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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Type II blowup solutions to the 5D semilinear heat equation with double power nonlinearity
双幂非线性 5D 双线性热方程 II型爆破解
2023/5/16
We will discuss the existence of blowup solutions to $u_t=\Delta u+|u|^\frac{4}{n-2}u-|u|^{q-1}u$ with $0We show that there are three kinds of blowup solutions in this equation. I... 
This note is related to Theorem 1 of the ICA-BSS Conference’paper “AR Processes and Sources can be Reconstructed from Degenerate Mixtures” [1]. Here we study further the uniqueness of the decompositio...
Energy-Efficient Power and Rate Control with QoS Constraints:A Game-Theoretic Approach
Energy-Efficient Power Rate Control QoS Constraints Game-Theoretic Approach
2015/9/29
A game-theoretic model is proposed to study the cross-layer problem of joint power and rate control with quality of service (QoS) constraints in multiple-access networks. In the proposed game, each us...
Power-like delay in time inhomogeneous Fisher-KPP equations
Power-like delay time inhomogeneous Fisher-KPP equations
2015/7/14
We consider solutions of the KPP equation with a time-dependent diffusivity of the formσ(t/T). For an initial condition that is compactly supported, we show that when σ(s) is increasing in time the fr...
POWER LAWS FOR MONKEYS TYPINGS RANDOMLY: THE CASE OF UNEQUAL PROBABILITIES
TYPINGS RANDOMLY UNEQUAL PROBABILITIES
2015/7/6
The case where letters are hit with unequal probability has been the subject of recent confusion, with
some suggesting that in this case the rank-frequency distribution follows a lognormal distributi...
The Power of Convex Relaxation:Near-Optimal Matrix Completion
Matrix completion low-rank matrices semidefinite programming duality in optimization nuclear norm minimization random matrices and techniques from random matrix theory free probability
2015/6/17
This paper is concerned with the problem of recovering an unknown matrix from a small fraction of its entries. This is known as the matrix completion problem, and comes up in a great number of applica...
Improving accuracy and power with transfer learning using a meta-analytic database
Meta-analysis,fMRI,multiple comparison,machine learning
2012/11/23
Typical cohorts in brain imaging studies are not large enough for systematic testing of all the information contained in the images. To build testable working hypotheses, investigators thus rely on an...
Improving power posterior estimation of statistical evidence
Marginal likelihood Markov chain Monte Carlo Power posteriors Statistical evidence Tempering Thermo dynamic integration
2012/11/22
The statistical evidence (or marginal likelihood) is a key quantity in Bayesian statistics, allowing one to assess the probability of the data given the model under investigation. This paper focuses o...
A practical recipe to fit discrete power-law distributions
practical recipe discrete power-law distributions
2012/11/22
Power laws pervade statistical physics and complex systems, but, traditionally, researchers in these fields have paid little attention to properly fit these distributions. Who has not seen (or even sh...
Power Tensor Theory and Continuous Wavelet Transform
Wavelets Tensor Electrical Power Power Electronic Power Quality
2013/1/30
A model for the definition of electrical Power is presented, which retrieves the concepts of homomorphism from the geometrical tensor approximation at the wavelet approach. Their definition here is ne...
On the power-bounded operators of classes $C_{0 \cdot}$ and $C_{1 \cdot}$
power-bounded operators C0 operators strongly stable operators Functional Analysis
2012/6/19
By a bounded backward sequence of the operator $T$ we mean a bounded sequence $\{x_n\}$ satisfying $Tx_{n+1}=x_n$. In \cite{Pa} we have characterized contractions with strongly stable nonunitary part ...
Computing power series expansions of modular forms
power series expansions of modular forms Number Theory
2012/5/9
We exhibit a method to numerically compute power series expansions of modular forms on a cocompact Fuchsian group, using the explicit computation a fundamental domain and linear algebra.
Some Critical Support for Power Laws and their variations
Some Critical Support Power Laws their variations Adaptation and Self-Organizing Systems
2012/4/26
The paper "Critical Truths About Power Laws" (Science, 335, pp665-666) by MPH Stumpf MPH and MA Porter is commented.
Loewy filtration and quantum de Rham cohomology over quantum divided power algebra
quantum divided power algebra Loewy filtration socle radical rigidity q-differentials
2012/4/18
As a continuation of \cite{HU}, we explore the submodule structures of the quantum divided power algebra $\mathcal{A}_q(n)$ introduced in \cite{HU} and its truncated objects $\mathcal{A}_q(n, \bold m)...
Heuristic and exact solutions to the inverse power index problem for small voting bodies
electoral systems simple games weighted voting games square root rule Penrose limit theorem
2012/2/29
Power indices are mappings that quantify the influence of the members of a voting body on collective decisions a priori. Their nonlinearity and discontinuity makes it difficult to compute inverse imag...