonstrate that the appearance of a convex dip in those cases can be traced back to a finite-size effect. The properties of the dip are markedly different from those associated with a first order transition and can be understood within a microcanonical finite-size scaling theory for continuous phase transitions. Results obtained from numerical simulations corroborate the predictions of the scaling theory.
In the present work we show that it is possible to arrive at a Ginzburg-Landau (GL) like equation from pure SU(2) gauge theory. This has a connection to the dual superconducting model for color confinement where color flux tubes permanently bind quarks into color neutral states. The GL Lagrangian with a spontaneous symmetry breaking potential, has such (Nielsen-Olesen) flux tube solutions. The spontaneous symmetry breaking requires a tachyonic mass for the effective scalar field. Such a tachyonic mass term is obtained from the condensation of ghost fields.
Recently, the Multilinear Compressive Learning (MCL) framework was proposed to efficiently optimize the sensing and learning steps when working with multidimensional signals, i.e. tensors. In Compressive Learning in general, and in MCL in particular, the number of compressed measurements captured by a compressive sensing device characterizes the storage requirement or the bandwidth requirement for transmission. This number, however, does not completely characterize the learning performance of a MCL system. In this paper, we analyze the relationship between the input signal resolution, the number of compressed measurements and the learning performance of MCL. Our empirical analysis shows that the reconstruction error obtained at the initialization step of MCL strongly correlates with the learning performance, thus can act as a good indicator to efficiently characterize learning performances obtained from different sensor configurations without optimizing the entire system.
The paper describes profile broadening and peak wavelength variation of diffuse interstellar bands (DIBs) measured for 46 lines of sight, probably caused by physical properties of intervening clouds. Full width at half maximum of four studied diffuse bands (5780, 5797, 6196 and 6614 \AA) demonstrate strong variability sometimes doubling the features' width. Despite the high magnitude of the effect, our current analysis is restricted to the strongest diffuse bands because the weaker ones require a much higher S/N ratio. The profile broadening in the studied DIBs moves the profile's centers towards longer wavelengths, probably due to the excitation of higher levels of the P branch of the unknown molecular carrier. Moreover, diffuse bands are broader in clouds with abundantly populated vibrationally excited states of the hydrogen molecules, i.e. DIB's broadening correlates with the rotational temperature estimated on H$_2$ $\nu$=2 vibrational level. However, objects demonstrating extremely broadened profiles of DIBs are scarce. The extreme peculiarity of DIBs' profiles was detected in Herschel~36. Here we show the gradual growths of the widths of diffuse bands, confirmed in spectra from different instruments.
Understanding how galaxies evolved from the early Universe through cosmic time is a fundamental part of modern astrophysics. In order to study this evolution it is important to sample the galaxies at various times in a consistent way through time. In regular luminosity selected samples, our analyses are biased towards the brightest galaxies at all times (as these are easier to observe and identify). A complementary method relies on the absorption imprint from neutral gas in galaxies, the so-called damped Ly-alpha absorbers (DLAs) seen towards distant bright objects. This thesis seeks to understand how the absorption selected galaxies relate to the emission selected galaxies by identifying the faint glow from the absorbing galaxies at redshift z~2.   In the last Chapter, a study of the more evolved, massive galaxies is presented. These galaxies are observed to be a factor of 2 to 6 times smaller than local galaxies of similar masses. A new spectroscopically selected sample is presented and the increased precision of the redshifts allows a more detailed measurement of the scatter in the mass-size relation. The size evolution of massive, quiescent galaxies is modelled by a `dilution' scenario, in which progressively larger galaxies at later times are added to the population of denser galaxies, causing an increase of the mean size of the population. This model describes the evolution of both sizes and number densities very well, however, the scatter in the model increases with time, contrary to the data. It is thus concluded that a combination of `dilution' and individual growth, e.g., through mergers, is needed.   For brevity, the individual chapters based on published peer-reviewed articles are omitted and a link to the given article is given instead.   Principal supervisor: Johan P. U. Fynbo
Within supersymmetric SU(5) Grand Unified Theory, we present several new scenarios with anomaly free flavor symmetry U(1)_F. Within each scenario, a variety of cases offer many possibilities for phenomenologically interesting model building. We present three concrete and economical models with anomaly free U(1)_F leading to natural understanding of observed hierarchies between charged fermion masses and CKM mixing angles.
In (1+1)-d CFTs, the 4-point function on the plane can be mapped to the pillow geometry and thereby crossing symmetry gets translated into a modular property. We use these modular features to derive a universal asymptotic formula for OPE coefficients in which one of the operators is averaged over heavy primaries. The coarse-grained heavy channel then reproduces features of the gravitational 2-to-2 S-matrix which has black holes as their intermediate states.
We prove that the variance of the current across a characteristic is of order t^{2/3} in a stationary asymmetric simple exclusion process, and that the diffusivity has order t^{1/3}. The proof proceeds via couplings to show the corresponding results for the expected deviations and variance of a second class particle.
The electronic structure of a quantum spin liquid compound, EtMe3Sb[Pd(dmit)2]2, has been studied with angle-resolved photoemission spectroscopy, together with two other Pd(dmit)2 salts in the valence bond solid or antiferromagnetic state. We have resolved several bands that have negligible dispersions and fit well to the calculated energy levels of an isolated [Pd(dmit)2]2 dimer. EtMe3Sb[Pd(dmit)2]2 being a Mott insulator, its lower Hubbard band is identified, and there is a small gap of ~ 50 meV between this band and the chemical potential. Moreover, the spectral features exhibit polaronic behavior with anomalously broad linewidth. Compared with existing theories, our results suggest that strong electron-boson interactions, together with smaller hopping and on-site Coulomb interaction terms have to be considered for a realistic modeling of the organic quantum spin liquid systems like the Pd(dmit)2 salt.
We discuss two important instability mechanisms that may lead to the limit-cycle oscillations of the luminosity of the accretion disks around compact objects: ionization instability and radiation-pressure instability. Ionization instability is well established as a mechanism of X-ray novae eruptions in black hole binary systems but its applicability to AGN is still problematic. Radiation pressure theory has still very weak observational background in any of these sources. In the present paper we attempt to confront the parameter space of these instabilities with the observational data. At the basis of this simple survey of sources properties we argue that the radiation pressure instability is likely to be present in several Galactic sources with the Eddington ratios above 0.15, and in AGN with the Eddington ratio above 0.025. Our results favor the parameterization of the viscosity through the geometrical mean of the radiation and gas pressure both in Galactic sources and AGN. More examples of the quasi-regular outbursts in the timescales of 100 seconds in Galactic sources, and hundreds of years in AGN are needed to formulate firm conclusions. We also show that the disk sizes in the X-ray novae are consistent with the ionization instability. This instability may also considerably influence the lifetime cycle and overall complexity in the supermassive black hole environment.
Stochastic dynamics of a quantum system driven by $N$ statistically independent random sudden quenches in a fixed time interval is studied. We reveal that with growing $N$ the system approaches a deterministic limit indicating self-averaging with respect to its temporal unitary evolution. This phenomenon is quantified by the variance of the unitary matrix governing the time evolution of a finite dimensional quantum system which according to an asymptotic analysis decreases at least as $1/N$. For a special class of protocols (when the averaged Hamiltonian commutes at different times), we prove that for finite $N$ the distance (according to the Frobenius norm) between the averaged unitary evolution operator generated by the Hamiltonian $H$ and the unitary evolution operator generated by the averaged Hamiltonian $\langle H \rangle$ scales as $1/N$. Numerical simulations enlarge this result to a broader class of the non-commuting protocols.
The study of the chemical evolution of gas and dust from pre-stellar dense cores to circumstellar disks around young stars forms an essential part of understanding star- and planet formation. Throughout the collapse- and protostellar phases, simple and complex molecules are formed, many of which deplete onto cold grains and are eventually incorporated into the icy planetesimals of new solar systems. Tracing this chemical evolution provides a wealth of information, not only about the chemical processing in primitive solar nebulae, but also about physical processes which occur in the immediate surroundings of young stellar objects (YSOs). Here we review the chemical processes which occur in the protostellar environment, and models and observations of the chemical structure of the various stages of star formation. We briefly discuss the way in which molecular abundances are derived from observations, and conclude with two examples: the low- to intermediate mass YSOs in Serpens, and the massive YSOs in W3.
Structured equations are a standard modeling tool in mathematical biology. They areintegro-differential equations where the unknown depends on one or several variables, representing the state or phenotype of individuals. A large literature has been devoted to many aspects of these equations and in particular to the study of measure solutions.Here we introduce a transport distance closely related to the Monge-Kantorovich distance,which appears to be non-expanding for several (mainly linear) examples of structured equations.