ShantanuT01/DACTYL-Pretraining huggingface dataset:
We determine the tree which maximizes the distance between characteristic set and subtree core over all trees on $n$ vertices. The asymptotic nature of this distance is also discussed. The problem of extremizing the distance between different central parts of trees on $n$ vertices with fixed diameter is studied
We report on near-infrared (IR) interferometric observations of the double-lined pre-main sequence (PMS) binary system DQ Tau. We model these data with a visual orbit for DQ Tau supported by the spectroscopic orbit & analysis of \citet{Mathieu1997}. Further, DQ Tau exhibits significant near-IR excess; modeling our data requires inclusion of near-IR light from an 'excess' source. Remarkably the excess source is resolved in our data, similar in scale to the binary itself ($\sim$ 0.2 AU at apastron), rather than the larger circumbinary disk ($\sim$ 0.4 AU radius). Our observations support the \citet{Mathieu1997} and \citet{Carr2001} inference of significant warm material near the DQ Tau binary.
Even though convolutional neural networks can classify objects in images very accurately, it is well known that the attention of the network may not always be on the semantically important regions of the scene. It has been observed that networks often learn background textures which are not relevant to the object of interest. In turn this makes the networks susceptible to variations and changes in the background which negatively affect their performance. We propose a new two-step training procedure called split training to reduce this bias in CNNs on both Infrared imagery and RGB data. Our split training procedure has two steps: using MSE loss first train the layers of the network on images with background to match the activations of the same network when it is trained using images without background; then with these layers frozen, train the rest of the network with cross-entropy loss to classify the objects. Our training method outperforms the traditional training procedure in both a simple CNN architecture, and deep CNNs like VGG and Densenet which use lots of hardware resources, and learns to mimic human vision which focuses more on shape and structure than background with higher accuracy.
We present a refined duality estimate for parabolic equations. This estimate entails new results for systems of reaction-diffusion equations, including smoothness and exponential convergence towards equilibrium for equations with quadratic right-hand sides in two dimensions. For general systems in any space dimension, we obtain smooth solutions of reaction-diffusion systems coming out of reversible chemistry under an assumption that the diffusion coefficients are sufficiently close one to another.
We show that, for general static or axisymmetric stationary spacetimes, a cosmological Killing horizon exists only if $R_{ab}n^{a}n^{b}< 0$ for a hypersurface orthogonal timelike $n^{a}$, at least over some portion of the region of interest of the manifold. This implies violation of the strong energy condition by the matter fields, the simplest example of which is a positive cosmological constant.
We study the existence of absolutely maximally entangled (AME) states in quantum mechanics and its applications to quantum information. AME states are characterized by being maximally entangled for all bipartitions of the system and exhibit genuine multipartite entanglement. With such states, we present a novel parallel teleportation protocol which teleports multiple quantum states between groups of senders and receivers. The notable features of this protocol are that (i) the partition into senders and receivers can be chosen after the state has been distributed, and (ii) one group has to perform joint quantum operations while the parties of the other group only have to act locally on their system. We also prove the equivalence between pure state quantum secret sharing schemes and AME states with an even number of parties. This equivalence implies the existence of AME states for an arbitrary number of parties based on known results about the existence of quantum secret sharing schemes.
We investigate the problem of teleporting an unknown qubit state to a recipient via a channel of $2\L$ qubits. In this procedure a protocol is employed whereby $\L$ Bell state measurements are made and information based on these measurements is sent via a classical channel to the recipient. Upon receiving this information the recipient determines a local gate which is used to recover the original state. We find that the $2^{2\L}$-dimensional Hilbert space of states available for the channel admits a decomposition into four subspaces. Every state within a given subspace is a perfect channel, and each sequence of Bell measurements projects $2\L$ qubits of the system into one of the four subspaces. As a result, only two bits of classical information need be sent to the recipient for them to determine the gate. We note some connections between these four subspaces and ground states of many-body Hamiltonian systems, and discuss the implications of these results towards understanding entanglement in multi-qubit systems.
Recently, Kawaguchi and Nakayama (KN) [Phys. Rev. E {\bf 88}, 022147 (2013)] showed that the hidden entropy production associated with a coarse-graining procedure obeys the integral fluctuation theorem (IFT) if the original process does not involve any odd-parity variable that changes its sign under time reversal. This was interpreted as the evidence that odd-parity variables play an important role in the derivation of irreversible stochastic dynamics from time-reversible deterministic dynamics. In this Comment, we show that KN's approach is inadequate for describing the origin of irreversible stochastic dynamics, which calls into question whether odd-parity variables are required for the emergence of macroscopic irreversibility.
We have observed room temperature ferromagnetism (FM) in In$_2$O$_3$ thin films doped with either 5 at.% Mn or Fe, prepared by pulsed laser deposition (PLD) at substrate temperatures ranging from 300 to 600$\,^{\circ}{\rm C}$. The dependence of saturation magnetization on grain size was investigated for both types of In$_2$O$_3$ films. It is revealed that, for the Mn-doped films, the magnetization was largest with small grains, indicating the importance of grain boundaries. In contrast, for Fe-doped films, the largest magnetization was observed with large grains.
The electronic structure and total energy were calculated for ordered and disordered MgO-CaO solid solutions within the multiple scattering theory in real space and the local density approximation. Based on the dependence of the total energy on the unit cell volume the equilibrium lattice parameter and formation energy were determined for different solution compositions. The formation energy of the solid solutions is found to be positive that is in agreement with the experimental phase diagram, which shows a miscibility gap.
Tests, independent of any solar model, can be made of whether solar neutrino experiments are consistent with the minimal Standard Model (stable, massless neutrinos). If the experimental uncertainties are correctly estimated and the sun is generating energy by light-element fusion in quasi-static equilibrium, the probability of a standard-physics solution is less than 2%. Even when the luminosity constraint is abandoned, the probability is not more than 4%. The sensitivity of the conclusions to input parameters is explored.
Starting from certain rational varieties blown-up from (P^1)^N, we construct a tropical, i.e., subtraction-free birational, representation of Weyl groups as a group of pseudo isomorphisms of the varieties. Furthermore, we develop an algebro-geometric framework of tau-functions as defining functions of exceptional divisors on the varieties. In the case where the corresponding root system is of affine type, our construction yields a class of (higher order) q-difference Painleve equations and its algebraic degree grows quadratically.
Extensive Monte Carlo simulation has been performed on a 2D modified XY model which behaves like a dense defect system. Topological defects are shown to introduce disorders in the system which makes the helicity modulus jump non-universal. The results corroborate the experimental observation of non-universal jump of the superconducting density in high-$T_c$ superconducting films.
In this work, we demonstrate the Wong-Zakai approximation results for two and three dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations forced by Hilbert space valued Wiener noise on bounded domains. Even though the existence and uniqueness of a pathwise strong solution to SCBF equations is known, the existence of a unique solution to the approximating system is not immediate from the solvability results of SCBF equations, and we prove it by using Faedo-Galerkin approximation technique and monotonicity arguments. Moreover, as an application of the Wong-Zakai approximation, we obtain the support of the distribution of solutions to SCBF equations.
Cosmological implications of asymmetry between particles and antiparticles are reviewed. Three possible mechanisms of CP-violation in cosmology are described. General features of kinetics of generation of cosmological charge asymmetry are discussed in detail. In particular, the cyclic balance condition, which plays the same role in time non-invariant theory as detailed balance does in T-invariant case, is derived. Several scenarios of baryogenesis are described with an emphasis on CP-violation mechanisms. Production of cosmic antimatter and a possibility of its ``living'' in our neighborhood is discussed.
We study a generalized Hadamard walk in one dimension with three inner states. The particle governed by the three-state quantum walk moves, in superposition, both to the left and to the right according to the inner state. In addition to these two degrees of freedom, it is allowed to stay at the same position. We calculate rigorously the wavefunction of the particle starting from the origin for any initial qubit state, and show the spatial distribution of probability of finding the particle. In contrast with the Hadamard walk with two inner states on a line, the probability of finding the particle at the origin does not converge to zero even after infinite time steps except special initial states. This implies that the particle is trapped near the origin after long time with high probability.
We give a description of supermembranes in nontrivial target-space geometries. A special class are the $AdS_4\times S^7$ and $AdS_7\times S^4$ spaces that have the maximal number of 32 supersymmetries.
To investigate the performance of quantum information tasks on networks whose topology changes in time, we study the spatial search algorithm by continuous time quantum walk to find a marked node on a random temporal network. We consider a network of $n$ nodes constituted by a time-ordered sequence of Erd\"os-R\'enyi random graphs $G(n,p)$, where $p$ is the probability that any two given nodes are connected: after every time interval $\tau$, a new graph $G(n,p)$ replaces the previous one. We prove analytically that for any given $p$, there is always a range of values of $\tau$ for which the running time of the algorithm is optimal, i.e.\ $\mathcal{O}(\sqrt{n})$, even when search on the individual static graphs constituting the temporal network is sub-optimal. On the other hand, there are regimes of $\tau$ where the algorithm is sub-optimal even when each of the underlying static graphs are sufficiently connected to perform optimal search on them. From this first study of quantum spatial search on a time-dependent network, it emerges that the non-trivial interplay between temporality and connectivity is key to the algorithmic performance. Moreover, our work can be extended to establish high-fidelity qubit transfer between any two nodes of the network. Overall, our findings show that one can exploit temporality to achieve optimal quantum information tasks on dynamical random networks.
With an atomic force microscope a ring geometry with self-aligned in-plane gates was directly written into a GaAs/AlGaAs-heterostructure. Transport measurements in the open regime show only one transmitting mode and Aharonov-Bohm oscillations with more than 50% modulation are observed in the conductance. The tuning via in-plane gates allows to study the Aharonov-Bohm effect in the whole range from the open ring to the Coulomb-blockade regime.
Steingrimsson's coloring complex and Jonsson's unipolar complex are interpreted in terms of hyperplane arrangements. This viewpoint leads to short proofs that all coloring complexes and a large class of unipolar complexes have convex ear decompositions. These convex ear decompositions impose strong new restrictions on the chromatic polynomials of all finite graphs. Similar results are obtained for characteristic polynomials of submatroids of type B_n arrangements.
In this short note we prove the following result: If a completely multiplicative function $f:\mathbb{N}\to[-1,1]$ is small on average in the sense that $\sum_{n\leq x}f(n)\ll x^{1-\delta}$, for some $\delta>0$, and if the Dirichlet series of $f$, say $F(s)$, is such that $F(1)=0$, then we obtain that for any $\epsilon>0$, $\sum_{p\leq x}(1+f(p))\log p\ll x^{1-\delta+\epsilon}$. Moreover, a necessary condition for the existence of such $f$ is that the Riemann zeta function $\zeta(s)$ has no zeros in the half plane $Re(s)>1-\delta$.
Motivated by recent experiments on superconducting circuits consisting of a dc-voltage biased Josephson junction in series with a resonator, quantum properties of these devices far from equilibrium are studied. This includes a crossover from a domain of incoherent to a domain of coherent Cooper pair tunneling, where the circuit realizes a driven nonlinear oscillator. Equivalently, weak photon-charge coupling turns into strong correlations captured by a single degree of freedom. Radiated photons offer a new tool to monitor charge flow and current noise gives access to nonlinear dynamics, which allows to analyze quantum-classical boundaries.
We present a multiscale approach to measurements of galaxy density, applied to a volume-limited sample constructed from SDSS DR5. We populate a rich parameter space by obtaining independent measurements of density on different scales for each galaxy, avoiding the implicit assumptions involved, e.g., in the construction of group catalogues. As the first application of this method, we study how the bimodality in galaxy colour distribution (u-r) depends on multiscale density. The u-r galaxy colour distribution is described as the sum of two gaussians (red and blue) with five parameters: the fraction of red galaxies (f_r) and the position and width of the red and blue peaks (mu_r, mu_b, sigma_r and sigma_b). Galaxies mostly react to their smallest scale (< 0.5 Mpc) environments: in denser environments red galaxies are more common (larger f_r), redder (larger mu_r) and with a narrower distribution (smaller sigma_r), while blue galaxies are redder (larger mu_b) but with a broader distribution (larger sigma_b). There are residual correlations of f_r and mu_b with 0.5 - 1 Mpc scale density, which imply that total or partial truncation of star formation can relate to a galaxy's environment on these scales. Beyond 1 Mpc (0.5 Mpc for mu_r) there are no positive correlations with density. However f_r (mu_r) anti-correlates with density on >2 (1) Mpc scales at fixed density on smaller scales. We examine these trends qualitatively in the context of the halo model, utilizing the properties of haloes within which the galaxies are embedded, derived by Yang et al, 2007 and applied to a group catalogue. This yields an excellent description of the trends with multiscale density, including the anti-correlations on large scales, which map the region of accretion onto massive haloes. Thus we conclude that galaxies become red only once they have been accreted onto haloes of a certain mass.
We consider the operator $\sL$ defined on $C^2(\bR^d)$ functions by \sL f(x)&=&{1/2}\sum_{i,j=1}^d a_{ij}(x)\frac{\partial^2f(x)}{\partial x_i\partial x_j}+\sum_{i=1}^d b_i(x)\frac{\partial f(x)}{\partial x_i} &+&\int_{\bR^d\backslash\{0\}}[f(x+h)-f(x)-1_{(|h|\leq1)}h\cdot \grad f(x)]n(x,h)dh. Under the assumption that the local part of the operator is uniformly elliptic and with suitable conditions on $n(x,h)$, we establish a Harnack inequality for functions that are nonnegative in $\bR^d$ and harmonic in a domain. We also show that the Harnack inequality can fail without suitable conditions on $n(x,h)$. A regularity theorem for those nonnegative harmonic functions is also proved
In an earlier work, the first author and Petsche used potential theoretic techniques to establish a lower bound for the height of algebraic numbers that satisfy splitting conditions, such as being totally real or p-adic, improving on earlier work of Bombieri and Zannier in the totally p-adic case. These bounds applied as the degree of the algebraic number over the rationals tended towards infinity. In this paper, we use discrete energy approximation techniques on the Berkovich projective line to make the dependence on the degree in these bounds explicit, and we establish lower bounds for algebraic numbers which depend only on local properties of the numbers.
A theoretical investigation is presented of the statistics of excitons in quantum dots (QDs) of different sizes. A formalism is developed to build the exciton creation operator in a dot from the single exciton wavefunction and it is shown how this operator evolves from purely fermionic, in case of a small QD, to purely bosonic, in case of large QDs. Nonlinear optical emission spectra of semiconductor microcavities containing single QDs are found to exhibit a peculiar multiplet structure which reduces to Mollow triplet and Rabi doublet in fermionic and bosonic limits, respectively.
We consider the capillary-gravity water wave equation in two dimensions. We assume that the fluid is inviscid, incompressible, irrotational and the air density is zero. We construct an energy functional and prove a local wellposedness result without assuming the Taylor sign condition. When the surface tension $\sigma$ is zero, the energy reduces to a lower order version of the energy obtained by Kinsey and Wu [23] and allows angled crest interfaces. For positive surface tension, the energy does not allow angled crest interfaces but admits initial data with large curvature of the order of $\sigma^{-\frac{1}{3} + \epsilon} $ for any $\epsilon >0$.
A study is made of the possible holonomy group types of a space-time for which the energy-momentum tensor corresponds to a null or non-null electromagnetic field, a perfect fluid or a massive scalar field. The case of an Einstein space is also included. The techniques developed are also applied to vacuum and conformally flat space-times and contrasted with already known results in these two cases. Examples are given.
We study thermoelectric phenomena in a system consisting of strongly correlated quantum dot coupled to external leads in the Kondo regime. We calculate linear and nonlinear electrical and thermal conductance and thermopower of the quantum dot and discuss the role of asymmetry in the couplings to external electrodes. In the linear regime electrical and thermal conductances are modified, while thermopower remains unchanged. In the nonlinear regime the Kondo resonance in differential conductance develops at non-zero source-drain voltage, which has important consequences on thermoelectric properties of the system and the thermopower starts to depend on the asymmetry. We also discuss Wiedemann-Franz relation, thermoelectric figure of merit and validity of the Mott formula for thermopower.
When searching for a marked vertex in a graph, Szegedy's usual search operator is defined by using the transition probability matrix of the random walk with absorbing barriers at the marked vertices. Instead of using this operator, we analyze searching with Szegedy's quantum walk by using reflections around the marked vertices, that is, the standard form of quantum query. We show we can boost the probability to 1 of finding a marked vertex in the complete graph. Numerical simulations suggests that the success probability can be improved for other graphs, like the two-dimensional grid. We also prove that, for a certain class of graphs, we can express Szegedy's search operator, obtained from the absorbing walk, using the standard query model.
The results of ART-P/Granat observations of the X-ray burster SLX1732-304 in the globular cluster Terzan 1 are presented. The X-ray (3-20 keV) fluxes from the source differed by more than a factor of 4 during the observing sessions on September 8 ($F_{\rm X}\simeq6.95\times10^{-10}$ erg cm$^{-2}$ s$^{-1}$) and October 6, 1990 ($F_{\rm X}\simeq1.64\times10^{-10}$ erg cm$^{-2}$ s$^{-1}$). The intensity variations of SLX1732-304 were apparently accompanied by variations in its hardness: whereas the source in its high state had the spectrum with a distinct exponential cutoff typical of bright low-mass X-ray binaries, its low-state spectrum could be satisfactorily described by a simple power law with a photon index $\alpha\simeq1.7$. During the ART-P observation on September 8, a type I X-ray burst was detected from SLX1732-304.
We show that the mass-metallicity relation observed in the local universe is due to a more general relation between stellar mass M*, gas-phase metallicity and SFR. Local galaxies define a tight surface in this 3D space, the Fundamental Metallicity Relation (FMR), with a small residual dispersion of ~0.05 dex in metallicity, i.e, ~12%. At low stellar mass, metallicity decreases sharply with increasing SFR, while at high stellar mass, metallicity does not depend on SFR. High redshift galaxies, up to z~2.5 are found to follow the same FMR defined by local SDSS galaxies, with no indication of evolution. The evolution of the mass-metallicity relation observed up to z=2.5 is due to the fact that galaxies with progressively higher SFRs, and therefore lower metallicities, are selected at increasing redshifts, sampling different parts of the same FMR. By introducing the new quantity mu_alpha=log(M*)-alpha log(SFR), with alpha=0.32, we define a projection of the FMR that minimizes the metallicity scatter of local galaxies. The same quantity also cancels out any redshift evolution up to z~2.5, i.e, all galaxies have the same range of values of mu_0.32. At z>2.5, evolution of about 0.6 dex off the FMR is observed, with high-redshift galaxies showing lower metallicities. The existence of the FMR can be explained by the interplay of infall of pristine gas and outflow of enriched material. The former effect is responsible for the dependence of metallicity with SFR and is the dominant effect at high-redshift, while the latter introduces the dependence on stellar mass and dominates at low redshift. The combination of these two effects, together with the Schmidt-Kennicutt law, explains the shape of the FMR and the role of mu_0.32. The small metallicity scatter around the FMR supports the smooth infall scenario of gas accretion in the local universe.
Equations of motion for the microscopic number density $\hat{\rho}({\bf x},t)$ and the momentum density $\hat{\bf g}({\bf x},t)$ of a fluid have been obtained in the past from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory. In the thermally averaged equation for the coarse grained density ${\rho}({\bf x},t)$, the related dependence on the bare interaction potential in Dean's equation is converted to that on the corresponding direct correlation functions of the density functional theory.