7 papers
Depth Separation for Neural Networks under Gaussian Measure
Cynthia Bortolotto, Francisco Ganacim, Roberto I. Oliveira
We revisit the problem of depth separation for neural networks, as studied by Eldan and Shamir, Daniely, and others. Specifically, we consider the natural setting of approxim…
A complex-analytic proof of square-restricted stable phase retrieval in Fock space
Cynthia Bortolotto, João P. G. Ramos
We give a short complex-analytic proof of a square-restricted form of local stable phase retrieval at the Gaussian in one-dimensional Fock space. The main estimate is a coercivity…
Modular Forms and Numerical Explorations of Rational Approximations to
Cynthia Bortolotto, Lucas Oliveira
We revisit Beukers' modular-form proof of the irrationality of from the point of view of the auxiliary weight two modular form. For the Fricke group , we show…
Intersections of random chords of a circle
Cynthia Bortolotto, Victor Souza
Where are the intersection points of diagonals of a regular -gon located? What is the distribution of the intersection point of two random chords of a circle? We investigate the…
On Extremal Problems Associated with Random Chords on a Circle
Cynthia Bortolotto, João P. G. Ramos
Inspired by the work of Karamata, we consider an extremization problem associated with the probability of intersecting two random chords inside a circle of radius $r, \, r \in (0,1…
Weyl sums with multiplicative coefficients and joint equidistribution
Matteo Bordignon, Cynthia Bortolotto, Bryce Kerr
In this paper we generalize a result of Montgomery and Vaughan regarding exponential sums with multiplicative coefcients to the setting of Weyl sums. As applications, we establish…
On the endpoint behaviour of oscillatory maximal function
Tainara Borges, Cynthia Bortolotto, João P. G. Ramos
Inspired by a question of Lie, we study boundedness in subspaces of of oscillatory maximal functions. In particular, we construct functions in w…