Classical-to-Quantum Sequence Encoding in Genomics

DNA sequencing allows for the determination of the genetic code of an organism, and therefore is an indispensable tool that has applications in Medicine, Life Sciences, Evolutionary Biology, Food Sciences and Technology, and Agriculture. In this paper, we present several novel methods of performing classical-to-quantum data encoding inspired by various mathematical fields, and we demonstrate these ideas within Bioinformatics. In particular, we introduce algorithms that draw inspiration from diverse fields such as Electrical and Electronic Engineering, Information Theory, Differential Geometry, and Neural Network architectures. We provide a complete overview of the existing data encoding schemes and show how to use them in Genomics. The algorithms provided utilise lossless compression, wavelet-based encoding, and information entropy. Moreover, we propose a contemporary method for testing encoded DNA sequences using Quantum Boltzmann Machines. To evaluate the effectiveness of our algorithms, we discuss a potential dataset that serves as a sandbox environment for testing against real-world scenarios. Our research contributes to developing classical-to-quantum data encoding methods in the science of Bioinformatics by introducing innovative algorithms that utilise diverse fields and advanced techniques. Our findings offer insights into the potential of Quantum Computing in Bioinformatics and have implications for future research in this area.Comment: 58 pages, 14 figure

Neural function approximation on graphs: shape modelling, graph discrimination & compression

Graphs serve as a versatile mathematical abstraction of real-world phenomena in numerous scientific disciplines. This thesis is part of the Geometric Deep Learning subject area, a family of learning paradigms, that capitalise on the increasing volume of non-Euclidean data so as to solve real-world tasks in a data-driven manner. In particular, we focus on the topic of graph function approximation using neural networks, which lies at the heart of many relevant methods. In the first part of the thesis, we contribute to the understanding and design of Graph Neural Networks (GNNs). Initially, we investigate the problem of learning on signals supported on a fixed graph. We show that treating graph signals as general graph spaces is restrictive and conventional GNNs have limited expressivity. Instead, we expose a more enlightening perspective by drawing parallels between graph signals and signals on Euclidean grids, such as images and audio. Accordingly, we propose a permutation-sensitive GNN based on an operator analogous to shifts in grids and instantiate it on 3D meshes for shape modelling (Spiral Convolutions). Following, we focus on learning on general graph spaces and in particular on functions that are invariant to graph isomorphism. We identify a fundamental trade-off between invariance, expressivity and computational complexity, which we address with a symmetry-breaking mechanism based on substructure encodings (Graph Substructure Networks). Substructures are shown to be a powerful tool that provably improves expressivity while controlling computational complexity, and a useful inductive bias in network science and chemistry. In the second part of the thesis, we discuss the problem of graph compression, where we analyse the information-theoretic principles and the connections with graph generative models. We show that another inevitable trade-off surfaces, now between computational complexity and compression quality, due to graph isomorphism. We propose a substructure-based dictionary coder - Partition and Code (PnC) - with theoretical guarantees that can be adapted to different graph distributions by estimating its parameters from observations. Additionally, contrary to the majority of neural compressors, PnC is parameter and sample efficient and is therefore of wide practical relevance. Finally, within this framework, substructures are further illustrated as a decisive archetype for learning problems on graph spaces.Open Acces

Remote Sensing Data Compression

A huge amount of data is acquired nowadays by different remote sensing systems installed on satellites, aircrafts, and UAV. The acquired data then have to be transferred to image processing centres, stored and/or delivered to customers. In restricted scenarios, data compression is strongly desired or necessary. A wide diversity of coding methods can be used, depending on the requirements and their priority. In addition, the types and properties of images differ a lot, thus, practical implementation aspects have to be taken into account. The Special Issue paper collection taken as basis of this book touches on all of the aforementioned items to some degree, giving the reader an opportunity to learn about recent developments and research directions in the field of image compression. In particular, lossless and near-lossless compression of multi- and hyperspectral images still remains current, since such images constitute data arrays that are of extremely large size with rich information that can be retrieved from them for various applications. Another important aspect is the impact of lossless compression on image classification and segmentation, where a reasonable compromise between the characteristics of compression and the final tasks of data processing has to be achieved. The problems of data transition from UAV-based acquisition platforms, as well as the use of FPGA and neural networks, have become very important. Finally, attempts to apply compressive sensing approaches in remote sensing image processing with positive outcomes are observed. We hope that readers will find our book useful and interestin

Asymptotically isometric codes for holography

The holographic principle suggests that the low energy effective field theory of gravity, as used to describe perturbative quantum fields about some background has far too many states. It is then natural that any quantum error correcting code with such a quantum field theory as the code subspace is not isometric. We discuss how this framework can naturally arise in an algebraic QFT treatment of a family of CFT with a large-$N$ limit described by the single trace sector. We show that an isometric code can be recovered in the $N \rightarrow \infty$ limit when acting on fixed states in the code Hilbert space. Asymptotically isometric codes come equipped with the notion of simple operators and nets of causal wedges. While the causal wedges are additive, they need not satisfy Haag duality, thus leading to the possibility of non-trivial entanglement wedge reconstructions. Codes with complementary recovery are defined as having extensions to Haag dual nets, where entanglement wedges are well defined for all causal boundary regions. We prove an asymptotic version of the information disturbance trade-off theorem and use this to show that boundary theory causality is maintained by net extensions. We give a characterization of the existence of an entanglement wedge extension via the asymptotic equality of bulk and boundary relative entropy or modular flow. While these codes are asymptotically exact, at fixed $N$ they can have large errors on states that do not survive the large-$N$ limit. This allows us to fix well known issues that arise when modeling gravity as an exact codes, while maintaining the nice features expected of gravity, including, among other things, the emergence of non-trivial von Neumann algebras of various types.Comment: 74 pages plus appendices, 7 figure

Restauration d'images en IRM anatomique pour l'étude préclinique des marqueurs du vieillissement cérébral

Les maladies neurovasculaires et neurodégénératives liées à l'âge sont en forte augmentation. Alors que ces changements pathologiques montrent des effets sur le cerveau avant l'apparition de symptômes cliniques, une meilleure compréhension du processus de vieillissement normal du cerveau aidera à distinguer l'impact des pathologies connues sur la structure régionale du cerveau. En outre, la connaissance des schémas de rétrécissement du cerveau dans le vieillissement normal pourrait conduire à une meilleure compréhension de ses causes et peut-être à des interventions réduisant la perte de fonctions cérébrales associée à l'atrophie cérébrale. Par conséquent, ce projet de thèse vise à détecter les biomarqueurs du vieillissement normal et pathologique du cerveau dans un modèle de primate non humain, le singe marmouset (Callithrix Jacchus), qui possède des caractéristiques anatomiques plus proches de celles des humains que de celles des rongeurs. Cependant, les changements structurels (par exemple, de volumes, d'épaisseur corticale) qui peuvent se produire au cours de leur vie adulte peuvent être minimes à l'échelle de l'observation. Dans ce contexte, il est essentiel de disposer de techniques d'observation offrant un contraste et une résolution spatiale suffisamment élevés et permettant des évaluations détaillées des changements morphométriques du cerveau associé au vieillissement. Cependant, l'imagerie de petits cerveaux dans une plateforme IRM 3T dédiée à l'homme est une tâche difficile car la résolution spatiale et le contraste obtenus sont insuffisants par rapport à la taille des structures anatomiques observées et à l'échelle des modifications attendues. Cette thèse vise à développer des méthodes de restauration d'image pour les images IRM précliniques qui amélioreront la robustesse des algorithmes de segmentation. L'amélioration de la résolution spatiale des images à un rapport signal/bruit constant limitera les effets de volume partiel dans les voxels situés à la frontière entre deux structures et permettra une meilleure segmentation tout en augmentant la reproductibilité des résultats. Cette étape d'imagerie computationnelle est cruciale pour une analyse morphométrique longitudinale fiable basée sur les voxels et l'identification de marqueurs anatomiques du vieillissement cérébral en suivant les changements de volume dans la matière grise, la matière blanche et le liquide cérébral.Age-related neurovascular and neurodegenerative diseases are increasing significantly. While such pathological changes show effects on the brain before clinical symptoms appear, a better understanding of the normal aging brain process will help distinguish known pathologies' impact on regional brain structure. Furthermore, knowledge of the patterns of brain shrinkage in normal aging could lead to a better understanding of its causes and perhaps to interventions reducing the loss of brain functions. Therefore, this thesis project aims to detect normal and pathological brain aging biomarkers in a non-human primate model, the marmoset monkey (Callithrix Jacchus) which possesses anatomical characteristics more similar to humans than rodents. However, structural changes (e.g., volumes, cortical thickness) that may occur during their adult life may be minimal with respect to the scale of observation. In this context, it is essential to have observation techniques that offer sufficiently high contrast and spatial resolution and allow detailed assessments of the morphometric brain changes associated with aging. However, imaging small brains in a 3T MRI platform dedicated to humans is a challenging task because the spatial resolution and the contrast obtained are insufficient compared to the size of the anatomical structures observed and the scale of the xpected changes with age. This thesis aims to develop image restoration methods for preclinical MR images that will improve the robustness of the segmentation algorithms. Improving the resolution of the images at a constant signal-to-noise ratio will limit the effects of partial volume in voxels located at the border between two structures and allow a better segmentation while increasing the results' reproducibility. This computational imaging step is crucial for a reliable longitudinal voxel-based morphometric analysis and for the identification of anatomical markers of brain aging by following the volume changes in gray matter, white matter and cerebrospinal fluid

Optical System Identification for Passive Electro-Optical Imaging

A statistical inverse-problem approach is presented for jointly estimating camera blur from aliased data of a known calibration target. Specifically, a parametric Maximum Likelihood (ML) PSF estimate is derived for characterizing a camera's optical imperfections through the use of a calibration target in an otherwise loosely controlled environment. The unknown parameters are jointly estimated from data described by a physical forward-imaging model, and this inverse-problem approach allows one to accommodate all of the available sources of information jointly. These sources include knowledge of the forward imaging process, the types and sources of statistical uncertainty, available prior information, and the data itself. The forward model describes a broad class of imaging systems based on a parameterization with a direct mapping between its parameters and physical imaging phenomena. The imaging perspective, ambient light-levels, target-reflectance, detector gain and offset, quantum-efficiency, and read-noise levels are all treated as nuisance parameters. The Cram'{e}r-Rao Bound (CRB) is derived under this joint model, and simulations demonstrate that the proposed estimator achieves near-optimal MSE performance. Finally, the proposed method is applied to experimental data to validate both the fidelity of the forward-models, as well as to establish the utility of the resulting ML estimates for both system identification and subsequent image restoration.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/153395/1/jwleblan_1.pd