arXiv subjects
Publications and source records attributed to Min Yan.
There are exactly eight edge-to-edge tilings of the sphere by congruent equilateral pentagons: three pentagonal subdivision tilings with 12, 24, 60 tiles; four earth map tilings with 16, 20, 24, 24 tiles; and one flip modification of the earth map tiling with 20 tiles.
There are fifteen edge-to-edge tilings of the sphere by congruent pentagons with the edge combination $a^3b^2$: five one-parameter families of pentagonal subdivision tilings, and ten flip modifications of three special cases of two pentagonal subdivision tilings.
Multi-human parsing aims to segment every body part of every human instance. Nearly all state-of-the-art methods follow the "detection first" or "segmentation first" pipelines. Different from them, we present an end-to-end and box-free pipeline from a new and more human-intuitive perspective. In training time, we directly do instance segmentation on humans and parts. More specifically, we introduce a notion of "indiscriminate objects with categorie" which treats humans and parts without distinction and regards them both as instances with categories. In the mask prediction, each binary mask is obtained by a combination of prototypes shared among all human and part categories. In inference time, we design a brand-new grouping post-processing method that relates each part instance with one single human instance and groups them together to obtain the final human-level parsing result. We name our method as Nondiscriminatory Treatment between Humans and Parts for Human Parsing (NTHP). Experiments show that our network performs superiorly against state-of-the-art methods by a large margin on the MHP v2.0 and PASCAL-Person-Part datasets.
We develop a theory of simple pentagonal subdivision of quadrilateral tilings, on orientable as well as non-orientable surfaces. Then we apply the theory to answer questions related to pentagonal tilings of surfaces, especially those related to pentagonal or double pentagonal subdivisions.
We show that there are no edge-to-edge tilings of the sphere by congruent pentagons beyond the minimal dodecahedron tiling, such that there is a tile with all vertices having degree 3 and the edge length combinations are three of the five possibilities.
Localized cavity resonances due to nanostructures at material surfaces can greatly enhance radiative heat transfer (RHT) between two closely placed bodies owing to stretching of cavity states in momentum space beyond light line. Based on such understanding, we numerically demonstrate the possibility of ultra-broadband super-Planckian RHT between two plates patterned with trapezoidal-shaped hyperbolic metamaterial (HMM) arrays. The phenomenon is rooted not only in HMM's high effective index for creating sub-wavelength resonators, but also its extremely anisotropic isofrequency contour. The two properties enable one to create photonic bands with a high spectral density to populate a desired thermal radiation window. At sub-micron gap sizes between such two plates, the artificial continuum states extend outside light cone, tremendously increasing overall RHT. Our study reveals that structured HMM offers unprecedented potential in achieving a controllable super-Planckian radiative heat transfer for thermal management at nanoscale.
Metamaterials possess artificial bulk and surface electromagnetic states. Tamed dispersion properties of surface waves allow one to achieve controllable super-Planckian radiative heat transfer (RHT) process between two closely spaced objects. We numerically demonstrate enhanced RHT between two 2D grooved metal plates by a full-wave scattering approach. The enhancement originates from both transverse magnetic spoof surface plasmon polaritons and a series of transverse electric bonding- and anti-bonding waveguide modes at surfaces. The RHT spectrum is frequency-selective, and highly geometrically tailorable. Our simulation also reveals thermally excited non-resonant surface waves in constituent materials can play a prevailing role for RHT at an extremely small separation between two plates, rendering metamaterial modes insignificant for the energy transfer process.
We report the effect of relaxation-type self-induced temperature oscillations in the system of two parallel plates of SiO$_2$ and VO$_2$ which exchange heat by thermal radiation in vacuum. The non-linear feedback in the self-oscillating system is provided by metal-insulator transition in VO$_2$. Using the method of fluctuational electrodynamics we show that under the action of an external laser of a constant power, the temperature of VO$_2$ plate oscillates around its phase transition value. The period and amplitude of oscillations depend on the geometry of the structure. We found that at 500\,nm vacuum gap separating bulk SiO$_2$ plate and 50 nm thick VO$_2$ plate, the period of self-oscillations is 2 s and the amplitude is 4 K which is determined by phase switching at threshold temperatures of phase transition.
A combinatorial tiling of the sphere is naturally given by an embedded graph. We study the case that each tile has exactly five edges, with the ultimate goal of classifying combinatorial tilings of the sphere by geometrically congruent pentagons. We show that the tiling cannot have only one vertex of degree >3. Moreover, we construct earth map tilings, which give classifications under the condition that vertices of degree >3 are at least of distance 4 apart, or under the condition that there are exactly two vertices of degree >3.
There is only one type of tilings of the sphere by $12$ congruent pentagons. These tilings are isohedral.
We study the local and global versions of the convexity, which is closely related to the problem of extending a convex function on a non-convex domain to a convex function on the convex hull of the domain and beyond the convex hull. We also give the parallel results for the convexity defined by positive definite Hessian.
We prove that under a very general setting, a system of ODE passes the Painleve test if and only if there is a good change of variable, such that the pole singularity solutions are converted to regular power series, while the converted ODE system is still kept regular. A consequence is that all principal balances of an ODE system converge. We also prove that the results are natural with respect to Hamiltonian systems.
A U(n)-manifold is multiaxial if the isotropy groups are always conjugate to unitary subgroups. The classification and the concordance of such manifolds have been studied by Davis, Hsiang and Morgan under much more strict conditions. We show that in general, without much extra condition, the homotopy classification of multiaxial manifolds can be split into a direct sum of the classification of pairs of adjacent strata, which can be computed by the classical surgery theory. Moreover, we also compute the homotopy classification for the case of the standard representation sphere. We also present the result for the similar multiaxial Sp(n)-manifolds.
We study edge-to-edge tilings of the sphere by edge congruent pentagons, under the assumption that there are tiles with all vertices having degree 3. We develop the technique of neighborhood tilings and apply the technique to completely classify edge congruent earth map tilings.
We show that in all dimensions >7 there are closed aspherical manifolds whose fundamental groups have nontrivial center but do not possess any topological circle actions. This disproves a conjectured converse (proposed by Conner and Raymond) to a classical theorem of Borel.
The tilings of the 2-dimensional sphere by congruent triangles have been extensively studied, and the edge-to-edge tilings have been completely classified. However, not much is known about the tilings by other congruent polygons. In this paper, we classify the simplest case, which is the edge-to-edge tilings of the 2-dimensional sphere by 12 congruent pentagons. We find one major class allowing two independent continuous parameters and four classes of isolated examples. The classification is done by first separately classifying the combinatorial, edge length, and angle aspects, and then combining the respective classifications together.
We find the bounds of the size of the union of n sets satisfying the condition that the intersection of any k sets is empty. We show that any number between the upper and lower bounds can be realised, and in the measure version, the realisation can be the most efficient. The realisation also holds for the counting version, but not always in the most efficient way. The elementary result should be known but surprisingly, we cannot find any reference.
We point out an apparently overlooked consequence of the boundary conditions obeyed by the electric displacement vector at air-metal interfaces: the continuity of the normal component combined with the quantum mechanical penetration of the electron gas in the air implies the existence of a surface on which the dielectric function vanishes. This, in turn, leads to an enhancement of the normal component of the total electric field. We study this effect for a planar metal surface, with the inhomogenous electron density accounted for by a Jellium model. We also illustrate the effect for equilateral triangular nanoislands via numerical solutions of the appropriate Maxwell equations, and show that the field enhancement is several orders of magnitude larger than what the conventional theory predicts.