ShantanuT01/DACTYL-Pretraining huggingface dataset:
Holoscopic 3D imaging is a promising technique for capturing full colour spatial 3D images using a single aperture holoscopic 3D camera. It mimics fly's eye technique with a microlens array, which views the scene at a slightly different angle to its adjacent lens that records three dimensional information onto a two dimensional surface. This paper proposes a method of depth map generation from a holoscopic 3D image based on graph cut technique. The principal objective of this study is to estimate the depth information presented in a holoscopic 3D image with high precision. As such, depth map extraction is measured from a single still holoscopic 3D image which consists of multiple viewpoint images. The viewpoints are extracted and utilised for disparity calculation via disparity space image technique and pixels displacement is measured with sub pixel accuracy to overcome the issue of the narrow baseline between the viewpoint images for stereo matching. In addition, cost aggregation is used to correlate the matching costs within a particular neighbouring region using sum of absolute difference SAD combined with gradient-based metric and winner takes all algorithm is employed to select the minimum elements in the array as optimal disparity value. Finally, the optimal depth map is obtained using graph cut technique. The proposed method extends the utilisation of holoscopic 3D imaging system and enables the expansion of the technology for various applications of autonomous robotics, medical, inspection, AR VR, security and entertainment where 3D depth sensing and measurement are a concern.
The deconfinement phase transition is studied in the FL model at finite temperature and chemical potential. At MFT approximation, the phase transition can only be the first order in the whole $\mu-T$ phase plane. By a Landau expansion we further study the phase transition order and the possible phase diagram of deconfinement. We discuss the possibilities of second order phase transitions in FL model. By our analysis the cubic term in the Landau expansion could be cancelled by the high order fluctuations. By an ansatz of the Landau parameters, we obtain the possible phase diagram with both first and second order phase transition including the tricritical point which is similar to that of the chiral phase transition.
We propose and employ a novel empirical method for determining chromospheric plage regions, which seems to better isolate plage from its surrounding regions compared to other methods commonly used. We caution that isolating plage from its immediate surroundings must be done with care in order to successfully mitigate statistical biases that, for instance, can impact quantitative comparisons between different chromospheric observables. Using this methodology, our analysis suggests that 1.25 mm wavelength free-free emission in plage regions observed with ALMA/Band6 may not form in the low chromosphere as previously thought, but rather in the upper chromospheric parts of dynamic plage features (such as spicules and other bright structures), i.e., near geometric heights of transition region temperatures. We investigate the high degree of similarity between chromospheric plage features observed in ALMA/Band6 (at 1.25 mm wavelength) and IRIS/Si IV at 1393\r{A}. We also show that IRIS/Mg II h and k is not as well correlated with ALMA/Band6 as was previously thought, and we discuss the discrepancies with previous works. Lastly, we report indications for chromospheric heating due to propagating shocks supported by the ALMA/Band6 observations.
We consider coagulation equations of Smoluchowski or Flory type where the total merge rate has a bilinear form $\pi(y)\cdot A\pi(x)$ for a vector of conserved quantities $\pi$, generalising the multiplicative kernel. For these kernels, a gelation transition occurs at a finite time $t_\mathrm{g}\in (0,\infty)$, which can be given exactly in terms of an eigenvalue problem in finite dimensions. We prove a hydrodynamic limit for a stochastic coagulant, including a corresponding phase transition for the largest particle, and exploit a coupling to random graphs to extend analysis of the limiting process beyond the gelation time.
Wavefront Coding has been applied as a means to increase the effective depth of focus of optical systems. In this note I discuss the potential for this technique to increase the depth of focus of the LSST and the resulting advantages for the construction and operation of the facility, as well as possible drawbacks. It may be possible to apply Wavefront Coding without changing the current LSST design, in which case Wavefront Coding might merit further study as a risk mitigation strategy.
We obtain homological properties of the second symmetric product of P^4 and the double cover of the symmetric determinantal quintic hypersurface in P^{14} (the double quintic symmetroids), which indicate the homological projective duality between (suitable noncommutative resolutions of) them. Among other things, we construct their good desingularizations and also (dual) Lefschetz collections in the derived categories of the desingularizations. These are expected to give (dual) Lefschetz decompositions of suitable noncommutative resolutions. The desingularization of the double quintic symmetroids also contains its interesting birational geometries.
An analytical method based on the classical ruin problem is developed to compute the mean reaction time between two walkers undergoing a generalized random walk on a 1d lattice. At each time step, either both walkers diffuse simultaneously with probability $p$ (synchronous event) or one of them diffuses while the other remains immobile with complementary probability (asynchronous event). Reaction takes place through same site occupation or position exchange. We study the influence of the degree of synchronicity $p$ of the walkers and the lattice size $N$ on the global reaction's efficiency. For odd $N$, the purely synchronous case ($p=1$) is always the most effective one, while for even $N$, the encounter time is minimized by a combination of synchronous and asynchronous events. This new parity effect is fully confirmed by Monte Carlo simulations on 1d lattices as well as for 2d and 3d lattices. In contrast, the 1d continuum approximation valid for sufficiently large lattices predicts a monotonic increase of the efficiency as a function of $p$. The relevance of the model for several research areas is briefly discussed.
Using spectroscopic ellipsometry measurements on GaP$_{1-x}$Bi$_{x}$/GaP epitaxial layers up to $x = 3.7$% we observe a giant bowing of the direct band gap ($E_{g}^{\Gamma}$) and valence band spin-orbit splitting energy ($\Delta_{\textrm{SO}}$). $E_{g}^{\Gamma}$ ($\Delta_{\textrm{SO}}$) is measured to decrease (increase) by approximately 200 meV (240 meV) with the incorporation of 1% Bi, corresponding to a greater than fourfold increase in $\Delta_{\textrm{SO}}$ in going from GaP to GaP$_{0.99}$Bi$_{0.01}$. The evolution of $E_{g}^{\Gamma}$ and $\Delta_{\textrm{SO}}$ with $x$ is characterised by strong, composition-dependent bowing. We demonstrate that a simple valence band-anticrossing model, parametrised directly from atomistic supercell calculations, quantitatively describes the measured evolution of $E_{g}^{\Gamma}$ and $\Delta_{\textrm{SO}}$ with $x$. In contrast to the well-studied GaAs$_{1-x}$Bi$_{x}$ alloy, in GaP$_{1-x}$Bi$_{x}$ substitutional Bi creates localised impurity states lying energetically within the GaP host matrix band gap. This leads to the emergence of an optically active band of Bi-hybridised states, accounting for the overall large bowing of $E_{g}^{\Gamma}$ and $\Delta_{\textrm{SO}}$ and in particular for the giant bowing observed for $x \lesssim 1$%. Our analysis provides insight into the action of Bi as an isovalent impurity, and constitutes the first detailed experimental and theoretical analysis of the GaP$_{1-x}$Bi$_{x}$ alloy band structure.
Validating whether a quantum device confers a computational advantage often requires classical simulation of its outcomes. The worst-case sampling cost of $L_1$-norm based simulation has plateaued at $\le(2+\sqrt{2})\xi_t \delta^{-1}$ in the limit that $t \rightarrow \infty$, where $\delta$ is the additive error and $\xi_t$ is the stabilizer extent of a $t$-qubit magic state. We reduce this prefactor 68-fold by a leading-order reduction in $t$ through correlated sampling. The result exceeds even the average-case of the prior state-of-the-art and current simulators accurate to multiplicative error. Numerical demonstrations support our proofs. The technique can be applied broadly to reduce the cost of $L_1$ minimization.
In this paper we revisit the Markovian queueing system with a single server, infinite capacity queue and the special queue skipping policy. Customers arrive in batches, but are served one by one according to any conservative discipline. The size of the arriving batch becomes known upon its arrival and at any time instant the total number of customers in the system is also known. According to the adopted queue skipping policy if a batch, which size is greater than the current system size, arrives to the system, all current customers in the system are removed from it and the new batch is placed in the queue. Otherwise the new batch is lost. The distribution of the total number of customers in the system is under consideration under assumption that the arrival intensity $\lambda(t)$ and/or the service intensity $\mu(t)$ are non-random functions of time. We provide the method for the computation of the upper bounds for the rate of convergence of system size to the limiting regime, whenever it exists, for any bounded $\lambda(t)$ and $\mu(t)$ (not necessarily periodic) and any distribution of the batch size. For periodic intensities $\lambda(t)$ and/or $\mu(t)$ and light-tailed distribution of the batch size it is shown how the obtained bounds can be used to numerically compute the limiting distribution of the queue size with the given error. Illustrating numerical examples are provided.
After deriving the classical Ward identity for the variation of the action under a change of the modulus of the torus we map the problem of the sphere with four sources to the torus. We extend the method previously developed for computing the classical conformal blocks for the sphere topology to the tours topology. We give the explicit results for the classical blocks up to the third order in the nome included and compare them with the classical limit of the quantum conformal blocks. The extension to higher orders is straightforward.
Modified gravitational forces in models that seek to explain cosmic acceleration without dark energy typically predict deviations in the abundance of massive dark matter halos. We conduct the first, simulation calibrated, cluster abundance constraints on a modified gravity model, specifically the modified action f(R) model. The local cluster abundance, when combined with geometric and high redshift data from the cosmic microwave background, supernovae, H_0 and baryon acoustic oscillations, improve previous constraints by nearly 4 orders of magnitude in the field amplitude. These limits correspond to a 2 order of magnitude improvement in the bounds on the range of the force modification from the several Gpc scale to the tens of Mpc scale.
By using row convex tableaux, we study the section rings of Bott-Samelson varieties of type A. We obtain flat deformations and standard monomial type bases of the section rings. In a separate section, we investigate a three dimensional Bott-Samelson variety in detail and compute its Hilbert polynomial and toric degenerations.
We study the structural correlations and the nonlinear response to a driving force of a two-dimensional phase-field-crystal model with random pinning. The model provides an effective continuous description of lattice systems in the presence of disordered external pinning centers, allowing for both elastic and plastic deformations. We find that the phase-field crystal with disorder assumes an amorphous glassy ground state, with only short-ranged positional and orientational correlations even in the limit of weak disorder. Under increasing driving force, the pinned amorphous-glass phase evolves into a moving plastic-flow phase and then finally a moving smectic phase. The transverse response of the moving smectic phase shows a vanishing transverse critical force for increasing system sizes.
In Kang (2015) we calculated the acceleration of cosmic-ray electrons and the ensuing radio synchrotron emission at weak spherical shocks that are expected to form in the outskirts of galaxy clusters.There we demonstrated that, at decelerating spherical shocks, the volume integrated spectra of both electrons and radiation deviate significantly from the test-particle power-laws predicted for constant planar shocks, because the shock compression ratio and the flux of injected electrons decrease in time. In this study, we consider spherical blast waves propagating into a constant density core surrounded by an isothermal halo with a decreasing density profile in order to explore how the deceleration rate of the shock speed affects the radio emission from accelerated electrons. The surface brightness profile and the volume-integrated radio spectrum of the model shocks are calculated by assuming a ribbon-like shock surface on a spherical shell and the associated downstream region of relativistic electrons. If the postshock magnetic field strength is about 7 microgauss, at the shock age of ~50 Myr, the volume-integrated radio spectrum steepens gradually with the spectral index from alpha_{inj} to alpha_{inj}+0.5 over 0.1-10 GHz, where alpha_{inj} is the injection index at the shock positionexpected from the diffusive shock acceleration theory. Such gradual steepening could explain the curved radio spectrum of the radio relic in cluster A2266, which was interpreted as a broken power-law by Trasatti et al. (2014), if the relic shock is young enough so that the break frequency falls in around 1 GHz.
We present numerical results of a model calculation for the 3He bilayer system, which captures the interplay between fast and slow dynamics of the different layers and incorporates an independent scale for the three body ring exchange. By means of Cluster-DMFT+CTQMC, we find remarkable similarities with the experiments: a suppression of the coherence temperature upon approaching the solidification point of the first layer accompanied by the onset of strong ferromagnetic correlations within the first layer. Based on the consistent results for different cluster sizes we conjecture a first-order transition cutting short the Kondo breakdown, which allows us to interpret the experimental observation of an intervening phase preempting the quantum critical point in terms of a phase separation.
We are concerned with the dimension reduction analysis for thin three-dimensional elastic films, prestrained via Riemannian metrics with weak curvatures.   For the prestrain inducing the incompatible version of the F\"oppl-von K\'arm\'an equations, we find the $\Gamma$-limits of the rescaled energies, identify the optimal energy scaling laws, and display the equivalent conditions for optimality in terms of both the prestrain components and the curvatures of the related Riemannian metrics. When the stretching-inducing prestrain carries no in-plane modes, we discover similarities with the previously described shallow shell models.   In higher prestrain regimes, we prove new energy upper bounds by constructing deformations as the Kirchhoff-Love extensions of the highly perturbative, H\"older-regular solutions to the Monge-Ampere equation obtained by means of convex integration.
Young tableaux are classical combinatorial objects playing recurring and varied roles in representation theory, algebraic geometry and commutative algebra. This article is a short exposition on Young tableaux, written for the "WHAT IS...?" series of the Notices of the American Mathematical Society. It describes some of their properties and applications.
We study a notion of local time for a continuous path, defined as a limit of suitable discrete quantities along a general sequence of partitions of the time interval. Our approach subsumes other existing definitions and agrees with the usual (stochastic) local times a.s. for paths of a continuous semimartingale. We establish pathwise version of the It\^o-Tanaka, change of variables and change of time formulae. We provide equivalent conditions for existence of pathwise local time. Finally, we study in detail how the limiting objects, the quadratic variation and the local time, depend on the choice of partitions. In particular, we show that an arbitrary given non-decreasing process can be achieved a.s. by the pathwise quadratic variation of a standard Brownian motion for a suitable sequence of (random) partitions; however, such degenerate behavior is excluded when the partitions are constructed from stopping times.
Water confined between two graphene layers with a small separation forms a two-dimensional ice structure,with an apparent square symmetry [Algara-Siller et al., Nature (London) 519, 443 (2015)], which is poorly understood. A density functional approach is applied to the water, but not to the water graphene interactions, since the two crystals are incommensurate. We thus need use a potential model for the interaction between water and graphene. We analyze the models for confinement of water by graphene, and find that even though the general features are well established, the detail is not so well understood. Using a representative range of potential models, we perform density-functional calculations and show that many ice-like configurations exist. In some cases these are unstable with respect to decay into a bi-layer structure, but we expect tunneling between such structures to be slow. It is shown that there is one good candidate for a square crystal, which is a peculiar anti-ferroelectric arrangement of water molecules.
A rearrangement of $n$ independent uniform $[0,1]$ random variables is a sequence of $n$ random variables $Y_1,...,Y_n$ whose vector of order statistics has the same distribution as that for the $n$ uniforms. We consider rearrangements satisfying the strong rank independence condition, that the rank of $Y_k$ among $Y_1,...,Y_k$ is independent of the values of $Y_1,...,Y_{k-1}$, for $k=1,...,n$. Nontrivial examples of such rearrangements are the travellers' processes defined by Gnedin and Krengel. We show that these are the only examples when $n=2$, and when certain restrictive assumptions hold for $n\geq 3$; we also construct a new class of examples of such rearrangements for which the restrictive assumptions do not hold.
We present new 3-mm continuum and molecular lines observations from the ATOMS survey towards the massive protostellar clump, MM1, located in the filamentary infrared dark cloud (IRDC), G034.43+00.24 (G34). The lines observed are the tracers of either dense gas (e.g. HCO+/H13CO+ J = 1-0) or outflows (e.g. CS J = 2-1). The most complete picture to date of seven cores in MM1 is revealed by dust continuum emission. These cores are found to be gravitationally bound, with virial parameter, $\alpha_{vir}<2$. At least four outflows are identified in MM1 with a total outflowing mass of $\sim 45 M_\odot$, and a total energy of $\sim 1\times 10^{47}$ erg, typical of outflows from a B0-type star. Evidence of hierarchical fragmentation, where turbulence dominates over thermal pressure, is observed at both the cloud and the clump scales. This could be linked to the scale-dependent, dynamical mass inflow/accretion on clump and core scales. We therefore suggest that the G34 cloud could be undergoing a dynamical mass inflow/accretion process linked to the multiscale fragmentation, which leads to the sequential formation of fragments of the initial cloud, clumps, and ultimately dense cores, the sites of star formation.
We address the cause of the unusual muon spin relaxation (muSR) results on molecular nanomagnets (MNMs). Through measurements on protonated and deuterated samples of the MNMs Cr7Mn (S=1) and Cr8 (S=0), we show that the muon spin for $S \neq 0$ MNMs is relaxed via dynamic fluctuations of the electronic spins. A freezing out of dynamic processes occurs on cooling and at low temperatures the muon spins are relaxed by the electronic spins which themselves are dephased by incoherent nuclear field fluctuations.We observe a transition to a state of static magnetic order of the MNM electronic spins in Cr7Mn below 2 K.
We show how the onset of a non-Slater antiferromagnetic ordering in a correlated material can be detected by optical spectroscopy. Using dynamical mean-field theory we identify two distinctive features: The antiferromagnetic ordering is associated with an enhanced spectral weight above the optical gap, and well separated spin-polaron peaks emerge in the optical spectrum. Both features are indeed observed in LaSrMnO_4 [G\"ossling et al., Phys. Rev. B 77, 035109 (2008)]
We consider new types of perfect shuffles wherein a deck is split in half, one half of the deck is "reversed", and then the cards are interlaced. Flip shuffles are when the reversal comes from flipping the half over so that we also need to account for face-up/face-down configurations while horseshoe shuffles are when the order of the cards are reversed but all cards still face the same direction. We show that these shuffles are closely related to faro shuffling and determine the order of the associated shuffling groups.
Suppose $E$ is an elliptic curve defined over $\Q$. At the 1983 ICM the first author formulated some conjectures that propose a close relationship between the explicit class field theory construction of certain abelian extensions of imaginary quadratic fields and an explicit construction that (conjecturally) produces almost all of the rational points on $E$ over those fields. Those conjectures are to a large extent settled by recent work of Vatsal and of Cornut, building on work of Kolyvagin and others. In this paper we describe a collection of interrelated conjectures still open regarding the variation of Mordell-Weil groups of $E$ over abelian extensions of imaginary quadratic fields, and suggest a possible algebraic framework to organize them.
The extraction of nuclear matter properties from measured nuclear masses is investigated in the energy density functional formalism of nuclei. It is shown that the volume energy $a_1$ and the nuclear incompressibility $K_0$ depend essentially on $\mu_n N+\bar{\mu}_p Z-2E_N$, whereas the symmetry energy $J$ and the density symmetry coefficient $L$ as well as symmetry incompressibility $K_s$ depend essentially on $\mu_n-\bar{\mu}_p$, where $\bar{\mu}_p=\mu_p-\partial E_C/\partial Z$, $\mu_n$ and $\mu_p$ are the neutron and proton chemical potentials respectively, $E_N$ the nuclear energy, and $E_C$ the Coulomb energy. The obtained symmetry energy is $J=28.5MeV$, while other coefficients are uncertain within ranges depending on the model of nuclear equation of state.