ShantanuT01/DACTYL-Pretraining huggingface dataset:
We derive a deterministic protocol to implement a general single-qubit POVM on near-term circuit-based quantum computers. The protocol has a modular structure, such that an $n$-element POVM is implemented as a sequence of $(n-1)$ circuit modules. Each module performs a $2$-element POVM. Two variations of the protocol are suggested, one optimal in terms of number of ancilla qubits, the other optimal in terms of number of qubit gate operations and quantum circuit depth. We use the protocol to implement $2$- and $3$-element POVMs on two publicly available quantum computing devices. The results we obtain suggest that implementing non-trivial POVMs could be within the reach of the current noisy quantum computing devices.
We show that thin horizontal arrays of single wall carbon nanotubes (SWNTs) suspended above the channel of silicon MOSFETs can be used as vibrating gate electrodes. This new class of nano-electromechanical system (NEMS) combines the unique mechanical and electronic properties of SWNTs with an integrated siliconbased motion detection. Its electrical response exhibits a clear signature of the mechanical resonance of SWNTs arrays (120-150 MHz) showing that these thin horizontal arrays behave as a cohesive, rigid and elastic body membrane with a Young modulus in the order of 1-10 GPa and ultra-low mass. The resonant frequency can be tuned by the gate voltage and its dependence is well understood within the continuum mechanics framework.
We review the observations of dust emission in supernova rem- nants (SNRs) and supernovae (SNe). Theoretical calculations suggest that SNe, particularly core-collapse, should make significant quantities of dust, perhaps as much as a solar mass. Observations of extragalactic SNe have yet to find anywhere near this amount, but this may be the result of observa- tional limitations. SN 1987A, in the process of transitioning from a SN to an SNR, does show signs of a significant amount of dust forming in its ejecta, but whether this dust will survive the passage of the reverse shock to be injected into the ISM is unknown. IR observations of SNRs have not turned up significant quantities of dust, and the dust that is observed is generally swept-up by the forward shock, rather than created in the ejecta. Because the shock waves also destroy dust in the ISM, we explore the question of whether SNe might be net destroyers, rather than net creators of dust in the universe.
We explicitly compute the effective resistances between any two vertices of a ladder graph by using circuit reductions. Using our findings, we obtain explicit formulas for Kirchhoff index and admissible invariants of a ladder graph considering it as a model of a metrized graph. Comparing our formula for Kirchhoff index and previous results in literature, we obtain an explicit sum formula involving trigonometric functions. We also expressed our formulas in terms of certain generalized Fibonacci numbers that are the values of the Chebyshev polynomials of the second kind at $2$.
Reaction-diffusion systems with reversible reactions generically display power-law relaxation towards chemical equilibrium. In this work we investigate through numerical simulations aging processes that characterize the non-equilibrium relaxation. Studying a model which excludes multiple occupancy of a site, we find that the scaling behavior of the two-time correlation and response functions are similar to that discovered previously in an exactly solvable version with no restrictions on the occupation numbers. Especially, we find that the scaling of the response depends on whether the perturbation conserves a certain quantity or not. Our results point to a high degree of universality in relaxation processes taking place in diffusion-limited systems with reversible reactions.
We propose a fully unsupervised multi-modal deformable image registration method (UMDIR), which does not require any ground truth deformation fields or any aligned multi-modal image pairs during training. Multi-modal registration is a key problem in many medical image analysis applications. It is very challenging due to complicated and unknown relationships between different modalities. In this paper, we propose an unsupervised learning approach to reduce the multi-modal registration problem to a mono-modal one through image disentangling. In particular, we decompose images of both modalities into a common latent shape space and separate latent appearance spaces via an unsupervised multi-modal image-to-image translation approach. The proposed registration approach is then built on the factorized latent shape code, with the assumption that the intrinsic shape deformation existing in original image domain is preserved in this latent space. Specifically, two metrics have been proposed for training the proposed network: a latent similarity metric defined in the common shape space and a learningbased image similarity metric based on an adversarial loss. We examined different variations of our proposed approach and compared them with conventional state-of-the-art multi-modal registration methods. Results show that our proposed methods achieve competitive performance against other methods at substantially reduced computation time.
We put forward a mechanism for current induced spin polarization for a hole in a quantum dot side-coupled to a quantum wire, that is based on the spin-orbit splitting of the valence band. We predict that in a stark contrast with the traditional mechanisms based on the linear in momentum spin-orbit coupling, an exponentially small bias applied to the quantum wire with heavy holes is enough to create the 100% spin polarization of a localized light hole. Microscopically, the effect is related with the formation of chiral quasi bound states and the spin dependent tunneling of holes from the quantum wire to the quantum dot. This novel current induced spin polarization mechanism is equally relevant for the GaAs, Si and Ge based semiconductor nanostructures.
In a wide range of physical phenomena, we find propagating surfaces {\Omega}t which need mathematical treatment. In this article, we review the theory of the system of kinematical conservation laws (KCL), which govern the evolution of these surfaces and have been developed by the second author and his collaborators. KCL are the most general equations in conservation form, governing the evolution of {\Omega}t with physically realistic singularities. A very special type of singularity is a kink, which is a point on {\Omega}t when {\Omega}t is a curve in R2 andisacurveon{\Omega}t when{\Omega}t isasurfaceinR3. Acrossakinkthenormalnto{\Omega}t and the normal velocity m on {\Omega}t are discontinuous. The main aim of this article is to identify density of the conserved variable and the flux for the KCL which we did not do earlier. The presentation of this article is like that in a popular article, which which aims at non-experts in the field.
Recent developments in astronomical radio telescopes opened new opportunities in imaging and spectroscopy of solar radio bursts at sub-second timescales. Imaging in narrow frequency bands has revealed temporal variations in the positions and source sizes that do not fit into the standard picture of type III solar radio bursts, and require a better understanding of radio-wave transport. In this paper, we utilise 3D Monte Carlo ray-tracing simulations that account for the anisotropic density turbulence in the inhomogeneous solar corona to quantitatively explain the image dynamics at the fundamental (near plasma frequency) and harmonic (double) plasma emissions observed at \sim 32~MHz. Comparing the simulations with observations, we find that anisotropic scattering from an instantaneous emission point source can account for the observed time profiles, centroid locations, and source sizes of the fundamental component of type III radio bursts (generated where f_{pe} \approx 32~MHz). The best agreement with observations is achieved when the ratio of the perpendicular to the parallel component of the wave vector of anisotropic density turbulence is around 0.25. Harmonic emission sources observed at the same frequency (\sim 32~MHz, but generated where f_{pe} \approx 16~MHz) have apparent sizes comparable to those produced by the fundamental emission, but demonstrate a much slower temporal evolution. The simulations of radio-wave propagation make it possible to quantitatively explain the variations of apparent source sizes and positions at sub-second time-scales both for the fundamental and harmonic emissions, and can be used as a diagnostic tool for the plasma turbulence in the upper corona.
We prove a sharp asymptotic formula for the mean exit time from a bounded domain $D\subset \mathbb R^d$ for the overdamped Langevin dynamics $$d X_t = -\nabla f(X_t) d t + \sqrt{2\ve} \ d B_t$$ when $\ve \to 0$ and in the case when $D$ contains a unique non degenerate minimum of $f$ and $\pa_{\mbf n}f>0$ on $\pa D$. This formula was actually first derived in~\cite{matkowsky-schuss-77} using formal computations and we thus provide, in the reversible case, the first proof of it. As a direct consequence, we obtain when $\ve \to 0$, a sharp asymptotic estimate of the smallest eigenvalue of the operator $$L_{\ve}=-\ve \Delta +\nabla f\cdot \nabla$$ associated with Dirichlet boundary conditions on $\pa D$. The approach does not require $f|_{\partial D}$ to be a Morse function. The proof is based on results from~\cite{Day2,Day4} and a formula for the mean exit time from $D$ introduced in~\cite{BEGK, BGK}.
We show that in every dimension $N\geq3$ there are many bounded domains $\Omega\subset\mathbb{R}^{N}$, having only finite symmetries, in which the Bahri-Coron problem \[-\Delta u=|u| ^{4/(N-2)}u\text{\in}\Omega,\text{\ \}u=0\text{\ on}\partial\Omega, \] has a prescribed number of solutions, one of them being positive and the rest sign changing.
We investigate thin and thick stellar disc formation in Milky-Way-mass galaxies using twelve FIRE-2 cosmological zoom-in simulations. All simulated galaxies experience an early period of bursty star formation that transitions to a late-time steady phase of near-constant star formation. Stars formed during the late-time steady phase have more circular orbits and thin-disc-like morphology at $z=0$, whilst stars born during the bursty phase have more radial orbits and thick-disc structure. The median age of thick-disc stars at $z=0$ correlates strongly with this transition time. We also find that galaxies with an earlier transition from bursty to steady star formation have a higher thin-disc fractions at $z=0$. Three of our systems have minor mergers with LMC-size satellites during the thin-disc phase. These mergers trigger short starbursts but do not destroy the thin disc nor alter broad trends between the star formation transition time and thin/thick disc properties. If our simulations are representative of the Universe, then stellar archaeological studies of the Milky Way (or M31) provide a window into past star-formation modes in the Galaxy. Current age estimates of the Galactic thick disc would suggest that the Milky Way transitioned from bursty to steady phase $\sim$6.5 Gyr ago; prior to that time the Milky Way likely lacked a recognisable thin disc.
We give a new proof for the well-known Blaschke--Petkantschin formula which is based on the polar decomposition of rectangular matrices and may be of interest in random matrix theory.
We present a measurement of the two-point autocorrelation function of photometrically-selected, high-$z$ quasars over $\sim$ 100 deg$^2$ on the Sloan Digitial Sky Survey Stripe 82 field. Selection is performed using three machine-learning algorithms, trained on known high-$z$ quasar colors, in a six-dimensional, optical/mid-infrared color space. Optical data from the Sloan Digitial Sky Survey is combined with overlapping deep mid-infrared data from the \emph{Spitzer} IRAC Equatorial Survey and the \emph{Spitzer}-HETDEX Exploratory Large-area survey. The selected quasar sample consists of 1378 objects and contains both spectroscopically-confirmed quasars and photometrically-selected quasar candidates. These objects span a redshift range of $2.9 \leq z \leq 5.1$ and are generally fainter than $i=20.2$; a regime which has lacked sufficient number density to perform autocorrelation function measurements of photometrically-classified quasars. We compute the angular correlation function of these data, marginally detecting quasar clustering. We fit a single power-law with an index of $\delta = 1.39 \pm 0.618$ and amplitude of $\theta_0 = 0.71 \pm 0.546$ arcmin. A dark-matter model is fit to the angular correlation function to estimate the linear bias. At the average redshift of our survey ($\langle z \rangle = 3.38$) the bias is $b = 6.78 \pm 1.79$. Using this bias, we calculate a characteristic dark-matter halo mass of 1.70--9.83$\times 10^{12}h^{-1} M_{\odot}$. Our bias estimate suggests that quasar feedback intermittently shuts down the accretion of gas onto the central super-massive black hole at early times. If confirmed, these results hint at a level of luminosity dependence in the clustering of quasars at high-$z$.
The fluctuations of the jamming coverage upon Random Sequential Adsorption (RSA) are studied using both analytical and numerical techniques. Our main result shows that these fluctuations (characterized by $\sigma_{\theta_J}$) decay with the lattice size according to the power-law $\sigma_{\theta_J} \propto L^{-1/ \nu}$. The exponent $\nu$ depends on the dimensionality $D$ of the substrate and the fractal dimension of the set where the RSA process actually takes place ($d_f$) according to $\nu = 2 / (2D - d_f)$.This theoretical result is confirmed by means of extensive numerical simulations applied to the RSA of dimers on homogeneous and stochastic fractal substrates. Furthermore, our predictions are in excellent agreement with different previous numerical results.   It is also shown that, studying correlated stochastic processes, one can define various fluctuating quantities designed to capture either the underlying physics of individual processes or that of the whole system. So, subtle differences in the definitions may lead to dramatically different physical interpretations of the results. Here, this statement is demonstrated for the case of RSA of dimers on binary alloys.
GRB 141221A was observed from infrared to soft gamma-ray bands. Here, we investigate its properties, in light of the standard model. We find that the optical light curve of the afterglow of this burst presents an unusual steep/quick rise. The broad band spectral energy distribution taken near the maximum of the optical emission presents either a thermal component or a spectral break. In the former case, the properties of the afterglow are then very unusual, but could explain the lack of apparent jet breaks in the Swift light curves. In the latter case, the afterglow properties of this burst are more usual, and we can see in the light curves the passing through of the injection and cooling frequencies within the optical bands, not masked by a reverse shock. This model also excludes the presence of a stellar wind, challenging either the stellar progenitor properties, or the very stellar nature of the progenitor itself. In all cases, this burst may be a part of a Rosetta stone that could help to explain some of the most striking features discovered by Swift during the last ten years.
We present our results on transverse momentum fluctuations and multiplicity fluctuations in the framework of the clustering of color sources. In this approach, elementary color sources -strings- overlap forming clusters, so the number of effective sources is modified. These clusters decay into particles with mean transverse momentum that depends on the number of elementary sources that conform each cluster and the area occupied by the cluster. We find a non-monotonic dependence of the $p_T$ and multiplicity fluctuations with the number of participants. In our approach, the physical mechanism responsible of these fluctuations is the same: the formation of clusters of strings that introduces correlations between the produced particles.
Based on the ideal of order rearrangement and block transmission of photons, we present a quantum secure direct communication scheme using single photons. The security of the present scheme is ensured by quantum no-cloning theory and the secret transmitting order of photons. The present scheme is efficient in that all of the polarized photons are used to transmit the sender's secret message except those chosen for eavesdropping check. We also generalize this scheme to a multiparty controlled quantum secret direct communication scheme which the sender's secret message can only be recovered by the receiver under the permission of all the controllers.
At the LHC, superpartners with the masses lighter than a few TeV may be found, and the masses of the supersymmetric (SUSY) particles and their interactions will be studied. The information would be the base to consider the SUSY breaking mechanism and cosmology related to the SUSY dark matter. We review the recent studies that aims for the ``precise SUSY study'' at the LHC.
Strange-metal phenomena often develop at the border of antiferromagnetic order in strongly correlated metals. It has been well established that they can originate from the fluctuations anchored by the point of continuous quantum phase transition out of the antiferromagnetic order, i.e., a quantum critical point. What has been unclear is how these phenomena can be associated with a potential new phase of matter at zero temperature. Here we show that magnetic frustration of the 4f-local moments in the distorted Kagome intermetallic compound CePdAl gives rise to such a paramagnetic quantum-critical phase. Moreover, we demonstrate that this phase turns into a Fermi liquid through a Mott-like crossover; in a two-dimensional parameter space of pressure and magnetic field, this crossover is linked to a line of zero-temperature 4f-electron localization-delocalization phase transitions at low and moderate pressures. Our discovery motivates a new design principle for strongly correlated metallic states with unconventional excitations that may underlie the development of such effects as high temperature superconductivity.
We map Eigen model of biological evolution [Naturwissenschaften {\bf 58}, 465 (1971)] into a one-dimensional quantum spin model with non-Hermitean Hamiltonian. Based on such a connection, we derive exact relaxation periods for the Eigen model to approach static energy landscape from various initial conditions. We also study a simple case of dynamic fitness function.
We compare evolved stellar models, which match Procyons mass and position in the HR diagram, to current ground-based asteroseismic observations. Diffusion of helium and metals along with two conventional core overshoot descriptions and the Kuhfuss nonlocal theory of convection are considered. We establish that one of the two published asteroseismic data reductions for Procyon, which mainly differ in their identification of even versus odd l-values, is a significantly more probable and self-consistent match to our models than the other. The most probable models according to our Bayesian analysis have evolved to just short of turnoff, still retaining a hydrogen convective core. Our most probable models include Y and Z diffusion and have conventional core overshoot between 0.9 and 1.5 pressure scale heights, which increases the outer radius of the convective core by between 22% to 28%, respectively. We discuss the significance of this comparatively higher than expected core overshoot amount in terms of internal mixing during evolution. The parameters of our most probable models are similar regardless of whether adiabatic or nonadiabatic model p-mode frequencies are compared to the observations, although, the Bayesian probabilities are greater when the nonadiabatic model frequencies are used. All the most probable models (with or without core overshoot, adiabatic or nonadiabatic model frequencies, diffusion or no diffusion, including priors for the observed HRD location and mass or not) have masses that are within one sigma of the observed mass 1.497+/-0.037 Msun.
In this note we discuss the possibility of detecting the accompanying X-ray emission from sources of fast radio bursts with the eROSITA telescope onboard the Spektr-RG observatory. It is shown that during four years of the survey program about 300 bursts are expected to appear in the field of view of eROSITA. About 1\% of them will be detected by ground-based radio telescopes. For a total energy release $\sim~10^{46}$~ergs depending on the spectral parameters and absorption in the interstellar and intergalactic media, an X-ray flare can be detected from distances from $\sim 1$~Mpc (thermal spectrum with $kT=200$~keV and strong absorption) up to $\sim1$~Gpc (power-law spectrum with photon index $\Gamma=2 $ and realistic absorption). Thus, eROSITA observations might help to provide important constraints on parameters of sources of fast radio bursts, or may even allow to identify the X-ray transient counterparts, which will help to constrain models of fast radio bursts generation.
Using a slitless spectroscopy method with the 8.2 m Subaru telescope and its FOCAS Cassegrain spectrograph, we have increased the number of planetary nebula (PN) detections and PN velocity measurements in the flattened elliptical galaxy NGC 821. A comparison with the detections reported previously by the Planetary Nebula Spectrograph (PN.S) group indicates that we have confirmed most of their detections. The velocities measured by the two groups, using different telescopes, spectrographs and slitless techniques, are in good agreement. We have built a combined sample of 167 PNs and have confirmed the keplerian decline of the line-of-sight velocity dispersion reported previously. We also confirm misaligned rotation from the combined sample. A dark matter halo may exist around this galaxy, but it is not needed to keep the PN velocities below the local escape velocity as calculated from the visible mass. We have measured the m(5007) magnitudes of 145 PNs and produced a statistically complete sample of 40 PNs in NGC 821. The resulting PN luminosity function (PNLF) was used to estimate a distance modulus of 31.4 mag, equivalent to 19 Mpc. We also estimated the PN formation rate. NGC 821 becomes the most distant galaxy with a PNLF distance determination. The PNLF distance modulus is smaller than the surface brightness fluctuation (SBF) distance modulus by 0.4 mag. Our kinematic information permits to rule out the idea that a shorter PNLF distance could be produced by the contamination of the PNLF by background galaxies with emission lines redshifted into the on-band filter transmission curve.