Research
Research
Research
Research
509+ open-access research outputs.
This article presents a partial differential equation (PDE) of Keller-Segel (KS) type that reproduces patterns commonly observed during the growth of brain microvasculature. We provide mathematical in…
The existence of global weak solutions to the compressible Navier-Stokes equations for the density of endothelial cells and their velocity, coupled to a reaction-diffusion equation for the concentrati…
We study the emergence of symmetric oscillatory behavior in multi-agent systems where each agent incorporates a continuous memory of its past states and past rates of change, modeled by distributed re…
While the classical Critical Depth Hypothesis (CDH) effectively explains the onset of blooms as transient instabilities, it does not fully capture the seasonal decoupling of biological rates and the l…
We derive a unidirectional asymptotic model for one-dimensional blood flow in viscoelastic arteries. We prove local well-posedness of strong solutions in Sobolev spaces for general parameters and mean…
In this paper we study a two-component coagulation equation that models the aggregation of rouleaux in blood. We consider product kernels that have homogeneity $2$ and we characterize the initial data…
We prove that if $A\subset \{1,\dots,N\}$ has no nontrivial three-term arithmetic progressions, then $|A|\leq \exp(-c\log(N)^{1/6}\log\log(N)^{-1})N$ for some absolute constant $c>0$. To obtain this b…
We provide a positive answer to an old problem of Jonathan K. Simon: if $K$ and $K'$ are two knots such that there is an epimorphism from the knot group of $K$ to the knot group of $K'$, then the genu…
We classify all maximal symmetry models of CR dimension 1, depending on their Bloom-Graham and Tanaka types, give coordinate realization to some of those models and prove a general extension principle…
How external stimulation is transformed into distributed reaction patterns remains unresolved at the level of propagation architecture. Existing large-scale control models quantify transition costs on…
Under-ice blooms in the Arctic can develop rapidly under conditions where conventional early warning signals based on critical slowing down fail due to strong noise or limited observational records. W…
Focusing on the assessment of benthic algae blooms that decay subexponentially, we propose a tractable (solvable in a closed form) and well-defined (that does not diverge) environmental index for the …
Pancreatic \b{eta}-cells secrete insulin in response to blood sugar levels to maintain glucose homeostasis. This vital insulin exocytosis is controlled by the cell's bursting behaviours, which are reg…
We present a unified mathematical framework for modeling blood and lymph flow in biological vessels, with a particular focus on lymph transport through lymphangions. Starting from first principles, we…
The world of primes has many gaps between evidence and theorems. Here, we review Legendre's conjecture on primes between consecutive squares and recent progress on the weaker question of primes betwee…
About 40 years ago Jonathan and Peter Borwein discovered the series identity $$ \sum_{n=0}^\infty \frac{(-1)^n(6n)!}{(3n)!(n!)^3} \frac{(A+nB)}{C^{n+1/2}} = \frac{1}{12\pi} $$ where \begin{align*} A&=…
We consider a Stokes flow coupled with advective-diffusive transport in an evolving domain with boundary conditions allowing for inflow and outflow. The evolution of the domain is induced by the trans…
Platelet extraction requires whole blood to be processed within six hours of donation. To meet this deadline, blood collection organizations must optimally route a fleet of vehicles to pick up blood u…
For integers $n,k \geq 1$, let $S_k(n)$ denote the power sum $1^k +2^k + \cdots + n^k$. In this note, we first recall the minimal recurrence relation connecting $S_k(n)$ and $S_{k-1}(n)$ established b…
Accumulation of amyloid beta proteins is a defining feature of Alzheimer's disease, and is usually accompanied by cerebrovascular pathology. Evidence suggests that amyloid beta and cerebrovascular pat…
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