he emergence of vascular networks is a long-standing problem which has been the subject of intense research in the past decades. One of the main reasons being the widespread applications that it has in tissue regeneration, wound…
Polytopes (also known in dimensions zero through three as "points", "line segments", “polygons", and “polyhedra") have been objects of interest to mathematicians throughout the recorded history of mathematics. Most notably,…
Let be a free associative algebra over generated by for in some indexing set and let be a poset. For and we define an action of on (the complex vector space with basis ) in a way such that either annihilates or…
Let Q be an orientation of a type A Dynkin diagram. An eta map corresponding to Q is a surjection from the weak order on permutations to a Cambrian lattice…
The Penrose triangle, also known as the impossible tribar is an icon for cohomology. It is literally the icon for Cech cohomology on Wikipedia. The idea goes back to a…
Much of the literature on the design and analysis of supersaturated designs (SSDs), in which the number of factors exceeds the number of runs, rests on design principles assuming a least-squares analysis. More…
Machine learning has become widely popular in fields like computer vision, natural language processing, and speech recognition, often performing tasks better than humans. A fundamental building block of many of…
Register now for a weekend anniversary celebration marking 130 years of mathematics education and research here at NC State. The history of mathematics at the university dates to 1889, when…
We present a general formula describing the joint distribution of two permutation statistics—the peak number and the descent number—over any set of permutations whose quasisymmetric generating function is a symmetric…
We prove that every rational homology cobordism class in the subgroup generated by lens spaces is represented by a unique connected sum of lens spaces whose first homology embeds in…
When running any iterative algorithm it is useful to know when to stop. Here we review LSQR and LSLQ, two iterative methods for solving \min_x \|Ax-b\|_2 based on the Golub-Kahan…
The ill-posedness and nonlinearity are two factors causing the phenomenon of multiple local minima and ravines of conventional least squares cost functionals for Coefficient Inverse Problems. Since any minimization method…
Mike Thompson, the Managing Director and CEO of First Analytics, will be giving a seminar on how machine learning and mathematics are used to handle large data analytics programs at First…
Chaos refers to seemingly random and unpredictable dynamics of a system that evolves in time. Certain chaotic systems exhibit an additional level of complexity: intermittent extreme events that are noticeably distinct…