A5101705485- Geometric Analysis and Curvature Flows
- Advanced Harmonic Analysis Research
- Point processes and geometric inequalities
- Nonlinear Partial Differential Equations
- Topological and Geometric Data Analysis
- Geometry and complex manifolds
- Advanced Differential Geometry Research
- Mathematical Dynamics and Fractals
- Advanced Topology and Set Theory
- Geometric and Algebraic Topology
- Online Learning and Analytics
- Polynomial and algebraic computation
- Genomics and Chromatin Dynamics
- Mathematical Analysis and Transform Methods
- Dermatological and Skeletal Disorders
- Advanced Banach Space Theory
- Analytical Chemistry and Chromatography
- Algebraic structures and combinatorial models
- Advanced Operator Algebra Research
- Advanced Graph Theory Research
- Commutative Algebra and Its Applications
- Algebraic Geometry and Number Theory
- AI in Service Interactions
- Mass Spectrometry Techniques and Applications
- Analytic Number Theory Research
University of Connecticut
2018-2023
The University of Western Australia
2022-2023
Massachusetts Institute of Technology
2023
Australian National University
2021
University of Michigan
2017
Michigan Medicine
2017
University of Chicago
2016
Johns Hopkins University
2014
Courant Institute of Mathematical Sciences
2009-2014
New York University
2013-2014
Designer Chromosome One of the ultimate aims synthetic biology is to build designer organisms from ground up. Rapid advances in DNA synthesis has allowed assembly complete bacterial genomes. Eukaryotic organisms, with their generally much larger and more complex genomes, present an additional challenge biologists. Annaluru et al. (p. 55 , published online 27 March) designed a eukaryotic chromosome based on yeast III. The chromosome, shorn destabilizing transfer RNA genes transposons, ∼14%...
Even though metal–organic frameworks (MOFs) derived from antiferromagnetic dimeric-Cu(II) building units and nonmagnetic molecular linkers are known to exhibit unexpected ferromagnetic behavior, a comprehensive understanding of the underlying mechanism remains elusive. Using combined theoretical experimental approach, here we reveal origin long-range coupling in series MOFs, constructed blocks. Our studies show that strong localization copper vacancy states favors spontaneous spin...
We show that if $G$ and $H$ are finitely generated groups whose Hilbert compression exponent is positive, then so the of wreath product $G \wr H$. also prove an analogous result for coarse embeddings products. In special case $G=\mathbb {Z}$, $H=\mathbb {Z} \mathbb {Z}$ our implies $\mathbb {Z}\wr (\mathbb {Z})$ at least $1/4$, answering a question posed by several authors.
Nous montrons que le groupe de Heisenberg ℍ ∞ dimension infinie est Markov 4-convexe et 1 3 (et donc aussi) n'est pas p-convexe pour tout p<4. Comme la convexité un invariant bilipschitzien les espaces Hilbert sont 2-convexes, on retrouve théorème classique Pansu Semmes sur l'absence plongement du dans espace euclidien.
Abstract Phenethylamine derivatives are being increasingly exploited for recreational use as “designer” stimulants designed to mimic psychostimulant properties of amphetamine or other illicit substances like 3,4‐methylenedioxymethamphetamine (MDMA [ecstasy]). Clandestine operations meticulously design phenethylamines so the user can bypass legal action when detected, many these yet be regulated by government authorities. Substituted 2C amines, N‐methoxybenzyl corresponding amines commonly...
We introduce a modified version of Jones's β $\beta$ -numbers for Carnot groups which we call stratified -numbers. show that an analogue traveling salesman theorem on 1-rectifiability sets holds any group if replace previous notions in with As generalize both directions the theorem, get characterization subsets lie finite length rectifiable curves. Our proof expands upon analysis Hebisch–Sikora norm groups. In particular, find new estimates drift between almost parallel line segments take...
We introduce a modified version of P. Jones's $\beta$-numbers for Carnot groups which we call {\it stratified $\beta$-numbers}. show that an analogue traveling salesman theorem on 1-rectifiability sets holds any group if replace previous notions in with $\beta$-numbers. As generalize both directions the theorem, get characterization subsets lie finite length rectifiable curves. Our proof expands upon analysis Hebisch-Sikora norm groups. In particular, find new estimates drift between almost...
We show that a sufficient condition for subset $E$ in the Heisenberg group (endowed with Carnot-Carath\'{e}odory metric) to be contained rectifiable curve is it satisfies modified analogue of Peter Jones's geometric lemma. Our estimates improve on those \cite{FFP}, by replacing power $2$ Jones-$\beta$-number any $r<4$. This complements (in an open ended way) our work \cite{Li-Schul-beta-leq-length}, where we showed such estimate was necessary, but $r=4$.
Abstract We continue to develop a program in geometric measure theory that seeks identify how measures space interact with canonical families of sets the space. In particular, extending theorem M. Badger and R. Schul Euclidean space, for an arbitrary locally finite Borel Carnot group , we tests part is carried by rectifiable curves singular curves. Our main result entwined extension analyst’s traveling salesman which characterizes subsets <m:math...
We compute the Markov convexity invariant of continuous infinite dimensional Heisenberg group $\mathbb{H}_\infty$ to show that it is 4-convex and cannot be $p$-convex for any $p < 4$. As a biLipschitz Hilbert space 2-convex, this gives different proof classical theorem Pansu Semmes does not admit embedding into Euclidean space. The lower bound will follow from exhibiting an explicit Laakso graphs $G_n$ has distortion at most $C n^{1/4} \sqrt{\log n}$. use if $X$ metric space, then balls...
Unexpected machine failures directly impact availability, which leads to phantom capacity, high maintenance cost, and risks factory profitability competitiveness. The collateral damage far exceeds the original downtime itself. This paper proposes a fractal based method for trend analysis performance control. AR (Auto Regression) model is applied data pre-process, rescaled range (R/S) Lo's modified are used Hurst exponent calculation, exponent, as well order exponents employed mathematical...
This paper contributes to the generalization of Rademacher's differentiability result for Lipschitz functions when domain is infinite dimensional and has nonabelian group structure. We introduce notion metric scalable groups which are our infinite-dimensional analogues Carnot groups. The in we will mostly be interested ones that admit a dense increasing sequence (finite-dimensional) subgroups. In fact, each these spaces show every function point Gâteaux differentiability. provide examples...
In recent work, Griffin, Ono, and Tsai constructs an L-series to prove that the proportion of short Weierstrass elliptic curves over ℚ with trivial Tamagawa product is 0.5054⋯ average 1.8183⋯. Following their we generalize arbitrary number fields K be
Identifying the molecular formula and fragmentation reactions of an unknown compound from its mass spectrum is crucial in areas such as natural product chemistry metabolomics. We propose a method for identifying correct candidate unidentified spectrum. The involves scoring plausibility parent formulae based on subformula graph (PSG), two possible metrics relating to number edges PSG. This applicable both electron-impact spectrometry (EI-MS) tandem (MS/MS) data. Additionally, this work...
Abstract We show that the β-numbers of intrinsic Lipschitz graphs Heisenberg groups <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub><m:mi>ℍ</m:mi><m:mi>n</m:mi></m:msub></m:math> {\mathbb{H}_{n}} are locally Carleson integrable when xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>n</m:mi><m:mo>≥</m:mo><m:mn>2</m:mn></m:mrow></m:math> {n\geq 2} . Our main bound uses a novel slicing argument to decompose into functions. A key ingredient in our proof is Euclidean...
What molecular formulae correspond to a given mass M? Here, we address this problem - the compomer of spectrometry. We describe, implement, and test straightforward practical aufbau algorithm which leads formula tree from all possible solutions may be obtained. The was inspired generating function method used in combinatorics, count number compomers. can generated linear time with regards elements N, quadratic respect M; demonstrate that memory requirements do not exceed standard laptop for...