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A fundamental problem from computational learning theory is to well-reconstruct an unknown function on the discrete hypercubes. One classical result of this problem for the random query model is the l...
The Zariski dense orbit conjecture of the arithmetic dynamic is to study the existence of a rational point P with a Zariski dense orbit of a dominant rational self-map f of a projective variety X. Whe...
A strong form of Arnold diffusion for two and a half degrees of freedom.
In this paper, we study small perturbations of a class of non-convex integrable Hamiltonians with two degrees offreedom, and we prove a result of diffusion for an open and dense set of perturbations, ...
We study the effective degrees of freedom of the lasso in the framework of Stein’s unbiased risk estimation (SURE). We show that the number of nonzero coefficients is an unbiased estimate for the degr...
A SEQUENTIAL IMPORTANCE SAMPLING ALGORITHM FOR GENERATING RANDOM GRAPHS WITH PRESCRIBED DEGREES
In a random graph model based on 3-interactions we give the joint asymptotic distribution of weights and degrees and prove scale-free property for the model. Moreover, we determine the asymptotics of ...
Abstract: We prove duality theorems for twisted Reidemeister torsions and twisted Alexander polynomials generalizing the results of Turaev. As a corollary we determine the parity of the degrees of twi...
DEGREES OF PERIODS     DEGREES OF PERIODS       2018/4/19
We introduce the concept of degree to classify the periods in the sense of Kontsevich.Using this notion we give some new understanding of some problems in transcendentalnumber theory.
We show that the 2  2  2 interference network, i.e., the multihop interference network formed by concatenation of two 2-user interference channels achieves the min-cut outer bound value of 2 DoF, fo...
The Severi variety parameterizes plane curves of degree d with  nodes.Its degree is called the Severi degree. For large enough d, the Severi degrees coincide with the Gromov-Witten invariants of CP2....
We provide a characterization of infinite algebraic Galois extensions of the rationals with uniformly bounded local degrees, giving a detailed proof of all the results announced in Checcoli and Zannie...
We present the solutions of equations of degrees 3 and 4 using Galois theory and some simple Fourier analysis for finite groups.
For a $K$-user interference channel with $M$ antenna at each transmitter and each receiver, the maximum total DoF of this channel has been previously determined to be $\max \sum_{k=1}^K d_k = MK/2$. H...

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