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This book introduces the basic fundamentals, models, emulators and analyses of mem-elements in the circuit theory with applications. The book starts reviewing the literature on mem-elements, models and their recent applications. It presents mathematical models, numerical results, circuit simulations, and experimental results for double-loop hysteresis behavior of mem-elements. The authors introduce a generalized memristor model in the fractional-order domain under different input and different designs for emulator-based mem-elements, with circuit and experimental results. The basic concept of memristive-based relaxation-oscillators in the circuit theory is also covered. The reader will moreover find in this book information on memristor-based multi-level digital circuits, memristor-based multi-level multiplier and memcapacitor-based oscillators and synaptic circuits.

Mathematical control systems --- Classical mechanics. Field theory --- Statistical physics --- Electrical engineering --- Applied physical engineering --- Information systems --- ICT (informatie- en communicatietechnieken) --- chaos --- toegepaste wiskunde --- theoretische fysica --- statistiek --- informatiesystemen --- ingenieurswetenschappen --- fysica --- elektrische circuits --- dynamica --- informatietheorie

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Fractional calculus. --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Calculus

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"Fractional-Order Design: Devices, Circuits, and Systems introduces applications from the design perspective so that the reader can learn about, and get ready to, design these applications. The book also includes the different techniques employed to comprehensively and straightforwardly design fractional-order systems/devices. Furthermore, a lot of mathematics is available in the literature for solving the fractional-order calculus for system application. However, a small portion is employed in the design of fractional-order systems. This book introduces the mathematics that has been employed explicitly for fractional-order systems."--

Fractional calculus. --- Electronic circuit design. --- Electronic circuits --- Derivatives and integrals, Fractional --- Differentiation of arbitrary order, Integration and --- Differintegration, Generalized --- Fractional derivatives and integrals --- Generalized calculus --- Generalized differintegration --- Integrals, Fractional derivatives and --- Integration and differentiation of arbitrary order --- Calculus --- Design

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Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation and experimental results. It is primarily meant for researchers from academia and industry, and for those working in areas such as control engineering, electrical engineering, computer science and information technology. This book is ideal for researchers working in the area of both continuous-time and discrete-time dynamics and chaotic systems.--

Fractional calculus.

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The brain is the most complex organ in the human body. It is a fascinating biological machine capable of processing massive amounts of information and performing a wide array of functions. In fact, it is so complex that we estimate that the number of connections between nerve cells (neurons) in the human brain to be about 100 times the number of stars in our neighboring Andromeda galaxy (1 trillion). However, like any other organ in our body, the brain can also be afflicted by various diseases, such as stroke, benign or malignant tumors, vascular, and structural malformations, among others. Many of these conditions require surgery for their treatment, thus it is not surprising that an estimated 13.4 million brain surgeries take place worldwide every year. Surgery is a double-edged sword because as much as it can be beneficial for treating diseases, it can also result in profound and potentially debilitating consequences. This is particularly true when it comes to brain surgery, as different parts of the brain serve specific functions, and if damaged can result in temporary or even permanent loss of function. In fact, it was brain damage in ancient times that provided us with our earliest insights into the brain's functional organization.To cope with this unique challenge, the fields of brain imaging and surgery have greatly evolved by exploiting modern advances in spatial localization, noninvasive imaging, tissue fluorescence, and computer vision. MRI is probably the most versatile noninvasive imaging modality available today, as it can generate images of brain structure in different contrasts, e.g., T1 weighted-images (WIs), which are excellent for evaluating the brain's anatomy, and T2 WIs, which improve detection and differentiation of pathology. MRI can also show brain function with blood-oxygen level dependent (BOLD) functional MRI (fMRI), and structural connections or nerve bundles can be visualized with diffusion MRI (dMRI) fiber tractography (FT), thus providing multimodal and multiscalar maps of the brain. Today it is typical for patients who need brain surgery to undergo presurgical imaging with computed tomography (CT) and/or MRI. In emergency cases, e.g., with acute traumatic contusions, hemorrhages, stroke, and brain herniation, where urgent surgery is needed, CT is typically used. MRI is typically used in elective, non-emergency cases, e.g., with epilepsy, vascular malformations, and neoplasms. An estimated 3.5 million non-emergency brain surgeries worldwide per year could potentially benefit from presurgical brain mapping with fMRI and dMRI. However, their use is typically reserved for a small percent of surgeries. This is because their acquisition and analysis are relatively time consuming and technically demanding, requiring well-trained personnel, highly equipped imaging centers and operation theaters. In addition, fMRI typically requires a cooperative patient to perform a task during the scan, which could be a problem in very young, uncooperative or cognitively impaired patients. The overarching goal of this doctoral thesis was to explore how automation and adoption of recent advances in the field can help make presurgical brain mapping less operator dependent, and less challenging for patients, thus potentially making it more applicable even in the absence of highly trained data analysts. We aimed to extend its applicability by using task-free or resting-state fMRI (rs-fMRI) for functional mapping instead of task-based fMRI (tbfMRI), and we aimed to improve the accuracy of white matter mapping with the use of more advanced dMRI methods. The first aim was to facilitate accurate automated analysis for structural brain images containing pathology like large brain tumors. In chapter 4 we detail the method used to achieve this and report on a proof-of-concept analysis using real data from 10 patients and 10 healthy individuals, and 200 artificial brain images derived from the real sample. The second aim was to define a virtual dissection protocol and associated atlas of 68 white matter tractograms using dMRI FT with constrained spherical deconvolution (CSD), and to study their variability and reproducibility in healthy data. These results are presented in chapter 5. We complemented this with an automated workflow for subject-specific FT that could be used for structurally normal and later on for clinical patients with focal pathology. The third aim was to investigate the benefits of using CSD FT compared to the widely used but relatively inaccurate diffusion tensor imaging (DTI) FT. In chapter 6, the methods outlined in chapters 4 and 5 were applied to data from 22 neurosurgical patients. Invasive brain mapping with direct electrical stimulation (DES) was used as the ground truth to compare the accuracy of DTI and CSD FT. This study showed that CSD resulted in improved sensitivity and accuracy of tractography for the corticospinal tract (CST) and arcuate fasciculus (AF) compared to DTI. The fourth aim was to investigate whether BOLD rs-fMRI could be used in clinical functional brain mapping, which could improve patient tolerability, and make presurgical functional mapping possible even if a task cannot be performed by the patient. In chapter 7, we compared the accuracy of task-based fMRI (tbfMRI), and two types of rs-fMRI, in a group of 16 neurosurgical patients with their DES results as the ground truth. This study showed no significant differences between any of the 3 fMRI methods, suggesting that rs-fMRI can achieve accurate functional mapping in presurgical patients. To conclude, this work showed that it is feasible to account for large focal pathology in automated structural mapping workflows. We presented a new CSD-based atlas of white matter bundles, which was translated to clinical patients, and using these two approaches we showed a clear improvement in white matter mapping with CSD over DTI. Finally, rs-fMRI was shown to be comparable to tbfMRI in terms of accuracy when compared to DES. However, the sample sizes in chapters 6 and 7 were rather limited, and DES data has proven to be rather sparse. Thus, future studies are advised to use larger sample sizes, possibly by pooling data from different sources, and to use denser sampling for ground truth mapping e.g., with electrocorticography (ECoG), or to rely on noninvasive methods e.g., transcranial magnetic stimulation (TMS).