ShantanuT01/DACTYL-Pretraining huggingface dataset:
We measure galaxy sizes on a sample of $\sim1200$ galaxies with confirmed spectroscopic redshifts $2 \leq z_{spec} \leq 4.5$ in the VIMOS Ultra Deep Survey (VUDS), representative of star-forming galaxies with $i_\mathrm{AB} \leq 25$. We first derive galaxy sizes applying a classical parametric profile fitting method using GALFIT. We then measure the total pixel area covered by a galaxy above a given surface brightness threshold, which overcomes the difficulty of measuring sizes of galaxies with irregular shapes. We then compare the results obtained for the equivalent circularized radius enclosing 100\% of the measured galaxy light $r_T^{100}$ to those obtained with the effective radius $r_{e,\mathrm{circ}}$ measured with GALFIT. We find that the sizes of galaxies computed with our non-parametric approach span a large range but remain roughly constant on average with a median value $r_T^{100}\sim2.2$ kpc for galaxies with $2<z<4.5$. This is in stark contrast with the strong downward evolution of $r_e$ with increasing redshift, down to sizes of $<1$ kpc at $z\sim4.5$. We analyze the difference and find that parametric fitting of complex, asymmetric, multi-component galaxies is severely underestimating their sizes. By comparing $r_T^{100}$ with physical parameters obtained through SED fitting we find that the star-forming galaxies that are the largest at any redshift are, on average, more massive and more star-forming. We discover that galaxies present more concentrated light profiles as we move towards higher redshifts. We interpret these results as the signature of several, possibly different, evolutionary paths of galaxies in their early stages of assembly, including major and minor merging or star-formation in multiple bright regions. (abridged)
Instability of a binary eutectic solidification front to morphological perturbations due to rejection of a ternary impurity leads to the formation of eutectic colonies. Whereas, the instability dynamics and the resultant mi- crostructural features are reasonably well understood for isotropic systems, several experimental observations point to the existence of colonies in systems with anisotropic interfaces. In this study, we extend the un- derstanding of eutectic colonies to anisotropic systems, where only certain orientations of the solid-liquid or solid-solid interfaces are thermodynamically stable. Through phase field simulations in 2D and 3D, we have systematically probed the colony formation dynamics and the resulting microstructures, as functions of the pulling velocity and the relative orientation of the equilibrium interfaces with that of the imposed tempera- ture gradient. We find that in 2D, stabler finger spacings are selected with an increase in the magnitude of anisotropy introduced, either in the solid-liquid or in the solid-solid interface. The fingers have a well-defined orientation for the case of anisotropy in the solid-liquid interface, with no fixed orientations for the lamellae constituting the colony. For the case where anisotropy exists in the solid-solid interface, the lamellae tend to orient themselves along the direction of the imposed temperature gradient, with tilted solid-liquid interfaces from the horizontal. The 3D simulations reveal existence of eutectic spirals which might become tilted under certain orientations of the equilibrium interfaces. Our simulations are able to explain several key features observed in our experimantal studies of solidification in Ni-Al-Zr alloy.
We investigate the cubic defocusing fourth order Schr\"odinger equation $iu_t + \Delta^2u + |u|^2u=0$ in arbitrary space dimension $\mathbb{R}^n$ for arbitrary $H^2$ initial data. We prove that the equation is globally well-posed when $n \le 8$ and ill-posed when $n \ge 9$, with the additional important information that scattering holds true when $5 \le n \le 8$.
We present new classes of permutation polynomials over finite fields.
Effects of the Fermi-sea polarization on the superfluidity in nuclear matter are studied in a framework of quantum hadrodynamics. The particle-hole polarization due to $\sigma$ and $\omega$ mesons enhances the peak value of the pairing gap contrary to the previous non-relativistic studies.
We study two functionals of a random matrix $\boldsymbol A$ with independent elements uniformly distributed over the cyclic group of integers $\{0,1,\ldots, M-1\}$ modulo $M$. One of them, $V_0(\boldsymbol A)$ with mean $\mu$, gives the total number of solutions for a generalised birthday problem, and the other, $W(\boldsymbol A)$ with mean $\lambda$, gives the number of solutions detected by Wagner's tree based algorithm.   We establish two limit theorems. Theorem 2.1 describes an asymptotical behaviour of the ratio $\lambda/\mu$ as $M\to\infty$. Theorem 2.2 suggests Chen-Stein bounds for the total variation distance between Poisson distribution and distributions of $V_{0}$ and $W$.
Some properties that nominally involve the eigenvalues of Gaussian Unitary Ensemble (GUE) can instead be phrased in terms of singular values. By discarding the signs of the eigenvalues, we gain access to a surprising decomposition: the singular values of the GUE are distributed as the union of the singular values of two independent ensembles of Laguerre type. This independence is remarkable given the well known phenomenon of eigenvalue repulsion.   The structure of this decomposition reveals that several existing observations about large $n$ limits of the GUE are in fact manifestations of phenomena that are already present for finite random matrices. We relate the semicircle law to the quarter-circle law by connecting Hermite polynomials to generalized Laguerre polynomials with parameter $\pm$1/2. Similarly, we write the absolute value of the determinant of the $n\times{}n$ GUE as a product n independent random variables to gain new insight into its asymptotic log-normality. The decomposition also provides a description of the distribution of the smallest singular value of the GUE, which in turn permits the study of the leading order behavior of the condition number of GUE matrices.   The study is motivated by questions involving the enumeration of orientable maps, and is related to questions involving powers of complex Ginibre matrices. The inescapable conclusion of this work is that the singular values of the GUE play an unpredictably important role that had gone unnoticed for decades even though, in hindsight, so many clues had been around.
The single electron transistor (SET) is a prime candidate for reading out the final state of a qubit in a solid state quantum computer. Such a measurement requires the detection of sub-electron charge motion in the presence of random charging events. We present a detection scheme where the signals from two SETs are cross-correlated to suppress unwanted artifacts due to charge noise. This technique is demonstrated by using the two SETs to detect the charge state of two tunnel junction - coupled metal dots, thereby simulating charge transfer and readout in a two qubit system. These measurements indicate that for comparable buried dopant semiconductor architectures the minimum measurement time required to distinguish between the two charge states is of the order of 10 ns.
Systematic pressure- and temperature-dependent infrared studies on the two-dimensional organic quantum spin-liquid $\beta^{\prime}$-EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ disclose the electronic and lattice evolution across the Mott insulator-metal transition. Increasing hydrostatic pressure continuously suppresses the insulating ground state; for $p>0.6$~GPa, a Drude-like component develops indicating the appearance of coherent quasiparticles at the Fermi level. In the vicinity of the Mott transition, not only the electronic state changes rapidly, but also the vibration modes exhibit a jump both in frequency and Fano constant, underlining the strong coupling between lattice and electrons. The anisotropy of the in-plane optical response becomes inverted above 0.6~GPa. The findings are discussed in detail and summarized in a phase diagram comprising different experimental approaches.
A variant of the accelerating cosmology reconstruction program is developed for $f(R)$ gravity. Reconstruction schemes in terms of e-foldings and by using an auxiliary scalar field are developed. An example of a model with a transient phantom behavior without real matter is explicitly discussed in both schemes. Detailed comparison of the two schemes of reconstruction is presented. It seems to support physical non-equivalence of the two frames.
We show that an inflation model in which a spectator axion field is coupled to an SU(2) gauge field produces a large three-point function (bispectrum) of primordial gravitational waves, $B_{h}$, on the scales relevant to the cosmic microwave background experiments. The amplitude of the bispectrum at the equilateral configuration is characterized by $B_{h}/P_h^2=\mathcal{O}(10)\times \Omega_A^{-1}$, where $\Omega_A$ is a fraction of the energy density in the gauge field and $P_h$ is the power spectrum of gravitational waves produced by the gauge field.
In recent years, the unified theory of information and thermodynamics has been intensively discussed in the context of stochastic thermodynamics. The unified theory reveals that information theory would be useful to understand non-stationary dynamics of systems far from equilibrium. In this letter, we have found a new link between stochastic thermodynamics and information theory well known as information geometry. By applying this link, an information geometric inequality can be interpreted as a thermodynamic uncertainty relationship between speed and thermodynamic cost. We have numerically applied an information geometric inequality to a thermodynamic model of biochemical enzyme reaction.
We report on the implementation of the Wannier Functions (WFs) formalism within the full-potential linearized augmented plane wave method (FLAPW), suitable for bulk, film and one-dimensional geometries. The details of the implementation, as well as results for the metallic SrVO3, ferroelectric BaTiO3 grown on SrTiO3, covalently bonded graphene and a one-dimensional Pt-chain are given. We discuss the effect of spin-orbit coupling on the Wannier Functions for the cases of SrVO3 and platinum. The dependency of the WFs on the choice of the localized trial orbitals as well as the difference between the maximally localized and "first-guess" WFs are discussed. Our results on SrVO3 and BaTiO3, e.g. the ferroelectric polarization of BaTiO3, are compared to results published elsewhere and found to be in excellent agreement.
The mass spectrum of the chargino--neutralino sector in the minimal supersymmetric standard model (MSSM) is calculated at the one-loop level, based on the complete set of one-loop diagrams. On-shell renormalization conditions are applied to determine the counterterms for the gaugino-mass-parameters $M_1, M_2$ and the Higgsino-mass parameter $\mu$. The input is fixed in terms of three pole masses (two charginos and one neutralino); the other pole masses receive a shift with respect to the tree-level masses, which can amount to several GeV. The detailed evaluation shows that both the fermionic/sfermionic loop contributions and the non-(s)fermionic loop contributions are of the same order of magnitude and are thus relevant for precision studies at future colliders.
Estimates of $H_0$ from Sunyaev-Zel'dovich effect (SZE) and X-ray surface brightness of galaxy clusters depends on the underlying cosmology. In the current $\Lambda$CDM flat cosmology, a possible technique to broke the degenerescency on the mass density parameter ($\Omega_{m}$) is to apply a joint analysis involving the baryon acoustic oscillations (BAO). By adopting this technique to the ($H_0, \Omega_m$) parameter space, we obtain new constraints on the Hubble constant $H_0$ from BAO signature as given by the Sloan Digital Sky Survey (SDSS) catalog. Our analysis based on the SZE/X-ray data for a sample of 25 clusters yields $H_0= 74^{+4}_{-3.5}$ km s$^{-1}$ Mpc$^{-1}$ ($1\sigma$, neglecting systematic uncertainties). This result is in good agreement with independent studies from the {\it{Hubble Space Telescope}} key project and the recent estimates of WMAP, thereby suggesting that the combination of these three independent phenomena provides an interesting method to constrain the Hubble constant.
In 1952, Dirac proved that every $2$-connected $n$-vertex graph with the minimum degree $k+1$ contains a cycle of length at least $\min\{n, 2(k+1)\}$. Here we obtain a stability version of this result by characterizing those graphs with minimum degree $k$ and circumference at most $2k+1$.   We present applications of the above-stated result by obtaining generalized Tur\'an numbers. In particular, for all $\ell \geq 5$ we determine how many copies of a five-cycle as well as four-cycle are necessary to guarantee that the graph has circumference larger than $\ell$. In addition, we give a new proof of Luo's Theorem for cliques using our stability result.
We study the number of two-dimensional sublattices of $\mathbb{Z^4}$ of a fixed covolume and construct the associated Dirichlet series. The latter is shown to be related to Eisenstein series on both $GL_4$ and its metaplectic double cover.
We study cosmological models involving scalar fields coupled to radiation and discuss their effect on the redshift evolution of the cosmic microwave background temperature, focusing on links with varying fundamental constants and dynamical dark energy. We quantify how allowing for the coupling of scalar fields to photons, and its important effect on luminosity distances, weakens current and future constraints on cosmological parameters. In particular, for evolving dark energy models, joint constraints on the dark energy equation of state combining BAO radial distance and SN luminosity distance determinations, will be strongly dominated by BAO. Thus, to fully exploit future SN data one must also independently constrain photon number non-conservation arising from the possible coupling of SN photons to the dark energy scalar field. We discuss how observational determinations of the background temperature at different redshifts can, in combination with distance measures data, set tight constraints on interactions between scalar fields and photons, thus breaking this degeneracy. We also discuss prospects for future improvements, particularly in the context of Euclid and the E-ELT and show that Euclid can, even on its own, provide useful dark energy constraints while allowing for photon number non-conservation.
In this paper, we derive the Jarzynski equality (JE) for an isolated quantum system in three different cases: (i) the full evolution is unitary with no intermediate measurements, (ii) with intermediate measurements of arbitrary observables being performed, and (iii) with intermediate measurements whose outcomes are used to modify the external protocol (feedback). We assume that the measurements will involve errors that are purely classical in nature. Our treatment is based on path probability in state space for each realization. This is in contrast to the formal approach based on projection operator and density matrices. We find that the JE remains unaffected in the second case, but gets modified in the third case where the mutual information between the measured values with the actual eigenvalues must be incorporated into the relation.
We extend the results presented by Ace\~na \textit{et al} in the afore mentioned paper, [arXiv:1012.2413], to the case of axisymmetric, maximal initial data which are invariant under an inversion transformation.
We theoretically explore nonresonantly pumped polaritonic graphene, a system consisting of a honeycomb lattice of micropillars in the regime of strong light-matter coupling. We demonstrate that, depending on the parameters of the structure, such as intensity of the pump and coupling strength between the pillars, the system shows rich variety of macroscopic ordering, including analogs of ferromagnetic, antiferromagnetic, and resonant valence bond phases. Transitions between these phases are associated with dramatic reshaping of the spectrum of the system connected with spontaneous appearance of topological order.
The sample of dwarf galaxies with measured central black hole masses $M$ and velocity dispersions $\sigma$ has recently doubled, and gives a close fit to the extrapolation of the $M \propto \sigma$ relation for more massive galaxies. We argue that this is difficult to reconcile with suggestions that the scaling relations between galaxies and their central black holes are simply a statistical consequence of assembly through repeated mergers. This predicts black hole masses significantly larger than those observed in dwarf galaxies unless the initial distribution of uncorrelated seed black hole and stellar masses is confined to much smaller masses than earlier assumed. It also predicts a noticeable flattening of the $M \propto \sigma$ relation for dwarfs, to $M \propto \sigma^2$ compared with the observed $M \propto \sigma^4$. In contrast black hole feedback predicts that black hole masses tend towards a universal $M \propto \sigma^4$ relation in all galaxies, and correctly gives the properties of powerful outflows recently observed in dwarf galaxies. These considerations emphasize once again that the fundamental physical black-hole -- galaxy scaling relation is between $M$ and $\sigma$. The relation of $M$ to the bulge mass $M_b$ is acausal, and depends on the quite independent connection between $M_b$ and $\sigma$ set by stellar feedback.
In this paper we consider a triangular array of branching processes with non-stationary immigration. We prove a weak convergence of properly normalized branching processes with immigration to deterministic function under assumption that immigration is rowwise $\psi-$mixing and the offspring mean tends to its critical value 1, immigration mean and variance controlled by regularly varying functions. Moreover, we obtain a fluctuation limit theorem for branching process with immigration when immigration is $m-$dependent where $m$ may tend to infinity with the row index at a certain rate. In this case the limiting process is a time-changed Wiener process. Our results extend and improve the previous known results in the literature.
We have studied the surface of pure and oxidized Pt$_3$Zr(0001) by scanning tunneling microscopy (STM), Auger electron microscopy, and density functional theory (DFT). The well-annealed alloy surface shows perfect long-range chemical order. Occasional domain boundaries are probably caused by nonstoichiometry. Pt$_3$Zr exhibits ABAC stacking along [0001]; only the A-terminated surfaces are seen by STM, in agreement with DFT results showing a lower surface energy for the A termination. DFT further predicts a stronger inward relaxation of the surface Zr than for Pt, in spite of the larger atomic size of Zr. A closed ZrO$_2$ film is obtained by oxidation in $10^{-7}$ mbar O$_2$ at 400 $^\circ$C and post-annealing at $\approx 800 ^\circ$C. The oxide consists of an O-Zr-O trilayer, equivalent to a (111) trilayer of the fluorite structure of cubic ZrO$_2$, but contracted laterally. The oxide forms a $(\sqrt{19} \times \sqrt{19})$R23$^\circ$ superstructure. The first monolayer of the substrate consists of Pt and contracts, similar to the metastable reconstruction of pure Pt(111). DFT calculations show that the oxide trilayer binds rather weakly to the substrate. In spite of the O-terminated oxide, bonding to the substrate mainly occurs via the Zr atoms in the oxide, which strongly buckle down towards the Pt substrate atoms, if near a Pt position. According to DFT, the oxide has a bandgap; STM indicates that the conduction band minimum lies $\approx 2.3$ eV above $E_\mathrm{F}$.
The cost of large scale data collection and annotation often makes the application of machine learning algorithms to new tasks or datasets prohibitively expensive. One approach circumventing this cost is training models on synthetic data where annotations are provided automatically. Despite their appeal, such models often fail to generalize from synthetic to real images, necessitating domain adaptation algorithms to manipulate these models before they can be successfully applied. Existing approaches focus either on mapping representations from one domain to the other, or on learning to extract features that are invariant to the domain from which they were extracted. However, by focusing only on creating a mapping or shared representation between the two domains, they ignore the individual characteristics of each domain. We suggest that explicitly modeling what is unique to each domain can improve a model's ability to extract domain-invariant features. Inspired by work on private-shared component analysis, we explicitly learn to extract image representations that are partitioned into two subspaces: one component which is private to each domain and one which is shared across domains. Our model is trained not only to perform the task we care about in the source domain, but also to use the partitioned representation to reconstruct the images from both domains. Our novel architecture results in a model that outperforms the state-of-the-art on a range of unsupervised domain adaptation scenarios and additionally produces visualizations of the private and shared representations enabling interpretation of the domain adaptation process.
omega Cen contains the largest population of very hot horizontal branch (HB) stars known in a globular cluster. Recent UV observations (Whitney et al. 1998; D'Cruz et al. 2000) show a significant population of hot stars below the zero-age horizontal branch (``blue hook'' stars), which cannot be explained by canonical stellar evolution. Stars which suffer unusually large mass loss on the red giant branch and thus experience the helium core flash while descending the white dwarf cooling curve could populate this region. Theory predicts that these ``late hot flashers'' should show higher temperatures than the hottest canonical HB stars and should have helium- and carbon-rich atmospheres. We obtained and analysed medium resolution spectra of a sample of blue hook stars to derive their atmospheric parameters. The blue hook stars are indeed both hotter (Teff > 35,000K) and more helium-rich than classical extreme HB stars. In addition we find indications for a large enhancement of the carbon abundance relative to the cluster abundance.
The redshifted 21-cm background is expected to be a powerful probe of the early Universe, carrying both cosmological and astrophysical information from a wide range of redshifts. In particular, the power spectrum of fluctuations in the 21-cm brightness temperature is anisotropic due to the line-of-sight velocity gradient, which in principle allows for a simple extraction of this information in the limit of linear fluctuations. However, recent numerical studies suggest that the 21-cm signal is actually rather complex, and its analysis likely depends on detailed model fitting. We present the first realistic simulation of the anisotropic 21-cm power spectrum over a wide period of early cosmic history. We show that on observable scales, the anisotropy is large and thus measurable at most redshifts, and its form tracks the evolution of 21-cm fluctuations as they are produced early on by Lyman-a radiation from stars, then switch to X-ray radiation from early heating sources, and finally to ionizing radiation from stars. In particular, we predict a redshift window during cosmic heating (at z ~ 15), when the anisotropy is small, during which the shape of the 21-cm power spectrum on large scales is determined directly by the average radial distribution of the flux from X-ray sources. This makes possible a model-independent reconstruction of the X-ray spectrum of the earliest sources of cosmic heating.