ShantanuT01/DACTYL-Pretraining huggingface dataset:
We measure the angular auto-correlation functions (w) of SDSS galaxies selected to have photometric redshifts 0.1 < z < 0.4 and absolute r-band magnitudes Mr < -21.2. We split these galaxies into five overlapping redshift shells of width 0.1 and measure w in each subsample in order to investigate the evolution of SDSS galaxies. We find that the bias increases substantially with redshift - much more so than one would expect for a passively evolving sample. We use halo-model analysis to determine the best-fit halo-occupation-distribution (HOD) for each subsample, and the best-fit models allow us to interpret the change in bias physically. In order to properly interpret our best-fit HODs, we convert each halo mass to its z = 0 passively evolved bias (bo), enabling a direct comparison of the best-fit HODs at different redshifts. We find that the minimum halo bo required to host a galaxy decreases as the redshift decreases, suggesting that galaxies with Mr < -21.2 are forming in halos at the low-mass end of the HODs over our redshift range. We use the best-fit HODs to determine the change in occupation number divided by the change in mass of halos with constant bo and we find a sharp peak at bo ~ 0.9 - corresponding to an average halo mass of ~ 10^12Msol/h. We thus present the following scenario: the bias of galaxies with Mr < -21.2 decreases as the Universe evolves because these galaxies form in halos of mass ~ 10^12Msol/h (independent of redshift), and the bias of these halos naturally decreases as the Universe evolves.
The BTW sandpile model is considered on three dimensional percolation lattice which is tunned with the occupation parameter $p$. Along with the three-dimensional avalanches, we study the energy propagation in two-dimensional cross-sections. We use the moment analysis to extract the exponents for two separate cases: the critical ($p=p_c\equiv p_c^{3D}$) and the off-critical ($p_c<p\leq 1$) cases. The three-dimensional avalanches at $p=p_c$ has exponents like the regular 2D BTW model, whereas the exponents for the 2D cross-sections have serious similarities with the 2D critical Ising model. The moment analysis show that finite size scaling theory is the fulfilled, and some hyper-scaling relations are confirmed. For the off-critical lattice, the exponents change logarithmically with $p-p_c$, for which the cut-off exponents $\nu$ drop discontinuously from $p=p_c$ to the other values. The analysis for the 2D cross-sections show a singular behavior at some $p_0\approx p_c^{2D}$ ($p_c^{3D}$ and $p_c^{2D}$ being three- and two-dimensional percolation thresholds). We argue that there are two separate phases in the cross-sections, namely $p_c^{3D}\leq p<p_c^{2D}$ which, due to lack of 2D percolation cluster, has no thermodynamic limit, and $p\geq p_c^{2D}$ having the chance to involve percolated clusters.
The recursive method of Berends and Giele to compute tree-level gluon amplitudes is revisited using the framework of ten-dimensional super Yang-Mills. First we prove that the pure spinor formula to compute SYM tree amplitudes derived in 2010 reduces to the standard Berends-Giele formula from the 80s when restricted to gluon amplitudes and additionally determine the fermionic completion. Second, using BRST cohomology manipulations in superspace, alternative representations of the component amplitudes are explored and the Bern-Carrasco-Johansson relations among partial tree amplitudes are derived in a novel way. Finally, it is shown how the supersymmetric components of manifestly local BCJ-satisfying tree-level numerators can be computed in a recursive fashion.
We study the zero-temperature magnetization curve (M-H curve) of the S=1 bilinear-biquadratic spin chain, whose Hamiltonian is given by $H=\sum_{i} S_i S_{i+1}+\beta (S_iS_{i+1})^2 with $0 \leq \beta <1$. We focus on validity of the delta-function bose-gas picture near the two critical fields: the saturation field $H_s$ and the lower critical field $H_c$ associated with the Haldane gap. Near $H_s$, we take ``low-energy effective S-matrix'' approach, which gives correct effective bose-gas coupling constant $c$, different from the spin-wave value. Comparing the M-H curve of the bose gas with the product-wavefunction renormalization group (PWFRG) calculation, excellent agreement is seen. Near $H_c$, comparing the PWFRG result with the bose-gas prediction, we find that there are two distinct regions of $\beta$ separated by a critical value $\beta_c(\approx 0.41)$. In the region $0<\beta<\beta_c$, the effective coupling $c$ is positive but rather small. The small value of $c$ makes the ``critical region'' of the square-root behavior $M\sim \sqrt{H-H_c}$ very narrow. Further, we find that in the $\beta \to \beta_c-0$, the square-root behavior transmutes to a different one, $M\sim (H-H_c)^{1/4}$. In the region $\beta_c<\beta <1$, the square-root behavior is rather distinct, but the effective coupling $c$ becomes negative.
Let Y be a normal projective variety and p a morphism from X to Y, which is a projective holomorphic symplectic resolution. Namikawa proved that the Kuranishi deformation spaces Def(X) and Def(Y) are both smooth, of the same dimension, and p induces a finite branched cover f from Def(X) to Def(Y). We prove that f is Galois. We proceed to calculate the Galois group G, when X is simply connected, and its holomorphic symplectic structure is unique, up to a scalar factor. The singularity of Y is generically of ADE-type, along every codimension 2 irreducible component B of the singular locus, by Namikawa's work. The modular Galois group G is the product of Weyl groups of finite type, indexed by such irreducible components B. Each Weyl group factor W_B is that of a Dynkin diagram, obtained as a quotient of the Dynkin diagram of the singularity-type of B, by a group of Dynkin diagram automorphisms.   Finally we consider generalizations of the above set-up, where Y is affine symplectic, or a Calabi-Yau threefold with a curve of ADE-singularities. We prove that the morphism f from Def(X) to Def(Y) is a Galois cover of its image. This explains the analogy between the above results and related work of Nakajima, on quiver varieties, and of Szendroi on enhanced gauge symmetries for Calabi-Yau threefolds.
We propose a new soft clustering scheme for classifying galaxies in different activity classes using simultaneously 4 emission-line ratios; log([NII ]/Ha), log([SII]/Ha), log([OI]/Ha) and log([OIII]/Hb). We fit 20 multivariate Gaussian distributions to the 4-dimensional distribution of these lines obtained from the Sloan Digital Sky Survey (SDSS) in order to capture local structures and subsequently group the multivariate Gaussian distributions to represent the complex multi-dimensional structure of the joint distribution of galaxy spectra in the 4 dimensional line ratio space. The main advantages of this method are the use of all four optical-line ratios simultaneously and the adoption of a clustering scheme. This maximises the available information, avoids contradicting classifications, and treats each class as a distribution resulting in soft classification boundaries and providing the probability for an object to belong to each class. We also introduce linear multi-dimensional decision surfaces using support vector machines based on the classification of our soft clustering scheme. This linear multi-dimensional hard clustering technique shows high classification accuracy with respect to our soft-clustering scheme.
This is a supplement to the paper "Goncharov's Relations in Bloch's higher Chow Group CH^3(F,5)" submitted as math.AG/0105084. We check the admissiblility of all the cycles appearing in the main article.
In light of recent work on particles fluctuating in linear viscoelastic fluids, we study a linear stochastic partial-integro-differential equation with memory that is driven by a stationary noise on a bounded, smooth domain. Using the framework of generalized stationary solutions introduced in~\cite{mckinley2018anomalous}, we provide sufficient conditions on the differential operator and the noise to obtain the existence as well as H\"older regularity of the stationary solutions for the concerned equation. As an application of the regularity results, we compare to analogous classical results for the stochastic heat equation. When the 1d stochastic heat equation is driven by white noise, solutions are continuous with space and time regularity that is H\"older $(1/2-\ep)$ and $(1/4-\ep)$ respectively. When driven by colored-in-space noise, solutions can have a range of regularity properties depending on the structure of the noise. Here, we show that the particular form of colored-in-time memory that arises in viscoelastic diffusion applications, satisfying what is called the Fluctuation--Dissipation relationship, yields sample paths that are H\"older $(1/2-\ep)$ and $(1/2-\ep)$ in space and time.
The harmonic oscillator is a powerful model that can appear as a limit case when examining a nonlinear system. A well known fact is, that without driving, the inclusion of a friction term makes the origin of the phase space -- which is a fixpoint of the system -- linearly stable. In this work we include a telegraph process as perturbation of the oscillator's frequency, for example to describe the motion of a particle with fluctuating charge gyrating in an external magnetic field. Increasing intensity of this colored noise is capable of changing the quality of the fixed point. To characterize the stability of the system, we use a stability measure, that describes the growth of the displacement of the system's phase space position and express it in a closed form. We expand the respective exponent for light friction and low noise intensity and compare both, the exact analytic solution and the expansion to numerical values. Our findings allow stability predictions for several physical systems.
We find four kinds of six-parameter family of coupled Painlev\'e VI systems in dimension four with affine Weyl group symmetry of types $B_6^{(1)}$, $D_6^{(1)}$ and $D_7^{(2)}$. Each system is the first example which gave higher-order Painlev\'e equations of types $B_l^{(1)},D_l^{(1)}$ and $D_l^{(2)}$, respectively. Each system can be expressed as a polynomial Hamiltonian system. We show that these systems are equivalent by an explicit birational and symplectic transformation, respectively. By giving each holomorphy condition, we can recover each system. These symmetries, holomorphy conditions and invariant divisors are new. We also give an explicit description of a confluence process from the system of type $D_6^{(1)}$ to the system of type $A_5^{(1)}$ by taking the coupling confluence process from the Painlev\'e VI system to the Painlev\'e V system.
Bragg coherent X-ray diffraction imaging (BCDI) is a non-destructive, lensless method for 3D-resolved, nanoscale strain imaging in micro-crystals. A challenge, particularly for new users of the technique, is accurate mapping of experimental data, collected in the detector reciprocal space coordinate frame, to more convenient orthogonal coordinates, e.g. attached to the sample. This is particularly the case since different coordinate conventions are used at every BCDI beamline. The reconstruction algorithms and mapping scripts composed for individual beamlines are not readily interchangeable. To overcome this, a BCDI experiment simulation with a plugin script that converts all beamline angles to a universal, right-handed coordinate frame is introduced, making it possible to condense any beamline geometry into three rotation matrices. The simulation translates a user-specified 3D complex object to different BCDI-related coordinate frames. It also allows the generation of synthetic coherent diffraction data that can be inserted into any BCDI reconstruction algorithm to reconstruct the original user-specified object. Scripts are provided to map from sample space to detector conjugated space, detector conjugated space to sample space and detector conjugated space to detector conjugated space for a different reflection. This provides the reader with the basis for a flexible simulation tool kit that is easily adapted to different geometries. It is anticipated that this will find use in the generation of tailor-made supports for phasing of challenging data and exploration of novel geometries or data collection modalities.
We construct partially ionized hydrogen atmosphere models for magnetized neutron stars in radiative equilibrium with fixed surface fields between B=10^12 and 2x10^13 G and effective temperatures logT_eff=5.5-6.8, as well as with surface B and T_eff distributions around these values. The models are based on the latest equation of state and opacity results for magnetized, partially ionized hydrogen plasmas. The atmospheres directly determine the characteristics of thermal emission from the surface of neutron stars. We also incorporate these model spectra into XSPEC, under the model name NSMAX, thus allowing them to be used by the community to fit X-ray observations of neutron stars.
We present the catalog of HI sources extracted from the ongoing Arecibo Legacy Fast ALFA (ALFALFA) extragalactic HI line survey, found within the sky region bounded by 9h36m < RA < 11h36m and +08deg < DEC < +12deg. The HI catalog presented here for this 118-deg^2 region is combined with ones derived from surrounding regions also covered by the ALFALFA survey to examine the large scale structure in the complex Leo region. Because of the combination of wide sky coverage and superior sensitivity, spatial and spectral resolution, the ALFALFA HI catalog of the Leo region improves significantly on the numbers of low HI mass sources as compared with those found in previous HI surveys. The HI mass function of the Leo I group presented here is dominated by low-mass objects: 45 of the 65 Leo I members have M_HI < 10^8 Msun, yielding tight constraints on the low-mass slope of the Leo I HI mass function. The best-fit slope is alpha < -1.41 + 0.2 - 0.1. A direct comparison between the ALFALFA HI line detections and an optical search of the Leo I region proves the advantage of the ALFALFA strategy in finding low mass, gas-rich dwarfs. These results suggest the existence of a significant population of low surface brightness, gas-rich, yet still very low HI mass galaxies, and may reflect the same type of morphological segregation as is seen in the Local Group. While the low mass end slope of the Leo I HI mass function is steeper than that determined for luminosity functions of the group, the slope still falls short of the values predicted by simulations of structure formation in the LCDM paradigm.
We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras $W_3$ and $W_3^{(2)}$ can be embedded as subalgebras into some {\em linear} algebras with finite set of currents. Using these linear algebras we find new field realizations of $W_3^{(2)}$ and $W_3$ which could be a starting point for constructing new versions of $W$-string theories. We also reveal a number of hidden relationships between $W_3$ and $W_3^{(2)}$. We conjecture that similar linear algebras can exist for other $W$-algebras as well.
An enhanced model, based on the Extended Boson Approximation, for the lowest-lying states in odd-mass nuclei is presented. Our approach is built on the Quasiparticle Phonon Model, extending it to take into account the ground state correlations due to the action of the Pauli principle more accurately than in the conventional theory. The derived interaction strengths between the quasiparticles and the phonons in this model depend on the quasiparticle occupation numbers explicitly coupling the odd-mass nucleus equations with those of the even-even core. Within this model we calculated the transition probabilities in several Te, Xe and Ba isotopes with A$\approx$130.
Net-proton number fluctuations can be measured experimentally and hence provide a source of important information about the matter created during relativistic heavy ion collisions. Particularly, they may give us clues about the conjectured QCD critical point. In this work the beam-energy dependence of ratios of the first four cumulants of the net-proton number is discussed. These quantities are calculated using a phenomenologically motivated model in which critical mode fluctuations couple to protons and anti-protons. Our model qualitatively captures both the monotonic behavior of the lowest-order ratio as well as the non-monotonic behavior of higher-order ratios, as seen in the experimental data from the STAR Collaboration. We also discuss the dependence of our results on the coupling strength and the location of the critical point.
A complete model of baryon production in an expanding, primordially symmetric hot Universe is constructed in the framework of general-relativistic kinetic theory. In this model specific model for a baryon is calculated and graphs of the value dependence are constructed.
We investigate the X-ray properties of the K-band-selected galaxies at redshift 2 < z < 4 by using our deep near-infrared images obtained in the MOIRCS Deep Survey project and the published Chandra X-ray source catalog. 61 X-ray sources with the 2-10 keV luminosity L_X = 10^{42}-10^{44} erg/s are identified with the K-selected galaxies and we found that they are exclusively (90%) associated with the massive objects with stellar mass larger than 10^{10.5} Msun. Our results are consistent with the idea that the M_BH/M_str ratio of the galaxies at z=2-4 is similar to the present-day value. On the other hand, the AGN detection rate among the very massive galaxies with the stellar mass larger than 10^{11} Msun is high, 33% (26/78). They are active objects in the sense that the black-hole mass accretion rate is ~ 1-50% of the Eddington limit if they indeed have similar M_BH/M_str ratio with those observed in the local universe. The active duration in the AGN duty cycle of the high-redshift massive galaxies seems large.
The phenomenon of super-radiance in quantum optics predicted by Dicke 50 years ago and observed experimentally has its counterparts in many-body systems on the borderline between discrete spectrum and continuum. The interaction of overlapping resonances through the continuum leads to the redistribution of widths and creation of broad super-radiant states and long-lived compound states. We explain the physics of super-radiance and discuss applications to weakly bound nuclei, giant resonances and widths of exotic baryons.
Three-dimensional integer partitions provide a convenient representation of codimension-one three-dimensional random rhombus tilings. Calculating the entropy for such a model is a notoriously difficult problem. We apply transition matrix Monte Carlo simulations to evaluate their entropy with high precision. We consider both free- and fixed-boundary tilings. Our results suggest that the ratio of free- and fixed-boundary entropies is $\sigma_{free}/\sigma_{fixed}=3/2$, and can be interpreted as the ratio of the volumes of two simple, nested, polyhedra. This finding supports a conjecture by Linde, Moore and Nordahl concerning the ``arctic octahedron phenomenon'' in three-dimensional random tilings.
We study a gas of hard rods on a ring, driven by an external thermostat, with either elastic or inelastic collisions, which exhibits sub-diffusive behavior $<x^2 > \sim t^{1/2}$. We show the validity of the usual Fluctuation-Dissipation (FD) relation, i.e. the proportionality between the response function and the correlation function, when the gas is elastic or diluted. On the contrary, in strongly inelastic or dense cases, when the tracer velocity is no more independent of the other degrees of freedom, the Einstein formula fails and must be replaced by a more general FD relation.
We present first results from the ongoing radio monitoring of SN 2008iz in M82. The VLBI images reveal a shell-like structure with circular symmetry, which expands in a self-similar way. There is strong evidence of a compact component with a steep spectrum at the center of the shell. The expansion curve obtained from our VLBI observations is marginally decelerated (m = 0.89) and can be modeled simultaneously with the available radio light curves. While the results of this simultaneous fitting are not conclusive (i.e. different combinations of values of the magnetic field, CSM density profile, and electron energy distribution, provide fits to the available data with similar quality), additional observations should allow a more robust and detailed modeling.
Natural language questions are inherently compositional, and many are most easily answered by reasoning about their decomposition into modular sub-problems. For example, to answer "is there an equal number of balls and boxes?" we can look for balls, look for boxes, count them, and compare the results. The recently proposed Neural Module Network (NMN) architecture implements this approach to question answering by parsing questions into linguistic substructures and assembling question-specific deep networks from smaller modules that each solve one subtask. However, existing NMN implementations rely on brittle off-the-shelf parsers, and are restricted to the module configurations proposed by these parsers rather than learning them from data. In this paper, we propose End-to-End Module Networks (N2NMNs), which learn to reason by directly predicting instance-specific network layouts without the aid of a parser. Our model learns to generate network structures (by imitating expert demonstrations) while simultaneously learning network parameters (using the downstream task loss). Experimental results on the new CLEVR dataset targeted at compositional question answering show that N2NMNs achieve an error reduction of nearly 50% relative to state-of-the-art attentional approaches, while discovering interpretable network architectures specialized for each question.
This paper is a continuation of previous work of the authors. We extend one of the theorems that gave a way to construct equilateral triangles whose vertices have integer coordinates to the general situation. An approximate extrapolation formula for the sequence ET(n) of all equilateral triangles with vertices in $\{0,1,2,...,n\}^3$ (A 102698) is given and the asymptotic behavior of this sequence is analyzed.
An expression for the Dalitz plot of the semileptonic decay of a charged kaon, including radiative corrections to order O[\alpha \pi)(q/M_1)], where q is the four-momentum transfer and M_1 is the mass of the decaying kaon, is obtained. Contributions of both the three- and four-body regions are accounted for. Besides, the emitted muon is considered to be polarized so the analysis is also focused on evaluating the radiative corrections to the longitudinal, transverse, and normal polarization components of the muon. The final formulas, with the triple integration of the bremsstrahlung photon variables ready to be performed numerically, are general enough to be used in model-independent experimental analyses whether or not the real photon is discriminated. With the numerical values of the weak form factors and slope parameters of the process, the radiative corrections to the components of the muon polarization are found to be very small compared to their respective uncorrected values.