Separable time-causal and time-recursive spatio-temporal receptive fields

We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, obtained by a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently truncated exponential filters coupled in cascade over the temporal domain. Compared to previous spatio-temporal scale-space formulations in terms of non-enhancement of local extrema or scale invariance, these receptive fields are based on different scale-space axiomatics over time by ensuring non-creation of new local extrema or zero-crossings with increasing temporal scale. Specifically, extensions are presented about parameterizing the intermediate temporal scale levels, analysing the resulting temporal dynamics and transferring the theory to a discrete implementation in terms of recursive filters over time.Comment: 12 pages, 2 figures, 2 tables. arXiv admin note: substantial text overlap with arXiv:1404.203

Time-causal and time-recursive spatio-temporal receptive fields

We present an improved model and theory for time-causal and time-recursive spatio-temporal receptive fields, based on a combination of Gaussian receptive fields over the spatial domain and first-order integrators or equivalently truncated exponential filters coupled in cascade over the temporal domain. Compared to previous spatio-temporal scale-space formulations in terms of non-enhancement of local extrema or scale invariance, these receptive fields are based on different scale-space axiomatics over time by ensuring non-creation of new local extrema or zero-crossings with increasing temporal scale. Specifically, extensions are presented about (i) parameterizing the intermediate temporal scale levels, (ii) analysing the resulting temporal dynamics, (iii) transferring the theory to a discrete implementation, (iv) computing scale-normalized spatio-temporal derivative expressions for spatio-temporal feature detection and (v) computational modelling of receptive fields in the lateral geniculate nucleus (LGN) and the primary visual cortex (V1) in biological vision. We show that by distributing the intermediate temporal scale levels according to a logarithmic distribution, we obtain much faster temporal response properties (shorter temporal delays) compared to a uniform distribution. Specifically, these kernels converge very rapidly to a limit kernel possessing true self-similar scale-invariant properties over temporal scales, thereby allowing for true scale invariance over variations in the temporal scale, although the underlying temporal scale-space representation is based on a discretized temporal scale parameter. We show how scale-normalized temporal derivatives can be defined for these time-causal scale-space kernels and how the composed theory can be used for computing basic types of scale-normalized spatio-temporal derivative expressions in a computationally efficient manner.Comment: 39 pages, 12 figures, 5 tables in Journal of Mathematical Imaging and Vision, published online Dec 201

Optimal free parameters in orthonormal approximations

We consider orthonormal expansions where the basis functions are governed by some free parameters. If the basis functions adhere to a certain differential or difference equation, then an expression can be given for a specific enforced convergence rate criterion as well as an upper bound for the quadratic truncation error. This expression is a function of the free parameters and some simple signal measurements. Restrictions on the differential or difference equation that make this possible are given. Minimization of either the upper bound or the enforced convergence criterion as a function of the free parameters yields the same optimal parameters, which are of a simple form. This method is applied to several continuous-time and discrete-time orthonormal expansions that are all related to classical orthogonal polynomial

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Measures of sympathetic and parasympathetic autonomic outflow from heartbeat dynamics

Reliable and effective noninvasive measures of sympathetic and parasympathetic peripheral outflow are of crucial importance in cardiovascular physiology. Although many techniques have been proposed to take up this long-lasting challenge, none has proposed a satisfying discrimination of the dynamics of the two separate branches. Spectral analysis of heart rate variability is the most currently used technique for such assessment. Despite its widespread use, it has been demonstrated that the subdivision in the low-frequency (LF) and high-frequency (HF) bands does not fully reflect separate influences of the sympathetic and parasympathetic branches, respectively, mainly due to their simultaneous action in the LF. Two novel heartbeat-derived autonomic measures, the sympathetic activity index (SAI) and parasympathetic activity index (PAI), are proposed to separately assess the time-varying autonomic nervous system synergic functions. Their efficacy is validated in landmark autonomic maneuvers generally employed in clinical settings. The novel measures move beyond the classical frequency domain paradigm through identification of a set of coefficients associated with a proper combination of Laguerre base functions. The resulting measures were compared with the traditional LF and HF power. A total of 236 ECG recordings were analyzed for validation, including autonomic outflow changes elicited by procedures of different nature and temporal variation, such as postural changes, lower body negative pressure, and handgrip tests. The proposed SAI-PAI measures consistently outperform traditional frequency-domain indexes in tracking expected instantaneous autonomic variations, both vagal and sympathetic, and may aid clinical decision making, showing reduced intersubject variability and physiologically plausible dynamics

Fast fluorescence lifetime imaging and sensing via deep learning

Error on title page – year of award is 2023.Fluorescence lifetime imaging microscopy (FLIM) has become a valuable tool in diverse disciplines. This thesis presents deep learning (DL) approaches to addressing two major challenges in FLIM: slow and complex data analysis and the high photon budget for precisely quantifying the fluorescence lifetimes. DL's ability to extract high-dimensional features from data has revolutionized optical and biomedical imaging analysis. This thesis contributes several novel DL FLIM algorithms that significantly expand FLIM's scope. Firstly, a hardware-friendly pixel-wise DL algorithm is proposed for fast FLIM data analysis. The algorithm has a simple architecture yet can effectively resolve multi-exponential decay models. The calculation speed and accuracy outperform conventional methods significantly. Secondly, a DL algorithm is proposed to improve FLIM image spatial resolution, obtaining high-resolution (HR) fluorescence lifetime images from low-resolution (LR) images. A computational framework is developed to generate large-scale semi-synthetic FLIM datasets to address the challenge of the lack of sufficient high-quality FLIM datasets. This algorithm offers a practical approach to obtaining HR FLIM images quickly for FLIM systems. Thirdly, a DL algorithm is developed to analyze FLIM images with only a few photons per pixel, named Few-Photon Fluorescence Lifetime Imaging (FPFLI) algorithm. FPFLI uses spatial correlation and intensity information to robustly estimate the fluorescence lifetime images, pushing this photon budget to a record-low level of only a few photons per pixel. Finally, a time-resolved flow cytometry (TRFC) system is developed by integrating an advanced CMOS single-photon avalanche diode (SPAD) array and a DL processor. The SPAD array, using a parallel light detection scheme, shows an excellent photon-counting throughput. A quantized convolutional neural network (QCNN) algorithm is designed and implemented on a field-programmable gate array as an embedded processor. The processor resolves fluorescence lifetimes against disturbing noise, showing unparalleled high accuracy, fast analysis speed, and low power consumption.Fluorescence lifetime imaging microscopy (FLIM) has become a valuable tool in diverse disciplines. This thesis presents deep learning (DL) approaches to addressing two major challenges in FLIM: slow and complex data analysis and the high photon budget for precisely quantifying the fluorescence lifetimes. DL's ability to extract high-dimensional features from data has revolutionized optical and biomedical imaging analysis. This thesis contributes several novel DL FLIM algorithms that significantly expand FLIM's scope. Firstly, a hardware-friendly pixel-wise DL algorithm is proposed for fast FLIM data analysis. The algorithm has a simple architecture yet can effectively resolve multi-exponential decay models. The calculation speed and accuracy outperform conventional methods significantly. Secondly, a DL algorithm is proposed to improve FLIM image spatial resolution, obtaining high-resolution (HR) fluorescence lifetime images from low-resolution (LR) images. A computational framework is developed to generate large-scale semi-synthetic FLIM datasets to address the challenge of the lack of sufficient high-quality FLIM datasets. This algorithm offers a practical approach to obtaining HR FLIM images quickly for FLIM systems. Thirdly, a DL algorithm is developed to analyze FLIM images with only a few photons per pixel, named Few-Photon Fluorescence Lifetime Imaging (FPFLI) algorithm. FPFLI uses spatial correlation and intensity information to robustly estimate the fluorescence lifetime images, pushing this photon budget to a record-low level of only a few photons per pixel. Finally, a time-resolved flow cytometry (TRFC) system is developed by integrating an advanced CMOS single-photon avalanche diode (SPAD) array and a DL processor. The SPAD array, using a parallel light detection scheme, shows an excellent photon-counting throughput. A quantized convolutional neural network (QCNN) algorithm is designed and implemented on a field-programmable gate array as an embedded processor. The processor resolves fluorescence lifetimes against disturbing noise, showing unparalleled high accuracy, fast analysis speed, and low power consumption

Advances in modeling and characterization of human neuromagnetic oscillations

Intracranial electrophysiological measurements as well as electromagnetic recordings from the scalp have shown that oscillatory activity in the human brain plays an important role in sensory and cognitive processing. Communication between distant brain regions seems to be mediated by oscillatory coherence and synchrony. Our brain is both reactive and reflexive: it reacts to changes in the external environment, but it is also influenced by its past and present internal state. On the one hand, task-related or induced modulations of oscillatory activity provide an important marker for cortical excitability and information processing of the reactive brain. On the other hand, spontaneous oscillatory dynamics subserves information processing of the reflexive brain. In this thesis, methods were developed to model and characterize task-related oscillatory changes, as well as spontaneous oscillatory activity measured using magnetoencephalography (MEG). In Publication I, we developed a predictive model to capture the suppression-rebound reactivity of the ~20 Hz mu rhythm originating in the sensorimotor cortex and applied this model to locate the cortical generators of the rhythm from independent measurements. In Publications II and III, we developed temporal and spatial variants of a data-driven method to characterize spatial, temporal, and spectral aspects of spontaneous MEG oscillations. Analysis of complex-valued Fourier coefficients identified well-known rhythms, such as the parieto-occipital ~10-Hz and the rolandic ~20-Hz rhythms consistently across subjects. In Publication IV, we applied independent component analysis to time-frequency representations of cortical current estimates computed from simulated as well as resting-state and naturalistic stimulation data. Group-level analysis of Fourier envelopes also identified the ~20-Hz bilateral sensorimotor network, a subset of the default-mode network at ~8 and ~15 Hz, and lateralized temporal-lobe sources at ~8 Hz. The methods developed here represent important advances in the modeling and characterization of the brain's oscillatory activity measured using non-invasive electrophysiological methods in healthy humans

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar

The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference

Bayesian Variational Regularisation for Dark Matter Reconstruction with Uncertainty Quantification

Despite the great wealth of cosmological knowledge accumulated since the early 20th century, the nature of dark-matter, which accounts for ~85% of the matter content of the universe, remains illusive. Unfortunately, though dark-matter is scientifically interesting, with implications for our fundamental understanding of the Universe, it cannot be directly observed. Instead, dark-matter may be inferred from e.g. the optical distortion (lensing) of distant galaxies which, at linear order, manifests as a perturbation to the apparent magnitude (convergence) and ellipticity (shearing). Ensemble observations of the shear are collected and leveraged to construct estimates of the convergence, which can directly be related to the universal dark-matter distribution. Imminent stage IV surveys are forecast to accrue an unprecedented quantity of cosmological information; a discriminative partition of which is accessible through the convergence, and is disproportionately concentrated at high angular resolutions, where the echoes of cosmological evolution under gravity are most apparent. Capitalising on advances in probability concentration theory, this thesis merges the paradigms of Bayesian inference and optimisation to develop hybrid convergence inference techniques which are scalable, statistically principled, and operate over the Euclidean plane, celestial sphere, and 3-dimensional ball. Such techniques can quantify the plausibility of inferences at one-millionth the computational overhead of competing sampling methods. These Bayesian techniques are applied to the hotly debated Abell-520 merging cluster, concluding that observational catalogues contain insufficient information to determine the existence of dark-matter self-interactions. Further, these techniques were applied to all public lensing catalogues, recovering the then largest global dark-matter mass-map. The primary methodological contributions of this thesis depend only on posterior log-concavity, paving the way towards a, potentially revolutionary, complete hybridisation with artificial intelligence techniques. These next-generation techniques are the first to operate over the full 3-dimensional ball, laying the foundations for statistically principled universal dark-matter cartography, and the cosmological insights such advances may provide

Nonlinear Systems

The editors of this book have incorporated contributions from a diverse group of leading researchers in the field of nonlinear systems. To enrich the scope of the content, this book contains a valuable selection of works on fractional differential equations.The book aims to provide an overview of the current knowledge on nonlinear systems and some aspects of fractional calculus. The main subject areas are divided into two theoretical and applied sections. Nonlinear systems are useful for researchers in mathematics, applied mathematics, and physics, as well as graduate students who are studying these systems with reference to their theory and application. This book is also an ideal complement to the specific literature on engineering, biology, health science, and other applied science areas. The opportunity given by IntechOpen to offer this book under the open access system contributes to disseminating the field of nonlinear systems to a wide range of researchers