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Geometrically continuous splines are piecewise polynomials defined on a collection of patches stitched together through transition maps. In this talk, we introduce an algebraic framework to study geom...
We consider the genealogical tree of a stationary continuous state branching process with immigration. For a sub-critical stable branching mechanism, we consider the genealogical tree of the extant po...
In these two talks, I will present a unified method to construct soliton solutions to NLS type equations by the KP-Toda reduction approach. I will take the NLS equation as a typical example and show h...
An important discovery of the 20th century mathematics is that many deterministic systems exhibit stochastic behavior. The stochasticity is caused by exponential divergence of nearby trajectories. Th...
We combine the technique of inducing with a method of Johnson boxes and construct new examples of S-unimodal maps ϕ which do not have a finite absolutely continuous invariant measure, but do have...
Respondent-driven sampling (RDS) is a network-based method for sampling hidden and hard-to-reach populations that has been shown to produce asymptotically unbiased population estimates when its ass...
We discuss a Continuous Curvelet Transform (CCT), a transform f → Γf(a, b, θ) of functions f(x1, x2) on R2, into a transform domain with continuous scale a > 0, location b ∈ R2, and orientation θ ∈...
We develop a unifying perspective on several decompositions exhibiting directional parabolic scaling. In each decomposition, the individual atoms are highly anisotropic at fine scales, with e&...
A coloring c:[X]n → Z is said to be irreducible if for every Y; X of equal cardinality c00[Y ]n = Z. The focus of this note will be to show that there are continuous irreducible colorings on sets of r...
On characterizations of Metropolis type algorithms in continuous time。
We develop a unifying perspective on several decompositions exhibiting directional parabolic scaling. In each decomposition, the individual atoms are highly anisotropic at fine scales, with effective ...
We discuss a Continuous Curvelet Transform (CCT), a transform f → Γf(a, b, θ) of functions f(x1, x2) on R2, into a transform domain with continuous scale a > 0, location b ∈ R2, and orientation θ ∈ [...
In probability theory, equalities are much less than inequalities. In this paper, we find a series of equalities which characterize the symmetry of the forming times of a family of similar cycles fo...

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