ShantanuT01/DACTYL-Pretraining huggingface dataset:
We propose a possible explanation of the recent diphoton excess reported by ATLAS and CMS collaborations, at around 750 GeV diphoton invariant mass, within the framework of $E_{6}$ motivated Alternative Left-Right Symmetric Model (ALRSM), which is capable of addressing the $B$ decay anomalies in the flavor sector, the $eejj$ and $e$ missing $p_{T}jj$ excesses reported by CMS in run 1 of LHC and has the feature of high scale leptogenesis. We find that gluon-gluon fusion can give the observed production rate of the 750 GeV resonance, $\tilde{n}$, through a loop of scalar leptoquarks ($\tilde{h}^{(c)}$) with mass below a few TeV range, while $\tilde{n}$ can subsequently decay into $\gamma\gamma$ final state via loops of $\tilde{h}^{(c)}$ and $\tilde{E}^{(c)}$. Interestingly, the $\tilde{E}^{(c)}$ loop can enhance the diphoton branching ratio significantly to successfully explain the observed cross section of the diphoton signal.
The behavior of the most probable values of the order parameter $x$ and the amplitude $\phi$ of conjugate force fluctuations is studied for a stochastic system with a colored multiplicative noise with absorbing states. The phase diagrams introduced as dependencies the noise self-correlation time vs temperature and noise growth velocity are defined. It is shown that phase half-plane $(x,\phi)$ can be split into isolated domains of large, intermediate, and small values of $x$. System behavior in these domains is studied by the probability represented as path integral. In the region $x\ll 1$, the trajectories converge to the point $x = \phi = 0$ for $0 < a < 1/2$ and to $x = 0$, $\phi\to\infty$ for $1/2 < a \le 1$. In the former case, the probability of realization of trajectories is finite, while in the latter case it is vanishingly small, and an absorbing state can be formed.
Contopoulos 2019 proposed that a dissipation zone develops in the magnetosphere of young pulsars at the edge of the closed-line region beyond the light cylinder. This is necessary in order to supply the charge carriers that will establish current closure through the equatorial and separatrix current-sheets. In the present work, we propose to investigate in greater detail this region with a simplified model that we would like to call the `ring-of-fire'. According to this simple model, the dissipation zone is a narrow reconnection layer where electrons and positrons are accelerated inwards and outwards respectively along Speiser orbits that are deflected in the azimuthal direction by the pulsar rotation. After they exit the reconnection layer, the accelerated positrons form the positively charged equatorial current-sheet, and the accelerated electrons form the negatively charged separatrix current-sheet along the boundary of the closed-line region. During their acceleration, particles lose only a small part of their energy to radiation. Most of their energy is lost outside the dissipation region, in the equatorial and separatrix current sheets. Our simple model allows us to obtain high-energy spectra and efficiencies. The radiation emitted by the positrons in the equatorial current-sheet forms a very-high energy tail that extends up to the TeV range.
We study the problem of writing Gaussian primes as the sum of two squares, both of which are interesting arithmetically, in particular, when one is the square of a prime and the other the square of an almost-prime.
We study the model of random permutations of $n$ objects with polynomially growing cycle weights, which was recently considered by Ercolani and Ueltschi, among others. Using saddle-point analysis, we prove that the total variation distance between the process which counts the cycles of size $1, 2, ..., b$ and a process $(Z_1, Z_2, ..., Z_b)$ of independent Poisson random variables converges to $0$ if and only if $b=o(\ell)$ where $\ell$ denotes the length of a typical cycle in this model. By means of this result, we prove a central limit theorem for the order of a permutation and thus extend the Erd\H{o}s-Tur\'an Law to this measure. Furthermore, we prove a Brownian motion limit theorem for the small cycles.
We address the intervention of classical-like behavior, well documented in experimental studies of strongly correlated electron systems of solids that emerges at temperatures $T$ far below the Debye temperature $T_D$. We attribute this unexpected phenomenon to spontaneous rearrangement of the conventional Landau state beyond a critical point at which the topological stability of this state breaks down, leading to the formation of an interaction-induced flat band adjacent to the nominal Fermi surface. We demonstrate that beyond the critical point, the quasiparticle picture of such correlated Fermi systems still holds, since the damping of single-particle excitations remains small compared with the Fermi energy $T_F=p^2_F/2m_e$. A Pitaevskii-style equation for determination of the rearranged quasiparticle momentum distribution $n_*({\bf p})$ is derived, which applies to explanation of the linear-in-$T$ behavior of the resistivity $\rho(T)$ found experimentally.
The primitive equations (PEs) model large scale dynamics of the oceans and the atmosphere. While it is by now well-known that the three-dimensional viscous PEs is globally well-posed in Sobolev spaces, and that there are solutions to the inviscid PEs (also called the hydrostatic Euler equations) that develop singularities in finite time, the qualitative description of the blowup still remains undiscovered. In this paper, we provide a full description of two blowup mechanisms, for a reduced PDE that is satisfied by a class of particular solutions to the PEs. In the first one a shock forms, and pressure effects are subleading, but in a critical way: they localize the singularity closer and closer to the boundary near the blow-up time (with a logarithmic in time law). This first mechanism involves a smooth blow-up profile and is stable among smooth enough solutions. In the second one the pressure effects are fully negligible; this dynamics involves a two-parameters family of non-smooth profiles, and is stable only by smoother perturbations.
In this paper, a new method based on probability generating functions is used to obtain multiple Stein operators for various random variables closely related to Poisson, binomial and negative binomial distributions. Also, Stein operators for certain compound distributions, where the random summand satisfies Panjer's recurrence relation, are derived. A well-known perturbation approach for Stein's method is used to obtain total variation bounds for the distributions mentioned above. The importance of such approximations is illustrated, for example, by the binomial convoluted with Poisson approximation to sums of independent and dependent indicator random variables.
In this manuscript we consider a porous medium equation with non-local diffusion effects given by a fractional heat operator $\partial_t + (-\Delta)^s$ in two space dimensions. Global in time existence of weak solutions is shown by employing a time semi-discretization of the equations, an energy inequality, a higher order integral estimate, and a generalized version of the Div-Curl lemma.
Quantum criticality of the spin-1/2 ferromagnetic-leg ladder 3-I-V [=3-(3-iodophenyl)-1,5-diphenylverdazyl] has been examined with respect to the antiferromagnetic to paramagnetic phase transition near the saturation field $H_{c}$. The phase boundary $T_{c}(H)$ follows the power-law $T_{c}(H)\propto H_{c}-H$ for a wide temperature range. This characteristic behavior is discussed as a quasi-one-dimensional (quasi-1D) Bose-Einstein condensation, which is predicted theoretically for weakly coupled quasi-1D ferromagnets. Thus, 3-I-V provides the first promising candidate for this attractive prediction.
Organic charge transfer salts based on the molecule Pd(dmit)2 display strong electronic correlations and geometrical frustration, leading to spin liquid, valence bond solid, and superconducting states, amongst other interesting phases. The low energy electronic degrees of freedom of these materials are often described by a single band model; a triangular lattice with a molecular orbital representing a Pd(dmit)2 dimer on each site. We use ab initio electronic structure calculations to construct and parametrize low energy effective model Hamiltonians for a class of Me(4-n) EtnX[Pd(dmit)2]2 (X=As,P,N,Sb) salts and investigate how best to model these systems by using variational Monte Carlo (VMC) simulations. Our findings suggest that the prevailing model of these systems as a t-t' triangular lattice is incomplete, and that a fully anisotropic triangular lattice (FATL) description produces importantly different results, including a significant lowering of the critical U of the spin-liquid phase.
We introduce the notion of a task-oriented maximally entangled state (TMES). This notion depends on the tasks for which a quantum state is used as the resource. This concept may be more fruitful than that of a general maximally entangled state in the case of a multipartite system. We illustrate this idea by giving an operational definition of maximally entangled states on the basis of communication tasks of teleportation and superdense coding. We also give examples and a procedure to obtain such TMESs for {\em n}-qubit systems.
In nuclear fusion and fission, fluctuation and dissipation arise due to the coupling of collective degrees of freedom with internal excitations. Close to the barrier, both quantum, statistical and non-Markovian effects are expected to be important. In this work, a new approach based on quantum Monte-Carlo addressing this problem is presented. The exact dynamics of a system coupled to an environment is replaced by a set of stochastic evolutions of the system density. The quantum Monte-Carlo method is applied to systems with quadratic potentials. In all range of temperature and coupling, the stochastic method matches the exact evolution showing that non-Markovian effects can be simulated accurately. A comparison with other theories like Nakajima-Zwanzig or Time-ConvolutionLess ones shows that only the latter can be competitive if the expansion in terms of coupling constant is made at least to fourth order. A systematic study of the inverted parabola case is made at different temperatures and coupling constants. The asymptotic passing probability is estimated in different approaches including the Markovian limit. Large differences with the exact result are seen in the latter case or when only second order in the coupling strength is considered as it is generally assumed in nuclear transport models. On opposite, if fourth order in the coupling or quantum Monte-Carlo method is used, a perfect agreement is obtained.
We describe a systematic way of computing the 't Hooft anomalies for continuous symmetries of Quantum Field Theories in even dimensions that can be geometrically engineered from M5-branes. Our approach is based on anomaly inflow, and characterizes the anomaly polynomial of the QFT in terms of the geometric definition of the field theory. In particular, when the QFT admits a holographic dual, the topological data of the solution is sufficient to compute the anomalies of the dual field theory, including finite terms in $N$. We study several classes of examples in four and six dimensions, with or without known M5-brane probe configurations.
Nowdays, multiferroic materials with magnetoelectric coupling have many real-world applications in the fields of novel memory devices. It is challenging is to create multiferroic materials with strongly coupled ferroelectric and ferrimagnetic orderings at room temperature. The single crystal of ferric selenide (Fe3Se4) shows type-II multiferroic due to the coexistence of ferroelectric as well as magnetic ordering at room temperature. We have investigated the lattice instability, electronic structure, ferroelectric, ferrimagnetic ordering and transport properties of ferroelectric metal Fe3Se4. The density of states shows considerable hybridization of Fe-3d and Se-4p states near the Fermi level confirming its metallic behavior. The magnetic moments of Fe cations follow a type-II ferrimagnetic and ferroelectric ordering with a calculated total magnetic moment of 4.25 per unit cell (Fe6Se8). The strong covalent bonding nature of Fe-Se leads to its ferroelectric properties. In addition, the symmetry analysis suggests that tilting of Fe sub-lattice with 3d-t2g orbital ordering is due to the Jahn-Teller (JT) distortion. This study provides further insight in the development of spintronics related technology using multiferroic materials.
In the framework of the effective field theory method, we use the experimental data and the perturbative unitarity bounds to determine the values and uncertainty of all the 11 chiral coefficients ($\al_i, i=0, ..., 10$) of the standard electroweak chiral Lagrangian. Up to linear terms in $\al_i$, we provide the one-loop renormalization group equations of all the chiral coefficients, which are calculated in the Feynman-'t Hooft gauge using the modified minimal subtraction scheme. With the improved renormalization group equations to sum over the logarithmic corrections, we analyze the current experimental uncertainty of oblique correction parameters, $S(\Lambda)$ and $T(\Lambda)$. We find that, due to the large uncertainty in the triple gauge-boson coupling measurements, the parameter space of positive $S(\Lambda)$ for $\Lambda > 1$ TeV is still allowed by the current experimental data. $T(\Lambda)$ tends to increase with $\Lambda$ even in the presence of the operators that contribute to the triple and quartic gauge-boson couplings.
We show that the variance of centred linear statistics of eigenvalues of GUE matrices remains bounded for large $n$ for some classes of test functions less regular than Lipschitz functions. This observation is suggested by the limiting form of the variance (which has previously been computed explicitly), but it does not seem to appear in the literature. We combine this fact with comparison techniques following Tao-Vu and Erd\"os, Yau, et al. and a Littlewood-Paley type decomposition to extend the central limit theorem for linear eigenvalue statistics to functions in the H\"older class $C^{1/2+\epsilon}$ in the case of matrices of Gaussian convolution type. We also give a variance bound which implies the CLT for test functions in the Sobolev space $H^{1+\epsilon}$ and $C^{1-\epsilon}$ for general Wigner matrices satisfying moment conditions. Previous results on the CLT impose the existence and continuity of at least one classical derivative.
On-road obstacle detection is an important field of research that falls in the scope of intelligent transportation infrastructure systems. The use of vision-based approaches results in an accurate and cost-effective solution to such systems. In this research paper, we propose a threat detection mechanism for autonomous self-driving cars using dashcam videos to ensure the presence of any unwanted obstacle on the road that falls within its visual range. This information can assist the vehicle's program to en route safely. There are four major components, namely, YOLO to identify the objects, advanced lane detection algorithm, multi regression model to measure the distance of the object from the camera, the two-second rule for measuring the safety, and limiting speed. In addition, we have used the Car Crash Dataset(CCD) for calculating the accuracy of the model. The YOLO algorithm gives an accuracy of around 93%. The final accuracy of our proposed Threat Detection Model (TDM) is 82.65%.
We prove that the facial nonrepetitive chromatic number of any outerplanar graph is at most 11 and of any planar graph is at most 22.
A complete characterization of the set of states that can be achieved through Thermal Processes (TP) is given by describing all vertices, edges and facets of the allowed set of states in the language of thermomajorization curves. TPs are linked to transportation matrices, which leads to the existance of extremal TPs that are not required in implemenation of any transition allowed by TPs, for every dimension $d\geq 4$ of the state space. A property of the associated graphs, biplanarity, which differentiates between these extremal TPs and the necessary ones, is identified.
We correct an error in our paper Phys. Rev. B 72, 104404 (2005) [cond-mat/0502215]. We show that a particular fermion bilinear is not related to the other ``competing orders'' of the algebraic spin liquid, and does not possess their slowly decaying correlations. For the square lattice staggered flux spin liquid (equivalently, d-wave RVB state), this observable corresponds to the uniform spin chirality.
We show that for a transitive unimodular graph, the number of ends is the same for every tree of the free minimal spanning forest. This answers a question of Lyons, Peres and Schramm.
We investigate the incompressible Navier-Stokes equations with variable density. The aim is to prove existence and uniqueness results in the case of discontinuous ini- tial density. In dimension n = 2, 3, assuming only that the initial density is bounded and bounded away from zero, and that the initial velocity is smooth enough, we get the local-in-time existence of unique solutions. Uniqueness holds in any dimension and for a wider class of velocity fields. Let us emphasize that all those results are true for piecewise constant densities with arbitrarily large jumps. Global results are established in dimension two if the density is close enough to a positive constant, and in n-dimension if, in addition, the initial velocity is small. The Lagrangian formula- tion for describing the flow plays a key role in the analysis that is proposed in the present paper.
The presence of A/F-type {\it Kepler} hybrid stars extending across the entire $\delta$ Sct-$\gamma$ Dor instability strips and beyond remains largely unexplained. In order to better understand these particular stars, we performed a multi-epoch spectroscopic study of 49 candidate A/F-type hybrid stars and one cool(er) hybrid object detected by the {\it Kepler} mission. We determined a lower limit of 27 % for the multiplicity fraction. For six spectroscopic systems, we also reported long-term variations of the time delays. For four systems, the time delay variations are fully coherent with those of the radial velocities and can be attributed to orbital motion. We aim to improve the orbital solutions for those systems with long orbital periods (order of 4-6 years) among the {\it Kepler} hybrid stars. The orbits are computed based on a simultaneous modelling of the RVs obtained with high-resolution spectrographs and the photometric time delays derived from time-dependent frequency analyses of the {\it Kepler} light curves. We refined the orbital solutions of four spectroscopic systems with A/F-type {\it Kepler} hybrid component stars: KIC 4480321, 5219533, 8975515 and KIC 9775454. Simultaneous modelling of both data types analysed together enabled us to improve the orbital solutions, obtain more robust and accurate information on the mass ratio, and identify the component with the short-period $\delta$ Sct-type pulsations. In several cases, we were also able to derive new constraints for the minimum component masses. From a search for regular frequency patterns in the high-frequency regime of the Fourier transforms of each system, we found no evidence of tidal splitting among the triple systems with close (inner) companions. However, some systems exhibit frequency spacings which can be explained by the mechanism of rotational splitting.
We present new Spitzer Space Telescope observations of the region NGC 2467, and use these observations to determine how the environment of an HII region affects the process of star formation. Our observations comprise IRAC (3.6, 4.5, 5.8, and 8.0 um) and MIPS (24 um) maps of the region, covering approximately 400 square arcminutes. The images show a region of ionized gas pushing out into the surrounding molecular cloud, powered by an O6V star and two clusters of massive stars in the region. We have identified as candidate Young Stellar Objects (YSOs) 45 sources in NGC 2467 with infrared excesses in at least two mid-infrared colors. We have constructed color-color diagrams of these sources and have quantified their spatial distribution within the region. We find that the YSOs are not randomly distributed in NGC 2467; rather, over 75% of the sources are distributed at the edge of the HII region, along ionization fronts driven by the nearby massive stars. The high fraction of YSOs in NGC 2467 that are found in proximity to gas that has been compressed by ionization fronts supports the hypothesis that a significant fraction of the star formation in NGC 2467 is triggered by the massive stars and the expansion of the HII region. At the current rate of star formation, we estimate at least 25-50% of the total population of YSOs formed by this process.
First-principles dynamical CPA (Coherent-Potential Approximation) for electron correlations has been developed further by taking into account higher-order dynamical corrections with use of the asymptotic approximation. The theory is applied to the investigations of a systematic change of excitation spectra in $3d$ transition metals from Sc to Cu at finite temperatures. It is shown that the dynamical effects damp main peaks in the densities of states (DOS) obtained by the local density approximation to the density functional theory, reduce the band broadening due to thermal spin fluctuations, create the Mott-Hubbard type bands in the case of fcc Mn and fcc Fe, and create a small hump corresponding to the `6 eV' satellite in the case of Co, Ni, and Cu. Calculated DOS explain the X-ray photoelectron spectroscopy data as well as the bremsstrahlung isochromat spectroscopy data. Moreover, it is found that screening effects on the exchange energy parameters are significant for understanding the spectra in magnetic transition metals.
The T^2 coefficient of electrical resistivity, A, is compared with the electronic specific-heat coefficient, \gamma, for a number of Yb-based compounds. It is revealed that many systems including YbCuAl, YbInCu4, YbAl3 and YbCu5 show A/\gamma^2 values close to 0.4*10^{-6} \mu\Omega cm(mol K/mJ)^2, which is remarkably smaller than that known as the Kadowaki-Woods relation, A/\gamma^2 = 1.0*10^{-5} \mu\Omega cm(mol K/mJ)^2. Empirically, the compounds with the smaller A/\gamma^2 values appear to show weak intersite magnetic-correlation and/or to have almost fully-degenerated (J = 5/2 or 7/2) ground states.
We show, for several fake projective planes with nontrivial automorphism group, that the bicanonical map is an embedding.
Arguments against the traditional Yukawa-type approach to $NN$ intermediate- and short-range interaction due to scalar-isoscalar meson exchange are presented. Instead of the Yukawa mechanism for intermediate-range attraction some new approach based on formation of the symmetric six-quark bag in the state $|(0s)^6[6]_X,L=0>$ dressed due to strong coupling to $\pi$, $\sigma$ and $\rho$ fields are suggested. These new mechanism offers a strong intermediate-range attraction which replaces the effective $\sigma$-exchange (or excitation of two isobars in the intermediate state) in traditional force models. A similar mechanism with vector $\rho$-meson production in the intermediate six-quark state is expected to lead to a strong short-range spin-orbital nonlocal interaction in the $NN$ system, which may resolve the long-standing puzzle of the spin-orbit force in baryons and in two-baryon systems. Illustrative examples are developed which demonstrate clearly how well the suggested new model can reproduce $NN$ data. Strong interrelations have been shown to exist between the proposed microscopic model and the one-component Moscow $NN$ potential developed by the authors previously and also with some hybrid models and the one-term separable Tabakin potential. The new implications of the proposed model for nuclear physics are discussed.