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Articles 1 - 8 of 8
Full-Text Articles in Mathematics
Homomorphism Obstructions For Satellite Maps, Allison N. Miller
Homomorphism Obstructions For Satellite Maps, Allison N. Miller
Mathematics & Statistics Faculty Works
A knot in a solid torus defines a map on the set of (smooth or topological) concordance classes of knots in S³. This set admits a group structure, but a conjecture of Hedden suggests that satellite maps never induce interesting homomorphisms: we give new evidence for this conjecture in both categories. First, we use Casson-Gordon signatures to give the first obstruction to a slice pattern inducing a homomorphism on the topological concordance group, constructing examples with every winding number besides ± 1. We then provide subtle examples of satellite maps which map arbitrarily deep into the n-solvable filtration …
Bifurcation From Infinity With Oscillatory Nonlinearity For Neumann Problems, M. Chhetri, Nsoki Mavinga, R. Pardo
Bifurcation From Infinity With Oscillatory Nonlinearity For Neumann Problems, M. Chhetri, Nsoki Mavinga, R. Pardo
Mathematics & Statistics Faculty Works
We consider a sublinear perturbation of an elliptic eigenvalue problem with Neumann boundary condition. We give sufficient conditions on the nonlinear perturbation which guarantee that the unbounded continuum, bifurcating from infinity at the first eigenvalue, contains an unbounded sequence of turning points as well as an unbounded sequence of resonant solutions. We prove our result by using bifurcation theory combined with a careful analysis of the oscillatory behavior of the continuum near the bifurcation point.
Fucik Spectrum With Weights And Existence Of Solutions For Nonlinear Elliptic Equations With Nonlinear Boundary Conditions, Nsoki Mavinga, Q. A. Morris, S. B. Robinson
Fucik Spectrum With Weights And Existence Of Solutions For Nonlinear Elliptic Equations With Nonlinear Boundary Conditions, Nsoki Mavinga, Q. A. Morris, S. B. Robinson
Mathematics & Statistics Faculty Works
We consider the boundary value problem −Δu + c(x)u = αm(x)u+ − βm(x)u− + f(x,u), x∈Ω, (∂u)/(∂η) + σ(x)u = αρ(x)u+ − βρ(x)u− + g(x,u), x∈∂Ω, where (α,β) ∈R2, c, m ∈ L∞(Ω), σ, ρ ∈ L∞(∂Ω), and the nonlinearities f and g are bounded …
Strongly Invertible Knots, Equivariant Slice Genera, And An Equivariant Algebraic Concordance Group, Allison N. Miller, M. Powell
Strongly Invertible Knots, Equivariant Slice Genera, And An Equivariant Algebraic Concordance Group, Allison N. Miller, M. Powell
Mathematics & Statistics Faculty Works
We use the Blanchfield form to obtain a lower bound on the equivariant slice genus of a strongly invertible knot. For our main application, let K be a strongly invertible genus one slice knot with nontrivial Alexander polynomial. We show that the equivariant slice genus of an equivariant connected sum #n K is at least n/4. We also formulate an equivariant algebraic concordance group, and show that the kernel of the forgetful map to the classical algebraic concordance group is infinite rank.
Structure And Dynamics That Specialize Neurons For High-Frequency Coincidence Detection In The Barn Owl Nucleus Laminaris, Ben Drucker , '22, Joshua H. Goldwyn
Structure And Dynamics That Specialize Neurons For High-Frequency Coincidence Detection In The Barn Owl Nucleus Laminaris, Ben Drucker , '22, Joshua H. Goldwyn
Mathematics & Statistics Faculty Works
A principal cue for sound source localization is the difference in arrival times of sounds at an animal’s two ears (interaural time difference, ITD). Neurons that process ITDs are specialized to compare the timing of inputs with submillisecond precision. In the barn owl, ITD processing begins in the nucleus laminaris (NL) region of the auditory brain stem. Remarkably, NL neurons are sensitive to ITDs in high-frequency sounds (kilohertz-range). This contrasts with ITD-based sound localization in analogous regions in mammals where ITD sensitivity is typically restricted to lower-frequency sounds. Guided by previous experiments and modeling studies of tone-evoked responses of NL …
Generalized Sasakian Structures From A Poisson Geometry Viewpoint, Janet Talvacchia
Generalized Sasakian Structures From A Poisson Geometry Viewpoint, Janet Talvacchia
Mathematics & Statistics Faculty Works
In this paper we define a canonical Poisson structure on a normal generalized contact metric space and use this structure to define a generalized Sasakian structure. We show also that this canonical Poisson structure enables us to distinguish generalized Sasakian structures from generalized coKähler structures.
New Insights Into Binocular Rivalry From The Reconstruction Of Evolving Percepts Using Model Network Dynamics, Kenneth Barkdoll , '24, Yuhua Lu , '24, Victor J. Barranca
New Insights Into Binocular Rivalry From The Reconstruction Of Evolving Percepts Using Model Network Dynamics, Kenneth Barkdoll , '24, Yuhua Lu , '24, Victor J. Barranca
Mathematics & Statistics Faculty Works
When the two eyes are presented with highly distinct stimuli, the resulting visual percept generally switches every few seconds between the two monocular images in an irregular fashion, giving rise to a phenomenon known as binocular rivalry. While a host of theoretical studies have explored potential mechanisms for binocular rivalry in the context of evoked model dynamics in response to simple stimuli, here we investigate binocular rivalry directly through complex stimulus reconstructions based on the activity of a two-layer neuronal network model with competing downstream pools driven by disparate monocular stimuli composed of image pixels. To estimate the dynamic percept, …
The Explorer–Director Game On Graphs, Pat Devlin, E. Meger, A. Raz, Polymath Reu Participants
The Explorer–Director Game On Graphs, Pat Devlin, E. Meger, A. Raz, Polymath Reu Participants
Mathematics & Statistics Faculty Works
The Explorer-Director game, first introduced by Nedev and Muthukrishnan, can be described as a game where two players—Explorer and Director—determine the movement of a token that is positioned on the vertices of some given graph. At each time step, the Explorer specifies a distance that the token must move with an aim to maximize the total number of vertices ultimately visited. However, the Director adversarially chooses where to move token in an effort to minimize this number. The game ends when no new vertices can be visited. Given a graph G and a starting vertex v, the number of vertices …