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- Allogrooming network (1)
- Apical meristems (1)
- Canalization (1)
- Category of relations (1)
- Cohomology (1)
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- Divergence angle (1)
- Dynamic social network (1)
- Evolutionary sociobiology (1)
- Fibonacci sequence (1)
- Frobenius algebra (1)
- Generalized graph splines (1)
- Groupoid (1)
- Hygienic behavior (1)
- Phyllotaxis (1)
- Simplicial set (1)
- Social grooming (1)
- Spiral patterns (1)
- Splines (1)
- Topological quantum field theory (1)
Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Phyllotaxis As Geometric Canalization During Plant Development, Christophe Godin, Christophe Golé, Stéphane Douady
Phyllotaxis As Geometric Canalization During Plant Development, Christophe Godin, Christophe Golé, Stéphane Douady
Mathematics Sciences: Faculty Publications
Why living forms develop in a relatively robust manner, despite various sources of internal or external variability, is a fundamental question in developmental biology. Part of the answer relies on the notion of developmental constraints: at any stage of ontogenesis, morphogenetic processes are constrained to operate within the context of the current organism being built. One such universal constraint is the shape of the organism itself, which progressively channels the development of the organism toward its final shape. Here, we illustrate this notion with plants, where strikingly symmetric patterns (phyllotaxis) are formed by lateral organs. This Hypothesis article aims first …
Frobenius Objects In The Category Of Relations, Rajan Amit Mehta, Ruoqi Zhang
Frobenius Objects In The Category Of Relations, Rajan Amit Mehta, Ruoqi Zhang
Mathematics Sciences: Faculty Publications
We give a characterization, in terms of simplicial sets, of Frobenius objects in the category of relations. This result generalizes a result of Heunen, Contreras, and Cattaneo showing that special dagger Frobenius objects in the category of relations are in correspondence with groupoids. As an additional example, we construct a Frobenius object in the category of relations whose elements are certain cohomology classes in a compact oriented Riemannian manifold.
Preparing For A Career At A Liberal Arts College, Julianna Tymoczko
Preparing For A Career At A Liberal Arts College, Julianna Tymoczko
Mathematics Sciences: Faculty Publications
No abstract provided.
A Formula For The Cohomology And K-Class Of A Regular Hessenberg Variety, Erik Insko, Julianna Tymoczko, Alexander Woo
A Formula For The Cohomology And K-Class Of A Regular Hessenberg Variety, Erik Insko, Julianna Tymoczko, Alexander Woo
Mathematics Sciences: Faculty Publications
Hessenberg varieties are subvarieties of the flag variety parametrized by a linear operator X and a nondecreasing function h. The family of Hessenberg varieties for regular X is particularly important: they are used in quantum cohomology, in combinatorial and geometric representation theory, in Schubert calculus and affine Schubert calculus. We show that the classes of a regular Hessenberg variety in the cohomology and K-theory of the flag variety are given by making certain substitutions in the Schubert polynomial (respectively Grothendieck polynomial) for a permutation that depends only on h. Our formula and our methods are different from a recent result …
How Emergent Social Patterns In Allogrooming Combat Parasitic Infections, Shelby N. Wilson, Suzanne S. Sindi, Heather Z. Brooks, Maryann E. Hohn, Candice R. Price, Ami E. Radunskaya, Nakeya D. Williams, Nina H. Fefferman
How Emergent Social Patterns In Allogrooming Combat Parasitic Infections, Shelby N. Wilson, Suzanne S. Sindi, Heather Z. Brooks, Maryann E. Hohn, Candice R. Price, Ami E. Radunskaya, Nakeya D. Williams, Nina H. Fefferman
Mathematics Sciences: Faculty Publications
Members of social groups risk infection through contact with those in their social network. Evidence that social organization may protect populations from pathogens in certain circumstances prompts the question as to how social organization affects the spread of ectoparasites. The same grooming behaviors that establish social bonds also play a role in the progression of ectoparasitic outbreaks. In this paper, we model the interactions between social organization and allogrooming efficiency to consider how ectoparasitic threats may have shaped the evolution of social behaviors. To better understand the impacts of social grooming on organizational structure, we consider several dynamic models of …
Analysis In Metric Spaces, Mario Bonk, Luca Capogna, Piotr Hajłasz, Nageswari Shanmugalingam, Jeremy Tyson
Analysis In Metric Spaces, Mario Bonk, Luca Capogna, Piotr Hajłasz, Nageswari Shanmugalingam, Jeremy Tyson
Mathematics Sciences: Faculty Publications
No abstract provided.
Three-Dimensional Viscoelastic Instabilities In A Four-Roll Mill Geometry At The Stokes Limit, Paloma Gutierrez-Castillo, Adam Kagel, Becca Thomases
Three-Dimensional Viscoelastic Instabilities In A Four-Roll Mill Geometry At The Stokes Limit, Paloma Gutierrez-Castillo, Adam Kagel, Becca Thomases
Mathematics Sciences: Faculty Publications
Three-dimensional numerical simulations of viscoelastic fluids in the Stokes limit with a four-roll mill background force (extended to the third dimension) were performed. Both the Oldroyd-B model and FENE-P model of viscoelastic fluids were used. Different temporal behaviors were observed depending on the Weissenberg number (non-dimensional relaxation time), model, and initial conditions. Temporal dynamics evolve on long time scales, and simulations were accelerated by using a Graphics Processing Unit (GPU). Previously, parameter explorations and long-time simulations in 3D were prohibitively expensive. For a small Weissenberg number, all the solutions are constant in the third dimension, displaying strictly two-dimensional temporal evolutions. …
Graphs Admitting Only Constant Splines, Katie Anders, Alissa S. Crans, Briana Foster-Greenwood, Blake Mellor, Julianna Tymoczko
Graphs Admitting Only Constant Splines, Katie Anders, Alissa S. Crans, Briana Foster-Greenwood, Blake Mellor, Julianna Tymoczko
Mathematics Sciences: Faculty Publications
We study generalized graph splines, introduced by Gilbert, Tymoczko, and Viel (2016). For a large class of rings, we characterize the graphs that only admit constant splines. To do this, we prove that if a graph has a particular type of cutset (e.g., a bridge), then the space of splines naturally decomposes as a certain direct sum of submodules. As an application, we use these results to describe splines on a triangulation studied by Zhou and Lai, but over a different ring than they used.
A Filtration On The Cohomology Rings Of Regular Nilpotent Hessenberg Varieties, Megumi Harada, Tatsuya Horiguchi, Satoshi Murai, Martha Precup, Julianna Tymoczko
A Filtration On The Cohomology Rings Of Regular Nilpotent Hessenberg Varieties, Megumi Harada, Tatsuya Horiguchi, Satoshi Murai, Martha Precup, Julianna Tymoczko
Mathematics Sciences: Faculty Publications
Let n be a positive integer. The main result of this manuscript is a construction of a filtration on the cohomology ring of a regular nilpotent Hessenberg variety in GL(n, C) / B such that its associated graded ring has graded pieces (i.e., homogeneous components) isomorphic to rings which are related to the cohomology rings of Hessenberg varieties in GL(n- 1 , C) / B, showing the inductive nature of these rings. In previous work, the first two authors, together with Abe and Masuda, gave an explicit presentation of these cohomology rings in terms of generators and relations. We introduce …