Mathematical Modelling of Optical Coherence Tomography

In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high resolution images of the inner structure of biological tissues. Images are obtained by measuring the time delay and the intensity of the backscattered light from the sample considering also the coherence properties of light. The scattering problem is considered for a weakly scattering medium located far enough from the detector. The inverse problem is to reconstruct the susceptibility of the medium given the measurements for different positions of the mirror. Different approaches are addressed depending on the different assumptions made about the optical properties of the sample. This procedure is applied to a full field OCT system and an extension to standard (time and frequency domain) OCT is briefly presented.Comment: 28 pages, 5 figures, book chapte

Formalization of Transform Methods using HOL Light

Transform methods, like Laplace and Fourier, are frequently used for analyzing the dynamical behaviour of engineering and physical systems, based on their transfer function, and frequency response or the solutions of their corresponding differential equations. In this paper, we present an ongoing project, which focuses on the higher-order logic formalization of transform methods using HOL Light theorem prover. In particular, we present the motivation of the formalization, which is followed by the related work. Next, we present the task completed so far while highlighting some of the challenges faced during the formalization. Finally, we present a roadmap to achieve our objectives, the current status and the future goals for this project.Comment: 15 Pages, CICM 201

Fast fluorescence microscopy for imaging the dynamics of embryonic development

Live imaging has gained a pivotal role in developmental biology since it increasingly allows real-time observation of cell behavior in intact organisms. Microscopes that can capture the dynamics of ever-faster biological events, fluorescent markers optimal for in vivo imaging, and, finally, adapted reconstruction and analysis programs to complete data flow all contribute to this success. Focusing on temporal resolution, we discuss how fast imaging can be achieved with minimal prejudice to spatial resolution, photon count, or to reliably and automatically analyze images. In particular, we show how integrated approaches to imaging that combine bright fluorescent probes, fast microscopes, and custom post-processing techniques can address the kinetics of biological systems at multiple scales. Finally, we discuss remaining challenges and opportunities for further advances in this field

Agency, qualia and life: connecting mind and body biologically

Many believe that a suitably programmed computer could act for its own goals and experience feelings. I challenge this view and argue that agency, mental causation and qualia are all founded in the unique, homeostatic nature of living matter. The theory was formulated for coherence with the concept of an agent, neuroscientific data and laws of physics. By this method, I infer that a successful action is homeostatic for its agent and can be caused by a feeling - which does not motivate as a force, but as a control signal. From brain research and the locality principle of physics, I surmise that qualia are a fundamental, biological form of energy generated in specialized neurons. Subjectivity is explained as thermodynamically necessary on the supposition that, by converting action potentials to feelings, the neural cells avert damage from the electrochemical pulses. In exchange for this entropic benefit, phenomenal energy is spent as and where it is produced - which precludes the objective observation of qualia

Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamics

We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition, defines twelve families of admissible models. When these models are coupled to gravity, the flat space classification leads to a complete characterization of the associated sets of gravitating electrostatic spherically symmetric solutions by their central and asymptotic behaviours. We focus on nine of these families, which support asymptotically Schwarzschild-like black hole configurations, for which the thermodynamic analysis is possible and pertinent. In this way, the thermodynamic laws are extended to the sets of black hole solutions of these families, for which the generic behaviours of the relevant state variables are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we find universal scaling laws (which hold and are the same for all the black hole solutions of models belonging to any of the nine families) running the thermodynamic variables with the electric charge and the horizon radius. These scale transformations form a one-parameter multiplicative group, leading to universal "renormalization group"-like first-order differential equations. The beams of characteristics of these equations generate the full set of black hole states associated to any of these gravitating nonlinear electrodynamics...Comment: 51 single column pages, 19 postscript figures, 2 tables, GRG tex style; minor corrections added; final version appearing in General Relativity and Gravitatio

Ribosomal oxygenases are structurally conserved from prokaryotes to humans

2-Oxoglutarate (2OG)-dependent oxygenases have important roles in the regulation of gene expression via demethylation of N-methylated chromatin components1,2 and in the hydroxylation of transcription factors3 and splicing factor proteins4. Recently, 2OG-dependent oxygenases that catalyse hydroxylation of transfer RNA5,6,7 and ribosomal proteins8 have been shown to be important in translation relating to cellular growth, TH17-cell differentiation and translational accuracy9,10,11,12. The finding that ribosomal oxygenases (ROXs) occur in organisms ranging from prokaryotes to humans8 raises questions as to their structural and evolutionary relationships. In Escherichia coli, YcfD catalyses arginine hydroxylation in the ribosomal protein L16; in humans, MYC-induced nuclear antigen (MINA53; also known as MINA) and nucleolar protein 66 (NO66) catalyse histidine hydroxylation in the ribosomal proteins RPL27A and RPL8, respectively. The functional assignments of ROXs open therapeutic possibilities via either ROX inhibition or targeting of differentially modified ribosomes. Despite differences in the residue and protein selectivities of prokaryotic and eukaryotic ROXs, comparison of the crystal structures of E. coli YcfD and Rhodothermus marinus YcfD with those of human MINA53 and NO66 reveals highly conserved folds and novel dimerization modes defining a new structural subfamily of 2OG-dependent oxygenases. ROX structures with and without their substrates support their functional assignments as hydroxylases but not demethylases, and reveal how the subfamily has evolved to catalyse the hydroxylation of different residue side chains of ribosomal proteins. Comparison of ROX crystal structures with those of other JmjC-domain-containing hydroxylases, including the hypoxia-inducible factor asparaginyl hydroxylase FIH and histone Nε-methyl lysine demethylases, identifies branch points in 2OG-dependent oxygenase evolution and distinguishes between JmjC-containing hydroxylases and demethylases catalysing modifications of translational and transcriptional machinery. The structures reveal that new protein hydroxylation activities can evolve by changing the coordination position from which the iron-bound substrate-oxidizing species reacts. This coordination flexibility has probably contributed to the evolution of the wide range of reactions catalysed by oxygenases

Sleep Enforces the Temporal Order in Memory

BACKGROUND: Temporal sequence represents the main principle underlying episodic memory. The storage of temporal sequence information is thought to involve hippocampus-dependent memory systems, preserving temporal structure possibly via chaining of sequence elements in heteroassociative networks. Converging evidence indicates that sleep enhances the consolidation of recently acquired representations in the hippocampus-dependent declarative memory system. Yet, it is unknown if this consolidation process comprises strengthening of the temporal sequence structure of the representation as well, or is restricted to sequence elements independent of their temporal order. To address this issue we tested the influence of sleep on the strength of forward and backward associations in word-triplets. METHODOLOGY/PRINCIPAL FINDINGS: Subjects learned a list of 32 triplets of unrelated words, presented successively (A-B-C) in the center of a screen, and either slept normally or stayed awake in the subsequent night. After two days, retrieval was assessed for the triplets sequentially either in a forward direction (cueing with A and B and asking for B and C, respectively) or in a backward direction (cueing with C and B and asking for B and A, respectively). Memory was better for forward than backward associations (p<0.01). Sleep did not affect backward associations, but enhanced forward associations, specifically for the first (AB) transitions (p<0.01), which were generally more difficult to retrieve than the second transitions. CONCLUSIONS/SIGNIFICANCE: Our data demonstrate that consolidation during sleep strengthens the original temporal sequence structure in memory, presumably as a result of a replay of new representations during sleep in forward direction. Our finding suggests that the temporally directed replay of memory during sleep, apart from strengthening those traces, could be the key mechanism that explains how temporal order is integrated and maintained in the trace of an episodic memory

A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Potential climatic transitions with profound impact on Europe

We discuss potential transitions of six climatic subsystems with large-scale impact on Europe, sometimes denoted as tipping elements. These are the ice sheets on Greenland and West Antarctica, the Atlantic thermohaline circulation, Arctic sea ice, Alpine glaciers and northern hemisphere stratospheric ozone. Each system is represented by co-authors actively publishing in the corresponding field. For each subsystem we summarize the mechanism of a potential transition in a warmer climate along with its impact on Europe and assess the likelihood for such a transition based on published scientific literature. As a summary, the ‘tipping’ potential for each system is provided as a function of global mean temperature increase which required some subjective interpretation of scientific facts by the authors and should be considered as a snapshot of our current understanding. <br/