ShantanuT01/DACTYL-Pretraining huggingface dataset:
Using a set of rephasing-invariant variables, it is shown that the renormalization group equations for quark mixing parameters can be written in a form that is compact, in addition to having simple properties under flavor permutation. We also found approximate solutions to these equations if the quark masses are hierarchical or nearly degenerate.
Consider a discrete-time quantum walk on the $N$-cycle subject to decoherence both on the coin and the position degrees of freedom. By examining the evolution of the density matrix of the system, we derive some new conclusions about the asymptotic behavior of the system. When $N$ is odd, the density matrix of the system tends, in the long run, to the maximally mixed state, independent of the initial state. When $N$ is even, although the behavior of the system is not necessarily asymptotically stationary, in this case too an explicit formulation is obtained of the asymptotic dynamics of the system. Moreover, this approach enables us to specify the limiting behavior of the mutual information, viewed as a measure of quantum entanglement between subsystems (coin and walker). In particular, our results provide efficient theoretical confirmation of the findings of previous authors, who arrived at their results through extensive numerical simulations. Our results can be attributed to an important theorem which, for a generalized random unitary operation, explicitly identifies the structure of all of its eigenspaces corresponding to eigenvalues of unit modulus.
My dissertation presents results from three recent investigations in the Hubble Ultra Deep Field (HUDF) focusing on understanding structural and physical properties of high redshift galaxies. Here I summarize results from these studies. This thesis work was conducted at Arizona State University under the guidance of Prof. Rogier Windhorst and Prof. Sangeeta Malhotra.
We discuss possible measurements and origins of single spin asymmetries in DIS and of some unusual spin properties of vector mesons produced in lepton- nucleon, photon-nucleon and photon-photon interactions. Such effects have already been observed in other processes.
We address representation learning for large-scale instance-level image retrieval. Apart from backbone, training pipelines and loss functions, popular approaches have focused on different spatial pooling and attention mechanisms, which are at the core of learning a powerful global image representation. There are different forms of attention according to the interaction of elements of the feature tensor (local and global) and the dimensions where it is applied (spatial and channel). Unfortunately, each study addresses only one or two forms of attention and applies it to different problems like classification, detection or retrieval.   We present global-local attention module (GLAM), which is attached at the end of a backbone network and incorporates all four forms of attention: local and global, spatial and channel. We obtain a new feature tensor and, by spatial pooling, we learn a powerful embedding for image retrieval. Focusing on global descriptors, we provide empirical evidence of the interaction of all forms of attention and improve the state of the art on standard benchmarks.
Recent observations revealed that small magnetic elements abundant at the solar surface move poleward with a velocity which seems to be lower than the plasma velocity $U_{\theta}$. Guerrero et al. (2011) explained this discrepancy as a consequence of diffusive spreading of the magnetic elements due to a positive radial gradient of $|U_{\theta}|$. As the gradient's sign (inferred by local helioseismology) is still unclear, cases with a negative gradient are studied in this paper. Under this condition, the velocity of the magnetic tracers turns out to be larger than the plasma velocity, in disagreement with the observations. Alternative mechanisms for explaining them independently are proposed. For the turbulent magnetic pumping it is shown that it has to be unrealistically strong to reconcile the model with the observations.
The aim of this short note is to extend the recent variational proof of partial regularity for optimal transport maps to the case of continuous densities.
Kinetics of separation between the low and high density phases in a single component Lennard-Jones model has been studied via molecular dynamics simulations, at a very low temperature, in the space dimension $d=2$. For densities close to the vapor (low density) branch of the coexistence curve, disconnected clusters of the high density phase exhibit ballistic motion, the kinetic energy distribution of the clusters being closely Maxwellian. Starting from nearly circular shapes, at the time of nucleation, these clusters grow via sticky collisions, gaining filament-like nonequilibrium structure at late times, with a very low fractal dimensionality. The origin of the latter is shown to lie in the low mobility of the constituent particles, in the corresponding cluster reference frame, due to the (quasi-long-range) crystalline order. Standard self-similarity in the domain pattern, typically observed in kinetics of phase transitions, is found to be absent in this growth process. This invalidates the common method, that provides a growth law same as in immiscible solid mixtures, of quantifying growth. An appropriate alternative approach, involving the fractality in the structure, quantifies the growth of the characteristic "length" to be a power-law with time, the exponent being surprisingly high. The observed growth law has been derived via a nonequilibrium kinetic theory.
Aims. In this paper we study the influence of the ionizing cluster mass on the emission line spectrum of Hii regions in order to determine the influence of low mass clusters on the integrated emission line spectra of galaxies. Methods. For this purpose, we present a grid of photoionization models that covers metallicities from Z = 0.001 to Z = 0.040, ages from 0.1 to 10 Ma (with a time step of 0.1 Ma), and cluster initial masses from 1 to 107 Mo. The stellar masses follow a Salpeter initial mass function (IMF) in an instantaneous burst mode of star formation. We obtain power-law scale-relations between emission-line luminosities and ionizing cluster masses from the grids and we evaluate the dependences on the ionizing cluster mass for some line luminosities, equivalent widths and line ratios. Results. Power-law scale-relations are shown to be useful tools to obtain robust diagnostics, as examples: (a) H?/H? ratio varies from the usually assumed value of 2.86, these variations imply the existence of a lower limit to the attainable precision in extinction estimations of ?E(B - V) ~ 0.1.; (b) EW(H?) is a good age indicator with a small dependence on cluster mass, while EW([O iii] 5007) shows a noteworthy mass dependence; (c) abundance estimations from R23 are practically unaffected by variations of the cluster mass; (d) estimations from S 23 and ?' would improve if the cluster mass dependences were considered and (e) [Oii] 3727/H? is a good star formation rate indicator for ages older than -4.5 Ma. We also show that the ionizing cluster mass dependence explains why empirical calibrations produce more reliable diagnostics of some emission lines than photoionization models grids. Finally, we show preliminary results about the contribution of low mass clusters (M < 104 Mo) to the integrated emission line spectra of galaxies, which can be as high as 80% for some relevant lines.
Let X be the complex Fermat variety of dimension n=2d and degree m>2. We investigate the submodule of the middle homology group of X with integer coefficients generated by the classes of standard d-dimensional subspaces contained in X, and give an algebraic (or rather combinatorial) criterion for the primitivity of this submodule.
We study the charge current transmitted through the correlated quantum dot characterized by a finite magnitude of the Coulomb interaction |U|. At low temperatures the correlations can lead to appearance of the spin (for U>0) or charge (for U<0) Kondo states qualitatively affecting the transport properties. We explore an influence of the charge Kondo effect on the electron pair tunneling introducing the auxiliary two-component model which describes the fluctuations between empty and doubly occupied states of the quantum dot.
We present results of sub-arcsec ALMA observations of CO(2-1) and CO(5-4) toward a massive main sequence galaxy at z = 1.45 in the SXDS/UDS field, aiming at examining the internal distribution and properties of molecular gas in the galaxy. Our target galaxy consists of the bulge and disk, and has a UV clump in the HST images. The CO emission lines are clearly detected and the CO(5-4)/CO(2-1) flux ratio (R_52) is ~1, similar to that of the Milky Way. Assuming a metallicity dependent CO-toH_2 conversion factor and a CO(2-1)/CO(1-0) flux ratio of 2 (the Milky Way value), the molecular gas mass and the gas mass fraction (f_gas = molecular gas mass / (molecular gas mass + stellar mass)) are estimated to be ~1.5x10^11 M_Sun and ~0.55, respectively. We find that R_52 peak coincides with the position of the UV clump and its value is approximately two times higher than the galactic average. This result implies high gas density and/or high temperature in the UV clump, which qualitatively agrees with a numerical simulation of a clumpy galaxy. The CO(2-1) distribution is well represented by a rotating disk model and its half-light radius is ~2.3 kpc. Compared to the stellar distribution, the molecular gas is more concentrated in the central region of the galaxy. We also find that f_gas decreases from ~0.6 at the galactic center to ~0.2 at 3xhalf-light radius, indicating that the molecular gas is distributed in more central region of the galaxy than stars and seems to associate with the bulge rather than the stellar disk.
Many areas of physics rely upon adiabatic state transfer protocols, allowing a quantum state to be moved between different physical systems for storage and retrieval or state manipulation. However, these state-transfer protocols suffer from dephasing and dissipation. In this thesis we go beyond the standard open-systems treatment of quantum dissipation allowing us to consider non-Markovian environments. We use adiabatic perturbation theory in order to give analytic descriptions for various quantum state-transfer protocols. The leading-order corrections will give rise to additional terms adding to the geometric phase preventing us from achieving a perfect fidelity. We obtain analytical descriptions for the effects of the geometric phase in non-Markovian regimes. The Markovian regime is usually treated by solving a standard Bloch-Redfield master equation, while in the non-Markovian regime, we perform a secular approximation allowing us to obtain a solution to the density matrix without solving master equations. This solution contains all the relevant phase information for our state-transfer protocol. After developing the general theoretical tools, we apply our methods to adiabatic state transfer between a four-level atom in a driven cavity. We explicitly consider dephasing effects due to unavoidable photon shot noise and give a protocol for performing a phase gate. These results will be useful to ongoing experiments in circuit quantum electrodynamics (QED) systems.
Let $T$ be a tree with a vertex set $\{ 1,2,\dots, N \}$. Denote by $d_{ij}$ the distance between vertices $i$ and $j$. In this paper, we present an explicit combinatorial formula of principal minors of the matrix $(t^{d_{ij}})$, and its applications to tropical geometry, study of multivariate stable polynomials, and representation of valuated matroids. We also give an analogous formula for a skew-symmetric matrix associated with $T$.
With camera resolution ever increasing and the need to rapidly recalibrate robotic platforms in less than ideal environments, there is a need for faster and more robust chessboard fiducial marker detectors. A new chessboard detector is proposed that is specifically designed for: high resolution images, focus/motion blur, harsh lighting conditions, and background clutter. This is accomplished using a new x-corner detector, where for the first time blur is estimated and used in a novel way to enhance corner localization, edge validation, and connectivity. Performance is measured and compared against other libraries using a diverse set of images created by combining multiple third party datasets and including new specially crafted scenarios designed to stress the state-of-the-art. The proposed detector has the best F1- Score of 0.97, runs 1.9x faster than next fastest, and is a top performer for corner accuracy, while being the only detector to have consistent good performance in all scenarios.
We prove a conjecture of Frenkel, Gaitsgory, Kazhdan and Vilonen, related to Fourier coefficients of spherical perverse sheaves on the affine Grassmannian associated to a a split reductive group. Our proof is an extension of the proof given by the first author in the case of GL(n) (see math/9801109); it relies on the study of certain resolutions of Schubert varieties in the affine Grassmannian, built from the so-called minuscule or quasi-minuscule cases.
For a graph $G$, a hypergraph $\mathcal{H}$ is a Berge copy of $G$ (or a Berge-$G$ in short), if there is a bijection $f : E(G) \rightarrow E(\mathcal{H})$ such that for each $e \in E(G)$ we have $e \subseteq f(e)$. We denote the family of $r$-uniform hypergraphs that are Berge copies of $G$ by $B^rG$.   For families of $r$-uniform hypergraphs $\mathbf{H}$ and $\mathbf{H}'$, we denote by $R(\mathbf{H},\mathbf{H}')$ the smallest number $n$ such that in any blue-red coloring of $\mathcal{K}_n^r$ (the complete $r$-uniform hypergraph on $n$ vertices) there is a monochromatic blue copy of a hypergraph in $\mathbf{H}$ or a monochromatic red copy of a hypergraph in $\mathbf{H}'$. $R^c(\mathbf{H})$ denotes the smallest number $n$ such that in any coloring of the hyperedges of $\mathcal{K}_n^r$ with $c$ colors, there is a monochromatic copy of a hypergraph in $\mathbf{H}$.   In this paper we initiate the general study of the Ramsey problem for Berge hypergraphs, and show that if $r> 2c$, then $R^c(B^rK_n)=n$. In the case $r = 2c$, we show that $R^c(B^rK_n)=n+1$, and if $G$ is a non-complete graph on $n$ vertices, then $R^c(B^rG)=n$, assuming $n$ is large enough. In the case $r < 2c$ we also obtain bounds on $R^c(B^rK_n)$. Moreover, we also determine the exact value of $R(B^3T_1,B^3T_2)$ for every pair of trees $T_1$ and $T_2$.
The orthant model is a directed percolation model on $\mathbb{Z}^d$, in which all clusters are infinite. We prove a sharp threshold result for this model: if $p$ is larger than the critical value above which the cluster of $0$ is contained in a cone, then the shift from $0$ that is required to contain the cluster of $0$ in that cone is exponentially small. As a consequence, above this critical threshold, a shape theorem holds for the cluster of $0$, as well as ballisiticity of the random walk on this cluster.
We report the discovery of large amplitude X-ray variability in the low luminosity AGN (LLAGN) MGC 7589, and present possible observational evidence for accretion mode transition in this source. Long-term X-ray flux variations by a factor of more than 50 are found using X-ray data obtained by Swift/XRT and XMM-Newton over 17 years. Results of long-term monitoring data in the UV, optical and infrared bands over ~20 years are also presented. The Eddington ratio increased from $10^{-3}$ to $\sim0.13$, suggesting a transition of the accretion flow from an ADAF to a standard thin accretion disc. Further evidence supporting the thin disc in the high luminosity state is found by the detection of a significant soft X-ray component in the X-ray spectrum. The temperature of this component ($\sim19^{+15}_{-7}$eV, fitted with a blackbody model) is in agreement with the predicted temperature of the inner region for a thin disc around a black hole (BH) with mass of $\sim10^{7}\,M_{\mathrm{Sun}}$. These results may indicate that NGC 7589 had experienced accretion mode transition over a timescale of a few years, suggesting the idea that similar accretion processes are at work for massive black hole and black hole X-ray binaries.
Motivated by a partition inequality of Bessenrodt and Ono, we obtain analogous inequalities for $k$-colored partition functions $p_{-k}(n)$ for all $k\geq2$. This enables us to extend the $k$-colored partition function multiplicatively to a function on $k$-colored partitions, and characterize when it has a unique maximum. We conclude with one conjectural inequality that strengthens our results.
The spin-1/2 Heisenberg kagome antiferromagnet is one of the paradigmatic playgrounds for frustrated quantum magnetism, with an extensive number of competing resonating valence bond (RVB) states emerging at low energies, including gapped and gapless spin liquids and valence bond crystals. Here we revisit the crossover from this quantum RVB phase to a semiclassical regime brought about by anisotropic Kitaev interactions, and focus on the precise mechanisms underpinning this crossover. To this end, we introduce a simple parametrization of the classical ground states (GSs) in terms of emergent Ising-like variables, and use this parametrizaton: i) to construct an effective low-energy description of the order-by-disorder mechanism operating in a large part of the phase diagram, and ii) to contrast, side by side, exact diagonalization data obtained from the full basis with that obtained from the restricted (orthonormalized) basis of classical GSs. The results reveal that fluctuation corrections from states outside the restricted basis are strongly quenched inside the semiclassical regime (due to the large anisotropy spin gaps), and that the RVB phase survives up to a relatively large value of Kitaev anisotropy $K$. We further find that the pure Kitaev model admits a subextensive number of one-dimensional symmetries, which explains naturally the absence of classical and quantum order by disorder reported previously.
A family of de Sitter vacua introduced in hep-th/0203198 as plausible initial conditions for inflation, are discussed from the point of view of de Sitter holography. The vacua are argued to be physically acceptable and the inflationary picture provides a physical interpretation of a subfamily of de Sitter invariant vacua. Some speculations on the issue of vacuum choice and the connection between the CMBR and holography are also provided.
We perform a weak-lensing study of the nearby cool-core galaxy clusters, Hydra A ($z=0.0538$) and A478 ($z=0.0881$), of which brightest cluster galaxies (BCGs) host powerful activities of active galactic nuclei (AGNs). For each cluster, the observed tangential shear profile is well described either by a single Navarro--Frenk--White model or a two-component model including the BCG as an unresolved point mass. For A478, we determine the BCG and its host-halo masses from a joint fit to weak-lensing and stellar photometry measurements. We find that the choice of initial mass functions (IMFs) can introduce a factor of two uncertainty in the BCG mass, whereas the BCG host halo mass is well constrained by data. We perform a joint analysis of weak-lensing and stellar kinematics data available for the Hydra A cluster, which allows us to constrain the central mass profile without assuming specific IMFs. We find that the central mass profile ($r<300$kpc) determined from the joint analysis is in excellent agreement with those from independent measurements, including dynamical masses estimated from the cold gas disk component, X-ray hydrostatic total mass estimates, and the central stellar mass estimated based on the Salpeter IMF. The observed dark-matter fraction around the BCG for Hydra A is found to be smaller than those predicted by adiabatic contraction models, suggesting the importance of other physical processes, such as the the AGN feedback and/or dissipationless mergers.
A real-time path integral for ultrasoft QCD is formulated. It exhibits a Feynman's influence functional. The statistical properties of the theory and the gauge symmetry are explicit. The correspondence is established with the alternative version, where a noise term enters a transport equation.
To every reduced (projective) curve X with planar singularities one can associate many fine compactified Jacobians, depending on the choice of a polarization on X, which are birational (possibly non-isomorphic) Calabi-Yau projective varieties with locally complete intersection singularities. We define a Poincare' sheaf on the product of any two (possibly equal) fine compactified Jacobians of X and show that the integral transform with kernel the Poincare' sheaf is an equivalence of their derived categories. In particular, any two fine compactified Jacobians are derived equivalent. When applied to the same fine compactified Jacobian, one gets a Fourier-Mukai autoequivalence, which generalizes the classical result of Mukai for Jacobians of smooth curves (or more generally abelian varieties) and of Arinkin for compactified Jacobians of integral curves, thus providing further evidence for the classical limit of the geometric Langlands conjecture (as formulated by R. Donagi and T. Pantev). As a corollary of our main result, we prove an autoduality result for fine compactified Jacobians: there is a natural equivariant open embedding of the connected component of the scheme parametrizing rank-1 torsion-free sheaves on X into the connected component of the algebraic space parametrizing rank-1 torsion-free sheaves on a given fine compactified Jacobian of X.
Large $N$ matrix models play an important role in modern theoretical physics, ranging from quantum chromodynamics to string theory and holography. However, they remain a difficult technical challenge because in most cases it is not known how to perform the sum over planar graphs, which dominate the models at large $N$. In this thesis, we study large $D$ matrix models, which provide a framework to build new limits for matrix models in which the sum over planar graphs simplifies when $D$ is large. The basic degrees of freedom are real matrices of size $N\times N$ with $r$ additional indices of range $D$. They can be interpreted as a real tensor of rank $R=r+2$ with indices of different ranges, making a compelling connection with tensor models. We define a new large $D$ limit for the sum over Feynman graphs of fixed genus in matrix models, based on an enhanced large $D$ scaling of the coupling constants. Then, we show that the resulting large $D$ expansion is well-defined and organized according to a half-integer called the index. When $N=D$, the result provides a new large $N$ limit for general $\text{O}(N)^R$ invariant tensor models. In the large $D$ limit, the sum over planar graphs of large $N$ matrix models simplifies to a non-trivial sum over generalized melonic graphs. This class of graphs extends the one obtained in tensor models with standard scaling and allows for a wider class of interactions, including all the maximally single-trace terms. The general classification of generalized melonic graphs remains an open problem. However, in the case of the complete interaction of order $R+1$ for $R$ a prime number, we identify them in detail and demonstrate that they exhibit the same important features as the SYK model with $q=(R+1)$-fold random interactions, including the emergent conformal symmetry in the infrared regime and maximal chaos.
The entanglement in a Hubbard chain of hardcore bosons is investigated. The analytic expression of the global entanglement in ground state is derived. The divergence of the derivative of the global entanglement shows the quantum criticality of the ground state. For the thermal equilibrium state, the bipartite and the multipartite entanglement are evaluated. The entanglement decreases to zero at a certain temperature. The thermal entanglement is rapidly decreasing with the increase of the number of sites in the lattice. The bipartite thermal entanglement approaches a constant value at a certain number of sites while the multipartite entanglement eventually vanishes.