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Full-Text Articles in Physical Sciences and Mathematics
On The Cyclically Fully Commutative Elements Of Coxeter Groups, T. Boothby, J. Burket, M. Eichwald, D. C. Ernst, R. M. Green, Matthew Macauley
On The Cyclically Fully Commutative Elements Of Coxeter Groups, T. Boothby, J. Burket, M. Eichwald, D. C. Ernst, R. M. Green, Matthew Macauley
Publications
Let W be an arbitrary Coxeter group. If two elements have expressions that are cyclic shifts of each other (as words), then they are conjugate (as group elements) in W. We say that w is cyclically fully commutative (CFC) if every cyclic shift of any reduced expression for w is fully commutative (i.e., avoids long braid relations). These generalize Coxeter elements in that their reduced expressions can be described combinatorially by acyclic directed graphs, and cyclically shifting corresponds to source-to-sink conversions. In this paper, we explore the combinatorics of the CFC elements and enumerate them in all Coxeter groups. …
2d Novel Structures Along An Opitcal Fiber, Charles-Julien Vandamme, S.C. Mancas
2d Novel Structures Along An Opitcal Fiber, Charles-Julien Vandamme, S.C. Mancas
Publications
By using spectral methods, we present seven classes of stable and unstable structures that occur in a dissipative media. By varying parameters and initial conditions we find ranges of existence of stable structures (spinning elliptic, pulsating, stationary, organized exploding), and unstable structures (filament, disorganized exploding, creeping). By varying initial conditions, vorticity, and parameters of the equation, we find a reacher behavior of solutions in the form of creeping-vortex (propellers), spinning rings and spinning “bean-shape” solitons. Each class differentiates from the other by distinctive features of their shape and energy evolution, as well as domain of existence.
Nested Canalyzing Depth And Network Stability, Lori Layne, Elena Dimitrova, Matthew Macauley
Nested Canalyzing Depth And Network Stability, Lori Layne, Elena Dimitrova, Matthew Macauley
Publications
We introduce the nested canalyzing depth of a function, which measures the extent to which it retains a nested canalyzing structure. We characterize the structure of functions with a given depth and compute the expected activities and sensitivities of the variables. This analysis quantifies how canalyzation leads to higher stability in Boolean networks. It generalizes the notion of nested canalyzing functions (NCFs), which are precisely the functions with maximum depth. NCFs have been proposed as gene regulatory network models, but their structure is frequently too restrictive and they are extremely sparse. We find that functions become decreasingly sensitive to input …
Vortex Patterns Beyond Hypergeometric, Andrei Ludu
Vortex Patterns Beyond Hypergeometric, Andrei Ludu
Publications
We prove that loop vortices are created by a point-like magnetic dipole in an infinite superconductor space. The geometry of the vortex system is obtained through analytic solutions of the linearized Ginzburg-Landau equation described in terms of Heun functions, generalizing the traditional hypergeometric behavior of such magnetic singularity.
Ace - A Model Centered Reu Program Standing On The Three Legs Of Cse: Analysis, Computation And Experiment, Hong P. Liu, Andrei Ludu
Ace - A Model Centered Reu Program Standing On The Three Legs Of Cse: Analysis, Computation And Experiment, Hong P. Liu, Andrei Ludu
Publications
Enhancing REU (research experience for undergraduates) has become a popular strategy for many selective universities to enhance quality of undergraduate education and recruit gifted new students. The university that the authors are affiliated has set REU as one of the major outcomes for our QEP (quality enhancement program) for next 5 years. This paper presents a model centered REU program entitled as ACE standing for Analysis, Computation and Experiment. As a work in progress, the program is planned to run for the next 5 years and to serve for 20-30 undergraduate students who are gifted in mathematics and computing annually. …