ShantanuT01/DACTYL-Pretraining huggingface dataset:
We develop a method to search for pair halos around active galactic nuclei (AGN) through a temporal analysis of gamma-ray data. The basis of our method is an analysis of the spatial distributions of photons coming from AGN flares and from AGN quiescent states and a further comparison of these two spatial distributions. This method can also be used for a reconstruction of a point spread function (PSF). We found no evidence for a pair halo component through this method by applying it to the Fermi-LAT data in the energy bands of 4.5-6, 6-10, and >10 GeV and set upper limits on the fraction of photons attributable to a pair halo component. An illustration of how to reconstruct the PSF of Fermi-LAT is given. We demonstrate that the PSF reconstructed by using this method is in good agreement with that which was obtained by using the gamma-ray data taken by LAT in the direction of the Crab pulsar and nebula.
Charge carriers in two-dimensional transition metal dichalcogenides (TMDs), such as WSe$_2$, have their spin and valley-pseudospin locked into an optically-addressable index that is proposed as a basis for future information processing. The manipulation of this spin-valley index requires tuning its energy, typically through external magnetic field (B), which is cumbersome. Thus, other efficient routes like all-optical control of spin-valley index are desirable. Here, we show that many-body interactions amongst interlayer excitons in WSe$_2$/MoSe$_2$ heterobilayer induce a steady-state valley Zeeman splitting corresponding to B $\sim$ 6 Tesla. This anomalous splitting, present at incident powers as low as $\mu$Ws, increases with power and enhances, suppresses or even flips the sign of a B-induced splitting. Moreover, the $\it{g}$-factor of valley Zeeman splitting can be tuned by $\sim$ 30 $\%$ with incident power. In addition to valleytronics, our results are relevant for achieving optical non-reciprocity using two-dimensional materials.
To a torus action on a complex vector space, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, called the GKZ hypergeometric system. Its solutions are GKZ hypergeometric functions. We study the $\ell$-adic counterpart of the GKZ hypergeometric system, which we call the $\ell$-adic GKZ hypergeometric sheaf. It is an object in the derived category of $\ell$-adic sheaves on the affine space over a finite field. Traces of Frobenius on stalks of this object at rational points of the affine space define the hypergeometric functions over the finite field introduced by Gelfand and Graev. We prove that the $\ell$-adic GKZ hypergeometric sheaf is perverse, calculate its rank, and prove that it is irreducible under the non-resonance condition. We also study the weight filtration of the GKZ hypergeometric sheaf, determine its lisse locus, and apply our result to the study of weights of twisted exponential sums.
A Latin square of order $n$ is an $n\times n$ array which contains $n$ distinct symbols exactly once in each row and column. We define the adjacent distance between two adjacent cells (containing integers) to be their difference modulo $n$, and inner distance of a Latin square to be the minimum of adjacent distances in the Latin square. By first establishing upper bounds and then constructing squares with said inner distance, we found the maximum inner distance of an $n \times n$ Latin square to be $\left\lfloor\frac{n-1}{2}\right\rfloor$. We then studied special kinds of Latin squares such as pandiagonals (also known as Knut-Vik designs), as well as Sudoku Latin squares. This research was conducted at the REU at Moravian College on Research Challenges of Computational and Experimental Mathematics, with support from the National Science Foundation.
We take a global view at substitution invariant Sturmian sequences. We show that homogeneous substitution invariant Sturmian sequences $s_{\alpha,\alpha}$ can be indexed by two binary trees, associated directly to Johannes Kepler's tree of harmonic fractions from 1619. We obtain similar results for the inhomogeneous sequences $s_{\alpha,1-\alpha}$ and $s_{\alpha,0}$.
In this communication we introduce a pair of coupled continuum equations to model overlayer growth with evaporation-accretion due to thermal or mechanical agitations of the substrate. We gain insight into the dynamics of growth via one-loop perturbative techniques. This allows us to analyze our numerical data. We conclude that there is a crossover behaviour from a roughening regime to a very long-time, large length scale smoothening regime.
Precision measurements of the stars in short-period orbits around the supermassive black hole at the Galactic Center are now being used to constrain general relativistic effects, such as the gravitational redshift and periapse precession. One of the largest systematic uncertainties in the measured orbits has been errors in the astrometric reference frame, which is derived from seven infrared-bright stars associated with SiO masers that have extremely accurate radio positions, measured in the Sgr A*-rest frame. We have improved the astrometric reference frame within 14'' of the Galactic Center by a factor of 2.5 in position and a factor of 5 in proper motion. In the new reference frame, Sgr A* is localized to within a position of 0.645 mas and proper motion of 0.03 mas/yr. We have removed a substantial rotation (2.25 degrees per decade), that was present in the previous less-accurate reference frame used to measure stellar orbits in the field. With our improved methods and continued monitoring of the masers, we predict that orbital precession predicted by General Relativity will become detectable in the next ~5 years.
The Galactic TeV $\gamma$-ray source HESS$\,$J1804$-$216 is currently an unidentified source. In an attempt to unveil its origin, we present here the most detailed study of interstellar gas using data from the Mopra Southern Galactic Plane CO Survey, 7 and 12$\,$mm wavelength Mopra surveys and Southern Galactic Plane Survey of HI. Several components of atomic and molecular gas are found to overlap HESS$\,$J1804$-$216 at various velocities along the line of sight. The CS(1-0) emission clumps confirm the presence of dense gas. Both correlation and anti-correlation between the gas and TeV $\gamma$-ray emission have been identified in various gas tracers, enabling several origin scenarios for the TeV $\gamma$-ray emission from HESS$\,$J1804$-$216. For a hadronic scenario, SNR$\,$G8.7$-$0.1 and the progenitor SNR of PSR$\,$J1803$-$2137 require cosmic ray (CR) enhancement factors of $\mathord{\sim} 50$ times the solar neighbour CR flux value to produce the TeV $\gamma$-ray emission. Assuming an isotropic diffusion model, CRs from both these SNRs require a slow diffusion coefficient, as found for other TeV SNRs associated with adjacent ISM gas. The morphology of gas located at 3.8$\,$kpc (the dispersion measure distance to PSR$\,$J1803$-$2137) tends to anti-correlate with features of the TeV emission from HESS$\,$J1804$-$216, making the leptonic scenario possible. Both pure hadronic and pure leptonic scenarios thus remain plausible.
The three- spin chain with Heisenberg XY- interaction is simulated in a three- qubit nuclear magnetic resonance (NMR) quantum computer. The evolution caused by the XY- interaction is decomposed into a series of single- spin rotations and the $J$- coupling evolutions between the neighboring spins. The perfect state transfer (PST) algorithm proposed by M. Christandl et al [Phys. Rev. Lett, 92, 187902(2004)] is realized in the XY- chain.
We compute the fundamental group of a toroidal compactification of a Hermitian locally symmetric space $D/\Gamma$, without assuming either that $\Gamma$is neat or that it is arithmetic. We also give bounds for the first Betti number.
We give an effective version with explicit constants of a mean value theorem of Vaughan related to the values of \psi(y, \chi), the twisted summatory function associated to the von Mangoldt function \Lambda and a Dirichlet character \chi. As a consequence of this result we prove an effective variant of the Bombieri-Vinogradov theorem with explicit constants. This effective variant has the potential to provide explicit results in many problems. We give examples of such results in several number theoretical problems related to shifted primes.
In the framework of causal perturbation theory renormalization consists of the extension of distributions. We give the explicit form of a Lorentz invariant extension of a scalar distribution, depending on one difference of space time coordinates.
Hybrid halide perovskites are currently under intense investigation due to their potential applications in optoelectronics and solar cells. Among them, MAPbI$_3$ where MA stands for the methylammonium cation, exhibits ideal properties for solar cells. In attempt to identify new lead-free halide perovskites we have studied using \textit{ab-initio} electronic structure calculations in conjunction with hybrid functionals a series of MABX$_3$ compounds where B is a divalent cation and X a halogen atom. Our results suggest that the compounds under study exhibit a variety of lattice constants and energy band gaps. Especially, MAZnCl$_3$, MACdBr$_3$, MAGeCl$_3$ and MAGeBr$_3$ are susceptible to replace MAPbI$_3$ in devices since they show comparable energy gaps. Further calculations on the mixed hybrid halide perovskites show that we can tune the values of the energy gap although no simplified pattern exists. Our results pave the way for further investigation on the use of these materials in technology relevant applications.
If $P(x)$ is the error term in the circle problem, then it is proved that $$\int_0^\infty P^2(x)e^{-x/T}dx = {1\over4}({T\over\pi})^{3/2} \sum_{n=1}^\infty r^2(n)n^{-3/2} - T + O_\epsilon(T^{2/3+\epsilon}), $$ improving the author's earlier exponent 5/6. The new bound is obtained by using results of F. Chamizo on the correlated sum $\sum_{n\le x}r(n)r(n+h)$, where $r(n)$ is the number of representations of $n$ as a sum of two squares.
We discuss the two-slit experiment and the Aharonov-Bohm (AB) experiment in the magnetic field. In such a case the electron moving in the magnetic field produces so called synchrotron radiation. In other words the photons are emitted from the points of the electron trajectory and it means that the trajectory of electron is visible in the synchrotron radiation spectrum. The axiomatic system of quantum mechanics does not enable to define the trajectory of the elementary particle. The two-slit experiment and AB experiment in a magnetic field was never performed and it means that they are the missing experiments of quantum mechanics. The extension of the discussion to the cosmical rays moving in the magnetic field of the Saturn magnetosphere and its rings is mentioned. It is related to the probe CASSINI. The solution of the problem in the framework of the hydrodynamical model of quantum mechanics and the nonlinear quantum mechanics is also mentioned.
We herein present the spin freezing dynamics of stuffed polycrystalline compound Dy$_2$Ti$_{1.8}$Mn$_{0.2}$O$_7$. In Dy$_2$Ti$_2$O$_7$, spin freezes with ice-like spin relaxations at a temperature around 3 K (T$_i$) along with another spin freezing at a temperature around 0.7 K (T\textless T$_i$). These relaxations can be observed prominently with an application of varying DC magnetic field bias and applied AC-field. We show here that with fractional inclusion of Mn at the Ti site in Dy$_2$Ti$_2$O$_7$, there is a significant shift in these temperatures. In Dy$_2$Ti$_{1.8}$Mn$_{0.2}$O$_7$ the T$_i$ shifts to a higher temperature around 5 K and freezing belonging to T\textless T$_i$ shifts to 2.5 K without any application of external DC Bias and/or AC-field. The inclusion of Mn at Ti site also enhances the ferromagnetic interaction for Dy$_2$Ti$_{1.8}$Mn$_{0.2}$O$_7$ as compared to Dy$_2$Ti$_2$O$_7$. Arrhenius fit of freezing temperature with frequency for Dy$_2$Ti$_{1.8}$Mn$_{0.2}$O$_7$ shows that these spin relaxations at T$_i$ and T\textless T$_i$ are thermally induced. Low-temperature structural change in lattice parameters and crystal field phonon coupling has been studied using synchrotron x-ray diffraction. Debye-Gruineisen analysis of temperature-dependent lattice volume shows the emergence of crystal field phonon coupling at a much higher temperature (70 K) in Dy$_2$Ti$_{1.8}$Mn$_{0.2}$O$_7$ in contrast to 40 K in Dy$_2$Ti$_2$O$_7$. These findings make Dy$_2$Ti$_{1.8}$Mn$_{0.2}$O$_7$ a suitable system to explore the application of the spin ice phenomenon at a workable temperature.
We present Fermi's golden rule calculations of the optical carrier injection and the coherent control of current injection in graphene nanoribbons with zigzag geometry, using an envelope function approach. This system possesses strongly localized states (flat bands) with a large joint density of states at low photon energies; for ribbons with widths above a few tens of nanometers, this system also posses large number of (non-flat) states with maxima and minima close to the Fermi level. Consequently, even with small dopings the occupation of these localized states can be significantly altered. In this work, we calculate the relevant quantities for coherent control at different chemical potentials, showing the sensitivity of this system to the occupation of the edge states. We consider coherent control scenarios arising from the interference of one-photon absorption at $2\hbar\omega$ with two-photon absorption at $\hbar\omega$, and those arising from the interference of one-photon absorption at $\hbar\omega$ with stimulated electronic Raman scattering (virtual absorption at $2\hbar\omega$ followed by emission at $\hbar\omega$). Although at large photon energies these processes follow an energy-dependence similar to that of 2D graphene, the zigzag nanoribbons exhibit a richer structure at low photon energies, arising from divergences of the joint density of states and from resonant absorption processes, which can be strongly modified by doping. As a figure of merit for the injected carrier currents, we calculate the resulting swarm velocities. Finally, we provide estimates for the limits of validity of our model.
We study eigenstate thermalization and related signatures of quantum chaos in the one-dimensional ferromagnetic transverse-field Ising model with power-law interactions. The presence of long-range interactions allows for a finite-temperature phase transition despite the one-dimensional geometry of the model. Unlike previous studies of eigenstate thermalization in non-disordered systems with finite temperature phase transitions, our model possesses sufficiently many energy eigenstates below the critical energy density to allow us to make a definitive statement about the presence of eigenstate thermalization and chaotic level statistics in the broken-symmetry phase.
The aim of this work is to perform a systematic study of the measures of the mass and concentration estimated by fitting the convergence profile of a large sample of mock galaxy cluster size lenses, created with the publicly available code MOKA. We found that the main contribution to the bias in mass and in concentration is due to the halo triaxiality and second to the presence of substructures within the host halo virial radius. We show that knowing the cluster elongation along the line of sight helps in correcting the mass bias, but still keeps a small negative bias for the concentration. If these mass and concentration biases will characterize the galaxy cluster sample of a wide field survey it will be difficult to well recover within one sigma the cosmological parameters that mainly influence the c - M relation, using as reference a 3D c - M relation measured in cosmological N-body simulation. In this work we propose how to correct the c - M relation for projection effects and for adiabatic contraction and suggest to use these as reference for real observed data. Correcting mass and concentration estimates, as we propose, gives a measurement of the cosmological parameter within 1 - {\sigma} confidence contours.
The antique Mills Futurity slot machine has two unusual features. First, if a player loses 10 times in a row, the 10 lost coins are returned. Second, the payout distribution varies from coup to coup in a manner that is nonrandom and periodic with period 10. It follows that the machine is driven by a 100-state irreducible period-10 Markov chain. Here, we evaluate the stationary distribution of the Markov chain, and this leads to a strong law of large numbers and a central limit theorem for the sequence of payouts. Following a suggestion of Pyke [In Mathematical Statistics and Applications: Festschrift for Constance van Eeden (2003) 185--216 Institute of Mathematical Statistics], we address the question of whether there exists a two-armed version of this ``one-armed bandit'' that obeys Parrondo's paradox. More precisely, is there such a machine with the property that the casino can honestly advertise that both arms are fair, yet when players alternate arms in certain random or nonrandom ways, the casino makes money in the long run? The answer is a qualified yes. Although this ``history-dependent'' game is conceptually simpler than the original such games of Parrondo, Harmer and Abbott [Phys. Rev. Lett. (2000) 85 5226--5229], it is nearly as complicated analytically, and open problems remain.
The solvent casted Poly(ethylene glycol) (PEG) and Poly(lactic acid) (PLA) blend was recrystallized by the thermal treatment of a heating and cooling cycle. The high PEG content blend (30\%wt) showed a striking dispersion behavior, that the materials rapidly dispersed and dissolved in the aqueous environment in a few hours. This phenomenon has not been reported by others, and was not observed in low PEG content samples of 5\%, 10\%, and 20\%, or quenched(amorphous) samples. We hypothesized the mechanism that the chain rearrangement during the thermal treatment leads to the phase separation. And with the phase separation in the recrystallized samples, the PEG potions rapidly dissolved in the aqueous environment, left out the small PLA spherulites being separated and dispersed in the solution. The same underlying reason can also be inferred from the degradation behaviors of other samples. Characterizations of DSC, XRD, and SEM have been done to validate our hypothesis.
The relations between TMDs and PDFs are obtained from the symmetry requirement: relativistic covariance combined with rotationally symmetric parton motion in the nucleon rest frame. This requirement is applied in the covariant parton model. Using the usual PDFs as an input, we are obtaining predictions for some polarized and unpolarized TMDs.
Many challenging Graver bases computations, like for multi-way tables in statistics, have a highly symmetric problem structure that is not exploited so far computationally. In this paper we present a Graver basis algorithm for sublattices of $\Z^n$ that exploits existing symmetry.
This paper is focused on studying the view-manifold structure in the feature spaces implied by the different layers of Convolutional Neural Networks (CNN). There are several questions that this paper aims to answer: Does the learned CNN representation achieve viewpoint invariance? How does it achieve viewpoint invariance? Is it achieved by collapsing the view manifolds, or separating them while preserving them? At which layer is view invariance achieved? How can the structure of the view manifold at each layer of a deep convolutional neural network be quantified experimentally? How does fine-tuning of a pre-trained CNN on a multi-view dataset affect the representation at each layer of the network? In order to answer these questions we propose a methodology to quantify the deformation and degeneracy of view manifolds in CNN layers. We apply this methodology and report interesting results in this paper that answer the aforementioned questions.
Top quark pair production close to threshold at a next linear collider is discussed, with special focus on the influence of rescattering corrections. Numerical results are shown for the differential cross-section, i.e. the momentum distribution and the forward backward asymmetry, and for moments of the angular distribution of leptons arising from the semileptonic top quark decay.
We present a theoretical study of the static and dynamical properties of the Kitaev magnet $\beta$-Li$_2$IrO$_3$ based on the minimal $J$-$K$-$\Gamma$ model. We argue that the incommensurate magnetic order of $\beta$-Li$_2$IrO$_3$ can be qualitatively understood in terms of a long-wavelength twisting of a nearby commensurate, period-3 state, that shares the same symmetry, propagation vector, counter-rotation of the two spin sublattices, and non-coplanarity. This period-3 state shows very different structure when either the Kitaev interaction $K$ or the off-diagonal exchange anisotropy $\Gamma$ is dominant, featuring in particular ferromagnetic or antiferromagnetic spin dimers, respectively. We compute the magnon excitation spectra and the dynamical spin structure factor for both structures. The results for the momentum and energy dependence of the neutron-scattering intensity provide distinctive qualitative and quantitative fingerprints of the $K$-dominant or $\Gamma$-dominant states and thus gives additional information on the relative strength of these interactions in $\beta$-Li$_2$IrO$_3$.
A system of $m$ nonzero vectors in $\mathbb{Z}^n$ is called an $m$-icube if they are pairwise orthogonal and have the same length. The paper describes $m$-icubes in $\mathbb{Z}^4$ for $2\le m\le 4$ using Hurwitz integral quaternions, counts the number of them with given edge length, and proves that unlimited extension is possible in $\mathbb{Z}^4$.
This paper presents a novel way to predict options price for one day in advance, utilizing the method of Quasi-Reversibility for solving the Black-Scholes equation. The Black-Scholes equation solved forwards in time with Tikhonov regularization as an ill-posed problem allows for extrapolation of option prices. This provides high-accuracy results, which can be further improved by applying Neural Network Machine Learning to the solution of the Black-Scholes equation as well as initial and boundary conditions and implied volatility. Using historical option and stock price data the results obtained from the method of Quasi-Reversibility and Machine Learning method are compared in terms of accuracy, precision and recall. It is shown that these methods can be applied to the real-world trading within a variety of trading strategies.
We present 3 mm and 2 mm band simultaneously spectroscopic observations of HCN 1-0, HCO$^{+}$ 1-0, HNC 1-0, and CS 3-2 with the IRAM 30 meter telescope, toward a sample of 70 sources as nearby galaxies with infrared luminosities ranging from several 10$^{5}L_{\odot}$ to more than 10$^{12}L_{\odot}$. After combining HCN 1-0, HCO$^{+}$ 1-0 and HNC 1-0 data from literature with our detections, relations between luminosities of dense gas tracers (HCN 1-0, HCO$^{+}$ 1-0 and HNC 1-0) and infrared luminosities are derived, with tight linear correlations for all tracers. Luminosities of CS 3-2 with only our observations also show tight linear correlation with infrared luminosities. No systematic difference is found for tracing dense molecular gas among these tracers. Star formation efficiencies for dense gas with different tracers also do not show any trend along different infrared luminosities. Our study also shows that HCN/HCO$^{+}$ line ratio might not be a good indicator to diagnose obscured AGN in galaxies.