Publications related to Formal sciences

Spatiotemporal energy‐density distribution of time‐reversed electromagnetic fields

Marcos Rubinstein, Farhad Rachidi-Haeri, Hamidreza Karami, Elias Per Joachim Le Boudec, Nicolas Mora Parra

Time reversal exploits the invariance of electromagnetic wave propagation in reciprocal and lossless media to localize radiating sources. Time-reversed measurements are back-propagated in a simulated domain and converge to the unknown source location. The ...

2024

Six-dimensional sphere packing and linear programming

Maryna Viazovska, Matthew De Courcy-Ireland, Maria Margarethe Dostert

We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn- Triantafillou [Math. Comp. 91 (2021), pp. 491 ...

Amer Mathematical Soc2024

Null energy constraints on two-dimensional RG flows

Grégoire Olivier Mathys

We study applications of spectral positivity and the averaged null energy condition (ANEC) to renormalization group (RG) flows in two-dimensional quantum field theory. We find a succinct new proof of the Zamolodchikov c-theorem, and derive further independ ...

New York2024

Geometric Learning: Leveraging differential geometry for learning and control

Bernardo Fichera

In this thesis, we concentrate on advancing high-level behavioral control policies for robotic systems within the framework of Dynamical Systems (DS). Throughout the course of this research, a unifying thread weaving through diverse fields emerges, and tha ...

EPFL2024

Stable cones in the thin one-phase problem

Xavier Fernandez-Real Girona

The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one -phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions n >= 3 is completely open. In this context, axial ...

Johns Hopkins Univ Press2024

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

Jan Sickmann Hesthaven, Federico Pichi

The present work proposes a framework for nonlinear model order reduction based on a Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) context, one is interested in obtaining real -time and many-query evaluations of parametric ...

San Diego2024

Formal Autograding in a Classroom (Experience Report)

Viktor Kuncak, Mario Bucev, Dragana Milovancevic, Samuel Chassot

We report our experience in enhancing automated grading in a functional programming course using formal verification. In our approach, we deploy a verifier for Scala programs to check equivalences between student submissions and reference solutions. Conseq ...

2024

Towards Trustworthy Deep Learning for Image Reconstruction

Alexis Marie Frederic Goujon

The remarkable ability of deep learning (DL) models to approximate high-dimensional functions from samples has sparked a revolution across numerous scientific and industrial domains that cannot be overemphasized. In sensitive applications, the good perform ...

EPFL2024

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Toyomu Matsuda

We give an extension of Le's stochastic sewing lemma. The stochastic sewing lemma proves convergence in

L_m

of Riemann type sums

\sum _{[s,t] \in \pi } A_{s,t}

for an adapted two-parameter stochastic process A, under certain conditions on the moments o ...

Cambridge Univ Press2024

Generation of entangled photon pairs from a silicon bichromatic photonic crystal cavity

Matteo Galli, Marco Clementi, Thanavorn Poempool

Integrated quantum photonics leverages the on-chip generation of nonclassical states of light to realize key functionalities of quantum devices. Typically, the generation of such nonclassical states relies on whispering gallery mode resonators, such as int ...

Melville2024

Formal sciences

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Spatiotemporal energy‐density distribution of time‐reversed electromagnetic fields

Six-dimensional sphere packing and linear programming

Null energy constraints on two-dimensional RG flows

Geometric Learning: Leveraging differential geometry for learning and control

Stable cones in the thin one-phase problem

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

Formal Autograding in a Classroom (Experience Report)

Towards Trustworthy Deep Learning for Image Reconstruction

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Generation of entangled photon pairs from a silicon bichromatic photonic crystal cavity

Six-dimensional sphere packing and linear programming

Spatiotemporal energy‐density distribution of time‐reversed electromagnetic fields

Null energy constraints on two-dimensional RG flows

Geometric Learning: Leveraging differential geometry for learning and control

Stable cones in the thin one-phase problem

Generation of entangled photon pairs from a silicon bichromatic photonic crystal cavity

A graph convolutional autoencoder approach to model order reduction for parametrized PDEs

Formal Autograding in a Classroom (Experience Report)

An extension of the stochastic sewing lemma and applications to fractional stochastic calculus

Towards Trustworthy Deep Learning for Image Reconstruction