ShantanuT01/DACTYL-Pretraining huggingface dataset:
The role of chiral transformations in effective theories modeling Quantum Chromo Dynamics is reviewed. In the context of the Nambu--Jona--Lasinio model the hidden gauge and massive Yang--Mills approaches to vector mesons are demonstrated to be linked by a special chiral transformation which removes the chiral field from the scalar--pseudoscalar sector. The role of this transformation in the presence of a topologically non--trivial chiral field is illuminated. The fermion determinant for such a field configuration is evaluated by summing the discretized eigenvalues of the Dirac Hamiltonian. This discretization is accomplished by demanding certain boundary conditions on the quark fields leaving a finite model space. The properties of two sets of boundary conditions are compared. When the topologically non-trivial chiral transformation is applied to the meson fields the associated transformation of the boundary conditions is shown to be indispensable. A constructive procedure for transforming the boundary conditions is developed.
Blazars have been regarded as one of the most powerful sources of the highest energy cosmic rays and also their byproducts, neutrinos. Provided that a magnetized filamentary system is established in a blazar jet as well, we could apply the mechanism of multi-stage diffusive shock acceleration to a feasible TeV emitter, Mrk 501 to evaluate the achievable maximum energy of protons. Taking conceivable energy restriction into account systematically, it seems adequate to say that EeV-protons are produced at this site by our present model. We also estimate neutrino fluxes generated by these accelerated protons and discuss the detectability based on an updated kilometre-scale telescope such as IceCube.
Providing an improved technique which can assist pathologists in correctly classifying meningioma tumours with a significant accuracy is our main objective. The proposed technique, which is based on optimum texture measure combination, inspects the separability of the RGB colour channels and selects the channel which best segments the cell nuclei of the histopathological images. The morphological gradient was applied to extract the region of interest for each subtype and for elimination of possible noise (e.g. cracks) which might occur during biopsy preparation. Meningioma texture features are extracted by four different texture measures (two model-based and two statistical-based) and then corresponding features are fused together in different combinations after excluding highly correlated features, and a Bayesian classifier was used for meningioma subtype discrimination. The combined Gaussian Markov random field and run-length matrix texture measures outperformed all other combinations in terms of quantitatively characterising the meningioma tissue, achieving an overall classification accuracy of 92.50%, improving from 83.75% which is the best accuracy achieved if the texture measures are used individually.
Phenomenological functions $\Sigma$ and $\mu$, also known as $G_{\rm light}/G$ and $G_{\rm matter}/G$, are commonly used to parameterize modifications of the growth of large-scale structure in alternative theories of gravity. We study the values these functions can take in Horndeski theories, i.e. the class of scalar-tensor theories with second order equations of motion. We restrict our attention to models that are in a broad agreement with tests of gravity and the observed cosmic expansion history. In particular, we require the speed of gravity to be equal to the speed of light today, as required by the recent detection of gravitational waves and electromagnetic emission from a binary neutron star merger. We examine the correlations between the values of $\Sigma$ and $\mu$ analytically within the quasi-static approximation, and numerically, by sampling the space of allowed solutions. We confirm that the conjecture made in [Pogosian:2016pwr], that $(\Sigma-1)(\mu -1) \ge 0$ in viable Horndeski theories, holds very well. Along with that, we check the validity of the quasi-static approximation within different corners of Horndeski theory. Our results show that, even with the tight bound on the present day speed of gravitational waves, there is room within Horndeski theories for non-trivial signatures of modified gravity at the level of linear perturbations.
A $d$-angulation is a planar map with faces of degree $d$. We present for each integer $d\geq 3$ a bijection between the class of $d$-angulations of girth $d$ (i.e., with no cycle of length less than $d$) and a class of decorated plane trees. Each of the bijections is obtained by specializing a "master bijection" which extends an earlier construction of the first author. Our construction unifies known bijections by Fusy, Poulalhon and Schaeffer for triangulations ($d=3$) and by Schaeffer for quadrangulations ($d=4$). For $d\geq 5$, both the bijections and the enumerative results are new. We also extend our bijections so as to enumerate \emph{$p$-gonal $d$-angulations} ($d$-angulations with a simple boundary of length $p$) of girth $d$. We thereby recover bijectively the results of Brown for simple $p$-gonal triangulations and simple $2p$-gonal quadrangulations and establish new results for $d\geq 5$. A key ingredient in our proofs is a class of orientations characterizing $d$-angulations of girth $d$. Earlier results by Schnyder and by De Fraysseix and Ossona de Mendez showed that simple triangulations and simple quadrangulations are characterized by the existence of orientations having respectively indegree 3 and 2 at each inner vertex. We extend this characterization by showing that a $d$-angulation has girth $d$ if and only if the graph obtained by duplicating each edge $d-2$ times admits an orientation having indegree $d$ at each inner vertex.
A class of scattered linearized polynomials covering infinitely many field extensions is exhibited. More precisely, the $q$-polynomial over $\mathbb F_{q^6}$, $q \equiv 1\pmod 4$ described in arXiv:1906.05611, arXiv:1910.02278 is generalized for any even $n\ge6$ to an $\mathbb F_q$-linear automorphism $\psi(x)$ of $\mathbb F_q^n$ of order $n$. Such $\psi(x)$ and some functional powers of it are proved to be scattered. In particular this provides new maximum scattered linear sets of the projective line $\mathrm{PG}(1,q^n)$ for $n=8,10$. The polynomials described in this paper lead to a new infinite family of MRD-codes in $\mathbb F_q^{n\times n}$ with minimum distance $n-1$ for any odd $q$ if $n\equiv0\pmod4$ and any $q\equiv1\pmod4$ if $n\equiv2\pmod4$.
The Coma cluster is the nearest massive ($M \gtrsim 10^{15}\,\mathrm{M_\odot}$) galaxy cluster, making it an excellent laboratory to probe the influence of the cluster environment on galaxy star formation. Here, we present a sample of 41 galaxies with disturbed morphologies consistent with ram pressure stripping. These galaxies are identified visually using high-quality, multi-band imaging from the Canada-France-Hawaii telescope covering ~9 $\mathrm{deg^2}$ of the Coma cluster. These "stripping candidates" are clear outliers in common quantitative morphological measures, such as concentration-asymmetry and Gini-$M_{20}$, confirming their disturbed nature. Based on the orientations of observed asymmetries, as well as the galaxy positions in projected phase-space, these candidates are consistent with galaxies being stripped shortly after infall onto the Coma cluster. Finally, the stripping candidates show enhanced star formation rates, both relative to "normal" star-forming Coma galaxies and isolated galaxies in the field. Ram pressure is likely driving an enhancement in star formation during the stripping phase, prior to quenching. On the whole, ram pressure stripping appears to be ubiquitous across all regions of the Coma cluster.
Kohn-Sham (KS) density functional theory (DFT) is a very efficient method for calculating various properties of solids as, for instance, the total energy, the electron density, or the electronic band structure. The KS-DFT method leads to rather fast calculations, however the accuracy depends crucially on the chosen approximation for the exchange and correlation (xc) functional $E_{\text{xc}}$ and/or potential $v_{\text{xc}}$. Here, an overview of xc methods to calculate the electronic band structure is given, with the focus on the so-called semilocal methods that are the fastest in KS-DFT and allow to treat systems containing up to thousands of atoms. Among them, there is the modified Becke-Johnson potential that is widely used to calculate the fundamental band gap of semiconductors and insulators. The accuracy for other properties like the magnetic moment or the electron density, that are also determined directly by $v_{\text{xc}}$, is also discussed.
Recently Barrow, and Tsagas [Phys Rev D 77: 107302, (2008)] have shown that slow decay of cosmological magnetic slowly decay in FRW universes on curvature scales as $B\sim{a^{-1}}$ in the context of general relativity (GR). This helps possible amplification of cosmic magnetic fields. In this paper starting from dynamo equations in spacetimes with torsion we obtain also slow decay of magnetic fields naturally on curvature-torsion scales of Riemann-Cartan spacetime on a de Sitter universe. In this case the constant of proportionality between the magnetic field and the curvature scale is the torsion in the present universe. Thus the B-field becomes $B\sim{\frac{{\eta}}{H_{0}}Ta^{-1}}$ where T is torsion vector modulus, $H_{0}$ is the Hubble constant and $\eta$ is the diffusive scale.
Magneto-curvature stresses could deform magnetic field lines and this would give rise to back reaction and restoring magnetic stresses [Tsagas, PRL (2001)]. Barrow et al [PRD (2008)] have shown in Friedman universe the expansion to be slow down in spatial section of negative Riemann curvatures.   From Chicone et al [CMP (1997)] paper, proved that fast dynamos in compact 2D manifold implies negatively constant Riemannian curvature, here one applies the Barrow-Tsagas ideas to cosmic dynamos. Fast dynamo covariant stretching of Riemann slices of cosmic Lobachevsky plane is given. Inclusion of advection term on dynamo equations [Clarkson et al, MNRAS (2005)] is considered. In absence of advection a fast dynamo is also obtained. Viscous and restoring forces on stretching particles decrease, as magnetic rates increase. From COBE data ($\frac{{\delta}B}{B}\approx{10^{-5}}$), one computes stretching $\frac{{\delta}V^{y}}{V^{y}}=1.5\frac{{\delta}B}{B}\approx{1.5{\times}10^{-5}}$. Zeldovich et al has computed the maximum magnetic growth rate as ${\gamma}_{max}\approx{8.0{\times}10^{-1}t^{-1}}$. From COBE data one computes a lower growth rate for the magnetic field as ${\gamma}_{COBE}\approx{6.0{\times}10^{-6}t^{-1}}$, well-within Zeldovich et al estimate. Instead of the Harrison value $B\approx{t^{{4/3}}}$ one obtains the lower primordial field $B\approx{10^{-6}t}$ which yields the $B\approx{10^{-6}G}$ at the $1s$ Big Bang time.
We analyze the distribution of PageRank on a directed configuration model and show that as the size of the graph grows to infinity it can be closely approximated by the PageRank of the root node of an appropriately constructed tree. This tree approximation is in turn related to the solution of a linear stochastic fixed point equation that has been thoroughly studied in the recent literature.
Galactic cosmic rays are believed to be accelerated at supernova remnant shocks. Though very popular and robust, this conjecture still needs a conclusive proof. The strongest support to this idea is probably the fact that supernova remnants are observed in gamma-rays, which are indeed expected as the result of the hadronic interactions between the cosmic rays accelerated at the shock and the ambient gas. However, also leptonic processes can, in most cases, explain the observed gamma-ray emission. This implies that the detections in gamma rays do not necessarily mean that supernova remnants accelerate cosmic ray protons. To overcome this degeneracy, the multi-wavelength emission (from radio to gamma rays) from individual supernova remnants has been studied and in a few cases it has been possible to ascribe the gamma-ray emission to one of the two processes (hadronic or leptonic). Here we adopt a different approach and, instead of a case-by-case study we aim for a population study and we compute the number of supernova remnants which are expected to be seen in TeV gamma rays above a given flux under the assumption that these objects indeed are the sources of cosmic rays. The predictions found here match well with current observational results, thus providing a novel consistency check for the supernova remnant paradigm for the origin of galactic cosmic rays. Moreover, hints are presented for the fact that particle spectra significantly steeper than E^-2 are produced at supernova remnants. Finally, we expect that several of the supernova remnants detected by H.E.S.S. in the survey of the galactic plane should exhibit a gamma-ray emission dominated by hadronic processes (i.e. neutral pion decay). The fraction of the detected remnants for which the leptonic emission dominates over the hadronic one depends on the assumed values of the physical parameters and can be as high as roughly a half.
We present 6 cm Very Large Array observations of the Greene & Ho (2004) sample of 19 low-mass active galaxies with high accretion rates. This is one of the only studies of a uniform sample of narrow-line Seyfert 1 (NLS1) galaxies with such high sensitivity and resolution. Although we detect only one source, the entire sample is very radio-quiet down to strong limits. GH10 was found to have a radio power of 8.5 x 10^21 W/Hz, and a ratio R = f(6 cm)/f(4400 A) of 2.8. The 3 sigma upper limits for the remaining nondetections correspond to radio powers from 3 x 10^20 to 8 x 10^21 W/Hz and 0.47 < R <9.9. Stacking all nondetections yields an even stronger upper limit of R < 0.27. An assessment of existing observations in the literature confirms our finding that NLS1s are consistently radio-quiet, with a radio-loud fraction of 0%-6%, which is significantly lower than the 10%-20% observed in the general quasar population. By analogy with stellar-mass black holes, we argue that AGNs undergo a state transition at L_bol/L_Edd~0.01. Below this value a radiatively inefficient accretion flow effectively drives an outflow, which disappears when the flow turns into an optically thick, geometrically thin disk, or a radiation pressure-dominated slim disk at still higher L_bol/L_Edd.
One aspect of Chebyshev's bias is the phenomenon that a prime number, $ q $, modulo another prime number, $ p$, experimentally seems to be slightly more likely to be a nonquadratic residue than a quadratic residue. We thought it would be interesting to model this residue bias as a "random" walk using Legendre symbol values as steps. Such a model would allow us to easily visualize the bias. In addition, we would be able to extend our model to other number fields.   In this report, we first outline underlying theory and some motivations for our research. In the second section, we present our findings in the rational prime numbers. We found evidence that Chebyshev's bias, if modeled as a Legendre symbol $ \left(\frac{q}{p}\right)$ walk, may be somewhat reduced by only allowing $ q$ to iterate over primes with nonquadratic residue (mod $ 4$). In the final section, we extend our Legendre symbol walks to the Gaussian primes and present our main findings. Let $ \pi_1 = \alpha+\beta i$ and $ \pi_2 = \beta+\alpha i$. We observed strong ($ \pm$) correlations between Gaussian Legendre symbol walks for $ \left[\frac{a+bi}{\pi_1}\right]$ and $ \left[\frac{a+bi}{\pi_2}\right]$ where $ N(\pi_1) = N(\pi_2)$ and $ a+bi$ iterates over Gaussian primes in the first quadrant. We attempt an explanation of why, for some norms, the plots for $ \pi_1$ and $ \pi_2$ have strong positive correlation, while, for other norms, the plots have strong negative correlation. We hope to have written in a way that makes our observations accessible to readers without prior formal training in number theory.
Cross-section and neutron-emission data from heavy-ion fusion-fission reactions are consistent with the fission of fully equilibrated systems with fission lifetime estimates obtained via a Kramers-modified statistical model which takes into account the collective motion of the system about the ground state, the temperature dependence of the location and height of fission transition points, and the orientation degree of freedom. If the standard techniques for calculating fission lifetimes are used, then the calculated excitation-energy dependence of fission lifetimes is incorrect. We see no evidence to suggest that the nuclear viscosity has a temperature dependence. The strong increase in the nuclear viscosity above a temperature of approximately 1.3 MeV deduced by others is an artifact generated by an inadequate fission model.
Launched on the 11th of June 2008, the Fermi Large Area Telescope (LAT) has made several outstanding scientific contributions to the high energy astrophysics community. One of these contributions was the high statistics measurement of the Galactic Cosmic Ray (GCR) electron + positron spectrum from 20 GeV to 1 TeV. The Fermi satellite is in a nearly circular orbit with an inclination of 25.6 degrees at an altitude of 565 km. Given this orbit it is possible to measure the GCR electrons + positrons down to roughly 5 GeV. However, this lower limit in energy is highly dependent on the orbital position of the LAT in geomagnetic coordinates due to the rigidity cutoff. In order to measure the spectrum down to these energies it is necessary to sample the population of electrons + positrons in several different geomagnetic positions. In this poster we present the analysis performed to extend the lower limit in energy of the GCR electron + positron spectrum measured by the Fermi LAT.
We consider $K^-$ nucleon elastic and inelastic scattering in isospin symmetric nuclear matter. It is found that the proper description of the $\Lambda(1405)$ resonance structure in nuclear matter requires a self-consistent approach. Then the $\Lambda (1405) $ resonance mass remains basically unchanged, however, the resonance acquires an increased decay width as nuclear matter is compressed. The elastic and inelastic scattering amplitudes show important medium modifications close to the kaon nucleon threshold. We also construct the $K^-$-nuclear optical potential appropriate for $K^-$ atoms. Our microscopic approach predicts a strong attractive non-local interaction strength.
A Monte Carlo program is presented for the computation of the most general cross section for two-photon production in e+e- collisions at fixed two-photon invariant mass W. Functions implemented for the five gamma* gamma* structure functions include three models of the total hadronic cross section and the lepton-pair production cross section. Prospects of a structure-function determination through a study of the azimuthal dependence between the two scattering planes are outlined. All dependences on the electron mass and the photon virtualities Q_i^2 are fully kept. Special emphasis is put on a numerically stable evaluation of all variables over the full Q_i^2 range from Q_{i\min}^2 \sim m_e^2 (W/\sqrt{s})^4 \ll m_e^2 up to Q_{i\max}^2 \sim s. A comparison is made with an existing Monte Carlo program for lepton-pair production and an equivalent-photon approximation for hadronic cross sections.
Mean field methods to calculate the nuclear mass are extended into the high spin regime to calculate the nuclear binding energy as a function of proton number, neutron number and angular momentum. Comparing the trend as a function of mass number for a selection of high-spin states, a similar agreement between theory and experiment is obtained as for ground state masses.
Recently, the possibility of an all electrical scheme of preparation and readout for a single spin state in a single quantum dot attached to spin biased leads has been shown [F. Chi et al., Phys. Rev. B 81, 075310 (2010)]. However, spin scattering mechanisms have been omitted. To remedy this lack we consider the influence of the spin-flip scattering process on the proposed preparation and readout scheme.
This paper proves that the $\mathbb{U}$-operator attached to a cocharacter is a right root of the corresponding Hecke polynomial. This result is an important ingredient in the proof of (i) the horizontal norm relations in the context of Gross--Gan--Prasad cycles and of (ii) the generalization of Eichler--Shimura relations.
It was generally assumed that weak van der Waals interactions exist between neighboring layers in the two-dimensional group-IV chalcogenides. Using PbSe as a prototypal example, however, we find additional strong coupling between the Pb-Pb layers, as evidenced by detailed analysis of the differential charge density. The coupling resembles covalent-like bond and exhibits strong harmonicity around the equilibrium distance, which can be fine tuned to obviously reduce the phonon thermal conductivity but slightly change the electronic transport of PbSe. As a consequence, a maximum ZT value of 2.5 can be realized at 900 K for the p-type system. Our work offers an effective and feasible design strategy to enhance the thermoelectric performance of similar layered structures.
We compare and validate COLA (COmoving Lagrangian Acceleration) simulations against existing emulators in the literature, namely Bacco and Euclid Emulator 2. Our analysis focuses on the non-linear response function, i.e., the ratio between the non-linear dark matter power spectrum in a given cosmology with respect to a pre-defined reference cosmology, which is chosen to be the Euclid Emulator 2 reference cosmology in this paper. We vary three cosmological parameters, the total matter density, the amplitude of the primordial scalar perturbations and the spectral index. By comparing the COLA non-linear response function with those computed from each emulator in the redshift range $0 \leq z \leq 3$, we find that the COLA method is in excellent agreement with the two emulators for scales up to $k \sim 1 \ h$/Mpc as long as the deviations of the matter power spectrum from the reference cosmology are not too large. We validate the implementation of massive neutrinos in our COLA simulations by varying the sum of neutrino masses to three different values, $0.0$ eV, $0.058$ eV and $0.15$ eV. We show that all three non-linear prescriptions used in this work agree at the $1\%$ level at $k \leq 1 \ h$/Mpc. We then introduce the Effective Field Theory of Dark Energy in our COLA simulations using the $N$-body gauge method. We consider two different modified gravity models in which the growth of structure is enhanced or suppressed at small scales, and show that the response function with respect to the change of modified gravity parameters depends weakly on cosmological parameters in these models.
It is proved that a three-dimensional double cone is a birationally rigid variety. We also compute the group of birational automorphisms of such a variety. This work is based on the method of "untwisting" maximal singularities of linear system.
We study resonance behavior of a two-dimensional fully frustrated Josephson-junction array driven by high alternating currents. The signal-to-noise ratio (SNR) is examined as the frequency of the driving current is varied; revealed is a certain frequency range where the SNR is enhanced. Such resonance behavior is explained by considering the dynamic order parameter at zero temperature. We also compute the work, which corresponds to the Ohmic dissipation of the energy due to external currents, and discuss its possibility as a measure of stochastic resonance.