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TBA

Wilson's algorithm allows efficient sampling of the uniform spanning tree (UST) by using loop-erased random walks. This connection gives a tractable method to study the UST. The strategy has been fruitful for scaling limits of the UST in the planar...

Abstract: A triangulation of a surface is a way to divide it into a finite number of triangles. Let us pick a random triangulation uniformly among all those with a fixed size and genus. What can be said about the behaviour of these random geometric...

Consider three gamblers with initial capital A,B,C. Each time, a pair of them is chosen at random, a fair coin is flipped and $1 is transferred. Classically, the chance that the first gambler wins all the money is A/ (A + B + C). Consider the first...

In his 1965 seminal paper on edge colouring, Vizing proved that a (Delta+1)-edge colouring can be reached from any given proper edge colouring through a series of Kempe changes, where Delta is the maximum degree of the graph. He concludes the paper...

Cells often chemotax, directing their motion in response to a chemical signal. We develop models of strategies for chemotaxis in complex environments. Groups of cells may cooperate to sense a chemical signal. One strategy is to specialize into leader...

The Schramm-Loewner evolution (SLE) is a random fractal curve in the plane that describes the scaling limit of interfaces in several statistical physics models. It is uniquely characterized by two properties known as conformal invariance and the...

It has been well established that the mechanical stiffness of the substrate with which cells interact affects various intracellular processes, including cell spread areas, speeds at which motile cells translocate, and the number and strength of cell...

Malaria is a leading cause of death in many low-income countries despite being preventable, treatable and curable. One of the major roadblocks to malaria elimination is the emergence and spread of antimalarial drug resistance, which evolves when...

Systemic chemotherapy is one of the main anticancer treatments used for most kinds of clinically diagnosed tumors. However, the efficacy of these drugs can be hampered by the physical attributes of the tumor tissue, such as tortuous vasculature...