ShantanuT01/DACTYL-Pretraining huggingface dataset:
For all positive non-square integer multiplier k, there is an infinity of multiples of triangular numbers which are also triangular numbers. With a simple change of variables, these triangular numbers can be found using solutions of Pell equations. With some conditions on parities of fundamental solutions of the simple and generalized Pell equations, only odd solutions of the generalized Pell equation are retained to provide many infinitely solutions found on branches corresponding to each of the generalized fundamental solutions. General algebraic expressions of fundamental solutions of the Pell equations are found for some values of the multiplier k in function of the closest natural square. Further, among the expressions of Pell equation solutions, a set of recurrent relations is identical to those found previously without the Pell equation solving method. It is found also that two constants of the problem of multiples of triangular numbers are directly related to the fundamental solutions of the simple Pell equation, which is an unexpected result as it means that simple Pell equation fundamental solutions in all generality are related to constants in recurrent relations of the problem of finding triangular numbers multiple of other triangular numbers.
Spiking behavior and a high degree of intensity correlation of frequency up- and down-converted directional radiation from population-inverted alkali vapors excited with a continuous-wave laser pumping are attributed to cooperative effects.
We theoretically investigate resonant dipole-dipole interaction (RDDI) between artificial atoms in a 1D geometry, implemented by N transmon qubits coupled through a transmission line. Similarly to the atomic cases, RDDI comes from exchange of virtual photons of the unexcited modes, and causes the so-called collective Lamb shift (CLS). To probe the shift, we effectively set one end of the transmission line as a mirror, and examine the reflection spectrum of the probe field from the other end. Our calculation shows that when a qubit is placed at the node of the standing wave formed by the incident and reflected waves, even though it is considered to be decoupled from the field, it results in large energy splitting in the spectral profile of a resonant qubit located elsewhere. This directly signals the interplay of virtual photon processes and explicitly demonstrates the CLS. We further derive a master equation to describe the system, which can take into account mismatch of participating qubits and dephasing effects. Our calculation also demonstrates the superradiant and subradiant nature of the atomic states, and how the CLS scales when more qubits are involved.
That muon neutrinos $\nu_{\mu}$ oscillating into the mixture of tau neutrinos $\nu_{\tau}$ and sterile neutrinos $\nu_{s}$ has been studied to explain the atmospheric $\nu_{\mu}$ disappearance. In this scenario, the effect of Earth matter is a key to determine the fraction of $\nu_{s}$. Considering that the Earth matter density has uncertainty and this uncertainty has significant effects in some neutrino oscillation cases, such as the CP violation in very long baseline neutrino oscillations and the day-night asymmetry for solar neutrinos, we study the effects caused by this uncertainty in the above atmospheric $\nu_{\mu}$ oscillation scenario. We find that this uncertainty seems to have no significant effects and that the previous fitting results need not to be modified fortunately.
Several recent studies have shown that the use of extra in-distribution data can lead to a high level of adversarial robustness. However, there is no guarantee that it will always be possible to obtain sufficient extra data for a selected dataset. In this paper, we propose a biased multi-domain adversarial training (BiaMAT) method that induces training data amplification on a primary dataset using publicly available auxiliary datasets, without requiring the class distribution match between the primary and auxiliary datasets. The proposed method can achieve increased adversarial robustness on a primary dataset by leveraging auxiliary datasets via multi-domain learning. Specifically, data amplification on both robust and non-robust features can be accomplished through the application of BiaMAT as demonstrated through a theoretical and empirical analysis. Moreover, we demonstrate that while existing methods are vulnerable to negative transfer due to the distributional discrepancy between auxiliary and primary data, the proposed method enables neural networks to flexibly leverage diverse image datasets for adversarial training by successfully handling the domain discrepancy through the application of a confidence-based selection strategy. The pre-trained models and code are available at: \url{https://github.com/Saehyung-Lee/BiaMAT}.
We present an analysis of the subpulse drift in PSR J1750-3503, which is characterized by abrupt transitions of drift direction. As the pulsar does not exhibit other mode changes or clear nulling, it is an ideal candidate system for studying the phenomenon of drift direction change. For $\sim 80\%$ of the time the subpulses are characterized by positive drift - from early to later longitudes - while the drift direction is negative in the other $\sim 20\%$. The subpulse separation for single pulses with positive drift, $P_2=(18.8\pm 0.1)^{\circ}$, is higher then for single pulses with negative drift, $P_2=(17.5\pm 0.2)^{\circ}$. When the drift is stable, the measured repetition time of the drift pattern is $P_3^{\rm obs}=(43.5 \pm 0.4) P$, where $P$ is pulsar period. We show that the observed data can be reproduced by a carousel models with subpulse rotation around the magnetic axis using purely dipolar configuration of surface magnetic field. The observed drift characteristics can be modeled assuming that the actual repetition time $P_3<2P$, such that we observe its aliased value. A small variation in $P_3$, of the order of $6\%$ (or less assuming higher alias orders), is enough to reproduce the characteristic drift direction changes we observe.
Observations are consistent with a significant fraction of heavy nuclei in the cosmic ray flux above a few times 10^19 eV. Such nuclei can be deflected considerably in the Galactic magnetic field, with important implications for the search of their sources. We perform detailed simulations of heavy nuclei propagation within recent Galactic magnetic field models. While such models are not yet sufficiently constrained to predict deflection maps in detail, we find general features of the distribution of (de-) magnified flux from sources. Since in most theoretical models sources of heavy nuclei are located in the local large scale structure of galaxies, we show examples of images of several nearby galaxy clusters and of the supergalactic plane. Such general features may be useful to develop efficient methods for source reconstruction from observed ultrahigh energy cosmic ray arrival directions.
MACHO project photometry shows the candidate Symbiotic Star V5485 Sagittarii's red giant component has a photometric orbital period of 270 days as evidenced by ellipsoidal variation of the lightcurve.
We present results of AO-assisted K-band IFU spectroscopy of the massive young star IRAS13481-6124 performed with ESO's VLT/SINFONI instrument. Our spectro-astrometric analysis of the Br{\gamma} line revealed a photo-center shift with respect to the adjacent continuum of \sim1 AU at a distance of 3.1 kpc. The position angle of this shift matches with that of the outflow which confirms that the massive star is indeed the driving source. Furthermore, a velocity gradient along the major disk axis was found which hints at the rotational sense of the ionized region, and thus of the disk as well. The gradient is not consistent with Keplerian motion but points to rigid rotation of the innermost disk. Notably, emission of H_2 is absent from source while both shocked and fluorescent H_2 emission are observed in its immediate surroundings.
We extend the duality between acyclic orientations and totally cyclic orientations on planar graphs to dualities on graphs on orientable surfaces by introducing boundary acyclic orientations and totally bi-walkable orientations. In addition, we provide a reciprocity theorem connecting local tensions and boundary acyclic orientations. Furthermore, we define the balanced flow polynomial which is connected with tension polynomial by duality and with totally bi-walkable orientations by reciprocity.
The translational Chern-Simons type three-form coframe torsion on a Riemann-Cartan spacetime is related (by differentiation) to the Nieh-Yan four-form. Following Chandia and Zanelli, two spaces with non-trivial translational Chern-Simons forms are discussed. We then demonstrate, firstly within the classical Einstein-Cartan-Dirac theory and secondly in the quantum heat kernel approach to the Dirac operator, how the Nieh-Yan form surfaces in both contexts, in contrast to what has been assumed previously.
DP-coloring (also known as correspondence coloring) is a generalization of list coloring developed recently by Dvo\v{r}\'ak and Postle. We introduce and study $(i,j)$-defective DP-colorings of simple graphs. Let $g_{DP}(i,j,n)$ be the minimum number of edges in an $n$-vertex DP-$(i,j)$-critical graph. In this paper we determine sharp bound on $g_{DP}(i,j,n)$ for each $i\geq3$ and $j\geq 2i+1$ for infinitely many $n$.
In recent years there has been some focus on quasi-stationary behaviour of an one-dimensional L\'evy process $X$, where we ask for the law $P(X_t\in dy | \tau^-_0>t)$ for $t\to\infty$ and $\tau_0^-=\inf\{t\geq 0: X_t<0\}$. In this paper we address the same question for so-called Parisian ruin time $\tau^\theta$, that happens when process stays below zero longer than independent exponential random variable with intensity $\theta$.
The Coriolis matrix elements responsible for mixing of the $1^+ K=1$ and $1^+ K=0$ states are calculated in the framework of the Quasiparticle Phonon Model for several Gd and Dy isotopes. In many considered cases these matrix elements are equal to several tens of keV and are comparable with energy distances between the mixed levels. The results obtained indicates that Gd isotopes could be more suitable for finding deviations from Alaga rules in M1 transitions from $1^+$ state to the states of the ground band.
A variational approach based on Bogoliubov inequality for the free energy is employed in order to treat the quantum spin-$1$ anisotropic ferromagnetic Heisenberg model in the presence of a crystal field. Within the Bogoliubov scheme an improved pair approximation has been used. The temperature dependent thermodynamic functions have been obtained and provide much better results than the previous simple mean-field scheme. In one dimension, which is still non-integrable for quantum spin-$1$, we get the exact results in the classical limit, or near-exact results in the quantum case, for the free energy, magnetization and quadrupole moment, as well for the transition temperature. In two and three dimensions the corresponding global phase diagrams have been obtained as a function of the parameters of the Hamiltonian. First-order transition lines, second-order transition lines, tricritical and tetracritical points, and critical endpoints have been located through the analysis of the minimum of the Helmholtz free energy and a Landau like expansion in the approximated free energy. Only first-order quantum transitions have been found at zero temperature. Limiting cases, such as isotropic Heisenberg, Blume-Capel and Ising models have been analyzed and compared to previous results obtained from other analytical approaches as well as from Monte Carlo simulations.
In this paper, we obtain luminosity distances by using ages of 32 old passive galaxies distributed over the redshift interval $0.11 < z < 1.84$ and test the cosmic conservation of photon number by comparing them with 580 distance moduli of type Ia supernovae (SNe Ia) from the so-called Union 2.1 compilation. Our analyses are based on the fact that the method of obtaining ages of galaxies relies on the detailed shape of galaxy spectra but not on galaxy luminosity. Possible departures from cosmic conservation of photon number is parametrized by $\tau(z) = 2 \epsilon z$ and $\tau(z) = \epsilon z/(1+z)$ (for $\epsilon =0$ the conservation of photon number is recovered). We find $\epsilon=0.016^{+0.078}_{-0.075}$ from the first parametrization and $\epsilon=-0.18^{+0.25}_{-0.24}$ from the second parametrization, both limits at 95\% c.l. In this way, no significant departure from cosmic conservation of photon number is verified. In addition, by considering the total age as inferred from Planck (2015) analysis, we find the incubation time $t_{inc}=1.66\pm0.29$ Gyr and $t_{inc}=1.23\pm0.27$ Gyr at 68\% c.l. for each parametrization, respectively.}
We present a study of the orbits, environments and morphologies of 13 ram-pressure stripped galaxies in the massive, intermediate redshift (z$\sim0.3-0.4$) galaxy clusters A2744 and A370, using MUSE integral-field spectroscopy and HST imaging from the Frontier Fields Program. We compare different measures of the locations and morphologies of the stripped sample with a sample of 6 poststarburst galaxies identified within the same clusters, as well as the general cluster population. We calculate the phase space locations of all cluster galaxies and carry out a substructure analysis, finding that the ram-pressure stripped galaxies in A370 are not associated with any substructures, but are likely isolated infalling galaxies. In contrast, the ram-pressure stripped galaxies in A2744 are strictly located within a high-velocity substructure, moving through a region of dense X-ray emitting gas. We conclude that their ram-pressure interactions are likely to be the direct result of the merger between two components of the cluster. Finally, we study the morphologies of the stripped and poststarburst galaxies, using numerical measures to quantify the level of visual disturbances. We explore any morphological deviations of these galaxies from the cluster population, particularly the weaker cases which have been confirmed via the presence of ionised gas tails to be undergoing ram-pressure stripping, but are not strongly visually disturbed in the broad-band data. We find that the stripped sample galaxies are generally divergent from the general cluster sample, with poststarburst galaxies being intermediary in morphology between stripped galaxies and red passive cluster members.
The conclusions of a recent paper by Olsson (Phys. Rev. Lett. 75, 2758 (1995), cond-mat/9506082) about the fully frustrated XY model in two dimensions are questioned. In particular, the evidence presented for having two separate chiral and U(1) phase transitions are critically considered.
We collect different examples reflect Bolzman--Jaynes theory of maximum entropy principle. This principle proposed that equillibrium of macrosystem (most probable macrostate of the invariant measure of macrosystem) can be find as a solution of the entropy linear programming problem. Among this examples one can find applications to the economics, sociology, linguistics, traffic flow theory, biology e.t.c. We also describe on examples the connection between Nash's equillibrium, Darwin's principle of natural selection and conception of equillibrium of macrosystem.
For the first time spectroscopic galaxy redshift surveys are reaching the scales where galaxies can be studied together with the nearest quasars. This gives an opportunity to study the dependence between the activity of a quasar and its environment in a more extensive way than before. We study the spatial distribution of galaxies and groups of galaxies in the environments of low redshift quasars in the Sloan Digital Sky Survey (SDSS). Our aim is to understand how the nearby quasars are embedded in the local and global density field of galaxies and how the environment affects quasar activity. We analyse the environments of nearby quasars using number counts of galaxies. We also study the dependence of group properties to their distance to the nearest quasar. The large scale environments are studied by analysing the locations of quasars in the luminosity density field. Our study of the number counts of galaxies in quasar environments shows an underdensity of bright galaxies at a few Mpc from quasars. Also, the groups of galaxies that have a quasar closer than 2Mpc are poorer and less luminous than in average. Our analysis on the luminosity density field shows that quasars clearly avoid rich superclusters. Nearby quasars seem to be located in outskirts of superclusters or in filaments connecting them. Our results suggest that quasar evolution may be affected by density variations both on supercluster scales and in the local environment.
Light-matter interacting quantum systems manifest strong correlations that lead to distinct cooperative spontaneous emissions of subradiance or superradiance. To demonstrate the essence of long-range correlations in such systems, we consider an atomic array under the resonant dipole-dipole interactions (RDDI) and apply an interpretable machine learning with the integrated gradients to identify the crossover between the subradiant and superradiant sectors. The machine shows that the next nearest-neighbor couplings in RDDI play as much as the roles of nearest-neighbor ones in determining the whole eigenspectrum within the training sets. Our results present the advantage of machine learning approach with explainable ability to reveal the underlying mechanism of correlations in quantum optical systems, which can be potentially applied to investigate many other strongly interacting quantum many-body systems.
We present LVG and non-local radiative transfer calculations involving the rotational and hyperfine structure of the spectrum of N$_2$H$^+$ with collisional rate coefficients recently derived by us. The goal of this study is to check the validity of the assumptions made to treat the hyperfine structure and to study the physical mechanisms leading to the observed hyperfine anomalies.   We find that the usual hypothesis of identical excitation temperatures for all hyperfine components of the $J$=1-0 transition is not correct within the range of densities existing in cold dense cores, i.e., a few 10$^4$ $\textless$ n(H$_2$) $\textless$ a few 10$^6$ cm$^{-3}$. This is due to different radiative trapping effects in the hyperfine components. Moreover, within this range of densities and considering the typical abundance of N$_2$H$^+$, the total opacity of rotational lines has to be derived taking into account the hyperfine structure. The error made when only considering the rotational energy structure can be as large as 100%. Using non-local models we find that, due to saturation, hyperfine anomalies appear as soon as the total opacity of the $J$=1-0 transition becomes larger than $\simeq$ 20. Radiative scattering in less dense regions enhance these anomalies, and particularly, induce a differential increase of the excitation temperatures of the hyperfine components. This process is more effective for the transitions with the highest opacities for which emerging intensities are also reduced by self-absorption effects. These effects are not as critical as in HCO$^+$ or HCN, but should be taken into account when interpreting the spatial extent of the N$_2$H$^+$ emission in dark clouds.
We use molecular dynamics to study the nucleation of cracks in a two dimensional material without pre-existing cracks. We study models with zero and non-zero shear modulus. In both situations the time required for crack formation obeys an Arrhenius law, from which the energy barrier and pre-factor are extracted for different system sizes. For large systems, the characteristic time of rupture is found to decrease with system size, in agreement with classical Weibull theory. In the case of zero shear modulus, the energy opposing rupture is identified with the breakage of a single atomic layer. In the case of non-zero shear modulus, thermally activated fracture can only be studied within a reasonable time at very high strains. In this case the energy barrier involves the stretching of bonds within several layers, accounting for a much higher barrier compared to the zero shear modulus case. This barrier is understood within adiabatic simulations.
The binding energies of the ground states and several excited states related to single-particle and -hole states in nuclei around ^{16}O are calculated taking charge dependence into account. Effective interactions on the particle basis are constructed from modern charge-dependent nucleon-nucleon interactions and the Coulomb force within the framework of the unitary-model-operator approach. Single-particle (-hole) energies are obtained from the energy differences of the binding energies between a particle (hole) state in ^{17}O or ^{17}F (^{15}N or ^{15}O) and the ground state of ^{16}O. The resultant spin-orbit splittings are small for the hole state and large for the particle state in comparison with the experimental values though the differences between the experimental and calculated values are not very large. The charge dependence of the calculated single-particle energies for the ground states are in good agreement with the experimental values. Furthermore, the Thomas-Ehrman shift due to the Coulomb force for the 1s_{1/2} states in ^{17}O and ^{17}F can be observed.
We examine the phenomenon of {\it entanglement sudden death} (ESD) for $(2 \times 3)$-dimensional systems. As for $2 \times 2$ systems, the negativity vanishes in finite time for some entangled pure as well as mixed states. While locally equivalent pure states do so asymptotically. Interference between the decay of the two upper levels to the lowest one in the qutrit adds further richness to ESD in this systems.
This note addresses the motivic nature of some classical cohomological results due to Lefschetz, namely the primitive decomposition (for the cohomology of smooth projective varieties), and, secondly, the splitting of the cohomology of a complete intersection into the "fixed" and "variable part".
Much is known about binomial coefficients where primes are concerned, but considerably less is known regarding prime powers and composites. This paper provides two conjectures in these directions, one about counting binomial coefficients modulo 16 and one about the value of Binomial[n, 2p] modulo n.
For the inverse square long-range ferromagnetic Ising chain in a transverse field, the thermal phase boundary of the floating Kosterlitz-Thouless phase is obtained for several values of the transverse field down to the quantum critical point. The sharp domain walls in the classical model are increasingly smeared out by the transverse field, which is evidenced by a pronounced broadening of the non-universal bump in the specific heat. The discernability of KT critical scaling in finite-size simulations is discussed.
The chromatic sum $\Sigma(G)$ of a graph $G$ is the smallest sum of colors among of proper coloring with the natural number. In this paper, we introduce a necessary condition for the existence of graph homomorphisms. Also, we present $\Sigma(G)<\chi_f(G)|G|$ for every graph $G$.