ShantanuT01/DACTYL-Pretraining huggingface dataset:
We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroedinger Equation $- \epsilon^2 \Delta \psi + V(x) \psi = |\psi|^{p-1} \psi$ on a manifold or in the Euclidean space. Here V represents the potential, p is an exponent greater than 1 and $\epsilon$ a small parameter corresponding to the Planck constant. As $\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase in highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In the first part of this work we identified the limit set and constructed approximate solutions, while here we give the complete proof of our main existence result.
During the 2014 HST/Swift and ground-based multi-wavelength monitoring campaign of NGC 5548 (AGN STORM), the UV-optical broad emission lines exhibited anomalous, decorrelated behaviour relative to the far-UV continuum flux variability. Here, we use key diagnostic emission lines (Ly-alpha and He II) for this campaign to infer a proxy for the all important, variable driving EUV continuum incident upon BLR clouds. The inferred driving continuum provides a crucial step towards the recovery of the broad emission line response functions in this AGN. In particular, the ionising continuum seen by the BLR was weaker and softer during the anomalous period than during the first third of the campaign, and apparently less variable than exhibited by the far-UV continuum. We also report the first evidence for anomalous behaviour in the longer wavelength (relative to 1157A) continuum bands. This is corroborative evidence that a significant contribution to the variable UV-optical continuum emission arises from a diffuse continuum emanating from the same gas that emits the broad emission lines.
This article describes a contour-based 3D tongue deformation visualization framework using B-mode ultrasound image sequences. A robust, automatic tracking algorithm characterizes tongue motion via a contour, which is then used to drive a generic 3D Finite Element Model (FEM). A novel contour-based 3D dynamic modeling method is presented. Modal reduction and modal warping techniques are applied to model the deformation of the tongue physically and efficiently. This work can be helpful in a variety of fields, such as speech production, silent speech recognition, articulation training, speech disorder study, etc.
Conformal blocks in any number of dimensions depend on two variables z, zbar. Here we study their restrictions to the special "diagonal" kinematics z = zbar, previously found useful as a starting point for the conformal bootstrap analysis. We show that conformal blocks on the diagonal satisfy ordinary differential equations, third-order for spin zero and fourth-order for the general case. These ODEs determine the blocks uniquely and lead to an efficient numerical evaluation algorithm. For equal external operator dimensions, we find closed-form solutions in terms of finite sums of 3F2 functions.
Interference between an unknown two-photon state (a "biphoton") and the two-photon component of a reference state gives a phase-sensitive arrival-time distribution containing full information about the biphoton temporal wave function. Using a coherent state as a reference, we observe this interference and reconstruct the wave function of single-mode biphotons from a low-intensity narrowband squeezed vacuum state.
The space of Bridgeland stability conditions on the bounded derived category of coherent sheaves on P2 has a principle connected component Stab^\dag(P2). We show that Stab^\dag(P2) is the union of geometric and algebraic stability conditions. As a consequence, we give a cell decomposition for Stab^\dag (P2) and show that Stab^\dag(P2) is contractible.
The classical Langevin dynamics of a particle in a periodic potential energy landscape are studied via the intermediate scattering function (ISF). By construction, the particle performs coupled vibrational and activated jump motion with a wide separation of the vibrational period and the mean residence time between jumps. The long time limit of the ISF is a decaying tail proportional to the function that describes ideal jump motion in the absence of vibrations. The amplitude of the tail is unity in idealized jump dynamics models, but is reduced from unity by the intra-well motion. Analytical estimates of the amplitude of the jump motion signature are provided by assuming a \textcolor{blue}{factorization of the conditional probability density of the particle position at long times, motivated by the separation of time scales associated with inter-cell and intra-cell motion}. The assumption leads to a factorization of the ISF at long correlation times, where one factor is an ideal jump motion signature, and the other component is the amplitude of the signature. The amplitude takes the form of a single-particle anharmonic Debye-Waller factor. The factorization approximation is exact at the diffraction conditions associated with the periodic potential. Numerical simulations of the Langevin equation in one and two spatial dimensions confirm that for a strongly corrugated potential the analytical approximation provides a good qualitative description of the trend in the jump signature amplitude, between the points where the factorization is exact.
The empirical-phenomenological quasi-deuteron photofission description is theoretically justified within the semiclassical, intermediate statistics model. The transmutational fermion (nucleon) - boson (quasi-deuteron) potential plays an essential role in the present context and is expressed in terms of thermodynamical and of microscopical quantities, analogous to those commonly used in the superfluid nuclear model.
We discuss the question of how the number of dimensions of space and time can influence the equilibrium configurations of stars. We find that dimensionality does increase the effect of mass but not the contribution of the pressure, which is the same in any dimension. In the presence of a (positive) cosmological constant the condition of hydrostatic equilibrium imposes a lower limit on mass and matter density. We show how this limit depends on the number of dimensions and suggest that $\Lambda > 0$ is more effective in 4D than in higher dimensions. We obtain a general limit for the degree of compactification (gravitational potential on the boundary) of perfect fluid stars in $D$-dimensions. We argue that the effects of gravity are stronger in 4D than in any other number of dimensions. The generality of the results is also discussed.
Using an effective-field-theory (nonlinear sigma model) description of interacting electrons in a disordered metal ring enclosing magnetic flux, we calculate the moments of the persistent current distribution, in terms of interacting Goldstone modes (diffusons and cooperons). At the lowest or Gaussian order we reproduce well-known results for the average current and its variance that were originally obtained using diagrammatic perturbation theory. At this level of approximation the current distribution can be shown to be strictly Gaussian. The nonlinear sigma model provides a systematic way of calculating higher-order contributions to the current moments. An explicit calculation for the average current of the first term beyond Gaussian order shows that it is small compared to the Gaussian result; an order-of-magnitude estimation indicates that the same is true for all higher-order contributions to the average current and its variance. We therefore conclude that the experimentally observed magnitude of persistent currents cannot be explained in terms of interacting diffusons and cooperons.
Equivariant tree models are statistical models used in the reconstruction of phylogenetic trees from genetic data. Here equivariant refers to a symmetry group imposed on the root distribution and on the transition matrices in the model. We prove that if that symmetry group is Abelian, then the Zariski closures of these models are defined by polynomial equations of bounded degree, independent of the tree. Moreover, we show that there exists a polynomial-time membership test for that Zariski closure. This generalises earlier results on tensors of bounded rank, which correspond to the case where the group is trivial, and implies a qualitative variant of a quantitative conjecture by Sturmfels and Sullivant in the case where the group and the alphabet coincide. Our proofs exploit the symmetries of an infinite-dimensional projective limit of Abelian star models.
This paper investigates quantitative estimates in the homogenization of second-order elliptic systems with periodic coefficients that oscillate on multiple separated scales. We establish large-scale interior and boundary Lipschitz estimates down to the finest microscopic scale via iteration and rescaling arguments. We also obtain a convergence rate in the $L^2$ space by the reiterated homogenization method.
Separable nucleon-nucleon potentials are calculated using inverse scattering techniques as presented in previously published work. The dependence of the potentials on the momentum cut-off of the scattering phase-shifts is studied. Some comparison is made with the V-low-k potential. The effect of the cut-off on nuclear matter binding energy calculated by standard Brueckner theory is also presented. It is foumd that a cut-off larger than about 4 fm-1 will keep the error to within one Mev around saturation density. While the potentials are cut-off dependent the effective interaction represented by the Brueckner K-matrix is less sensitive to this cut-off. This is in particular found to be the case for the 1S0 state.
Macroscopic traversable wormhole solutions to Einstein's field equations in $(2+1)$ and $(3+1)$ dimensions with a cosmological constant are investigated. Ensuring traversability severely constrains the material used to generate the wormhole's spacetime curvature. Although the presence of a cosmological constant modifies to some extent the type of matter permitted (for example it is possible to have a positive energy density for the material threading the throat of the wormhole in $(2+1)$ dimensions), the material must still be ``exotic'', that is matter with a larger radial tension than total mass-energy density multiplied by $c^2$. Two specific solutions are applied to the general cases and a partial stability analysis of a $(2+1)$ dimensional solution is explored.
We study dispersion for the defocusing gKdV equation. It is expected that it is not possible for the bulk of the $L^2-$mass to concentrate in a small interval for a long time. We study a variance-type functional exploiting Tao's monotonicity formula in the spirit of earlier work by Tao as well as Kwon & Shao and quantify its growth in terms of sublevel estimates.
Based on an idea in Hironaka's proof of resolution of singularities, we present an algorithmic smoothness test for algebraic varieties. The test is inherently parallel and does not involve the calculation of codimension-sized minors of the Jacobian matrix of the variety. We also describe a hybrid method which combines the new method with the Jacobian criterion, thus making use of the strengths of both approaches. We have implemented all algorithms in the computer algebra system Singular, and compare the different approaches with respect to timings and memory usage. The test examples originate from questions in algebraic geometry, where the use of the Jacobian criterion is impractical due to the number and size of the minors involved.
A classical-kind phase-space formalism is developed to address the tiny intrinsic dynamical deviation from what is predicted by Wilczek-Zee theorem during quantum adiabatic evolution on degeneracy levels. In this formalism, the Hilbert space and the aggregate of degenerate eigenstates become the classical-kind phase-space and a high-dimensional subspace in the phase-space, respectively. Compared with the previous same study by a different method, the current result is qualitatively different in that the first-order deviation derived here is always perpendicular to the degeneracy subspace. A tripod scheme Hamiltonian with two degenerate dark states is employed to illustrate the adiabatic deviation with degeneracy levels.
Swift J1753.5-0127 (J1753) is a candidate black hole low-mass X-ray binary (BH-LMXB) that was discovered in outburst in May 2005. It remained in outburst for $\sim12$ years, exhibiting a wide range of variability on various timescales, before entering quiescence after two short-lived, low-luminosity "mini-outbursts" in April 2017. The unusually long outburst duration in such a short-period ($P_{\rm orb}\approx3.24$ hrs) source, and complex variability observed during this outburst period, challenges the predictions of the widely accepted disc-instability model, which has been shown to broadly reproduce the behaviour of LMXB systems well. The long-term behaviour observed in J1753 is reminiscent of the Z Cam class of dwarf novae, whereby variable mass transfer from the companion star drives unusual outbursts, characterized by stalled decays and abrupt changes in luminosity. Using sophisticated modelling of the multi-wavelength light curves and spectra of J1753, during the $\sim12$ years the source was active, we investigate the hypothesis that periods of enhanced mass transfer from the companion star may have driven this unusually long outburst. Our modelling suggests that J1753 is in fact a BH-LMXB analogue to Z Cam systems, where the variable mass transfer from the companion star is driven by the changing irradiation properties of the system, affecting both the disc and companion star.
Sparsity plays a central role in recent developments in signal processing, linear algebra, statistics, optimization, and other fields. In these developments, sparsity is promoted through the addition of an $L^1$ norm (or related quantity) as a constraint or penalty in a variational principle. We apply this approach to partial differential equations that come from a variational quantity, either by minimization (to obtain an elliptic PDE) or by gradient flow (to obtain a parabolic PDE). Also, we show that some PDEs can be rewritten in an $L^1$ form, such as the divisible sandpile problem and signum-Gordon. Addition of an $L^1$ term in the variational principle leads to a modified PDE where a subgradient term appears. It is known that modified PDEs of this form will often have solutions with compact support, which corresponds to the discrete solution being sparse. We show that this is advantageous numerically through the use of efficient algorithms for solving $L^1$ based problems.
The equation describing the stochastic motion of a classical particle in 1+1-dimensional space-time is connected to the Dirac equation with external gauge fields. The effects of assigning different turning probabilities to the forward and the backward moving particles in time are discussed.
La0.7Ce0.3MnO3 (LCeMO) is known usually called an electron doped colossal magnetotesistance material, which contains multiphase of n-type LCeMO, CeO2 and Mn-O. However, the present energy dispersion spectroscopy measurement shows that the La0.85Ce0.017MnO3+delta is the main phase in the bulk solid of material, which does not have the LCeMO phase. This finding is consistent with the XRD data analysis which indicates that the composition is La0.87Ce0.014MnO2.93. Since the highly localized f electrons of Ce ions may not be transferred to Mn ions significant oxygen deficiency is needed to drive La0.87Ce0.014MnO2.93 into n-type state that, which conflicts with the observation of a low TC fact of the vacuum annealed sample and to the natural tendency for the absorption of excess oxygen that yields a positive delta. Similar properties are also found in La1-xTexMnO3+delta, La1-xSnxMnO3+delta and La1-xZrxMnO3+delta systems. The present study casts doubt on the interpretation of n-ype electronic property in bulk solid of LCeMO and proposed that the n-type CMR may be formed in metastable state.
The elementary quadratic plus inverse sextic interaction containing a strongly singular repulsive core in the origin is made regular by a complex shift of coordinate $x = s-{\rm i}\varepsilon$. The shift $\varepsilon>0$ is fixed while the value of $s$ is kept real and potentially observable, $s \in (-\infty,\infty)$. The low-lying energies of bound states are found in closed form for the large couplings $g$. Within the asymptotically vanishing ${\cal O}(g^{-1/4})$ error bars these energies are real so that the time-evolution of the system may be expected unitary in an {\em ad hoc} physical Hilbert space.
When a rotating neutron star loses angular momentum, the reduction in the centrifugal force makes it contract. This perturbs each fluid element, raising the local pressure and originating deviations from beta equilibrium that enhance the neutrino emissivity and produce thermal energy. This mechanism is named rotochemical heating and has previously been studied for neutron stars of non-superfluid matter, finding that they reach a quasi-steady state in which the rate that the spin-down modifies the equilibrium concentrations is the same to that of the neutrino reactions restoring the equilibrium. On the other hand, the neutron star interior is believed to contain superfluid nucleons, which affect the thermal evolution of the star by suppressing the neutrino reactions and the specific heat, and opening new Cooper pairing reactions.   In this work we describe the thermal effects of Cooper pairing with spatially uniform energy gaps of neutrons and protons on rotochemical heating in millisecond pulsars (MSPs) when only modified Urca reactions are allowed. We find that the chemical imbalances grow up to a value close to the energy gaps, which is higher than the one of the nonsuperfluid case. Therefore, the surface temperatures predicted with Cooper pairing are higher and explain the recent measurement of MSP J0437-4715.
Fooling images are a potential threat to deep neural networks (DNNs). These images are not recognizable to humans as natural objects, such as dogs and cats, but are misclassified by DNNs as natural-object classes with high confidence scores. Despite their original design concept, existing fooling images retain some features that are characteristic of the target objects if looked into closely. Hence, DNNs can react to these features. In this paper, we address the question of whether there can be fooling images with no characteristic pattern of natural objects locally or globally. As a minimal case, we introduce single-color images with a few pixels altered, called sparse fooling images (SFIs). We first prove that SFIs always exist under mild conditions for linear and nonlinear models and reveal that complex models are more likely to be vulnerable to SFI attacks. With two SFI generation methods, we demonstrate that in deeper layers, SFIs end up with similar features to those of natural images, and consequently, fool DNNs successfully. Among other layers, we discovered that the max pooling layer causes the vulnerability against SFIs. The defense against SFIs and transferability are also discussed. This study highlights the new vulnerability of DNNs by introducing a novel class of images that distributes extremely far from natural images.
Backward stochastic differential equations (BSDEs) in the sense of Pardoux-Peng [Backward stochastic differential equations and quasilinear parabolic partial differential equations, Lecture Notes in Control and Inform. Sci., 176, 200--217, 1992] provide a non-Markovian extension to certain classes of non-linear partial differential equations; the non-linearity is expressed in the so-called driver of the BSDE. Our aim is to deal with drivers which have very little regularity in time. To this end we establish continuity of BSDE solutions with respect to rough path metrics in the sense of Lyons [Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14, no. 2, 215--310, 1998] and so obtain a notion of "BSDE with rough driver". Existence, uniqueness and a version of Lyons' limit theorem in this context are established. Our main tool, aside from rough path analysis, is the stability theory for quadratic BSDEs due to Kobylanski [Backward stochastic differential equations and partial differential equations with quadratic growth. Ann. Probab., 28(2):558--602, 2000].
We report the detection of accreting ionized gas at the disk-halo interface of the nearby galaxy M33. We analyze HST/COS absorption-line spectra of seven ultraviolet-bright stars evenly distributed across the disk of M33. We find Si IV absorption components consistently redshifted relative to the bulk M33's ISM absorption along all the sightlines. The Si IV detection indicates an enriched, disk-wide, ionized gas inflow toward the disk. This inflow is most likely multi-phase as the redshifted components can also be observed in ions with lower ionization states (e.g., S II, P II, Fe II, Si II). Kinematic modeling of the inflow is consistent with an accreting layer at the disk-halo interface of M33, which has an accretion velocity of 110$^{+15}_{-20}$ km s$^{-1}$ at a distance of 1.5$^{+1.0}_{-1.0}$ kiloparsec above the disk. The modeling indicates a total mass of $\sim3.9\times10^7$ M$_{\odot}$ for the accreting material at the disk-halo interface on the near side of the M33 disk , with an accretion rate of $\sim2.9$ M$_{\odot}$ yr$^{-1}$. The high accretion rate and the level of metal-enrichment suggest the inflow is likely to be the fall back of M33 gas from a galactic fountain and/or the gas pulled loosed during a close interaction between M31 and M33. Our study of M33 is the first to unambiguously reveal the existence of a disk-wide, ionized gas inflow beyond the Milky Way, providing a better understanding of gas accretion in the vicinity of a galaxy disk.
A covariant causal set (c-causet) is a causal set that is invariant under labeling. Such causets are well-behaved and have a rigid geometry that is determined by a sequence of positive integers called the shell sequence. We first consider the microscopic picture. In this picture, the vertices of a c-causet have integer labels that are unique up to a label isomorphism. This labeling enables us to define a natural metric $d(a,b)$ between time-like separated vertices $a$ and $b$. The time metric $d(a,b)$ results in a natural definition of a geodesic from $a$ to $b$. It turns out that there can be $n\ge 1$ such geodesics. Letting $a$ be the origin (the big bang), we define the curvature $K(b)$ of $b$ to be $n-1$. Assuming that particles tend to move along geodesics, $K(b)$ gives the tendency that vertex $b$ is occupied. In this way, the mass distribution is determined by the geometry of the c-causet. We next consider the macroscopic picture which describes the growth process of c-causets. We propose that this process is governed by a quantum dynamics given by complex amplitudes. At present, these amplitudes are unknown. But if they can be found, they will determine the (approximate) geometry of the c-causet describing our particular universe. As an illustration, we present a simple example of an amplitude process that may have physical relevance. We also give a discrete analogue of Einstein's field equations.
We observe that a lemma used in the study of even sets of nodes on surfaces applies almost verbatim to prove a celebrated formula of Gauss on the 2-torsion of the class group of a quadratic field.