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Score-based generative modeling (SGM) is a highly successful approach for learning a probability distribution from data and generating further samples, based on learning the score function (gradient o...
In the 2nd part of the series talks, I will introduce the new phenomena of weak-kink and its interaction with regular peakons which we recently developed. Such models include cubic Camassa-Holm (CH) t...
In this talk, I will majorly focus on the scalar peakon models developed in the last 30 years. Most integrable peakon equations come from the negative order flow in the hierarchy. I will take some exa...
Linear mixed model is a popular and common modeling method in statistical analysis. It is computationally difficult to obtain parameter estimates in linear mixed model for big data. The current subsam...
We show the existence of a trivial, strongly minimal (and thus uncountably categorical) theory for which the prime model is computable and each of the other countable models computes 0 00. This res...
The rise and fall of uncountable models.
Given a complete, superstable theory, we distinguish a class P of regular types, typically closed under automorphisms of C and non- orthogonality. We define the notion of P-NDOP, which is a weakenin...
We work in the context of ω-stable theories. We obtain a natural, algebraic equivalent of ENI-NDOP and discuss recent joint proofs with S. Shelah that if an ω-stable theory has either ENI-DOP or is ...
We characterize the stable theories T for which the saturated models of T admit decompositions. In particular, we show that countable, shallow, stable theories with NDOP have this property.
As has been known since at least [?] and is carefully spelled out in Chapter 6 of [?], for every complete sentence ψ of Lω1,ω (in a countable vocabulary τ ) there is a complete, first order theory T...
A first-order theory T has the Schr╫der-Bernstein (SB) property if any pair of elementarily bi-embeddable models are isomorphic. We prove that T has an expansion by constants with the SB property if...
A class of models combining a pharmacokinetic compartmental model and a pharmacodynamic Emax model is introduced. One 4- parameter and another 5-parameter models in this class are studied. These mo...
PROVIDENCE, R.I. [Brown University] — Mathematicians from Brown University have introduced a new element of uncertainty into an equation used to describe the behavior of fluid flows. While being as ce...
Forcing is a methodology for building models of Set Theory satisfying certain properties. Since its inception by Paul Cohen, in the early 1960s, it has been applied to several areas in Mathematical Lo...
A first-order theory T has the Schr\"oder-Bernstein (SB) property if any pair of elementarily bi-embeddable models are isomorphic. We prove that T has an expansion by constants that has the SB propert...

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