Results 1 to 10 of about 302,286 (174)

Algebraic Systems Biology: A Case Study for the Wnt Pathway

, 2015
Steady state analysis of dynamical systems for biological networks give rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here the
Gross, Elizabeth, Harrington, Heather A., Rosen, Zvi, Sturmfels, Bernd   +3 more
core   +1 more source

The rank of sparse symmetric matrices over arbitrary fields

Random Structures &Algorithms, Volume 66, Issue 1, January 2025.
Abstract Let 𝔽 be an arbitrary field and (Gn,d/n)n$$ {\left({\boldsymbol{G}}_{n,d/n}\right)}_n $$ be a sequence of sparse weighted Erdős–Rényi random graphs on n$$ n $$ vertices with edge probability d/n$$ d/n $$, where weights from 𝔽∖{0} are assigned to the edges according to a matrix Jn$$ {J}_n $$.
Remco van der Hofstad, Noela Müller, Haodong Zhu   +2 more
wiley   +1 more source

On Sequences With Exponentially Distributed Gaps

Random Structures &Algorithms, Volume 66, Issue 1, January 2025.
ABSTRACT It is well known that a sequence (xn)n∈ℕ⊆[0,1]$$ {\left({x}_n\right)}_{n\in \mathbb{N}}\subseteq \left[0,1\right] $$ which has Poissonian correlations of all orders necessarily has exponentially distributed nearest‐neighbor gaps. It is natural to ask whether this implication also holds in the other direction, that is, whether a sequence with ...
Christoph Aistleitner, Manuel Hauke, Agamemnon Zafeiropoulos   +2 more
wiley   +1 more source

Dispersion on the Complete Graph

Random Structures &Algorithms, Volume 66, Issue 1, January 2025.
ABSTRACT We consider a synchronous process of particles moving on the vertices of a graph G$$ G $$, introduced by Cooper et al. Initially, M$$ M $$ particles are placed on a vertex of G$$ G $$. At the beginning of each time step, for every vertex inhabited by at least two particles, each of these particles moves independently to a neighbor chosen ...
Umberto De Ambroggio, Tamás Makai, Konstantinos Panagiotou   +2 more
wiley   +1 more source

A systematic literature review on the mathematical underpinning of model‐based systems engineering

Systems Engineering, Volume 28, Issue 1, Page 134-153, January 2025.
Abstract The International Council on Systems Engineering (INCOSE) has initiated a Future of Systems Engineering (FuSE) program that includes a stream for advancing the theoretical foundations of the discipline of Systems Engineering (SE). A near‐term goal of FuSE is to assess the adequacy of current theoretical foundations of SE.
Paul Wach, Taylan G. Topcu, Sukhwan Jung, Brandt Sandman, Aditya U. Kulkarni, Alejandro Salado   +5 more
wiley   +1 more source

Chow rings of matroids as permutation representations

Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.
Abstract Given a matroid with a symmetry group, we study the induced group action on the Chow ring of the matroid with respect to symmetric building sets. This turns out to always be a permutation action. Work of Adiprasito, Huh and Katz showed that the Chow ring satisfies Poincaré duality and the Hard Lefschetz theorem.
Robert Angarone, Anastasia Nathanson, Victor Reiner   +2 more
wiley   +1 more source

CAT(0) and cubulated Shephard groups

Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.
Abstract Shephard groups are common generalizations of Coxeter groups, Artin groups, and graph products of cyclic groups. Their definition is similar to that of a Coxeter group, but generators may have arbitrary order rather than strictly order 2. We extend a well‐known result that Coxeter groups are CAT(0)$\mathrm{CAT}(0)$ to a class of Shephard ...
Katherine M. Goldman
wiley   +1 more source

The Combinatorics of Iterated Loop Spaces

, 2003
It is well known since Stasheff's work that 1-fold loop spaces can be described in terms of the existence of higher homotopies for associativity (coherence conditions) or equivalently as algebras of contractible non-symmetric operads.
Batanin, M. A.
core   +1 more source

The Poincaré‐extended ab$\mathbf {a}\mathbf {b}$‐index

Journal of the London Mathematical Society, Volume 111, Issue 1, January 2025.
Abstract Motivated by a conjecture concerning Igusa local zeta functions for intersection posets of hyperplane arrangements, we introduce and study the Poincaré‐extended ab$\mathbf {a}\mathbf {b}$‐index, which generalizes both the ab$\mathbf {a}\mathbf {b}$‐index and the Poincaré polynomial.
Galen Dorpalen‐Barry, Joshua Maglione, Christian Stump   +2 more
wiley   +1 more source

Ibadan Lectures on Toric Varieties

, 2017
Toric varieties are perhaps the most accessible class of algebraic varieties. They often arise as varieties parameterized by monomials, and their structure may be completely understood through objects from geometric combinatorics.
Sottile, Frank
core