ShantanuT01/DACTYL-Pretraining huggingface dataset:
We investigate a probabilistic model for routeing of messages in relay-augmented multihop ad-hoc networks, where each transmitter sends one message to the origin. Given the (random) transmitter locations, we weight the family of random, uniformly distributed message trajectories by an exponential probability weight, favouring trajectories with low interference (measured in terms of signal-to-interference ratio) and trajectory families with little congestion (measured in terms of the number of pairs of hops using the same relay). Under the resulting Gibbs measure, the system targets the best compromise between entropy, interference and congestion for a common welfare, instead of an optimization of the individual trajectories.   In the limit of high spatial density of users, we describe the totality of all the message trajectories in terms of empirical measures. Employing large deviations arguments, we derive a characteristic variational formula for the limiting free energy and analyse the minimizer(s) of the formula, which describe the most likely shapes of the trajectory flow. The empirical measures of the message trajectories well describe the interference, but not the congestion; the latter requires introducing an additional empirical measure. Our results remain valid under replacing the two penalization terms by more general functionals of these two empirical measures.
The Vapnik-\v{C}ervonenkis dimension is a complexity measure of set-systems, or hypergraphs. Its application to graphs is usually done by considering the sets of neighborhoods of the vertices (cf. Alon et al. (2006) and Chepoi, Estellon, and Vaxes (2007)), hence providing a set-system. But the graph structure is lost in the process. The aim of this paper is to introduce the notion of paired VC-dimension, a generalization of VC-dimension to set-systems endowed with a graph structure, hence a collection of pairs of subsets.   The classical VC-theory is generally used in combinatorics to bound the transversality of a hypergraph in terms of its fractional transversality and its VC-dimension. Similarly, we bound the chromatic number in terms of fractional transversality and paired VC-dimension. This approach turns out to be very useful for a class of problems raised by Erd\H{o}s and Simonovits (1973) asking for H-free graphs with minimum degree at least cn and arbitrarily high chromatic number, where H is a fixed graph and c a positive constant.   We show how the usual VC-dimension gives a short proof of the fact that triangle-free graphs with minimum degree at least n/3 have bounded chromatic number, where $n$ is the number of vertices. Using paired VC-dimension, we prove that if the chromatic number of $H$-free graphs with minimum degree at least cn is unbounded for some positive c, then it is unbounded for all c<1/3. In other words, one can find H-free graphs with unbounded chromatic number and minimum degree arbitrarily close to n/3. These H-free graphs are derived from a construction of Hajnal. The large chromatic number follows from the Borsuk-Ulam Theorem.
We calculate the large deviation function of the end-to-end distance and the corresponding extension-versus-force relation for (isotropic) random walks, on and off-lattice, with and without persistence, and in any spatial dimension. For off-lattice random walks with persistence, the large deviation function undergoes a first order phase transition in dimension $d> 5$. In the corresponding force-versus-extension relation, the extension becomes independent of the force beyond a critical value. The transition is anticipated in dimensions $d=4$ and $d=5$, where full extension is reached at a finite value of the applied stretching force. Full analytic details are revealed in the run-and-tumble limit. Finally, on-lattice random walks with persistence display a softening phase in dimension $d=3$ and above, preceding the usual stiffening appearing beyond a critical value of the force.
We present a detailed derivation of Fourier's law in a class of stochastic energy exchange systems that naturally characterize two-dimensional mechanical systems of locally confined particles in interaction. The stochastic systems consist of an array of energy variables which can be partially exchanged among nearest neighbours at variable rates. We provide two independent derivations of the thermal conductivity and prove this quantity is identical to the frequency of energy exchanges. The first derivation relies on the diffusion of the Helfand moment, which is determined solely by static averages. The second approach relies on a gradient expansion of the probability measure around a non-equilibrium stationary state. The linear part of the heat current is determined by local thermal equilibrium distributions which solve a Boltzmann-like equation. A numerical scheme is presented with computations of the conductivity along our two methods. The results are in excellent agreement with our theory.
We present a systematic analysis of perturbative Hexagonal(HG) mixing for describing recent global fit neutrino mixing data with normal and inverted hierarchy. The corrections to unperturbed mixing are parameterized in terms of small orthogonal rotations (R) with modified PMNS matrix of the forms \big($R_{\alpha\beta}^l\cdot V_{HG},~V_{HG}\cdot R_{\alpha\beta}^r,~V_{HG}\cdot R_{\alpha\beta}^r \cdot R_{\gamma\delta}^r,~R_{\alpha\beta}^l \cdot R_{\gamma\delta}^l \cdot V_{HG}$,~$R_{\alpha\beta}^l\cdot V_{HG}\cdot R_{\gamma\delta}^r$\big ). Here $R_{\alpha\beta}^{l, r}$ is rotation in ij sector and $V_{HG}$ is unperturbed Hexagonal mixing matrix. The detailed numerical investigation of all possible cases is performed with scanning of parameter space using $\chi^2$ approach. We found that the perturbative schemes governed by single rotation are unable to fit the mixing angle data even at $3\sigma$ level. The mixing schemes which involves two rotation matrices, only \big($R_{12}^l \cdot R_{13}^l \cdot V_{HG}$, ~$R_{13}^l \cdot R_{12}^l \cdot V_{HG}$,~$R_{13}^l \cdot V_{HG} \cdot R_{12}^r$,~$R_{12}^l \cdot V_{HG} \cdot R_{12}^r$, ~$R_{13}^l \cdot V_{HG} \cdot R_{13}^r$\big ) are successful in fitting all neutrino mixing angles within $1\sigma$ range for normal hierarchy(NH). However for inverted hierarchy(IH), only $R_{13}^l \cdot V_{HG} \cdot R_{13}^r$ is most preferable as it can fit all mixing angles at $1\sigma$ level. The remaining perturbative cases are either excluded at 3$\sigma$ level or successful in producing mixing angles only at $2-3\sigma$ level. To study the impact of phase parameter, we also looked into CP violating effects for single rotation case. The predicted value of $\delta_{CP}$ lies in the range $39.0^\circ(40.4^\circ) \le |\delta_{CP}| \le 78.7^\circ(79.2^\circ)$ for $U_{12}^l\cdot V_{HM}$ and $U_{13}^l\cdot V_{HM}$ case with Normal(Inverted) Hierarchy.
The quantum nature of the Big Bang is reexamined in the framework of Loop Quantum Cosmology. The strict application of a regularization procedure to the Hamiltonian, originally developed for the Hamiltonian in loop quantum gravity, leads to a qualitative modification of the bounce paradigm. Quantum gravity effects still lead to a quantum bounce connecting deterministically large classical Universes. However, the evolution features a large epoch of de Sitter Universe, with emergent cosmological constant of Planckian order, smoothly transiting into a flat expanding Universe.
The covariant form of the non-Abelian gauge anomaly on noncommutative R2n is computed for U(N) groups. Its origin and properties are analyzed. Its connection with the consistent form of the gauge anomaly is established. We show along the way that bi-fundamental $U(N)\times U(M)$ chiral matter carries no mixed anomalies, and interpret this result as a consequence of the half-dipole structure which characterizes the charged non-commutative degrees of freedom.
Quantile clocks are defined as convolutions of subordinators $L$, with quantile functions of positive random variables. We show that quantile clocks can be chosen to be strictly increasing and continuous and discuss their practical modeling advantages as business activity times in models for asset prices. We show that the marginal distributions of a quantile clock, at each fixed time, equate with the marginal distribution of a single subordinator. Moreover, we show that there are many quantile clocks where one can specify $L$, such that their marginal distributions have a desired law in the class of generalized $s$-self decomposable distributions, and in particular the class of self-decomposable distributions. The development of these results involves elements of distribution theory for specific classes of infinitely divisible random variables and also decompositions of a gamma subordinator, that is of independent interest. As applications, we construct many price models that have continuous trajectories, exhibit volatility clustering and have marginal distributions that are equivalent to those of quite general exponential L\'{e}vy price models. In particular, we provide explicit details for continuous processes whose marginals equate with the popular VG, CGMY and NIG price models. We also show how to perfectly sample the marginal distributions of more general classes of convoluted subordinators when $L$ is in a sub-class of generalized gamma convolutions, which is relevant for pricing of European style options.
We estimate the initial He content in about 30% of the Galactic globular clusters (GGCs) from new star counts we have performed on the recently published HST snapshot database of Colour Magnitude Diagrams (Piotto et al. 2002). More in detail, we use the so-called $R$-parameter and estimate the He content from a calibration based on a recently updated set of stellar models. We performed an accurate statistical analysis in order to assess whether GGCs show a statistically significant spread in their initial He abundances, and whether there is a correlation with the metallicity. We do not find any significant dependence of the He abundance on the GC metallicity; this provides an important constraint for models of Galaxy formation and evolution. Apart from GGCs with the bluest HB morphology, the observed spread in the individual He abundances is statistically compatible with the individual errors. This means that either there is no intrinsic He spread among the GGCs, or that this is masked by the errors. In the latter case we have estimated a firm 1$\sigma$ upper limit of 0.019 to the possible intrinsic spread. In case of the GGCs with the bluest HB morphology we detect a significant spread towards higher abundances inconsistent with the individual errors. In the hypothesis that the intrinsic dispersion on the individual He abundances is zero, taking into account the errors on the individual R-parameter estimates, as well as the uncertainties on the GGC [M/H] scale and theoretical calibration, we have determined an initial He abundance Y(GGC)=0.250\pm0.006 a value in perfect agreement with current estimates based on CMB radiation analyses and cosmological nucleosynthesis computations.
Continued gravitational collapse gives rise to curvature singularities. If a curvature singularity is globally naked then the space-time may be causally future ill-behaved admitting closed time-like or null curves which extend to asymptotic distances and generate a Cosmic Time Machine (de Felice (1995) Lecture Notes in Physics 455, 99). The conjecture that Cosmic Time Machines give rise to high energy impulsive events is here considered in more details.
This article traces a brief history of the use of single electron spins to compute. In classical computing schemes, a binary bit is represented by the spin polarization of a single electron confined in a quantum dot. If a weak magnetic field is present, the spin orientation becomes a binary variable which can encode logic 0 and logic 1. Coherent superposition of these two polarizations represent a qubit. By engineering the exchange interaction between closely spaced spins in neighboring quantum dots, it is possible to implement either classical or quantum logic gates.
We consider supersymmetric configurations in Type IIB supergravity obtained by the beackreaction of fundamental strings ending on a stack of D3-branes and smeared uniformly in the three spatial directions along the D3-branes. These automatically include a distribution of D5-brane baryon vertices necessary to soak up string charge. The backgrounds are static, preserving eight supersymmetries, an SO(5) global symmetry and symmetry under spatial translations and rotations. We obtain the most general BPS configurations consistent with the symmetries. We show that the solutions to the Type IIB field equations are completely specified by a single function (the dilaton) satisfying a Poisson-like equation in two dimensions. We further find that the equation admits a class of solutions displaying Lifshitz-like scaling with dynamical critical exponent z=7. The equations also admit an asymptotically AdS_5 x S^5 solution deformed by the presence of backreacted string sources that yield a uniform density of heavy quarks in N=4 SYM.
The work presents an experimental demonstration of time-reversal asymmetry of electron states propagating along boundary separating areas with opposite magnetic fields. For this purpose we have fabricated a hybrid ferromagnet-semiconductor device in form of a Hall cross with two ferromagnets deposited on top. The magnets generated two narrow magnetic barriers of opposite polarity in the active Hall area. We have observed that if the signs of the barriers are reversed, the bend resistance changes its sign. Using the Landauer-Buttiker theory, we have demonstrated that this is a direct consequence of asymmetric transmission of the "snake" and the "cycloidal" trajectories formed the boundary separating the regions with opposite magnetic field directions.
Recognition of epileptic focal point is the important diagnosis when screening the epilepsy patients for latent surgical cures. The accurate localization is challenging one because of the low spatial resolution images with more noisy data. Positron Emission Tomography (PET) has now replaced the issues and caring a high resolution. This paper focuses the research of automated localization of epileptic seizures in brain functional images using symmetry based cluster approach. This approach presents a fully automated symmetry based brain abnormality detection method for PET sequences. PET images are spatially normalized to Digital Imaging and Communications in Medicine (DICOM) standard and then it has been trained using symmetry based cluster approach using Medical Image Processing, Analysis & Visualization (MIPAV) tool. The performance evolution is considered by the metric like accuracy of diagnosis. The obtained result is surely assists the surgeon for the automated identification of seizures focus.
We develop a theory of the reversible switching of the magnetic state of the ferromagnet-insulator-normal metalferromagnet (FINF) nanostructure. The switching is controlled by tuning the Coulomb blockade strength via the gate voltage on the normal metal granule. The proposed mechanism allows for realizing the switching without passing a dissipative current through the structure.
The fine-structure constant alpha does not vary as Friedmann Universes evolve, a conclusion based on assessments of quantum mechanics and electrodynamics. alpha = e^2/(4pi epsilon hbar c), where e is the charge of the electron, epsilon is vacuum permittivity, c is the speed of light, and hbar is Planck's constant divided by 2pi. This inquiry was motivated by Schrodinger's (1939) prediction that all quantum wave functions coevolve with Friedmann geometry and a similar prediction by Sumner (1994) for vacuum permittivity. The functional form of variations in quantum wave functions found by Schrodinger is enough to show that alpha does not vary. Electrodynamics also predicts that alpha does not vary. Evolutionary changes in c exactly cancel those in vacuum permittivity and other factors in alpha do not change. Since alpha appears in all first-order perturbation formulas for atomic energy levels, comparisons of the atomic spectra of distant atoms with those in laboratories provide an experimental measure of this prediction. Most experiments find changes in alpha that are either statistically zero or very small. These results and estimates of the Hubble constant and deceleration parameter from precision redshift/magnitude data support a major assumption of this paper that the Friedmann solution to Einstein's theory of general relativity without cosmological constant is an adequate approximation to spacetime geometry and its long term evolution at quantum scales.
We study spin pumping in a $\mathrm{Y_3Fe_5O_{12}(YIG)/Pt/Ni_{81}Fe_{19}(Py)}$ trilayer film by means of the inverse spin Hall effect (ISHE). When the ferromagnets are not excited simultaneously by a microwave, ISHE-induced voltage is of the opposite sign at each ferromagnetic resonance (FMR). The opposite sign is consistent with spin pumping of bilayer films. On the other hand, the voltage is of the same sign at each FMR when both the ferromagnets are excited simultaneously. Futhermore, the voltage greatly increases in magnitude. The observed voltage is unconventional; neither its sign nor magnitude can be expected from spin pumping of bilayer films. Control experiments show that the unconventional voltage is dominantly induced by spin pumping at the Py/Pt interface. Interaction between YIG and Py layers is a possible origin of the unconventional voltage.
We study relations between geometric embeddings of graphs and the spectrum of associated matrices, focusing on outerplanar embeddings of graphs. For a simple connected graph $G=(V,E)$, we define a "good" $G$-matrix as a $V\times V$ matrix with negative entries corresponding to adjacent nodes, zero entries corresponding to distinct nonadjacent nodes, and exactly one negative eigenvalue. We give an algorithmic proof of the fact that it $G$ is a 2-connected graph, then either the nullspace representation defined by any "good" $G$-matrix with corank 2 is an outerplanar embedding of $G$, or else there exists a "good" $G$-matrix with corank 3.
Let $Q$ be a positive-definite quaternary quadratic form with prime discriminant. We give an explicit lower bound on the number of representations of a positive integer $n$ by $Q$. This problem is connected with deriving an upper bound on the Petersson norm $\langle C, C \rangle$ of the cuspidal part of the theta series of $Q$. We derive an upper bound on $\langle C, C \rangle$ that depends on the smallest positive integer not represented by the dual form $Q^{*}$. In addition, we give a non-trivial upper bound on the sum of the integers $n$ excepted by $Q$.
This article is concerned with a system of semilinear parabolic equations with two free boundaries describing the spreading fronts of the invasive species in a mutualistic ecological model. The local existence and uniqueness of a classical solution are obtained and the asymptotic behavior of the free boundary problem is studied. Our results indicate that two free boundaries tend monotonically to finite or infinite at the same time, and the free boundary problem admits a global slow solution with unbounded free boundaries if the inter-specific competitions are strong, while if the inter-specific competitions are weak, there exist the blowup solution and global fast solution.
The enumeration of lattice paths in wedges poses unique mathematical challenges. These models are not translationally invariant, and the absence of this symmetry complicates both the derivation of a functional recurrence for the generating function, and solving for it. In this paper we consider a model of partially directed walks from the origin in the square lattice confined to both a symmetric wedge defined by $Y = \pm pX$, and an asymmetric wedge defined by the lines $Y= pX$ and Y=0, where $p > 0$ is an integer. We prove that the growth constant for all these models is equal to $1+\sqrt{2}$, independent of the angle of the wedge. We derive functional recursions for both models, and obtain explicit expressions for the generating functions when $p=1$. From these we find asymptotic formulas for the number of partially directed paths of length $n$ in a wedge when $p=1$.   The functional recurrences are solved by a variation of the kernel method, which we call the ``iterated kernel method''. This method appears to be similar to the obstinate kernel method used by Bousquet-Melou. This method requires us to consider iterated compositions of the roots of the kernel. These compositions turn out to be surprisingly tractable, and we are able to find simple explicit expressions for them. However, in spite of this, the generating functions turn out to be similar in form to Jacobi $\theta$-functions, and have natural boundaries on the unit circle.
Modern theories of galaxy formation predict that galaxies impact on their gaseous surroundings, playing the fundamental role of regulating the amount of gas converted into stars. While star-forming galaxies are believed to provide feedback through galactic winds, Quasi-Stellar Objects (QSOs) are believed instead to provide feedback through the heat generated by accretion onto a central supermassive black hole. A quantitative difference in the impact of feedback on the gaseous environments of star-forming galaxies and QSOs has not been established through direct observations. Using the Sherwood cosmological simulations, we demonstrate that measurements of neutral hydrogen in the vicinity of star-forming galaxies and QSOs during the era of peak galaxy formation show excess LyA absorption extending up to comoving radii of about 150 kpc for star-forming galaxies and 300 - 700 kpc for QSOs. Simulations including supernovae-driven winds with the wind velocity scaling like the escape velocity of the halo account for the absorption around star-forming galaxies but not QSOs.
The probabilistic investigation on record values and record times of a sequence of random variables defined on the same probability space has received much attention from 1952 to now. A great deal of such theory focused on \textit{iid} or independent real-valued random variables. There exists a few results for real-valued dependent random variables. Some papers deal also with multivariate random variables. But a large theory regarding vectors and dependent data has yet to be done. In preparation of that, the probability laws of records are investigated here, without any assumption on the dependence structure. The results are extended sequences with values in partially ordered spaces whose order is compatible with measurability. The general characterizations are checked in known cases mostly for \textit{iid} sequences. The frame is ready for undertaking a vast study of records theory in high dimensions and for types of dependence.
This review discusses the techniques used in single-dish and interferometric radiometric observations of the Sunyaev-Zel'dovich effects, the pitfalls that arise, the systematic and other sources of error in the data, and the uncertainties in the interpretation of the results.