ShantanuT01/DACTYL-Pretraining huggingface dataset:
We provide a microscopic description of the fusion reactions between $^{40,48}$Ca and $^{78}$Ni. The internuclear potentials are obtained using the density-constrained (DC) time-dependent Hartree-Fock (TDHF) approach and fusion cross sections are calculated via the incoming wave boundary condition method. By performing DC-TDHF calculations at several selected incident energies, the internuclear potentials for both systems are obtained and the energy-dependence of fusion barrier are revealed. The influence of tensor force on internuclear potentials of $^{48}\mathrm{Ca}+{}^{78}\mathrm{Ni}$ is more obvious than those of $^{40}\mathrm{Ca}+{}^{78}\mathrm{Ni}$. By comparing the calculated fusion cross sections between $^{40}\mathrm{Ca}+{}^{78}\mathrm{Ni}$ and $^{48}\mathrm{Ca}+{}^{78}\mathrm{Ni}$, an interesting enhancement of sub-barrier fusion cross sections for the former system is found, which can be explained by the narrow width of internuclear potential for $^{40}\mathrm{Ca}+{}^{78}\mathrm{Ni}$ while the barrier heights and positions are very close to each other. The tensor force suppresses the sub-barrier fusion cross sections of both two systems.
We study the effect of final state interactions at the threshold of Higgs boson pair production in the Glashow-Weinberg-Salam model. We consider three major processes of the pair production in the model: lepton pair annihilation, ZZ fusion, and WW fusion. We find that the corrections caused by the effect for these processes are markedly different. According to our results, the effect can cause non-negligible corrections to the cross sections for lepton pair annihilation and small corrections for ZZ fusion, and this effect is negligible for WW fusion.
Using the recently found hA amplitude, single and double inclusive jet production rates on the nucleus are studied in the perturbative QCD with $N_c\to\infty$. Jet multiplicities are found to grow with $A$ and energy as $A^{2/9}s^\Delta$ where $\Delta$ is the BFKL intercept. Long range correlations are found to behave as $A^{4/9}s^{2\Delta}$ and change from negative to positive at a certain high energy.
We present a sample of 45 Damped Lyman-$\alpha$ system (DLA, \nhi\ $ \geq 2 \times 10^{20} {\rm cm}^{-2}$) counterparts (33 detections, 12 upper limits) which host gamma-ray bursts (GRB-DLAs) in order to investigate star-formation and metallicity within galaxies hosting DLAs. Our sample spans $z \sim 2-6$ and is nearly three times larger than any previously detected DLA counterparts survey based on quasar line-of-sight searches (QSO-DLAs). We report star formation rates (SFRs) from rest-frame UV photometry and SED modeling. We find that DLA counterpart SFRs are not correlated with either redshift or HI column density. Thanks to the combination of \hst\ and ground-based observations, we also investigate DLA host star-formation efficiency. Our GRB-DLA counterpart sample spans both higher efficiency and low efficiency star formation regions compared to the local Kennicutt-Schmidt relation, local star formation laws, and $z \sim 3$ cosmological simulations. We also compare the depletion times of our DLA hosts sample to other objects in the local Universe, our sample appears to deviate from the star formation efficiencies measured in local spiral and dwarf galaxies. Furthermore, we find similar efficiencies as local inner disks, SMC, and LBG outskirts. Finally, our enrichment time measurements show a spread of systems with under- and over-abundance of metals which may suggest that these systems had episodic star formation and a metal enrichment/depletion as a result of strong stellar feedback and/or metal inflow/outflow.
Measurements on entangled quantum systems necessarily yield outcomes that are intrinsically unpredictable if they violate a Bell inequality. This property can be used to generate certified randomness in a device-independent way, i.e., without making detailed assumptions about the internal working of the quantum devices used to generate the random numbers. Furthermore these numbers are also private, i.e., they appear random not only to the user, but also to any adversary that might possess a perfect description of the devices. Since this process requires a small initial random seed, one usually speaks of device-independent randomness expansion.   The purpose of this paper is twofold. First, we point out that in most real, practical situations, where the concept of device-independence is used as a protection against unintentional flaws or failures of the quantum apparatuses, it is sufficient to show that the generated string is random with respect to an adversary that holds only classical-side information, i.e., proving randomness against quantum-side information is not necessary. Furthermore, the initial random seed does not need to be private with respect to the adversary, provided that it is generated in a way that is independent from the measured systems. The devices, though, will generate cryptographically-secure randomness that cannot be predicted by the adversary and thus one can, given access to free public randomness, talk about private randomness generation.   The theoretical tools to quantify the generated randomness according to these criteria were already introduced in [S. Pironio et al, Nature 464, 1021 (2010)], but the final results were improperly formulated. The second aim of this paper is to correct this inaccurate formulation and therefore lay out a precise theoretical framework for practical device-independent randomness expansion.
We present the results of extensive multi-frequency monitoring of the radio galaxy 3C 111 between 2004 and 2010 at X-ray (2.4--10 keV), optical (R band), and radio (14.5, 37, and 230 GHz) wave bands, as well as multi-epoch imaging with the Very Long Baseline Array (VLBA) at 43 GHz. Over the six years of observation, significant dips in the X-ray light curve are followed by ejections of bright superluminal knots in the VLBA images. This shows a clear connection between the radiative state near the black hole, where the X-rays are produced, and events in the jet. The X-ray continuum flux and Fe line intensity are strongly correlated, with a time lag shorter than 90 days and consistent with zero. This implies that the Fe line is generated within 90 light-days of the source of the X-ray continuum. The power spectral density function of X-ray variations contains a break, with steeper slope at shorter timescales. The break timescale of 13 (+12,-6) days is commensurate with scaling according to the mass of the central black hole based on observations of Seyfert galaxies and black hole X-ray binaries (BHXRBs). The data are consistent with the standard paradigm, in which the X-rays are predominantly produced by inverse Compton scattering of thermal optical/UV seed photons from the accretion disk by a distribution of hot electrons --- the corona --- situated near the disk. Most of the optical emission is generated in the accretion disk due to reprocessing of the X-ray emission. The relationships that we have uncovered between the accretion disk and the jet in 3C 111, as well as in the FR I radio galaxy 3C 120 in a previous paper, support the paradigm that active galactic nuclei and Galactic BHXRBs are fundamentally similar, with characteristic time and size scales proportional to the mass of the central black hole
Exclusive processes of heavy meson production and spacelike and timelike deeply virtual Compton scattering allow us to investigate the hadron structure in terms of Generalized Parton Distributions (GPDs). We review recent developments in the NLO description of such processes.
A simple model is proposed as a possible explanation for the checkerboard pattern of modulations in the hole density observed in recent tunneling experiments on underdoped cuprates. Two assumptions are made; first, an enhanced hole density near the acceptor dopants and secondly short range correlations in the positions of these dopants caused by their electrostatic and anisotropic elastic interactions. Together these can lead to a structure factor in qualitative agreement with experiment.
We describe a Schubert induction theorem, a tool for analyzing intersections on a Grassmannian over an arbitrary base ring. The key ingredient in the proof is the Geometric Littlewood-Richardson rule, described in a companion paper.   Schubert problems are among the most classical problems in enumerative geometry of continuing interest. As an application of Schubert induction, we address several long-standing natural questions related to Schubert problems, including: the "reality" of solutions; effective numerical methods; solutions over algebraically closed fields of positive characteristic; solutions over finite fields; a generic smoothness (Kleiman-Bertini) theorem; and monodromy groups of Schubert problems. These methods conjecturally extend to the flag variety.
A subset of leaves of a rooted tree induces a new tree in a natural way. The density of a tree $D$ inside a larger tree $T$ is the proportion of such leaf-induced subtrees in $T$ that are isomorphic to $D$ among all those with the same number of leaves as $D$. The inducibility of $D$ measures how large this density can be as the size of $T$ tends to infinity. In this paper, we explicitly determine the inducibility in some previously unknown cases and find general upper and lower bounds, in particular in the case where $D$ is balanced, i.e., when its branches have at least almost the same size. Moreover, we prove a result on the speed of convergence of the maximum density of $D$ in strictly $d$-ary trees $T$ (trees where every internal vertex has precisely $d$ children) of a given size $n$ to the inducibility as $n \to \infty$, which supports an open conjecture.
In this work, we introduce new combinatorial objects called Dyck tableaux, which present a natural insertion algorithm. These tools may be useful to describe statistics which are relevant in the study of the physical model named PASEP.
We consider a renewal process with regularly varying stationary and weakly dependent steps, and prove that the steps made before a given time $t$, satisfy an interesting invariance principle. Namely, together with the age of the renewal process at time $t$, they converge after scaling to the Pitman--Yor distribution. We further discuss how our results extend the classical Dynkin--Lamperti theorem.
The following notion of growth rate can be seen as a generalization of joint spectral radius: Given a bilinear map $*:\mathbb R^d\times\mathbb R^d\to\mathbb R^d$ with nonnegative coefficients and a nonnegative vector $s\in\mathbb R^d$, denote by $g(n)$ the largest possible entry of a vector obtained by combining $n$ instances of $s$ using $n-1$ applications of $*$. Let $\lambda$ denote the growth rate $\limsup_{n\to\infty} \sqrt[n]{g(n)}$, Rosenfeld showed that the problem of checking $\lambda\le 1$ is undecidable by reducing the problem of joint spectral radius.   In this article, we provide a simpler reduction using the observation that matrix multiplication is actually a bilinear map. Suppose there is no restriction on the signs, an application of this reduction is that the problem of checking if the system can produce a zero vector is undecidable by reducing the problem of checking the mortality of a pair of matrices. This answers a question asked by Rosenfeld. Another application is that the problem does not become harder when we introduce more bilinear maps or more starting vectors, which was remarked by Rosenfeld.   It is known that if the vector $s$ is strictly positive, then the limit superior $\lambda$ is actually a limit. However, we show that when $s$ is only nonnegative, the problem of checking the validity of the limit is undecidable. This also answers a question asked by Rosenfeld.   We provide a formula for the growth rate $\lambda$. A condition is given so that the limit is always ensured. This actually gives a simpler proof for the limit $\lambda$ when $s>0$. An important corollary of the formula is the computability of the growth rate, which answers another question by Rosenfeld. Also, we relate the finiteness property of a set of matrices to a special structure called "linear pattern" for the problem of bilinear system.
We study the perturbative renormalizability of chiral two pion exchange for the singlet and triplet channels within effective field theory, provided that the one pion exchange piece of the interaction has been fully iterated. We determine the number of counterterms/subtractions needed in order to obtain finite results when the cut-off is removed, resulting in three counterterms for the singlet channel and six for the triplet. The results show that chiral two pion exchange can be treated perturbatively up to a center-of-mass momentum of k ~ 200-300 MeV in the singlet channel and k ~ 300-400 in the triplet.
We derive the optical luminosity, colors, and ratios of the blue and red helium burning (HeB) stellar populations from archival Hubble Space Telescope observations of nineteen starburst dwarf galaxies and compare them with theoretical isochrones from Padova stellar evolution models across metallicities from Z=0.001 to 0.009. We find that the observational data and the theoretical isochrones for both blue and red HeB populations overlap in optical luminosities and colors and the observed and predicted blue to red HeB ratios agree for stars older than 50 Myr over the time bins studied. These findings confirm the usefulness of applying isochrones to interpret observations of HeB populations. However, there are significant differences, especially for the red HeB population. Specifically we find: (1) offsets in color between the observations and theoretical isochrones of order 0.15 mag (0.5 mag) for the blue (red) HeB populations brighter than M_V ~ -4 mag, which cannot be solely due to differential extinction; (2) blue HeB stars fainter than M_V ~ -3 mag are bluer than predicted; (3) the slope of the red HeB sequence is shallower than predicted by a factor of ~3; and (4) the models overpredict the ratio of the most luminous blue to red HeB stars corresponding to ages <50 Myr. Additionally, we find that for the more metal-rich galaxies in our sample (Z> 0.5 Zsolar) the red HeB stars overlap with the red giant branch stars in the color magnitude diagrams, thus reducing their usefulness as indicators of star formation for ages >100 Myr.
I discuss the recent exciting results of discovery of TeV photons from several galactic and extragalactic sources, and highlight some objectives of VHE gamma ray astronomy that can be achieved in the near future by means of new generation ground-based detectors.
By devising a novel framework, we present a comprehensive theoretical study of solubilities of alkali (Li, Na, K, Rb, Cs) and alkaline earth (Be, Ca, Sr, Ba) metals in the he boron-rich Mg-B system. The study is based on first-principle calculations of solutes formation energies in MgB$_2$, MgB$_4$, MgB$_7$ alloys and subsequent statistical-thermodynamical evaluation of solubilities. The advantage of the approach consists in considering all the known phase boundaries in the ternary phase diagram. Substitutional Na, Ca, and Li demonstrate the largest solubilities, and Na has the highest (0.5-1 % in MgB$_7$ at $T=650-1000$ K). All the considered interstitials have negligible solubilities. The solubility of Be in MgB$_7$ can not be determined because the corresponding low-solubility formation energy is negative indicating the existence of an unknown ternary ground state. We have performed a high-throughput search of ground states in binary Mg-B, Mg-$A$, and B-$A$ systems, and we construct the ternary phase diagrams of Mg-B-$A$ alloys based on the stable binary phases. Despite its high temperature observations, we find that Sr$_{9}$Mg$_{38}$ is not a low-temperature equilibrium structure. We also determine two new possible ground states CaB$_{4}$ and RbB$_{4}$, not yet observed experimentally.
Given an oriented graph G, the modular flow polynomial counts the number of nowhere-zero Z_k-flows of G. We give a description of the modular flow polynomial in terms of (open) Ehrhart polynomials of lattice polytopes. Using Ehrhart-Macdonald reciprocity we give a combinatorial interpretation for the values of the modular flow polynomial at negative arguments which answers a question of Beck and Zaslavsky (2006). Our construction extends to Z_l-tensions and we recover Stanley's reciprocity theorem for the chromatic polynomial. Combining the combinatorial reciprocity statements for flows and tensions, we give an enumerative interpretation for positive evaluations of the Tutte polynomial of G.
Tetrahedrite-based ($\textrm{Cu}_{12}\textrm{Sb}_{4}\textrm{S}_{13}$) materials are candidates for good thermoelectric generators due to their intrinsic, very low thermal conductivity and high power factor. One of the current limitations is virtual absence of tetrahedrites exhibiting n--type conductivity. In this work, first-principles calculations are carried out to study Mg-doped tetrahedrite, $\textrm{Mg}_{x}\textrm{Cu}_{12}\textrm{Sb}_{4}\textrm{S}_{13}$ with possibility of predicting n--type material in mind. Different concentrations and modifications of the structure are investigated for their formation energies, preferred site occupation and change in local environment around dopants. Mg atoms tend to occupy 6b site, while introduced excess Cu prefers 24g site. Introduction of elements in those sites display different effect on nearby rattling Cu(2) atom. Topological analysis shows that tetrahedrite exhibits ionic, closed-shell bonds with some degree of covalency. Majority of the bonds weakens with increasing content of Mg; structure becomes increasingly less stable, which is also expressed by global instability and bond strain indexes. Achieving n--type conductivity was predicted by the calculations for structures with $x>1.0$, however increasing enthalpy of formation and lack of stability might suggest limit of solubility and difficulties in obtaining those experimentally.
In this paper we review some recent results, obtained jointly with Stu Whittington, for a mathematical model describing a copolymer in an emulsion. The copolymer consists of hydrophobic and hydrophilic monomers, concatenated randomly with equal density. The emulsion consists of large blocks of oil and water, arranged in a percolation-type fashion. To make the model mathematically tractable, the copolymer is allowed to enter and exit a neighboring pair of blocks only at diagonally opposite corners. The energy of the copolymer in the emulsion is minus $\alpha$ times the number of hydrophobic monomers in oil minus $\beta$ times the number of hydrophilic monomers in water. Without loss of generality we may assume that the interaction parameters are restricted to the cone $\{(\alpha,\beta)\in \mathbb{R}^2\colon |\beta|\leq\alpha\}$.   We show that the phase diagram has two regimes: (1) in the supercritical regime where the oil blocks percolate, there is a single critical curve in the cone separating a localized and a delocalized phase; (2) in the subcritical regime where the oil blocks do not percolate, there are three critical curves in the cone separating two localized phases and two delocalized phases, and meeting at two tricritical points. The different phases are characterized by different behavior of the copolymer inside the four neighboring pairs of blocks.
First, we consider a nonnegative homogeneous block tri-diagonal matrix and obtain its convergence parameter, where some results in the field of matrix analytic method are extended to the case where block matrices have countably infinite dimension. Second, we apply our results to a multi-dimensional QBD process and obtain lower bounds for the directional asymptotic decay rates of the stationary distribution.
We present a new approach for a single view, image-based object pose estimation. Specifically, the problem of culling false positives among several pose proposal estimates is addressed in this paper. Our proposed approach targets the problem of inaccurate confidence values predicted by CNNs which is used by many current methods to choose a final object pose prediction. We present a network called CullNet, solving this task. CullNet takes pairs of pose masks rendered from a 3D model and cropped regions in the original image as input. This is then used to calibrate the confidence scores of the pose proposals. This new set of confidence scores is found to be significantly more reliable for accurate object pose estimation as shown by our results. Our experimental results on multiple challenging datasets (LINEMOD and Occlusion LINEMOD) reflects the utility of our proposed method. Our overall pose estimation pipeline outperforms state-of-the-art object pose estimation methods on these standard object pose estimation datasets. Our code is publicly available on https://github.com/kartikgupta-at-anu/CullNet.
. The choice of a suitable random matrix model of a complex system is very sensitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wide range of random matrix ensembles which is not an easy task. It is highly desirable, if possible, to identify a common mathematcal structure among all the ensembles and analyze it to gain information about the ensemble- properties. Our successful search in this direction leads to Calogero Hamiltonian, a one-dimensional quantum hamiltonian with inverse-square interaction, as the common base. This is because both, the eigenvalues of the ensembles, and, a general state of Calogero Hamiltonian, evolve in an analogous way for arbitrary initial conditions. The varying nature of the complexity is reflected in the different form of the evolution parameter in each case. A complete investigation of Calogero Hamiltonian can then help us in the spectral analysis of complex systems.
Pistons are elementary components of a wide variety of thermal engines, allowing to convert input fuel into rotational motion. Here, we propose a single-piston engine where the rotational degree of freedom is effectively realized by the flux of a Josephson loop -- a quantum rotor -- while the working volume corresponds to the effective length of a superconducting resonator. Our autonomous design implements a Carnot cycle, relies solely on standard thermal baths and can be implemented with circuit quantum electrodynamics. We demonstrate how the engine is able to extract a net positive work via its built-in synchronicity using a filter cavity as an effective valve, eliminating the need for external control.
In this paper, we study the regularity of the solutions of Maxwell's equations in a bounded domain. We consider several different types of low regularity assumptions to the coefficients which are all less than Lipschitz. We first develop a new approach by giving $\mathcal{H}^1$ estimate when the coefficients are $\mathcal{L}^{\infty}$ bounded; and then we derive $\mathcal{W}^{1,p}$ estimates for every $p > 2$ when one of the leading coefficients is simply continuous; Finally, we extend the result to $\mathcal{C}^{1,\alpha}$ almost everywhere for the solution of the homogeneous Maxwell's equations when the coefficients are $\mathcal{W}^{1,p}, \, p>3$ and close to the identity matrix in the sense of $\mathcal{L}^{\infty}$ norm. The last two estimates are new, and the techniques and methods developed here can also be applied to other problems with similar difficulties.
We study the generalized $n$ component model of a driven diffusive system with annealed random drive in the large $n$ limit. This non-equilibrium model also describes conserved order parameter dynamics of an equilibrium model of ferromagnets with dipolar interaction. In this limit, at zero temperature a saddle point approximation becomes exact. The length scale in the direction transverse to the driving field acquires an additional logarithmic correction in this limit.
We survey some recent progress on rigorously establishing the universality of various spectral statistics of Wigner random matrix ensembles, focusing in particular on the Four Moment Theorem and its applications.