ShantanuT01/DACTYL-Pretraining huggingface dataset:
Single-electron spin qubits employ magnetic fields on the order of 1 Tesla or above to enable quantum state readout via spin-dependent-tunnelling. This requires demanding microwave engineering for coherent spin resonance control and significant on-chip real estate for electron reservoirs, both of which limit the prospects for large scale multi-qubit systems. Alternatively, singlet-triplet (ST) readout enables high-fidelity spin-state measurements in much lower magnetic fields, without the need for reservoirs. Here, we demonstrate low-field operation of metal-oxide-silicon (MOS) quantum dot qubits by combining coherent single-spin control with high-fidelity, single-shot, Pauli-spin-blockade-based ST readout. We discover that the qubits decohere faster at low magnetic fields with $T_{2}^{Rabi}=18.6$~$\mu$s and $T_2^*=1.4$~$\mu$s at 150~mT. Their coherence is limited by spin flips of residual $^{29}$Si nuclei in the isotopically enriched $^{28}$Si host material, which occur more frequently at lower fields. Our finding indicates that new trade-offs will be required to ensure the frequency stabilization of spin qubits and highlights the importance of isotopic enrichment of device substrates for the realization of a scalable silicon-based quantum processor.
We present a theory of the intrinsic anomalous Hall effect in a model of a doped Weyl semimetal, which serves here as the simplest toy model of a generic three-dimensional metallic ferromagnet with Weyl nodes in the electronic structure. We analytically evaluate the anomalous Hall conductivity as a function of doping, which allows us to explicitly separate the Fermi surface and non Fermi surface contributions to the Hall conductivity by carefully evaluating the zero frequency and zero wavevector limits of the corresponding response function. We show that this separation agrees with the one suggested a long time ago in the context of the quantum Hall effect by Streda.
We present a kinematic analysis of the dense molecular gas in the central 200 parsecs of the nearby galaxy NGC1097, based on Cycle 0 observations with the Atacama Large Millimeter/sub-millimeter Array (ALMA). We use the HCN(4-3) line to trace the densest interstellar molecular gas, and quantify its kinematics, and estimate an inflow rate for the molecular gas. We find a striking similarity between the ALMA kinematic data and the analytic spiral inflow model that we have previously constructed based on ionized gas velocity fields on larger scales. We are able to follow dense gas streaming down to 40 pc distance from the supermassive black hole in this Seyfert 1 galaxy. In order to fulfill marginal stability, we deduce that the dense gas is confined to a very thin disc, and we derive a dense gas inflow rate of 0.09 Msun/yr at 40 pc radius. Combined with previous values from the Ha and CO gas, we calculate a combined molecular and ionized gas inflow rate of 0.2 Msun/yr at 40 pc distance from the central supermassive black hole of NGC1097.
Generalizing the 't Hooft and Veltman method of unitary regulators, we demonstrate for the first time the existence of local, Lorentz-invariant, physically motivated Lagrangians of quantum-electrodynamic phenomena such that: (i) Feynman diagrams are finite and equal the diagrams of QED but with regularized propagators. (ii) N-point Green functions are causal. (iii) S-matrix relates only electrons, positrons and photons, is unitary and Lorentz-invariant, and conserves charge and total four-momentum.
In this work we introduce a differential rendering module which allows neural networks to efficiently process cluttered data. The module is composed of continuous piecewise differentiable functions defined as a sensor array of cells embedded in 3D space. Our module is learnable and can be easily integrated into neural networks allowing to optimize data rendering towards specific learning tasks using gradient based methods in an end-to-end fashion. Essentially, the module's sensor cells are allowed to transform independently and locally focus and sense different parts of the 3D data. Thus, through their optimization process, cells learn to focus on important parts of the data, bypassing occlusions, clutter and noise. Since sensor cells originally lie on a grid, this equals to a highly non-linear rendering of the scene into a 2D image. Our module performs especially well in presence of clutter and occlusions. Similarly, it deals well with non-linear deformations and improves classification accuracy through proper rendering of the data. In our experiments, we apply our module to demonstrate efficient localization and classification tasks in cluttered data both 2D and 3D.
We study, theoretically and numerically, the onset and development of modulational instability in an incoherently pumped spatially homogeneous polariton condensate. Within the framework of mean-field theory, we identify regimes of modulational instability in two cases: 1) Strong feedback between the condensate and reservoir, which may occur in scalar condensates, and 2) Parametric scattering in the presence of polarization splitting in spinor condensates. In both cases we investigate the instability induced textures in space and time including non-equilibrium dynamics of phase dislocations and vortices. In particular we discuss the mechanism of vortex destabilization and formation of spiraling waves. We also identify the presence of topological defects, which take the form of half-vortex pairs in the spinor case, giving an "eyelet" structure in intensity and dipole type structure in the spin polarization. In the modulationally stable parameter domains, we observe formation of the phase defects in the process of condensate formation from an initially spatially incoherent low-density state. In analogy to the Kibble-Zurek type scaling for nonequilibrium phase transitions, we find that the defect density scales with the pumping rate.
We consider the 3D hyperviscous Navier-Stokes equations in vorticity form, where the dissipative term $-\Delta \vec \xi$ of the Navier-Stokes equations is substituted by $(-\Delta)^{1+c} \vec \xi $. We investigate how big the correction term $c$ has to be in order to prove, by means of Girsanov transform, that the vorticity equations are equivalent (in law) to easier reference equations obtained by neglecting the stretching term. This holds as soon as $c>\frac 12$, improving previous results obtained with $c>\frac 32$ in a different setting in [5,14].
We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is unambiguous, i. e. error-free, discrimination with a minimum probability of getting an inconclusive outcome, where the measurement fails to give a definite answer. For distinguishing between two mixed quantum states, we investigate the relation between the minimum error probability achievable in conclusive discrimination, and the minimum failure probability that can be reached in unambiguous discrimination of the same two states. The latter turns out to be at least twice as large as the former for any two given states. As an example, we treat the case that the state of the quantum system is known to be, with arbitrary prior probability, either a given pure state, or a uniform statistical mixture of any number of mutually orthogonal states. For this case we derive an analytical result for the minimum probability of error and perform a quantitative comparison to the minimum failure probability.
We prove that in presence of $L^2$ Gaussian estimates, so-called Davies-Gaffney estimates, on-diagonal upper bounds imply precise off-diagonal Gaussian upper bounds for the kernels of analytic families of operators on metric measure spaces.
Let $N$ be the smallest integer such that there is a non-tautological cohomology class of even degree on $\mathcal{\bar M}_{2,N}$. We remark that there is such a non-tautological class on $\mathcal{\bar M}_{2,20}$, by work of Graber and Pandharipande. We show that $\mathcal{\bar M}_{2,N}$ has non-tautological cohomology only in one degree, which is not the middle degree. In particular, it follows that the tautological ring of $\mathcal{\bar M}_{2,N}$ is not Gorenstein. We present some evidence suggesting that N=20 holds.
We summarize recent progress in the studies of the short-rang correlations (SRC) in nuclei in high energy electron and hadron nucleus scattering and suggest directions for the future high energy studies aimed at establishing detailed structure of two-nucleon SRCs, revealing structure of three nucleon SRC correlations and discovering non-nucleonic degrees of freedom in nuclei.
We report the discovery of a protocluster at z~6 containing at least eight cluster member galaxies with spectroscopic confirmations in the wide-field image of the Subaru Deep Field (SDF). The overdensity of the protocluster is significant at the 6 sigma level, based on the surface number density of i'-dropout galaxies. The overdense region covers ~36 sq. arcmin, and includes 30 i'-dropout galaxies. Follow-up spectroscopy revealed that 15 of these are real z~6 galaxies (5.7 < z < 6.3). Eight of the 15 are clustering in a narrow redshift range centered at z=6.01, corresponding to a seven-fold increase in number density over the average in redshift space. We found no significant difference in the observed properties, such as Ly-alpha luminosities and UV continuum magnitudes, between the eight protocluster members and the seven non-members. The velocity dispersion of the eight protocluster members is 647 km/s, which is about three times higher than that predicted by the standard cold dark matter model. This discrepancy could be attributed to the distinguishing three-dimensional distribution of the eight protocluster members. We discuss two possible explanations for this discrepancy: either the protocluster is already mature, with old galaxies at the center, or it is still immature and composed of three subgroups merging to become a larger cluster. In either case, this concentration of z=6.01 galaxies in the SDF may be one of the first sites of formation of a galaxy cluster in the universe.
We study the one-dimensional Hubbard model with nearest-neighbor and next-nearest-neighbor hopping integrals by using the density-matrix renormalization group (DMRG) method and Hartree-Fock approximation. Based on the calculated results for the spin gap, total-spin quantum number, and Tomonaga-Luttinger-liquid parameter, we determine the ground-state phase diagram of the model in the entire filling and wide parameter region. We show that, in contrast to the weak-coupling regime where a spin-gapped liquid phase is predicted in the region with four Fermi points, the spin gap vanishes in a substantial region in the strong-coupling regime. It is remarkable that a large variety of phases, such as the paramagnetic metallic phase, spin-gapped liquid phase, singlet and triplet superconducting phases, and fully polarized ferromagnetic phase, appear in such a simple model in the strong-coupling regime.
The metal-insulator transition in manganites is strongly influenced by the concentration of holes present in the system. Based upon an orbitally degenerate Mott-Hubbard model we analyze two possible localization scenarios to account for this doping dependence: First, we rule out that the transition is initiated by a disorder-order crossover in the orbital sector, showing that its effect on charge itineracy is only small. Second, we introduce the idea of orbital polarons originating from a strong polarization of orbitals in the vicinity of holes. Considering this direct coupling between charge and orbital degree of freedom in addition to lattice effects we are able to explain well the phase diagram of manganites for low and intermediate hole concentrations.
The cross sections for photo- and pion-induced production of baryon resonances and their partial decay widths to the two--body and multi--body final states are calculated in the framework of the operator expansion method. The approach is fully relativistic invariant, and it allows us to perform combined analyses of different reactions imposing directly the analyticity and unitarity constraints. All formulae are given explicitly in the form used by the Crystal Barrel collaboration in the partial wave analysis.
We prove that a sequence of semi-discrete approximations converges to a multiplicative functional for reflected Brownian motion, which intuitively represents the Lyapunov exponent for the corresponding stochastic flow. The method of proof is based on a study of the deterministic version of the problem and the excursion theory.
Interpreting the coordinates of the quantum Euclidean space R_q^4 [the SO_q(4)-covariant noncommutative space] as the entries of a ``q-quaternion matrix'' we construct (anti)instanton solutions of a would-be q-deformed su(2) Yang-Mills theory on R_q^4. Since the (anti)selfduality equations are covariant under the quantum group of deformed rotations, translations and scale change, by applying the latter we can respectively generate ``gauge equivalent'' or ``inequivalent'' solutions from the one centered at the origin and with unit size. We also construct multi-instanton solutions. As these solutions depend on noncommuting parameters playing the roles of `sizes' and `coordinates of the centers' of the instantons, this indicates that the moduli space of a complete theory should be a noncommutative manifold. Similarly, as the (global) gauge transformations relating ``gauge equivalent'' solutions depend on the generators of two copies of SU_q(2), this suggests that gauge transformations should be allowed to depend on additional noncommutative parameters.
We use a suite of high-resolution cosmological dwarf galaxy simulations to test the accuracy of commonly-used mass estimators from Walker et al.(2009) and Wolf et al.(2010), both of which depend on the observed line-of-sight velocity dispersion and the 2D half-light radius of the galaxy, $Re$. The simulations are part of the the Feedback in Realistic Environments (FIRE) project and include twelve systems with stellar masses spanning $10^{5} - 10^{7} M_{\odot}$ that have structural and kinematic properties similar to those of observed dispersion-supported dwarfs. Both estimators are found to be quite accurate: $M_{Wolf}/M_{true} = 0.98^{+0.19}_{-0.12}$ and $M_{Walker}/M_{true} =1.07^{+0.21}_{-0.15}$, with errors reflecting the 68% range over all simulations. The excellent performance of these estimators is remarkable given that they each assume spherical symmetry, a supposition that is broken in our simulated galaxies. Though our dwarfs have negligible rotation support, their 3D stellar distributions are flattened, with short-to-long axis ratios $ c/a \simeq 0.4-0.7$. The accuracy of the estimators shows no trend with asphericity. Our simulated galaxies have sphericalized stellar profiles in 3D that follow a nearly universal form, one that transitions from a core at small radius to a steep fall-off $\propto r^{-4.2}$ at large $r$, they are well fit by S\'ersic profiles in projection. We find that the most important empirical quantity affecting mass estimator accuracy is $Re$ . Determining $Re$ by an analytic fit to the surface density profile produces a better estimated mass than if the half-light radius is determined via direct summation.
Automated emotion recognition in the wild from facial images remains a challenging problem. Although recent advances in Deep Learning have supposed a significant breakthrough in this topic, strong changes in pose, orientation and point of view severely harm current approaches. In addition, the acquisition of labeled datasets is costly, and current state-of-the-art deep learning algorithms cannot model all the aforementioned difficulties. In this paper, we propose to apply a multi-task learning loss function to share a common feature representation with other related tasks. Particularly we show that emotion recognition benefits from jointly learning a model with a detector of facial Action Units (collective muscle movements). The proposed loss function addresses the problem of learning multiple tasks with heterogeneously labeled data, improving previous multi-task approaches. We validate the proposal using two datasets acquired in non controlled environments, and an application to predict compound facial emotion expressions.
The minimum rank of a graph G is the minimum rank over all real symmetric matrices whose off-diagonal sparsity pattern is the same as that of the adjacency matrix of G. In this note we present the first exact algorithm for the minimum rank of an arbitrary graph G. In particular, we use the notion of determinantal rank to transform the minimum rank problem into a system of polynomial equations that can be solved by computational tools from algebraic geometry and commutative algebra. We provide computational results, explore possibilities for improvement, and discuss how the algorithm can be extended to other problems such as finding the minimum positive semidefinite rank of a graph.
In the Standard Model a Dark Matter candidate is missing, but it is relatively simple to enlarge the model including one or more suitable particles. We consider in this paper one such extension, inspired by simplicity and by the goal to solve more than just the Dark Matter issue. Indeed we consider a local $U(1) $ extension of the SM providing an axion particle to solve the strong CP problem and including RH neutrinos with appropriate mass terms. One of the latter is decoupled from the SM leptons and can constitute stable sterile neutrino DM. In this setting, the PQ symmetry arises only as an accidental symmetry but its breaking by higher order operators is sufficiently suppressed to avoid introducing a large $ \theta $ contribution. The axion decay constant and the RH neutrino masses are related to the same v.e.v.s and the PQ scale and both DM densities are determined by the parameters of the axion and scalar sector. The model predicts in general a mixed Dark Matter scenario with both axion and sterile neutrino DM and is characterised by a reduced density and observational signals from each single component.
The Erd\H{o}s--Faber--Lov\'{a}sz Conjecture, posed in 1972, states that if a graph $G$ is the union of $n$ cliques of order $n$ (referred to as defining $n$-cliques) such that two cliques can share at most one vertex, then the vertices of $G$ can be properly coloured using $n$ colours. Although still open after almost 50 years, it can be easily shown that the conjecture is true when every shared vertex belongs to exactly two defining $n$-cliques. We here provide a quick and easy algorithm to colour the vertices of $G$ in this case, and discuss connections with clique-decompositions and edge-colourings of graphs.
This paper links at the formal level the entropy structure of a multi-species cross-diffusion system of Shigesada-Kawasaki-Teramoto (SKT) type satisfying the detailed balance condition with the entropy structure of a reversible microscopic many-particle Markov process on a discretised space. The link is established by first performing a mean-field limit to a master equation over discretised space. Then the spatial discretisation limit is performed in a completely rigorous way. This by itself provides a novel strategy for proving global existence of weak solutions to a class of cross-diffusion systems.
In this paper we describe in detail the computational algorithm used by our parallel multigrid elliptic equation solver with adaptive mesh refinement. Our code uses truncation error estimates to adaptively refine the grid as part of the solution process. The presentation includes a discussion of the orders of accuracy that we use for prolongation and restriction operators to ensure second order accurate results and to minimize computational work. Code tests are presented that confirm the overall second order accuracy and demonstrate the savings in computational resources provided by adaptive mesh refinement.
We have studied the ground state properties (binding energy and charge radius) using relativistic mean filed formalism (RMF) for Mg-isotopes in the valley of stability to drip line region. The RMF densities have been analyzed in context of reaction dynamics. The calculated results of $^{24-40}$Mg+$^{12}$C reactions at projectile energy 240 AMeV using Glauber model with the conjunction of densities from relativistic mean field formalism are compared with experimental data. We found remarkable agreement of estimated values of reaction cross sections with experimental data except for $^{37}$Mg isotope. In view of this, the halo status of $^{37}$Mg is examined through higher magnitude of rms radius and small value of longitudinal momentum distribution. Finally, an effort is made to explore the structure of $^{37}$Mg halo candidate using Glauber few body formalism.
The wind driven by the intense neutrino emission from a protoneutron star (PNS) is an important site for producing nuclei heavier than the Fe group. Because of certain features in the neutrino angular distributions, the so-called fast flavor oscillations may occur very close to the PNS surface, effectively resetting the neutrino luminosities and energy spectra that drive the wind.   Using the unoscillated neutrino emission characteristics from two core-collapse supernova simulations representative of relevant progenitors at the lower and higher mass end, we study the potential effects of fast flavor oscillations on neutrino-driven winds and their nucleosynthesis.   We find that such oscillations can increase the total mass loss by factors up to ~ 1.5-1.7 and lead to significantly more proton-rich conditions. The latter effect can greatly enhance the production of 64Zn and the so-called light p-nuclei 74Se, 78Kr, and 84Sr. Implications for abundances in metal-poor stars, Galactic chemical evolution in general, and isotopic anomalies in meteorites are discussed.
We prove a result on lower bounds in large dimensions.
After briefly reviewing the impact of various parameters on photoionization models, we illustrate the importance of the nebular geometry by two examples: we first compare the results from models with thin shell and full shell geometry, and we study the influence of a diffuse ionized medium in the integrated spectra of galaxies at large redshift. Finally, we show how the calibration of the strong line method for deriving oxygen abundances depends on the assumed average properties of the ionizing star cluster and on the density distribution of the nebular gas.
For a reductive group G, the products of projective rational varieties homogeneous under G that are spherical for G have been classified by Stembridge. We consider the B-orbit closures in these spherical varieties and prove that under some mild restrictions they are normal, Cohen-Macaulay and have a rational resolution.
Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent and saturating number variance behaviour. We derive a general expression for the number variance for the spatial particle configurations arising from these systems and this enables us to deduce various limiting distribution results for the fluctuations of the associated counting functions. In particular, knowledge of the number variance allows us to introduce and characterize a novel family of centered, long memory Gaussian processes. We obtain fractional Brownian motion as a weak limit of these constructed processes.