ShantanuT01/DACTYL-Pretraining huggingface dataset:
An effective practical model with two characteristic parameters is presented to describe both of the tidally induced shape and spin alignments of the galactic halos with the large-scale tidal fields. We test this model against the numerical results obtained from the Small MultiDark Planck simulation on the galactic mass scale of $0.5\le M/(10^{11}\,h^{-1}\,M_{\odot})\le 50$ at redshift $z=0$. Determining empirically the parameters from the numerical data, we demonstrate how successfully our model describes simultaneously and consistently the amplitudes and behaviors of the probability density functions of three coordinates of the shape and spin vectors in the principal frame of the large scale tidal field. Dividing the samples of the galactic halos into multiple subsamples in four different mass ranges and four different types of the cosmic web, and also varying the smoothing scale of the tidal field from $5\,h^{-1}$Mpc to $10,\ 20,\ 30\,h^{-1}$Mpc, we perform repeatedly the numerical tests with each subsample at each scale. Our model is found to match well the numerical results for all of the cases of the mass range, smoothing scale and web type and to properly capture the scale and web dependence of the spin flip phenomenon.
The current cosmological paradigm sees the formation and evolution of the cosmic large-scale structure as governed by the gravitational attraction of the Dark Matter (DM) and the repulsion of the Dark Energy (DE).   We characterize the relative importance of uniform and constant dark energy, as given by the Lambda term in the standard LCDM cosmology, in galaxy systems of different scales, from groups to superclusters.   An instructive "Lambda significance graph" is introduced where the matter-DE density ratio <rho_M>/rho_Lambda for different galaxy systems is plotted against the radius R. This presents gravitation and DE dominated regions and shows directly the zero velocity radius, the zero-gravity radius, and the Einstein-Straus radius for any fixed value of mass.   Example galaxy groups and clusters from the local universe illustrate the use of the Lambda significance graph. These are generally located deep in the gravity-dominated region <rho_M}>/rho_Lambda > 2, being virialized. Extended clusters and main bodies of superclusters can reach down near the border line between gravity-dominated and DE dominated regions <rho_M>/rho_Lambda = 2. The scale--mass relation from the standard 2-point correlation function intersects this balance line near the correlation lenght.   The log <rho_M>/rho_Lambda vs. log R diagram is a useful and versatile way to characterize the dynamical state of systems of galaxies within the Lambda dominated expanding universe.
We apply a new entropic scheme to study the critical behavior of the square-lattice Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions. Estimates of the present scheme are compared with those of the Metropolis algorithm. We consider interactions in the range where superantiferromagnetic (SAF) order appears at low temperatures. A recent prediction of a first-order transition along a certain range (0.5-1.2) of the interaction ratio $(R=J_{nnn}/J_{nn})$ is examined by generating accurate data for large lattices at a particular value of the ratio $(R=1)$. Our study does not support a first-order transition and a convincing finite-size scaling analysis of the model is presented, yielding accurate estimates for all critical exponents for R=1 . The magnetic exponents are found to obey ``weak universality'' in accordance with a previous conjecture.
Positions of protons in DNA hydrogen bonds are fundamental for the fidelity of the replication process. Because the hydrogen bond is partially covalent the electronic structure of DNA plays an important role in the replication process. Current studies of electron transfer in DNA have shown that simple pictures based on independent electron physics are not sufficient to account for the experimental data. In this paper we propose a model for electron-proton interaction in DNA and its relationship to mutagenesis. We argue that mutations will be more frequent in DNA sequences where electron delocalization occurs. To test our theory we calculate the heat capacity of DNA at low temperatures and compare with the available experimental data in hydrated DNA. We find that our model is in good agreement with the data. We also propose new measurements of infrared absorption which would further test our ideas.
By applying the Hamiltonian reduction scheme we recover the R-matrix of the trigonometric and elliptic Calogero-Moser system.
Current state-of-the-art object detectors are at the expense of high computational costs and are hard to deploy to low-end devices. Knowledge distillation, which aims at training a smaller student network by transferring knowledge from a larger teacher model, is one of the promising solutions for model miniaturization. In this paper, we investigate each module of a typical detector in depth, and propose a general distillation framework that adaptively transfers knowledge from teacher to student according to the task specific priors. The intuition is that simply distilling all information from teacher to student is not advisable, instead we should only borrow priors from the teacher model where the student cannot perform well. Towards this goal, we propose a region proposal sharing mechanism to interflow region responses between the teacher and student models. Based on this, we adaptively transfer knowledge at three levels, \emph{i.e.}, feature backbone, classification head, and bounding box regression head, according to which model performs more reasonably. Furthermore, considering that it would introduce optimization dilemma when minimizing distillation loss and detection loss simultaneously, we propose a distillation decay strategy to help improve model generalization via gradually reducing the distillation penalty. Experiments on widely used detection benchmarks demonstrate the effectiveness of our method. In particular, using Faster R-CNN with FPN as an instantiation, we achieve an accuracy of $39.0\%$ with Resnet-50 on COCO dataset, which surpasses the baseline $36.3\%$ by $2.7\%$ points, and even better than the teacher model with $38.5\%$ mAP.
Measures of entanglement can be employed for the analysis of numerous quantum information protocols. Due to computational convenience, logarithmic negativity is often the choice in the case of continuous variable systems. In this work, we analyse a continuous variable measurement-based entanglement distillation experiment using a collection of entanglement measures. This includes: logarithmic negativity, entanglement of formation, distillable entanglement, relative entropy of entanglement, and squashed entanglement. By considering the distilled entanglement as a function of the success probability of the distillation protocol, we show that the logarithmic negativity surpasses the bound on deterministic entanglement distribution at a relatively large probability of success. This is in contrast to the other measures which would only be able to do so at much lower probabilities, hence demonstrating that logarithmic negativity alone is inadequate for assessing the performance of the distillation protocol. In addition to this result, we also observed an increase in the distillable entanglement by making use of upper and lower bounds to estimate this quantity. We thus demonstrate the utility of these theoretical tools in an experimental setting.
An ordered graph is a simple graph with an ordering on its vertices. Define the ordered path $P_n$ to be the monotone increasing path with $n$ edges. The ordered size Ramsey number $\tilde{r}(P_r,P_s)$ is the minimum number $m$ for which there exists an ordered graph $H$ with $m$ edges such that every two-coloring of the edges of $H$ contains a red copy of $P_r$ or a blue copy of $P_s$. For $2\leq r\leq s$, we show $\frac{1}{8}r^2s\leq \tilde{r}(P_r,P_s)\leq Cr^2s(\log s)^3$, where $C>0$ is an absolute constant. This problem is motivated by the recent results of Buci\'c-Letzter-Sudakov and Letzter-Sudakov for oriented graphs.
The purpose of this note is to establish a Central Limit Theorem for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on the correct aymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson, and its extension to large families of Wigner matrices by means of the Tao and Vu Four Moment Theorem and recent localization results by Erd\"os, Yau and Yin.
In this paper we give an asymptotic bound of the cardinality of Zariski multiples of particular plane singular curves. These curves have only nodes and cusps as singularities and are obtained as branched curves of ramified covering of the plane by surfaces isogenous to a product of curves with group $(\mathbb{Z}/2\mathbb{Z})^k$. The knowledge of the moduli space of these surfaces will enable us to produce Zariski multiplets whose number grows subexponentialy in function of their degree.
We have investigated the electronic structure of the dilute magnetic semiconductor (DMS) $Ga_{0.98}Mn_{0.02}P$ and compared it to that of an undoped $GaP$ reference sample, using hard X-ray photoelectron spectroscopy (HXPS) and hard X-ray angle-resolved photoemission spectroscopy (HARPES) at energies of about 3 keV. We present experimental data, as well as theoretical calculations, in order to understand the role of the Mn dopant in the emergence of ferromagnetism in this material. Both core-level spectra and angle-resolved or angle-integrated valence spectra are discussed. In particular, the HARPES experimental data are compared to free-electron final-state model calculations and to more accurate one-step photoemission theory. The experimental results show differences between $Ga_{0.98}Mn_{0.02}P$ and $GaP$ in both angle-resolved and angle-integrated valence spectra. The $Ga_{0.98}Mn_{0.02}P$ bands are broadened due to the presence of Mn impurities that disturb the long-range translational order of the host $GaP$ crystal. Mn-induced changes of the electronic structure are observed over the entire valence band range, including the presence of a distinct impurity band close to the valence-band maximum of the DMS. These experimental results are in good agreement with the one-step photoemission calculations, and a prior HARPES study of $Ga_{0.97}Mn_{0.03}As$ and $GaAs$ (Gray et al. Nature Materials 11, 957 (2012)), demonstrating the strong similarity between these two materials. The Mn 2p and 3s core-level spectra also reveal an essentially identical state in doping both $GaAs$ and $GaP$.
Effect of quantum fluctuations concerned with the orbital degrees of freedom is discussed for the model with SU(4) symmetry in one dimension. An effective Hamiltonian is derived from the orbitally degenerate Hubbard model at quarter filling. This model is equivalent to the Bethe soluble SU(4) exchange model. Quantum numbers of the ground state and the lowest branch of excitations are determined. The spin-spin correlation functions are obtained numerically by the density matrix renormalization group method. It shows a power-law decay with oscillations of the period of four sites. The period originates from the interference between the spin and orbital degrees of freedom. The exponent of the power-law decay estimated from the finite size data is consistent with the prediction by the conformal field theory.
In this paper, we investigate the Unruh radiation in the Bohmian field theory on a shape dynamics background setting. Since metric and metric momentum are real quantities, the integral kernel to invert the Lichnerowicz-York equation for first order deviations due to existence of matter terms turns out to be real. This fact makes the interaction Hamiltonian real. On the other hand, the only contribution to guarantee the existence of Unruh radiation has to come from the imaginary part of the temporal part of the wave functional. We have proved the existence of Unruh radiation in this setting. It is also important that we have found the Unruh radiation via an Unruh-DeWitt detector in a theory where there is no Lorentz symmetry and no conventional space-time structure.
The primal cohomology $\mathbb{K}_\mathbb{Q}$ of the theta divisor $\Theta$ of a principally polarized abelian fivefold (ppav) is the direct sum of its invariant and anti-invariant parts $\mathbb{K}_\mathbb{Q}^{+1}$, resp. $\mathbb{K}_\mathbb{Q}^{-1}$ under the action of $-1$. For smooth $\Theta$, these have dimension $6$ and $72$ respectively. We show that $\mathbb{K}_\mathbb{Q}^{+1}$ consists of Hodge classes and, for a very general ppav, $\mathbb{K}_\mathbb{Q}^{-1}$ is a simple Hodge structure of level $2$.
We study the differential equations governing mirror symmetry of elliptic curves, and obtain a characterization of the ODEs which give rise to the integral ${\bf q}$-expansion of mirror maps. Through theta function representation of the defining equation, we express the mirror correspondence in terms of theta constants. By investigating the elliptic curves in $X_9$-family, the identification of the Landau-Ginzburg potential with the spectral curve of Ising model is obtained. Through the Jacobi elliptic function parametrization of Boltzmann weights in the statistical model, an exact Jacobi form-like formula of mirror map is described .
The SUSY flavor, CP, gravitino and proton-decay problems are all solved to varying degrees by a decoupling solution wherein first/second generation matter scalars would exist in the multi-TeV regime. Recent models of natural SUSY presumably allow for a co-existence of naturalness with the decoupling solution. We show that: if sfermions are heavier than $\sim 10$ TeV, then a small first/second generation contribution to electroweak fine-tuning (EWFT) requires a rather high degree of intra-generational degeneracy of either 1. (separately) squarks and sleptons, 2. (separately) left- and right-type sfermions, 3. members of SU(5) multiplets, or 4. all members of a single generation as in SO(10). These (partial) degeneracy patterns required by naturalness hint at the necessity of an organizing principle, and highlight the limitations of models such as the pMSSM in the case of decoupled first/second generation scalars.
NGC 1316 (Fornax A) is a prominent merger remnant in the outskirts of the Fornax cluster. The cluster system has not yet been studied in its entirety. We therefore present a wide-field study of the globular cluster system of NGC 1316, investigating its properties in relation to the global morphology of NGC 1316. We used the MOSAIC II camera at the 4-m Blanco telescope at CTIO in the filters Washington C and Harris R. We identify globular cluster candidates and study their color distribution and the structural properties of the system. In an appendix, we also make morphological remarks, present color maps, and present new models for the brightness and color profiles of the galaxy. The cluster system is well confined to the optically visible outer contours of NGC 1316. The color distribution of the entire sample is unimodal, but the color distribution of bright subsamples in the bulge shows two peaks that, by comparison with theoretical Washington colors with solar metallicity, correspond to ages of about 2 Gyr and 0.8 Gyr, respectively. We also find a significant population of clusters in the color range 0.8 < C-R < 1.1 which must be populated by clusters younger than 0.8 Gyr, unless they are very metal-poor. The color interval 1.3 < C-R < 1.6 hosts the bulk of intermediate-age clusters which show a surface density profile with a sharp decline at about 4 arcmin. The outer cluster population shows an unimodal color distribution with a peak at C-R=1.1, indicating a larger contribution of old, metal-poor clusters. Their luminosity function does not show the expected turn-over, so the fraction of younger clusters is still significant. Cluster formation in NGC 1316 has continued after an initial burst, presumably related to the main merger. A toy model with two bursts of ages 2 Gyr and 0.8 Gyr is consistent with photometric properties and dynamical M/L-values.
Let $G=(V,E)$ be a multigraph (it has multiple edges, but no loops). The edge connectivity, denoted by $\lambda(G)$, is the cardinality of a minimum edge-cut of $G$. We call $G$ maximally edge-connected if $\lambda(G)=\delta(G)$, and $G$ super edge-connected if every minimum edge-cut is a set of edges incident with some vertex. The restricted edge-connectivity $\lambda'(G)$ of $G$ is the minimum number of edges whose removal disconnects $G$ into non-trivial components. If $\lambda'(G)$ achieves the upper bound of restricted edge-connectivity, then $G$ is said to be $\lambda'$-optimal. A bipartite multigraph is said to be half-transitive if its automorphism group is transitive on the sets of its bipartition. In this paper, we will characterize maximally edge-connected half-transitive multigraphs, super edge-connected half-transitive multigraphs, and $\lambda'$-optimal half-transitive multigraphs.
We find that the statistics of levels undergoing metal-insulator transition in systems with multi-parametric Gaussian disorders and non-interacting electrons behaves in a way similar to that of the single parametric Brownian ensembles \cite{dy}. The latter appear during a Poisson $\to$ Wigner-Dyson transition, driven by a random perturbation. The analogy provides the analytical evidence for the single parameter scaling of the level-correlations in disordered systems as well as a tool to obtain them at the critical point for a wide range of disorders.
Using the Singwi-Tosi-Land-Sjolander theory we have studied the many-body effects in the two-dimensional electron gas with arbitrary polarization at finite temperatures. We have calculated the structure factors, pair correlation functions, local-field factors and the Helmholtz free energy for different values of spin polarization, temperature and density parameter. We have shown that the spin polarization and finite temperature effects are remarkable and in the low temperature or paramagnetic case our results match closely with those obtained in earlier papers .
Pion-meson-exchange nucleon-nucleon potentials are derived for two nucleons in the intermediate states. The mesons we include are (i) pseudoscalar mesons: $\pi, \eta, \eta'$; (ii) vector mesons: $\rho, \omega, \phi$; (iii) scalar mesons: $a_{0}(980), \varepsilon(760), f_{0}(975)$; and (iv) the $J=0$ contribution from the Pomeron. Strong dynamical pair suppression is assumed, and at the nucleon-nucleon-meson vertices Gaussian form factors are incorporated into the relativistic two-body framework using a dispersion representation for the pion- and meson-exchange amplitudes. The Fourier transformations are performed using factorization techniques for the energy denominators. The potentials are first calculated in the adiabatic approximation to all planar and crossed three-dimensional momentum-space $\pi$-meson diagrams. Next, we calculate the $1/M$ corrections.
Several experiments and experimental proposals for the production of macroscopic superpositions naturally lead to states of the general form $|\phi_1>^{\otimes N}+|\phi_2>^{\otimes N}$, where the number of subsystems $N$ is very large, but the states of the individual subsystems have large overlap, $|{\l}\phi_1|\phi_2 \r|^2=1-\epsilon^2$. We propose two different methods for assigning an effective particle number to such states, using ideal Greenberger--Horne--Zeilinger (GHZ)-- states of the form $|0\r^{\otimes n}+|1\r^{\otimes n}$ as a standard of comparison. The two methods are based on decoherence and on a distillation protocol respectively. Both lead to an effective size $n$ of the order of $N \epsilon^2$.
The motion of knots in astrophysical jets is commonly interpreted as shock waves moving along it. Observations of the HST-1 knot during extended periods of time have produced complicated light curves on many wavelengths which are difficult to account using standard hydrodynamical models. Here we reproduce these light curves using the semi-analytical approach developed by Mendoza et al. (2009), developed to reproduce light curves of working surfaces moving along relativistic jets. These working surfaces are generated by periodic oscillations of the injected flow velocity and discharge at the base of the jet. In particular, we use this approach to reproduce the exotic observed features of the light curves of the HST-1 knot in M87. We show that the complicated fits to the light curves are reproduced with high accuracy in all wavelengths. As a bonus, we show that this model is also able to reproduce the light curve of the micro-qsr A06200-00 with high accuracy.
Using a sample of galaxies from the Sloan Digital Sky Survey (SDSS) Data Release 4, we study the trends relating surface brightness profile type and apparent axis ratio to the local galaxy environment. We use the SDSS parameter `fracDeV' to quantify the profile type. We find that galaxies with M_r > -18 are mostly described by exponential profiles in all environments. Galaxies with -21 < M_r < -18 mainly have exponential profiles in low density environments and de Vaucouleurs profiles in high density environments. The most luminous galaxies, with M_r < -21, are mostly described by de Vaucouleurs profiles in all environments. For galaxies with M_r < -19, the fraction of de Vaucouleurs galaxies is a monotonically increasing function of local density, while the fraction of exponential galaxies is monotonically decreasing. For a fixed surface brightness profile type, apparent axis ratio is frequently correlated with environment. As the local density of galaxies increases, we find that for -20 < M_r < -18, galaxies of all profile types become slightly rounder, on average; for -22 < M_r < -20, galaxies with exponential profiles tend to become flatter, while galaxies with de Vaucouleurs profiles become rounder; for M_r < -22, galaxies with exponential profiles become flatter, while the de Vaucouleurs galaxies become rounder in their inner regions, yet exhibit no change in their outer regions. We comment on how the observed trends relate to the merger history of galaxies.
The main general relativistic effects in the motion of the Moon are briefly reviewed. The possibility of detection of the solar gravitomagnetic contributions to the mean motions of the lunar node and perigee is discussed.
We study the flow of a weakly-interacting Bose-Einstein condensate around an obstacle by numerical solution of the Gross-Pitaevskii equation. We observe vortex emission and the formation of bow waves leading to pressure drag. We compare the drag law with that of an ideal Bose gas, and show that interactions reduce the drag force. This reduction can be explained in terms of a `collisional screening' of the obstacle.
In lepton-number-violating supersymmetric models, there is no natural choice of basis to distinguish the down-type Higgs and lepton superfields. We employ basis-independent techniques to identify the massless majoron and associated light scalar in the case of spontaneously-broken lepton number (L). When explicit L-violation is added, these two scalars can acquire masses of order the electroweak scale and can be identified as massive sneutrinos.