ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we study the variations of group galaxy properties according to the assembly history in SDSS-DR6 selected groups. Using mock SDSS group catalogues, we find two suitable indicators of group formation time: i) the isolation of the group, defined as the distance to the nearest neighbor in terms of its virial radius, and ii) the concentration, measured as the group inner density calculated using the fifth nearest bright galaxy to the group centre. Groups within narrow ranges of mass in the mock catalogue show increasing group age with isolation and concentration. However, in the observational data the stellar age, as indicated by the spectral type, only shows a correlation with concentration. We study groups of similar mass and different assembly history, finding important differences in their galaxy population. Particularly, in high mass SDSS groups, the number of members, mass-to-light ratios, red galaxy fractions and the magnitude difference between the brightest and second brightest group galaxies, show different trends as a function of isolation and concentration, even when it is expected that the latter two quantities correlate with group age. Conversely, low mass SDSS groups appear to be less sensitive to their assembly history. The correlations detected in the SDSS are not consistent with the trends measured in the mock catalogues. However, discrepancies can be explained in terms of the disagreement found in the age-isolation trends, suggesting that the model might be overestimating the effects of environment.We discuss how the modeling of the cold gas in satellite galaxies could be responsible for this problem. These results can be used to improve our understanding of the evolution of galaxies in high-density environments.
We define a large class of quantum sources and prove a quantum analog of the asymptotic equipartition property. Our proof relies on using local measurements on the quantum source to obtain an associated classical source. The classical source provides an upper bound for the dimension of the relevant subspace of the quantum source, via the Shannon-McMillan noiseless coding theorem. Along the way we derive a bound for the von Neumann entropy of the quantum source in terms of the Shannon entropy of the classical source, and we provide a definition of ergodicity of the quantum source. Several explicit models of quantum sources are also presented.
Given a generic family $Q$ of 2-dimensional quadrics over a smooth 3-dimensional base $Y$ we consider the relative Fano scheme $M$ of lines of it. The scheme $M$ has a structure of a generically conic bundle $M \to X$ over a double covering $X \to Y$ ramified in the degeneration locus of $Q \to Y$. The double covering $X \to Y$ is singular in a finite number of points (corresponding to the points $y \in Y$ such that the quadric $Q_y$ degenerates to a union of two planes), the fibers of $M$ over such points are unions of two planes intersecting in a point. The main result of the paper is a construction of a semiorthogonal decomposition for the derived category of coherent sheaves on $M$. This decomposition has three components, the first is the derived category of a small resolution $X^+$ of singularities of the double covering $X \to Y$, the second is a twisted resolution of singularities of $X$ (given by the sheaf of even parts of Clifford algebras on $Y$), and the third is generated by a completely orthogonal exceptional collection.
A theory of the circular photogalvanic effect caused by spin splitting in quantum wells is developed. Direct interband transitions between the hole and electron size-quantized subbands are considered. It is shown that the photocurrent value and direction depend strongly on the form of the spin-orbit interaction. The currents induced by structure-, bulk-, and interface-inversion asymmetry are investigated. The photocurrent excitation spectra caused by spin splittings in both conduction and valence bands are calculated.
We have extended the density matrix renormalization group (DMRG) approach to two-fluid open many-fermion systems governed by complex-symmetric Hamiltonians. The applications are carried out for three- and four-nucleon (proton-neutron) systems within the Gamow Shell Model (GSM) in the complex-energy plane. We study necessary and sufficient conditions for the GSM+DMRG method to yield the correct ground state eigenvalue and discuss different truncation schemes within DMRG. The proposed approach will enable configuration interaction studies of weakly-bound and unbound strongly interacting complex systems which, because of a prohibitively large size of Fock space, cannot be treated by means of the direct diagonalization.
We study the large time behavior of solutions $v:\Omega\times(0,\infty)\rightarrow \mathbb{R}$ of the PDE $\partial_t(|v|^{p-2}v)=\Delta_pv.$ We show that $e^{\left(\lambda_p/(p-1)\right)t}v(x,t)$ converges to an extremal of a Poincar\'e inequality on $\Omega$ with optimal constant $\lambda_p$, as $t\rightarrow \infty$. We also prove that the large time values of solutions approximate the extremals of a corresponding "dual" Poincar\'e inequality on $\Omega$. Moreover, our theory allows us to deduce the large time asymptotics of related doubly nonlinear flows involving various boundary conditions and nonlocal operators.
Applying elastic deformation can tune a material physical properties locally and reversibly. Spatially modulated lattice deformation can create a bandgap gradient, favouring photo-generated charge separation and collection in optoelectronic devices. These advantages are hindered by the maximum elastic strain that a material can withstand before breaking. Nanomaterials derived by exfoliating transition metal dichalcogenides TMDs are an ideal playground for elastic deformation, as they can sustain large elastic strains, up to a few percent. However, exfoliable TMDs with highly strain-tunable properties have proven challenging for researchers to identify. We investigated 1T-ZrS2 and 1T-ZrSe2, exfoliable semiconductors with large bandgaps. Under compressive deformation, both TMDs dramatically change their physical properties. 1T-ZrSe2 undergoes a reversible transformation into an exotic three-dimensional lattice, with a semiconductor-to-metal transition. In ZrS2, the irreversible transformation between two different layered structures is accompanied by a sudden 14 % bandgap reduction. These results establish that Zr-based TMDs are an optimal strain-tunable platform for spatially textured bandgaps, with a strong potential for novel optoelectronic devices and light harvesting.
We prove that the modular symbols appropriately normalized and ordered have an asymptotical normal distribution for all cocompact subgroups of SL_2(R). We introduce hyperbolic Eisenstein series in order to calculate the moments of the modular symbols.
The success of deep neural networks often relies on a large amount of labeled examples, which can be difficult to obtain in many real scenarios. To address this challenge, unsupervised methods are strongly preferred for training neural networks without using any labeled data. In this paper, we present a novel paradigm of unsupervised representation learning by Auto-Encoding Transformation (AET) in contrast to the conventional Auto-Encoding Data (AED) approach. Given a randomly sampled transformation, AET seeks to predict it merely from the encoded features as accurately as possible at the output end. The idea is the following: as long as the unsupervised features successfully encode the essential information about the visual structures of original and transformed images, the transformation can be well predicted. We will show that this AET paradigm allows us to instantiate a large variety of transformations, from parameterized, to non-parameterized and GAN-induced ones. Our experiments show that AET greatly improves over existing unsupervised approaches, setting new state-of-the-art performances being greatly closer to the upper bounds by their fully supervised counterparts on CIFAR-10, ImageNet and Places datasets.
We investigate the synthesis of kesterite Cu2ZnSnS4 (CZTS) polycrystalline thin films using cosputtering from binary sulfide targets followed by annealing in sulfur vapor at 500 {\deg}C to 650 {\deg}C. The films are the kesterite CZTS phase as indicated by x-ray diffraction, Raman scattering, and optical absorption measurements. The films exhibit (112) fiber texture and preferred low-angle and Sigma3 grain boundary populations which have been demonstrated to reduce recombination in Cu(In,Ga)Se2 and CdTe films. The grain growth kinetics are investigated as functions of temperature and the addition of Na. Significantly, lateral grain sizes above 1 um are demonstrated for samples grown on Na-free glass,demonstrating the feasibility for CZTS growth on substrates other than soda lime glass.
In this paper we consider two ways to generalize the mathematical expectation of a random variable, the Choquet expectation and Peng's g-expectation. An open question has been, after making suitable restrictions to the class of random variables acted on by the Choquet expectation, for what class of expectation do these two definitions coincide? In this paper we provide a necessary and sufficient condition which proves that the only expectation which lies in both classes is the traditional linear expectation. This settles another open question about whether Choquet expectation may be used to obtain Monte Carlo-like solution of nonlinear PDE: It cannot, except for some very special cases.
The main purpose of this paper is the analytical study of self-shrinker solutions of the one-dimensional Landau-Lifshitz-Gilbert equation (LLG), a model describing the dynamics for the spin in ferromagnetic materials. We show that there is a unique smooth family of backward self-similar solutions to the LLG equation, up to symmetries, and we establish their asymptotics. Moreover, we obtain that in the presence of damping, the trajectories of the self-similar profiles converge to great circles on the sphere $\mathbb{S}^2$, at an exponential rate. In particular, the results presented in this paper provide examples of blow-up in finite time, where the singularity develops due to rapid oscillations forming limit circles.
We present an experimental and theoretical study of the conduction states of crystalline Si films confined within amorphous SiO_2 barriers, using the Si-2p core-level excitations. The spectral peaks near the conduction band minimum are compared with the bulk silicon spectrum. In the Si quantum wells, it is found that the conduction band minimum and the low-lying peaks undergo a blue shift while all higher peaks remain unshifted. The experimental results are supported by calculations using recent first-principles structural models for Si/SiO_2 superlattices. The experimental results suggest that all conduction states up to a given conduction band offset become confined and blue-shifted while those at higher energies are not confined and undergo no shift. These results provide unambiguous evidence that the visible-light emitting properties of Si/SiO_2 structures depend strongly on electron confinement effects.
We present a new comprehensive model of the physics of galaxy formation designed for large-scale hydrodynamical simulations of structure formation using the moving mesh code AREPO. Our model includes primordial and metal line cooling with self-shielding corrections, stellar evolution and feedback processes, gas recycling, chemical enrichment, a novel subgrid model for the metal loading of outflows, black hole (BH) seeding, BH growth and merging procedures, quasar- and radio-mode feedback, and a prescription for radiative electro-magnetic (EM) feedback from active galactic nuclei (AGN). The metal mass loading of outflows can be adjusted independently of the wind mass loading. This is required to simultaneously reproduce the stellar mass content of low mass haloes and their gas oxygen abundances. Radiative EM AGN feedback is implemented assuming an average spectral energy distribution and a luminosity-dependent scaling of obscuration effects. This form of feedback suppresses star formation more efficiently than continuous thermal quasar-mode feedback alone, but is less efficient than mechanical radio-mode feedback in regulating star formation in massive haloes. We contrast simulation predictions for different variants of our galaxy formation model with key observations. Our best match model reproduces, among other things, the cosmic star formation history, the stellar mass function, the stellar mass - halo mass relation, g-, r-, i-, z-band SDSS galaxy luminosity functions, and the Tully-Fisher relation. We can achieve this success only if we invoke very strong forms of stellar and AGN feedback such that star formation is adequately reduced in both low and high mass systems. In particular, the strength of radio-mode feedback needs to be increased significantly compared to previous studies to suppress efficient cooling in massive, metal-enriched haloes.
Unveiling new topological phases of matter is one of the current objectives in condensed matter physics. Recent experimental discoveries of Dirac and Weyl semimetals prompt to search for other exotic phases of matter. Here we present a systematic angle-resolved photoemission spectroscopy (ARPES) study of ZrSiS, a prime topological nodal semimetal candidate. Our wider Brillouin zone (BZ) mapping shows multiple Fermi surface pockets such as the diamond-shaped Fermi surface, ellipsoidal-shaped Fermi surface, and a small electron pocket encircling at the zone center (G) point, the M point and the X point of the BZ, respectively. We experimentally establish the spinless nodal fermion semimetal phase in ZrSiS, which is supported by our first-principles calculations. Our findings evidence that the ZrSiS-type of material family is a new platform to explore exotic states of quantum matter, while these materials are expected to provide an avenue for engineering two-dimensional topological insulator systems.
We theoretically investigate the dynamics of wave packets in a generic, non-Hermitian, optically anisotropic exciton-polariton system that exhibits degeneracies of its complex-valued eigenenergies in the form of pairs of exceptional points in momentum space. We observe the self-acceleration and reshaping of the wave packets governed by their eigenenergies. We further find that the exciton-polariton wave packets tend to self-organize into the eigenstate with the smaller decay rate, then propagate towards the minima of the decay rates in momentum space, resulting in directional transport in real space. We also describe the formation of pseudospin topological defects on the imaginary Fermi arc, where the decay rates of the two eigenstate coincide in momentum space. These effects of non-Hermiticity on the dynamics of exciton polaritons can be observed experimentally in a microcavity with optically anisotropic cavity spacer or exciton-hosting materials.
Here we report on a novel chemical route to synthesize homogenous cobalt doped titanate nanotubes (CoTNT), using an amorphous Co-doped precursor. The influence of the synthesis temperature, autoclave dwell time and metal doping on the structural and microstructural as well as on the optical properties of the synthesized titanate nanotubes is studied and discussed. The optical band gaps of the CoTNT samples are red shifted in comparison with the values determined for the undoped samples, such red shifts bringing the absorption edge of the CoTNT samples into the visible region. CoTNT materials also demonstrate particular high adsorption ability for methylene blue, the amount of the adsorbed dye being higher than the one predictable for a monolayer formation. This suggests the possibility of intercalation of the dye molecule between the TiO6 layers of the TNT structure. It is also shown that the methylene blue sensitized Co-doped nanostructures are highly stable under UV radiation and present a strong and broad absorption in the visible region.
Given a finite set $A\subseteq \mathbb{N}$, define the sum set $$A+A = \{a_i+a_j\mid a_i,a_j\in A\}$$ and the difference set $$A-A = \{a_i-a_j\mid a_i,a_j\in A\}.$$ The set $A$ is said to be sum-dominant if $|A+A|>|A-A|$. Hegarty used a nontrivial algorithm to find that $8$ is the smallest cardinality of a sum-dominant set. Since then, Nathanson has asked for a human-understandable proof of the result. However, due to the complexity of the interactions among numbers, it is still questionable whether such a proof can be written down in full without computers' help. In this paper, we present a computer-free proof that a sum-dominant set must have at least $7$ elements. We also answer the question raised by the author of the current paper et al about the smallest sum-dominant set of primes, in terms of its largest element. Using computers, we find that the smallest sum-dominant set of primes has $73$ as its maximum, smaller than the value found before.
We performed a search of star-forming sites influenced by external factors, such as SNRs, HII regions, and cloud-cloud collisions, to understand the star-forming activity in the Galactic center region using the NRO Galactic Center Survey in SiO $v=0, J=2-1$, H$^{13}$CO$^+ J=1-0$, and CS $J=1-0$ emission lines obtained by the Nobeyama 45-m telescope. We found a half-shell like feature (HSF) with a high integrated line intensity ratio of $ int T_{ mathrm B}$(SiO $v=0, J=2-1$)$dv$/$ int T_{ mathrm B}$(H$^{13}$CO$^+ J=1-0$)$dv sim6-8$ in the 50 km s$^{-1}$ molecular cloud, which is a most conspicuous molecular cloud in the region and harbors an active star-forming site seen as several compact HII regions. The high ratio in the HSF indicates that the cloud contains huge shocked molecular gas. The HSF is also seen as a half-shell feature in the position-velocity diagram. A hypothesis explaining the chemical and kinetic properties of the HSF is that the feature is originated by a cloud-cloud collision (CCC). We analyzed the CS $J=1-0$ emission line data obtained by Nobeyama Millimeter Array to reveal the relation between the HSF and the molecular cloud cores in the cloud. We made a cumulative core mass function (CMF) of the molecular cloud cores within the HSF. The CMF in the CCC region is not truncated at least up to $ sim2500M_ odot$ although the CMF of the non-CCC region reaches the upper limit of $ sim1500M_ odot$. Most massive molecular cores with $M_{ mathrm{gas}}>750 M_{ odot}$ are located only around the ridge of the HSF and adjoin the compact HII region. These may be a sign of massive star formation induced by CCC in the Galactic center region.
We present results of optical polarization observations performed with the MASTER robotic net for three types of objects: gamma-ray bursts, supernovae, and blazars. For the Swift gamma-ray bursts GRB100906A, GRB110422A, GRB121011A, polarization observations were obtained during very early stages of optical emission. For GRB100906A it was the first prompt optical polarization observation in the world. Photometry in polarizers is presented for Type Ia Supernova 2012bh during 20 days, starting on March 27, 2012. We find that the linear polarization of SN 2012bh at the early stage of the envelope expansion was less than 3%. Polarization measurements for the blazars OC 457, 3C 454.3, QSO B1215+303, 87GB 165943.2+395846 at single nights are presented. We infer the degree of the linear polarization and polarization angle. The blazars OC 457 and 3C 454.3 were observed during their periods of activity. The results show that MASTER is able to measure substantially polarized light; at the same time it is not suitable for determining weak polarization (less than 5%) of dim objects (fainter than 16$^m$). Polarimetric observations of the optical emission from gamma-ray bursts and supernovae are necessary to investigate the nature of these transient objects.
The spin-polarized homogeneous electron gas with densities $\rho_\uparrow$ and $\rho_\downarrow$ for electrons with spin `up' ($\uparrow$) and spin `down' ($\downarrow$), respectively, is systematically analyzed with respect to its lowest-order reduced densities and density matrices and their mutual relations. The three 2-body reduced density matrices $\gamma_{\uparrow\uparrow}$, $\gamma_{\downarrow\downarrow}$, $\gamma_a$ are 4-point functions for electron pairs with spins $\uparrow\uparrow$, $\downarrow\downarrow$, and antiparallel, respectively. From them, three functions $G_{\uparrow\uparrow}(x,y)$, $G_{\downarrow\downarrow}(x,y)$, $G_a(x,y)$, depending on only two variables, are derived. These functions contain not only the pair densities but also the 1-body reduced density matrices. The contraction properties of the 2-body reduced density matrices lead to three sum rules to be obeyed by the three key functions $G_{ss}$, $G_a$. These contraction sum rules contain corresponding normalization sum rules as special cases. The momentum distributions $n_\uparrow(k)$ and $n_\downarrow(k)$, following from $f_\uparrow(r)$ and $f_\downarrow(r)$ by Fourier transform, are correctly normalized through $f_s(0)=1$. In addition to the non-negativity conditions $n_s(k),g_{ss}(r),g_a(r)\geq 0$ [these quantities are probabilities], it holds $n_s(k)\leq 1$ and $g_{ss}(0)=0$ due to the Pauli principle and $g_a(0)\leq 1$ due to the Coulomb repulsion. Recent parametrizations of the pair densities of the spin-unpolarized homogeneous electron gas in terms of 2-body wave functions (geminals) and corresponding occupancies are generalized (i) to the spin-polarized case and (ii) to the 2-body reduced density matrix giving thus its spectral resolutions.
We present a new tool to compute the number $\phi_\A (\b)$ of integer solutions to the linear system $$ \x \geq 0 \qquad \A \x = \b $$ where the coefficients of $\A$ and $\b$ are integral. $\phi_\A (\b)$ is often described as a \emph{vector partition function}. Our methods use partial fraction expansions of Euler's generating function for $\phi_\A (\b)$. A special class of vector partition functions are Ehrhart (quasi-)polynomials counting integer points in dilated polytopes.
The objective of this paper is to characterize harmonic Hardy spaces and a boundary behavior of harmonic functions on a smooth domain in real Euclidean space.
Jacobian conjectures (that nonsingular implies invertible) for rational everywhere defined maps of real n-space to itself are considered, with no requirement for a constant Jacobian determinant or a rational inverse. The associated extension of rational function fields must be of odd degree and must have no nontrivial automorphisms. The extensions for the Pinchuk counterexamples to the strong real Jacobian conjecture have no nontrivial automorphisms, but are of degree six. The birational case is proved, the Galois case is clarified but the general case of odd degree remains open. However, certain topological conditions are shown to be sufficient. Reduction theorems to specialized forms are proved.
Spin-related electronics using two dimensional (2D) van der Waals (vdW) materials as a platform are believed to hold great promise for revolutionizing the next generation spintronics. Although many emerging new phenomena have been unravelled in 2D electronic systems with spin long-range orderings, the scarcely reported room temperature magnetic vdW material has thus far hindered the related applications. Here, we show that intrinsic ferromagnetically aligned spin polarization can hold up to 316 K in a metallic phase of 1$T$-CrTe$_{2}$ in the few-layer limit. This room temperature 2D long range spin interaction may be beneficial from an itinerant enhancement. Spin transport measurements indicate an in-plane room temperature negative anisotropic magnetoresistance (AMR) in few-layered CrTe$_{2}$, but a sign change in the AMR at lower temperature, with -0.6$\%$ at 300 K and +5$\%$ at 10 K, respectively. This behavior may originate from the specific spin polarized band structure of CrTe$_{2}$. Our findings provide insights into magnetism in few-layered CrTe$_{2}$, suggesting potential for future room temperature spintronic applications of such 2D vdW magnets.