Residual Network based Aggregation Model for Skin Lesion Classification

We recognize that the skin lesion diagnosis is an essential and challenging sub-task in Image classification, in which the Fisher vector (FV) encoding algorithm and deep convolutional neural network (DCNN) are two of the most successful techniques. Since the joint use of FV and DCNN has demonstrated proven success, the joint techniques could have discriminatory power on skin lesion diagnosis as well. To this hypothesis, we propose the aggregation algorithm for skin lesion diagnosis that utilize the residual network to extract the local features and the Fisher vector method to aggregate the local features to image-level representation. We applied our algorithm on the International Skin Imaging Collaboration 2018 (ISIC2018) challenge and only focus on the third task, i.e., the disease classification.Comment: ISIC2018 task

Algebro-geometric solution of the coupled Burgers equation

We derive theta function representation of algebro-geometric solution of a Coupled Burgers equation which the second nonlinear evolution equation in a hierarchy. We also derive the algebro-geometric characters of the meromorphic function {\phi} and the Baker-Akhiezer vector {\Psi}.Comment: 16 page

Partial linearization for nonautonomous differential equations

In this paper, we prove the partial linearization for n-dimensional nonautonomous differential equations. The conditions are formulated in terms of the dichotomy spectrum

A two-component generalization of Burgers equation with Quasi-periodic solutions

In this paper, we aim for the theta function representation of quasi-periodic solution and related crucial quantities for a two-component generalization of Burgers equation. Our tools include the theory of algebraic curve, the meromorphic function, Baker-Akhiezer functions, the Dubrovin-type equations for auxiliary divisor, with these tools, the explicit representa- tions for above quantities are obtained.Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1406.623

Inverse Erdos-Fuchs theorem for k-fold sumsets

We generalize a result of Ruzsa on the inverse Erdos-Fuchs theorem for k-fold sumsets

Divisibility of some binomial sums

With help of $q$-congruence, we prove the divisibility of some binomial sums. For example, for any integers $\rho,n\geq 2$, $$\sum_{k=0}^{n-1}(4k+1) \binom{2k}{k}^\rho \cdot (-4)^{\rho(n-1-k)} \equiv 0\pmod{2^{\rho-2}n\binom{2n}{n}}.$$Comment: This is a very preliminary, which maybe contains some minor mistake

Some symmetric qq-congruences

We prove some symmetric $q$-congruences.Comment: 11 pages. This is a very very preliminary manuscript. And some results will be added in the future verision

On the convergence of the time average for skew-product structure and multiple ergodic system

In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity sets of transformation and observation function are neglected in some measure-theoretical sense. The theorems extend the classical results which have been established for continuous dynamical systems or continuous observation functions. Meanwhile, on the torus $\mathbb{T}^{d}$ with special rotation, we prove the pointwise convergence of multiple ergodic average \disp \f 1 N \sum_{n=0}^{N-1} f_{1}(R_{\alpha}^{n}x)f_{2}(R_{\alpha}^{2n}x) in $\mathbb{T}^{d}$

Ergodic behaviour of nonconventional ergodic averages for commuting transformations

Based on T.Tao's result of norm convergence of multiple ergodic averages for commut-ing transformation, we obtain there is a subsequence which converges almost everywhere. Meanwhile, the ergodic behaviour, which the time average is equal to the space average, of diagonal measures is obtained and we give different result according to the classification of transformations. Additionally, on the torus with special rotation. we can not only get the convergence in T.Tao's paper for every point in Td, but also get a beautiful result for ergodic behaviour

Finite quasiprimitive permutation groups with a metacyclic transitive subgroup

In this paper, we classify finite quasiprimitive permutation groups with a metacyclic transitive subgroup, solving a problem initiated by Wielandt in 1949. It also involves the classification of factorizations of almost simple groups with a metacyclic factor.Comment: 25 page