Fourier Analysis of the microvascular function of women with and without migraine

Erasmus MC is conducting a study on the increased risk of cardiovascular disease in women who have migraine. For this purpose, 50 healthy women and 50 women with migraine in age category of 40-60 years were compared using measurements of their dermal blood flow.<br/>These measurements are done using two different imaging devices: Laser Speckle...

FCT-GAN: Fourier Neural Operator for Global Relation Enhancement in Tabular Data Synthesizing using Generative Adversarial Networks

Since the regularization of data privacy (e.g., GDPR), the effectiveness of data sharing has decreased. A promising technique to circumvent this problem is tabular data synthesis (i.e., the generation of fake tabular data that statistically resembles the original data). However, the state-of-the-art tabular data synthesis model, CTAB-GAN, fails...

Fourier Ring Correlation with a single image

As super-resolution methods make it possible to capture images at a resolution beyond the diffraction limit, they have no straightforward measure for optical resolution. Consequently, signal-to-noise ratio-based methods to determine resolution such as Fourier Ring Correlation (FRC) have seen increased<br/>use. We look at a new method, called...

Signal-processing of audio for speech-recognition

The transcription of voice using neural networks is a technique that deserves attention, as speech assistants are becoming increasingly popular. Neural networks have often difficulty with determining the differences between a talking person and noise. Humans have a much better understanding of this and could possibly apply their knowledge of the...

Using object-specific frequency information from labeled data to improve a CNN’s robustness to adversarial attacks

Convolutional Neural Networks are particularly vulnerable to attacks that manipulate their data, which are usually called adversarial attacks. In this paper, a method of filtering images using the Fast Fourier Transform is explored, along with its potential to be used as a defense mechanism to such attacks. The main contribution that differs...

Using frequency information to improve accuracy of object detectors

This research paper analyses the effect that using frequency information can have on object detectors. The latter are complex networks that learn information about objects from images and are then able to predict the location of these objects in new, unseen images. There are, however, certain datasets that are hard to learn on, partly because...

Injecting prior frequency information in DETR for wheat head detection

Wheat is among the most important grains worldwide. For the assessment of wheat fields, image detection of spikes atop the plant containing grain is used. Previous work in deep learning for precision agriculture employs the already established object detectors, Faster R-CNN and YOLO, adapted for the given context. However, these models suffer...

Fourier analysis on finite groups and the irreducible representations of the symmetric group

In this paper we will naturally extend the concept of Fourier analysis to functions on arbitrary groups. We will generalise the idea of a convolution and try to find a formula for Fourier coefficients in such way that the coefficients of the convolution can easily be calculated. In the first section we will start off in familiar territory as we...

A numerical Fourier cosine method for forward backward stochastic differential equations with jumps

In financial and egineering problems, we are often faced with solving Partial-Integro Differential Equations (PIDEs). Rarely we can find an analytic solution in a closed form expression for these PIDEs, hence we turn to numerical schemes to accurately approximate the solution instead. Classically these methods are based on finite difference...

On Covariant Emergent Gravity

This Bachelor thesis is on Covariant Emergent Gravity (CEG): a covariant formulation by Sabine Hossenfelder of the ideas of Erik Verlinde on gravity as an emergent force. In this work, the ideas of Erik Verlinde are presented as well as the field equations of CEG. The aim of this thesis is to find experimentally verifiable results for CEG. From...

Eclipses by exomoons

The aim of this research is to study a method to find exomoons and to find specific characteristics that point to the existence of exomoons. Exomoons are natural satellites orbiting an extrasolar (exo)planet in an extrasolar system. By looking at eclipses on exoplanets, we can find these characteristics.<br/>We consider the reflected light...

Scaling limit of the odometer of correlated Gaussians on the torus

In the divisible sandpile model, we consider a collection of i.i.d. Gaussian heights on a finite graph. It was shown by Levine et al. (2015) that the odometer function in this case equals a discrete, bi-Laplacian field. Subsequently, Cipriani et al. (2016) proved that the scaling limit of the odometer is a continuum bi-Laplacian field, this time...

Boundary values of analytic functions on the disc

In this bachelor's thesis we will solve the Dirichlet problem with an L^p(T) boundary function. First, we will focus on the holomorphic version of the Dirichlet problem and introduce Hardy space theory, from which will follow a sufficient condition on the Fourier coefficients of the boundary function. Then we will prove the...

Brownian Motion and the Airy Function

Deriving the location of the maximum of a Brownian Motion with downward quadratic drift. Proving it is welldefined then finding an algorithmic method to simplify expressions of the moments.

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