Periodic space-time homogenisation of the $φ^4_2$ equation

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This thesis investigates Noisy Gradient Descent (NGD), an idealized version of Stochastic Gradient Descent in three different settings. While commonly understood as an undesirable artifact, we demonstrate that the noise in NGD can be harnessed to ensure convergence to equilibrium in multiagent games with limited feedback, as well as to guarantee generalization of the outputs of a learning scheme, and, that it can serve as an essential tool for generative modeling. We explore these benefits by progressively

Digital memcomputing machines (DMMs) have been designed to solve complex combinatorial optimization problems. Since DMMs are fundamentally classical dynamical systems, their ordinary differential equations (ODEs) can be efficiently simulated on modern computers. This provides a unique platform to study their performance under various conditions. An aspect that has received little attention so far is how their performance is affected by the numerical errors in the solution of their ODEs and the physical nois

A pipelined-SAR ADC is a popular front-end solution for highresolution, low-power loT sensors, as it combines the noise relaxation property of residue amplification with the robustness of SAR ADCs, enabling excellent energy efficiency and high-resolution readout. Residue amplifiers (RAs) are the key innovation point for these ADCs, as recent efforts have focused on replacing statically powered RAs with dynamic amplifiers, such as ring amplifiers [1–4], floating inverter amplifiers (FIAs) [5–7], or various o

In the context of Uncertainty Quantification, simulating high-dimensional stochastic dynamical systems remains a challenging task owing to the high computational cost they incur. The Dynamical Low-Rank (DLR) method, which has gained increasing attention in recent years, has characteristics that are naturally adapted to that setting. The method approximates a random field u(t, x, w) by Sum_{i=1}^R U_i(t, x) Y_i(t, w), where both the physical bases {U_i}{i=1}^R and stochastic bases {Y_i}{i=1}^R evolve in ti

This semester's project aims to explore the potential of the Vaisala CL61 ceilometer with polarization capacity for characterizing atmospheric observations. To achieve this, a Python pipeline was developed to classify atmospheric targets. The noise was filtered out from the data, enabling an efficient application of K-means clustering. Each cluster was classified by fixing thresholds on attenuated backscatter and linear depolarization ratio. The results show differentiation between liquid and solid scatteri

Human communication entails an efficient way of simultaneously processing voice and reducing the impact of environmental noise. By manipulating background noise, we aimed at clarifying the neural mechanisms allowing voice comprehension in noisy situations. Our results point to spatial and temporal coexistence of lateral and medial temporal cortex networks when voice is easily detected in highly noisy conditions, revealing the necessary neural underpinnings of human communication in realistic situations.

Extreme natural or man-made disasters are events caused by factors that injure, displace people and damage property. Victims of such events are often forced to live in temporary emergency shelters for prolonged time. It is therefore important to evaluate the indoor environmental quality in emergency shelters, which is the objective of this project. In addition to literature review, this project includes testing and integration of sensing modules that will be installed inside and outside of different emergen

The present work concerns the approximation of the solution map S associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution of the Helmholtz equation. We introduce a least squares rational Padé-type approximation technique applicable to any meromorphic Hilbert space-valued univariate map, and we prove the uniform convergence of the Padé approximation error on any compact subset

We study the accuracy of the discrete least-squares approximation on a finite dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. The convergence estimates are given in mean-square sense with respect to the sampling measure. The noise may be correlated with the location of the evaluation and may have nonzero mean (offset). We consider both cases of bounded or square-integrable noise /

We propose a new approach to semi-automated delineation of curvilinear structures in a wide range of imaging modalities. Earlier approaches lack robustness to imaging noise, do not provide radius estimates for the structures and operate only on single channel images. In contrast, ours makes use of the color information, when available, and generates accurate centreline location and radius estimates with minimal supervision. We demonstrate this on a wide range of datasets ranging from a 2D dataset of aerial

Behavioral and brain responses to identical stimuli can vary with experimental and task parameters, including the context of stimulus presentation or attention. More surprisingly, computational models suggest that noise-related random fluctuations in brain responses to stimuli would alone be sufficient to engender perceptual differences between physically identical stimuli. In two experiments combining psychophysics and EEG in healthy humans, we investigated brain mechanisms whereby identical stimuli are (e

This paper presents a MEMS-based 5th-order Delta Sigma capacitive accelerometer. The Delta Sigma loop is implemented in mixed signal, the global 5th-order filter having a 2nd-order analog and a 3rd-order digital part. The system can be used with a wide range of sensors, because the mixed-signal front-end is programmable. The developed ASIC comprises a voltage-mode preamplifier, two parallel demodulators implementing CDS, and a 7-bit internally non-linear flash ADC. The latter drives a 3rd-order digital filt

The purpose of this report is to present the study of a linguistic network based on the relation of synonymy. The network has been extracted from a dictionary of synonyms in French. Due to errors and ambiguities in the data, the synonyms are not always grouped into distinct components. To refine the results, we apply a clustering algorithm to the network. Each densely connected cluster is considered to correspond to a general concept in the language. Finally we develop a new general method, based on the int

Musical and audio signals in general form a major part of the large amount of data exchange taking place in our information-based society. Transmission of high quality audio signals through narrow-band channels, such as the Internet, requires refined methods for modeling and coding sound. The first important step is the development of new analysis techniques able to discriminate between sound components according to effective perceptual criteria. Our ultimate goal is to develop an optimal representation in

An analytical model is proposed that can predict the shape of the poststimulus time histogram (PSTH) response to a current pulse of a neuron subjected to uncorrelated background input. The model is based on an explicit description of noise in the form of an escape rate and corresponding hazard function. Two forms of the model are presented. The full model is nonlinear and can be integrated numerically while a linearized version, while the linearized version can be solved analytically. In the linearized vers

This paper examines a number of chaos shift keying methods Different approaches for the optimization of the transmitter and the receiver (based on statistical arguments) are compared through simulation. Based on the results, The tradeoff between computational comnplexity and performance is discussed. As usual, the performance measure considered is the bit error rate for a given noise level. Also, various limit cases are considered, among them the case where the channel noise is large

The multi-band processing paradigm for noise robust ASR was originally motivated by the observation that human recognition appears to be based on independent processing of separate frequency sub-bands, and also by

missing data'' results which have shown that ASR can be made significantly more robust to band-limited noise if noisy sub-bands can be detected and then ignored. Of the different multi-band models which have been proposed, only the

Full Combination'' or ``all-wise'' multi-band HMM/ANN hybrid a

The resoln. limit of fluorescence correlation spectroscopy for two-component solns. is investigated theor. and exptl. The autocorrelation function for two different particles in soln. were computed, statistical noise was added, and the resulting curve was fitted with a least squares fit. These simulations show that the ability to distinguish between two different mol. species in soln. depends strongly on the no. of photons detected from each particle, their difference in size, and the concn. of each compone

Periodic space-time homogenisation of the $φ^4_2$ equation

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Noisy Gradient Descent in Machine Learning: generalization, games, and sampling

On the solvable–unsolvable transition due to noise-induced chaos in digital memcomputing

A 78.2/90.0dB-SNDR/SFDR Pipelined-SAR ADC with Noise-Reducing Stacked Dynamic Source-Follower Amplifiers

Advances in Dynamical Low-Rank Approximations for random PDEs and Data Assimilation

Ceilometer data processing and analysis

Functional and causal neural mechanisms of human voice perception in noisy situations

A comparative study of indoor environmental quality in temporary emergency shelters

MATHICSE Technical Report :Convergence analysis of Padé approximations for Helmholtz frequency response problems

MATHICSE Technical Report : Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Semi-Automated Reconstruction of Curvilinear Structures in Noisy 2D images and 3D image stacks

Noise in brain activity engenders perception and influences discrimination sensitivity

A Navigation-Grade MEMS Accelerometer based on a Versatile Front End

Analysis of a Synonymy Network

Fractal additive synthesis : spectral modeling of sound for low rate coding of quality audio

Noise and the PSTH response to current transients: I. General theory and application to the integrate-and-fire neuron

Comparison of different chaos shift keying methods

From Multi-Band Full Combination to Multi-Stream Full Combination Processing in Robust ASR

Resolution of fluorescence correlation measurements