Alignment of spatial genomics and histology data using deep Gaussian processes

Spatially-resolved genomic technologies have allowed us to study the physical organization of cells and tissues, and promise an understanding of the local interactions between cells. However, it remains difficult to precisely align spatial observations across slices, samples, scales, individuals, and technologies. Here, we propose a probabilistic model that aligns a set of spatially-resolved genomics and histology slices onto a known or unknown common coordinate system into which the samples are aligned both spatially and in terms of the phenotypic readouts (e.g., gene or protein expression levels, cell density, open chromatin regions). Our method consists of a two-layer Gaussian process: the first layer maps the observed samples' spatial locations into a common coordinate system, and the second layer maps from the common coordinate system to the observed readouts. Our approach also allows for slices to be mapped to a known template coordinate space if one exists. We show that our registration approach enables complex downstream spatially-aware analyses of spatial genomics data at multiple resolutions that are impossible or inaccurate with unaligned data, including an analysis of variance, differential expression across the z-axis, and association tests across multiple data modalities.

Dirac particle in Aharonov–Bohm–Coulomb field: Path integral treatment

Exact Green’s function related to a Dirac particle submitted to the combination of Aharonov–Bohm and Coulomb potentials in [Formula: see text]) coordinate space is analytically calculated via path integral formalism. The Pauli matrices which describe the spin dynamics are replaced by two fermionic oscillators via the Schwinger model. The energy spectrum as well as the corresponding normalized wave functions are extracted following this approach. The interesting properties of the spinors are thus deduced after symmetrization. According to the symmetric form for Green’s function, it is shown that the non-relativistic limit of the Dirac particle is undertaken with much ease.

Self-consistent description of the halo nature of 31Ne with continuum and pairing correlations

Using a Glauber model with our relativistic fully microscopic structure model input, we give a full description of the halo nature of $^{31}$Ne that includes a self-consistent use of pairing and continuum contributions that makes predictions consistent with reaction cross section measurements. Our predictions of total reaction and one-neutron removal cross sections of $^{31}$Ne on a Carbon target were significantly enhanced compared with those of neighboring Neon isotopes, agreeing with measurements at 240 MeV/nucleon and consistent with a single neutron halo. Furthermore, our calculations of the inclusive longitudinal momentum distribution of the $^{30}$Ne and valence neutron residues from the $^{31}$Ne breakup reaction indicate a dilute density distribution in coordinate space, another halo signature.

Affine connection representation of gauge fields

There are two ways to unify gravitational field and gauge field. One is to represent gravitational field asprincipal bundle connection, and the other is to represent gauge field as affine connection. Poincaré gauge theoryand metric-affine gauge theory adopt the first approach. This paper adopts the second. In this approach:(i) Gauge field and gravitational field can both be represented by affine connection; they can be described by aunified spatial frame.(ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space andexternal coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as ageometric theory of distribution of gradient directions. Hence, gauge theory, gravitational theory, and quantumtheory all reflect intrinsic geometric properties of manifold.(iii) Coupling constants, chiral asymmetry, PMNS mixing and CKM mixing arise spontaneously as geometricproperties in affine connection representation, so they are not necessary to be regarded as direct postulates in theLagrangian anymore.(iv) The unification theory of gauge fields that are represented by affine connection can avoid the problem thata proton decays into a lepton in theories such as SU(5).(v) There exists a geometric interpretation to the color confinement of quarks.In the affine connection representation, we can get better interpretations to the above physical properties,therefore, to represent gauge fields by affine connection is probably a necessary step towards the ultimate theory ofphysics.

Revealing topology with transformation optics

Symmetry deepens our insight into a physical system and its interplay with topology enables the discovery of topological phases. Symmetry analysis is conventionally performed either in the physical space of interest, or in the corresponding reciprocal space. Here we borrow the concept of virtual space from transformation optics to demonstrate how a certain class of symmetries can be visualised in a transformed, spectrally related coordinate space, illuminating the underlying topological transitions. By projecting a plasmonic system in a higher-dimensional virtual space onto a lower-dimensional system in real space, we show how transformation optics allows us to construct a topologically non-trivial system by inspecting its modes in the virtual space. Interestingly, we find that the topological invariant can be controlled via the singularities in the conformal mapping, enabling the intuitive engineering of edge states. The confluence of transformation optics and topology here can be generalized to other wave realms beyond photonics.

On pion mass and decay constant from theory

We calculate the pion mass from Goldstone modes in the Higgs mechanism related to the neutron decay. The Goldstone pion modes acquire mass by a vacuum misalignment of the Higgs field. The size of the misalignment is controlled by the ratio between the electronic and the nucleonic energy scales. The nucleonic energy scale is involved in the neutron to proton transformation and the electronic scale is involved in the related creation of the electronic state in the course of the electroweak neutron decay. The respective scales influence the mapping of the intrinsic configuration spaces used in our description. The configuration spaces are the Lie groups U(3) for the nucleonic sector and U(2) for the electronic sector. These spaces are both compact and lead to periodic potentials in the Hamiltonians in coordinate space. The periodicity and strengths of these potentials control the vacuum misalignment and leads to a pion mass of 135.2(1.5) MeV with an uncertainty mainly from the fine structure coupling at pionic energies. The pion decay constant 92 MeV results from comparing the fourth order self-coupling in an effective pion field theory with the corresponding fourth order term in the Higgs potential. We suggest analogies with the Goldberger-Treiman relation.

Surface properties for Ne, Na, Mg, Al and Si isotopes in the Coherent Density Fluctuation Model using the relativistic mean field densities

We have systematically studied the surface properties, such as symmetry energy, neutron pressure, and symmetry energy curvature coefficient for Ne, Na, Mg, Al, and Si nuclei from the proton to neutron drip-lines. The Coherent Density Fluctuation Model (CDFM) is used to estimate these quantities taking the relativistic mean-field densities as inputs. The Br ¨uckner energy density functional is taken for the nuclear matter binding energy and local density approximation is applied for its conversion to coordinate space. The symmetry energy again decomposed to the volume and surface components within the liquid drop model formalism to the volume and surface parts separately. Before calculating the surface properties of finite nuclei, the calculated bulk properties are compared with the experimental data, whenever available. The NL3* parameter set with the BCS pairing approach in an axially deformed frame-work is used to take care of the pairing correlation when needed. The deformed density is converted to its spherical equivalent with a two Gaussian fitting, which is used as an input for the calculation of weight function in the CDFM approximation. With the help of the symmetry energy for the recently isotopes ²⁹F, ²⁸Ne, ^29,30Na and ^31,35,36Mg are considered to be within the island of inversion emphasized [Phys. Lett. B 772, 529 (2017)]. Although we get large symmetric energies corresponding to a few neutron numbers for this isotopic chain as expected, an irregular trend appears for all these considered nuclei. The possible reason behind this abnormal behavior of symmetry energy for these lighter mass nuclei is also included in the discussion, which gives a direction for future analysis.

Research on 3D reconstruction method of wear particle dynamic image based on multi contour space mapping

Aiming at the problems of current image monitoring methods of lubrication oil wear particles, this paper designs and builds a dynamic monitoring system for oil wear particles based on microfluidic microscopic images. A contour-based 3D reconstruction method of debris particle images is proposed. The image sequences of rotating wear particles tracked by a single target are used as data, and the contour of the wear particle is extracted and the data is stored. The minimum area external rectangle method is used to correct the rotation of the particle images for the problem of deflection. And an algorithm based on cylindrical coordinate space conversion is used to convert the discrete contour point data into three-dimensional space. Complete the 3D model reconstruction of microfluidic wear particles. The ability to analyse wear particles in oil online monitoring technology is improved, which also shows new ideas for wear status monitoring and fault diagnosis technology.

The impact of transverse Slavnov-Taylor identities on dynamical chiral symmetry breaking

We extend earlier studies of transverse Ward-Fradkin-Green-Takahashi identities in QED, their usefulness to constrain the transverse fermion-boson vertex and their importance for multiplicative renormalizability, to the equivalent gauge identities in QCD. To this end, we consider transverse Slavnov-Taylor identities that constrain the transverse quark-gluon vertex and derive its eight associated scalar form factors. The complete vertex can be expressed in terms of the quark’s mass and wave-renormalization functions, the ghost-dressing function, the quark-ghost scattering amplitude and a set of eight form factors. The latter parametrize the hitherto unknown nonlocal tensor structure in the transverse Slavnov-Taylor identity which arises from the Fourier transform of a four-point function involving a Wilson line in coordinate space. We determine the functional form of these eight form factors with the constraints provided by the Bashir-Bermudez vertex and study the effects of this novel vertex on the quark in the Dyson-Schwinger equation using lattice QCD input for the gluon and ghost propagators. We observe significant dynamical chiral symmetry breaking and a mass gap that leads to a constituent mass of the order of 500 MeV for the light quarks. The flavor dependence of the mass and wave-renormalization functions as well as their analytic behavior on the complex momentum plane is studied and as an application we calculate the quark condensate and the pion’s weak decay constant in the chiral limit. Both are in very good agreement with their reference values.

Method for the Coordination of Referencing of Autonomous Underwater Vehicles to Man-Made Objects Using Stereo Images

The use of an autonomous underwater vehicle (AUV) to inspect underwater industrial infrastructure requires the precise, coordinated movement of the AUV relative to subsea objects. One significant underwater infrastructure system is the subsea production system (SPS), which includes wells for oil and gas production, located on the seabed. The present paper suggests a method for the accurate navigation of AUVs in a distributed SPS to coordinate space using video information. This method is based on the object recognition and computation of the AUV coordinate references to SPS objects. Stable high accuracy during the continuous movement of the AUV in SPS space is realized through the regular updating of the coordinate references to SPS objects. Stereo images, a predefined geometric SPS model, and measurements of the absolute coordinates of a limited number of feature points of objects are used as initial data. The matrix of AUV coordinate references to the SPS object coordinate system is computed using 3D object points matched with the model. The effectiveness of the proposed method is estimated based on the results of computational experiments with virtual scenes generated in the simulator for AUV, and with real data obtained by the Karmin2 stereo camera (Nerian Vision, Stuttgart, Germany) in laboratory conditions.