CAS: Mathematics & Statistics: Scholarly Papers
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URI: http://hdl.handle.net/2144/1002
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Assessing dynamics, spatial scale, and uncertainty in task-related brain network analyses
The brain is a complex network of interconnected elements, whose interactions evolve dynamically in time to cooperatively perform specific functions. A common technique to probe these interactions involves multi-sensor ... -
Characterizing the spiking dynamics of subthalamic nucleus neurons in Parkinson's disease using generalized linear models
(Frontiers Media, 2012-06-20)Accurately describing the spiking patterns of neurons in the subthalamic nucleus (STN) of patients suffering from Parkinson's disease (PD) is important for understanding the pathogenesis of the disease and for achieving ... -
Non-stationary self-similar Gaussian processes as scaling limits of power law shot noise processes and generalizations of fractional Brownian motion
We study shot noise processes with Poisson arrivals and non-stationary noises. The noises are conditionally independent given the arrival times, but the distribution of each noise does depend on its arrival time. We establish ... -
Slopes of modular forms and the ghost conjecture, II
(American Mathematical Society (AMS), 2018)In a previous article we constructed an entire power series over 𝑷 -adic weight space (the ghost series) and conjectured, in the 𝚪₀ (𝑵) -regular case, that this series encodes the slopes of overconvergent modular forms ... -
Arithmetic properties of Fredholm series for 𝑝-adic modular forms
(Oxford University Press, 2016)We study the relationship between recent conjectures on slopes of overconvergent 𝑝-adic modular forms "near the boundary" of 𝑝-adic weight space. We also prove in tame level 1 that the coeffcients of the Fredholm series ... -
Explicit computations of Hida families via overconvergent modular symbols
(Springer International Publishing, 2016-12-01)In Pollack and Stevens (Ann Sci Éc Norm Supér 44(1):1–42, 2011), efficient algorithms are given to compute with overconvergent modular symbols. These algorithms then allow for the fast computation of 𝑝-adic 𝐿-functions ... -
On the freeness of anticyclotomic selmer groups of modular forms
(World Scientific Publishing, 2017-07-01)We establish the freeness of certain anticyclotomic Selmer groups of modular forms. The freeness of these Selmer groups plays a key role in the Euler system arguments introduced by Bertolini and Darmon in their work on the ... -
A remark on non-integral 𝑝-adic slopes for modular forms
(2017-03-10)We give a sufficient condition, namely “Buzzard irregularity”, for there to exist a cuspidal eigenform which does not have integral 𝑝-adic slope. -
Localized mirror functor constructed from a Lagrangian torus
(Elsevier BV, 2019-02)Fixing a weakly unobstructed Lagrangian torus in a symplectic manifold 𝘟, we define a holomorphic function 𝘞 known as the Floer potential. We construct a canonical 𝑨∞ -functor from the Fukaya category of 𝘟 to the ... -
Matched filters for noisy induced subgraph detection
We consider the problem of finding the vertex correspondence between two graphs with different number of vertices where the smaller graph is still potentially large. We propose a solution to this problem via a graph matching ...
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