ShantanuT01/DACTYL-Pretraining huggingface dataset:
We have developed a semi-analytic framework to model the large-scale evolution of the first Population III (Pop III) stars and the transition to metal-enriched star formation. Our model follows dark matter halos from cosmological N-body simulations, utilizing their individual merger histories and three-dimensional positions, and applies physically motivated prescriptions for star formation and feedback from Lyman-Werner (LW) radiation, hydrogen ionizing radiation, and external metal enrichment due to supernovae winds. This method is intended to complement analytic studies, which do not include clustering or individual merger histories, and hydrodynamical cosmological simulations, which include detailed physics, but are computationally expensive and have limited dynamic range. Utilizing this technique, we compute the cumulative Pop III and metal-enriched star formation rate density (SFRD) as a function of redshift at $z \geq 20$. We find that varying the model parameters leads to significant qualitative changes in the global star formation history. The Pop III star formation efficiency and the delay time between Pop III and subsequent metal-enriched star formation are found to have the largest impact. The effect of clustering (i.e. including the three-dimensional positions of individual halos) on various feedback mechanisms is also investigated. The impact of clustering on LW and ionization feedback is found to be relatively mild in our fiducial model, but can be larger if external metal enrichment can promote metal-enriched star formation over large distances.
Parsing an image into a hierarchy of objects, parts, and relations is important and also challenging in many computer vision tasks. This paper proposes a simple and effective capsule autoencoder to address this issue, called DPR-CAE. In our approach, the encoder parses the input into a set of part capsules, including pose, intensity, and dynamic vector. The decoder introduces a novel dynamic part representation (DPR) by combining the dynamic vector and a shared template bank. These part representations are then regulated by corresponding capsules to composite the final output in an interpretable way. Besides, an extra translation-invariant module is proposed to avoid directly learning the uncertain scene-part relationship in our DPR-CAE, which makes the resulting method achieves a promising performance gain on $rm$-MNIST and $rm$-Fashion-MNIST. % to model the scene-object relationship DPR-CAE can be easily combined with the existing stacked capsule autoencoder and experimental results show it significantly improves performance in terms of unsupervised object classification. Our code is available in the Appendix.
We investigate the impurity scattering induced quasiparticle interference in the ($\pi, 0$) spin-density wave phase of the iron pnictides. We use a five orbital tight binding model and our mean field theory in the clean limit captures key features of the Fermi surface observed in angle-resolved photoemission. We use a t-matrix formalism to incorporate the effect of doping induced impurities on this state. The impurities lead to a spatial modulation of the local density of states about the impurity site, with a periodicity of $\sim 8a_{{\rm Fe}-{\rm Fe}}$ along the antiferromagnetic direction. The associated momentum space quasiparticle interference pattern is anisotropic, with major peaks located at $\sim (\pm \pi/4,0)$, consistent with spectroscopic imaging scanning tunneling microscopy. We trace the origin of this pattern to an elliptical contour of constant energy around momentum (0,0), with major axis oriented along the (0,1) direction, in the mean field electronic structure.
We present results of a calculation of absorption of 10-500 GeV gamma-rays at high redshifts. This calculation requires the determination of the high- redshift evolution of the full spectral energy distribution of the intergalactic photon field. For this, we have primarily followed the recent analysis of Fall, Charlot and Pei. We give our results for the gamma-ray opacity as a function of redshift out to a redshift of 3. We then give predicted gamma-ray spectra for selected blazars and also extend our results on the background from unresolved blazars to an energy of 500 GeV. Absorption effects are predicted to significantly steepen the background spectrum above 20 GeV. Our absorption calculations can be used to place limits on the redshifts of gamma-ray bursts. Our background calculations can be used to determine the observability of multi-GeV lines from dark matter neutralino particles.
The self-consistent treatment of real and imaginary renormalizations in the dynamic spin susceptibility for the frustrated Heisenberg model reproduces for cuprates at low doping: a spin spectrum, a saddle point for q near (pi/2,pi/2), nearly constant q-integrated susceptibility for energy less than 150 meV and a scaling law. Frustration increase (optimally doped case) leads to a stripe scenario with a saddle point at q near (pi,pi/2) and $\chi_{2D}(\omega)$ peak near 30meV. The obtained $\chi (\mathbf{q},\omega)$ describes neutron scattering results and leads to well-known temperature transport anomalies in doped cuprates.
In this paper we use Jacobi fields to describe the motion of a charged particle in the classical gravitational, electromagnetic, and Yang-Mills fields.
Landauer's formula relates the conductance of a quantum wire or interface to transmission probabilities. Total transmission probabilities are frequently calculated using Green function techniques and an expression first derived by Caroli. Alternatively, partial transmission probabilities can be calculated from the scattering wave functions that are obtained by matching the wave functions in the scattering region to the Bloch modes of ideal bulk leads. An elegant technique for doing this, formulated originally by Ando, is here generalized to any Hamiltonian that can be represented in tight-binding form. A more compact expression for the transmission matrix elements is derived and it is shown how all the Green function results can be derived from the mode matching technique. We illustrate this for a simple model which can be studied analytically, and for an Fe|vacuum|Fe tunnel junction which we study using first-principles calculations.
In a recent paper, Gerbner, Patk\'{o}s, Tuza and Vizer studied regular $F$-saturated graphs. One of the essential questions is given $F$, for which $n$ does a regular $n$-vertex $F$-saturated graph exist. They proved that for all sufficiently large $n$, there is a regular $K_3$-saturated graph with $n$ vertices. We extend this result to both $K_4$ and $K_5$ and prove some partial results for larger complete graphs. Using a variation of sum-free sets from additive combinatorics, we prove that for all $k \geq 2$, there is a regular $C_{2k+1}$-saturated with $n$ vertices for infinitely many $n$. Studying the sum-free sets that give rise to $C_{2k+1}$-saturated graphs is an interesting problem on its own and we state an open problem in this direction.
The derivative of self-intersection local time (DSLT) for Brownian motion was introduced by Rosen and subsequently used by others to study the $L^2$ and $L^3$ moduli of continuity of Brownian local time. A version of the DSLT for fractional Brownian motion (fBm) has also appeared in the literature. In the present work, we further its study by proving a Tanaka-style formula for it. In the course of this endeavor we provide a Fubini theorem for integrals with respect to fBm. The Fubini theorem may be of independent interest, as it generalizes (to Hida distributions) similar results previously seen in the literature. Finally, we also give an explicit Wiener chaos expansion for the DSLT of fBm
In this article we present some particularly important issues regarding the CeCo$_{1-x}$Fe$_{x}$Ge$_{3}$ alloys. Firstly, the electrical resistivity below 2 K, down to 500 mK is studied to confirm the non-Fermi-liquid behavior around the critical substitution range x~0.65. Secondly, the scheme of the crystal electric field (CEF) levels has been investigated employing methods like inelastic neutron scattering, specific heat, and magnetic susceptibility. It aims to clarify different reports on the parent CeCoGe$_{3}$ compound and to provide first data concerning CEF in the entire CeCo$_{1-x}$Fe$_{x}$Ge$_{3}$ series. Third, the effect of hydrogenation, especially around the quantum critical point (QCP) (x~0.65) is verified.
The condition of plane polynomial curve to be a line in well-known Abhyankar-Moh Theorem is replaced by weaker ones. A criterion of embedded line is obtained from this strong theorem: Two polynomials can generate the entire polynomial ring iff their derivatives can be generated.
In this paper, we apply the moving plane method to some degenerate elliptic equations to get a Liouville type theorem. As an application, we derive the a priori bounds for positive solutions of some semi-linear degenerate elliptic equations.
With the increased size and frequency of wildfire eventsworldwide, accurate real-time prediction of evolving wildfirefronts is a crucial component of firefighting efforts and for-est management practices. We propose a wildfire spreadingmodel that predicts the evolution of the wildfire perimeter in24 hour periods. The fire spreading simulation is based ona deep convolutional neural network (CNN) that is trainedon remotely sensed atmospheric and environmental time se-ries data. We show that the model is able to learn wildfirespreading dynamics from real historic data sets from a seriesof wildfires in the Western Sierra Nevada Mountains in Cal-ifornia. We validate the model on a previously unseen wild-fire and produce realistic results that significantly outperformhistoric alternatives with validation accuracies ranging from78% - 98%
We obtain a new bound on the location of eigenvalues for a non-self-adjoint Schr\"odinger operator with complex-valued potentials by obtaining a weighted $L^2$ estimate for the resolvent of the Laplacian.
Let $q>r\ge1$ be coprime integers. Let ${\mathbb P}_c={\mathbb P}_c(q,r,{\cal H})$ be an increasing sequence of primes $p$ satisfying two conditions: (i) $p\equiv r$ (mod $q$) and (ii) $p$ starts a prime $k$-tuple with a given pattern ${\cal H}$. Let $\pi_c(x)$ be the number of primes in ${\mathbb P}_c$ not exceeding $x$. We heuristically derive formulas predicting the growth trend of the maximal gap $G_c(x)=\max_{p'\le x}(p'-p)$ between successive primes $p,p'\in{\mathbb P}_c$. Extensive computations for primes up to $10^{14}$ show that a simple trend formula $$G_c(x) \sim {x\over\pi_c(x)}\cdot(\log \pi_c(x) + O_k(1))$$ works well for maximal gaps between initial primes of $k$-tuples with $k\ge2$ (e.g., twin primes, prime triplets, etc.) in residue class $r$ (mod $q$). For $k=1$, however, a more sophisticated formula $$G_c(x) \sim {x\over\pi_c(x)}\cdot\big(\log{\pi_c^2(x)\over x}+O(\log q)\big)$$ gives a better prediction of maximal gap sizes. The latter includes the important special case of maximal gaps in the sequence of all primes ($k=1$, $q=2$, $r=1$). The distribution of appropriately rescaled maximal gaps $G_c(x)$ is close to the Gumbel extreme value distribution. Computations suggest that almost all maximal gaps satisfy a generalized strong form of Cramer's conjecture. We also conjecture that the number of maximal gaps between primes in ${\mathbb P}_c$ below $x$ is $O_k(\log x)$.
Historical optical data are combined with more recent optical, extreme ultraviolet, and X-ray data to update the spin ephemeris of the cataclysmic variable EX Hya.
We have established the relations between the baryon-baryon scattering phase shifts and the two-particle energy spectrum in the elongated box. We have studied the cases with both the periodic boundary condition and twisted boundary condition in the center of mass frame. The framework is also extended to the system of nonzero total momentum with periodic boundary condition in the moving frame. This will be helpful to extract the phase shifts in the continuum from lattice QCD data using asymmetric volumes.
The prominent blue shifts of Ne viii associated with the junctions of the magnetic network in the quiet Sun are still not well understood. By comparing the coronal magnetic-field structures as obtained by a potential-field reconstruction with the conspicuous blue-shift patches on the dopplergram of Ne viii as observed in an equatorial quiet-Sun region, we find that most of the regions with significant upflow are associated with the funnel-like legs of magnetic loops and co-spatial with increments of the line width. These quasi-steady upflows can be regarded as the signatures of mass supply to coronal loops. By using the square-root of the line intensity as a proxy for the plasma density, the mass flux of the upflow in each funnel can be estimated. We find that the mass flux is anti-correlated with the funnel's expansion factor as determined from the extrapolated magnetic field. One of the loop systems is associated with a coronal bright point, which was observed by several instruments and exhibited various morphologies in different wavelengths and viewing directions. A remarkable agreement between its magnetic structure and the associated EUV emission pattern was found, suggesting an almost potential-field nature of the coronal magnetic field. We also report the direct detection of a small-scale siphon flow by both STEREO satellites. However, this transient siphon flow occurred in a weak mixed-polarity-field region, which was outside the adjacent magnetic funnel, and thus it is perhaps not related to plasma upflow in the funnel. Based on these observations, we suggest that at upper-TR temperatures the dominant flows in quiet-Sun coronal loops are long-lasting upflows rather than siphon flows. We also discuss the implications for coronal heating and unresolved magnetic structures.
First, we establish an abstract ergodic result on $\mR^d$. Classical ergodic results on $\mR^d$ require that the process is irreducible, we weaken it to some weak form of irreducibility in this article. The main method used in this article is coupling. Then, we apply our abstract ergodic result to stochastic differential equations driven by a L\'evy noise and obtain a new result.
We have derived the Bethe-Salpeter (BS) equations for the collective-mode spectrum of a mixture of fermion atoms of two hyperfine states loaded into a moving optical lattice. The collective excitation spectrum exhibits rotonlike minimum and the Landau instability takes place when the energy of the rotonlike minimum hits zero. The BS approach is compared with the other existing methods for calculating the collective-mode spectrum. In particular, it is shown that the spectrum obtained by the BS equations in an excellent agreement with corresponding spectrum obtained by the perturbation theory, while the Green's function formalism provides slightly different results for the collective excitations.
We study a generic spin-fermion model, where a two-level system (spin) is coupled to two metallic leads with different chemical potentials, in the presence of monochromatic driving fields. The real-time dynamics of the system is simulated beyond the Markovian limit by an iterative numerically exact influence functional path integral method. Our results show that although both system-bath coupling and chemical potential difference contribute to dissipation, their effects are distinct. In particular, under certain drivings the asymptotic Floquet states of the system exhibit robustness against a range of system-bath coupling strength: the asymptotic behaviors of the system are insensitive to different system-bath coupling strength, while they are highly tunable by the chemical potential difference of baths. Further simulations show that such robustness may be essentially a result of the interplay between driving, bath electronic structure and system-bath coupling. Therefore the robustness could break down depending on the characteristics of the interplay. In addition, under fast linearly polarized driving the quantum stochastic resonance is demonstrated that stronger system-bath coupling (stronger dissipation) enhances rather than suppresses the amplitude of coherent oscillations of the system.
We compute a rigorous asymptotic expansion of the energy of a point defect in a 1D chain of atoms with second neighbour interactions. We propose the Confined Lennard-Jones model for interatomic interactions, where it is assumed that nearest neighbour potentials are globally convex and second neighbour potentials are globally concave. We derive the {\Gamma}-limit for the energy functional as the number of atoms per period tends to infinity and derive an explicit form for the first order term in a {\Gamma}-expansion in terms of an infinite cell problem. We prove exponential decay properties for minimisers of the energy in the infinite cell problem, suggesting that the perturbation to the deformation introduced by the defect is confined to a thin boundary layer.
Electronic structures of the filled-skutterudite compounds PrRu$_4$P$_{12}$ and SmRu$_4$P$_{12}$, which undergo a metal-insulator transition (MIT) at $T_{\rm MI}$ = 60 K and 16 K, respectively, have been studied by means of optical spectroscopy. Their optical conductivity spectra develop an energy gap of $\sim$ 10 meV below $T_{\rm MI}$. The observed characteristics of the energy gap are qualitatively different from those of the Kondo semiconductors. In addition, optical phonon peaks in the spectra show anomalies upon the MIT, including broadening and shifts at $T_{\rm MI}$ and an appearance of new peaks below $T_{\rm MI}$. These results are discussed in terms of density waves or orbital ordering previously predicted for these compounds.
In quantum zero knowledge, the assumption was made that the verifier is only using unitary operations. Under this assumption, many nice properties have been shown about quantum zero knowledge, including the fact that Honest-Verifier Quantum Statistical Zero Knowledge (HVQSZK) is equal to Cheating-Verifier Quantum Statistical Zero Knowledge (QSZK) (see [Wat02,Wat06]).   In this paper, we study what happens when we allow an honest verifier to flip some coins in addition to using unitary operations. Flipping a coin is a non-unitary operation but doesn't seem at first to enhance the cheating possibilities of the verifier since a classical honest verifier can flip coins. In this setting, we show an unexpected result: any classical Interactive Proof has an Honest-Verifier Quantum Statistical Zero Knowledge proof with coins. Note that in the classical case, honest verifier SZK is no more powerful than SZK and hence it is not believed to contain even NP. On the other hand, in the case of cheating verifiers, we show that Quantum Statistical Zero Knowledge where the verifier applies any non-unitary operation is equal to Quantum Zero-Knowledge where the verifier uses only unitaries.   One can think of our results in two complementary ways. If we would like to use the honest verifier model as a means to study the general model by taking advantage of their equivalence, then it is imperative to use the unitary definition without coins, since with the general one this equivalence is most probably not true. On the other hand, if we would like to use quantum zero knowledge protocols in a cryptographic scenario where the honest-but-curious model is sufficient, then adding the unitary constraint severely decreases the power of quantum zero knowledge protocols.
According to the Onsager principle a matrix of kinetic coefficients is symmetric in a system not violating time inversion symmetry. The antisymmetry is possible in systems with broken time inversion symmetry f.i. in systems in external magnetic field. An exception to this rule is presented here. It is shown that in a tetragonal metals with point group $C_{4v}$ not violating time inversion the conductivity tensor is antisymmetric. The corresponding optical properties are considered.
The dynamics of a non-Markovian open quantum system described by a general time-local master equation is studied. The propagation of the density operator is constructed in terms of two processes: (i) deterministic evolution and (ii) evolution of a probability density functional in the projective Hilbert space. The analysis provides a derivation for the jump probabilities used in the recently developed non-Markovian quantum jump (NMQJ) method (Piilo et al 2008 Phys. Rev. Lett. 100 180402).
About half of carbon and s-process enhanced metal-poor stars (CEMP-s) show a high r-process enrichment (CEMP-s/r), incompatible with a pure s-process contribution. CEMP-s stars are of low mass (M < 0.9 Msun) and belong to binary systems. The C and s-process enrichment results from mass transfer by the winds of the primary AGB companion (now a white dwarf). The nucleosynthesis of the r-process, instead, is believed to occur in massive stars exploding as Supernovae of Type II. The most representative r-process element is Eu (95% of solar Eu). We suggest that the r-process enrichment was already present by local SNII pollution in the molecular cloud from which the binary system formed. The initial r-enrichment does not affect the s-process nucleosynthesis. However, the s-process indicators [hs/ls] (where ls is defined as the average of Y and Zr; hs as the average of La, Nd, Sm) and [Pb/hs] may depend on the initial r-enhancement. For instance, the hs-peak has to account of an r-process contribution estimated to be 30% for solar La, 40% for solar Nd, and 70% for solar Sm. A large spread of [Eu/Fe] is observed in unevolved halo stars up to [Eu/Fe] ~ 2. In presence of a very high initial r-enrichment of the molecular cloud, the maximum [hs/Fe] predicted in CEMP-s/r stars may increase up to 0.3 dex. Instead, the spread of [Y,Zr/Fe] observed in unevolved halo stars reaches a maximum of only ~ 0.5 dex, not affecting much the predicted [ls/Fe]. This is in agreement with observations of CEMP-s/r stars that show an observed [hs/ls] in average higher than that observed in CEMP-s. Preliminary results are presented.
Dual supermassive black holes (SMBHs) with kiloparsec scale separations in merger-remnant galaxies are informative tracers of galaxy evolution, but the avenue for identifying them in large numbers for such studies is not yet clear. One promising approach is to target spectroscopic signatures of systems where both SMBHs are fueled as dual active galactic nuclei (AGNs), or where one SMBH is fueled as an offset AGN. Dual AGNs may produce double-peaked narrow AGN emission lines, while offset AGNs may produce single-peaked narrow AGN emission lines with line-of-sight velocity offsets relative to the host galaxy. We search for such dual and offset systems among 173 Type 2 AGNs at z<0.37 in the AGN and Galaxy Evolution Survey (AGES), and we find two double-peaked AGNs and five offset AGN candidates. When we compare these results to a similar search of the DEEP2 Galaxy Redshift Survey and match the two samples in color, absolute magnitude, and minimum velocity offset, we find that the fraction of AGNs that are dual SMBH candidates increases from z=0.25 to z=0.7 by a factor of ~6 (from 2/70 to 16/91, or 2.9% to 18%). This may be associated with the rise in the galaxy merger fraction over the same cosmic time. As further evidence for a link with galaxy mergers, the AGES offset and dual AGN candidates are tentatively ~3 times more likely than the overall AGN population to reside in a host galaxy that has a companion galaxy (from 16/173 to 2/7, or 9% to 29%). Follow-up observations of the seven offset and dual AGN candidates in AGES will definitively distinguish velocity offsets produced by dual SMBHs from those produced by narrow-line region kinematics, and will help sharpen our observational approach to detecting dual SMBHs.