A direct comparison of high-speed methods for the numerical Abel transform

The Abel transform is a mathematical operation that transforms a cylindrically symmetric three-dimensional (3D) object into its two-dimensional (2D) projection. The inverse Abel transform reconstructs the 3D object from the 2D projection. Abel transforms have wide application across numerous fields of science, especially chemical physics, astronomy, and the study of laser-plasma plumes. Consequently, many numerical methods for the Abel transform have been developed, which makes it challenging to select the ideal method for a specific application. In this work eight transform methods have been incorporated into a single, open-source Python software package (PyAbel) to provide a direct comparison of the capabilities, advantages, and relative computational efficiency of each transform method. Most of the tested methods provide similar, high-quality results. However, the computational efficiency varies across several orders of magnitude. By optimizing the algorithms, we find that some transform methods are sufficiently fast to transform 1-megapixel images at more than 100 frames per second on a desktop personal computer. In addition, we demonstrate the transform of gigapixel images.Comment: 9 pages, 5 figure

Energy Density-Flux Correlations in an Unusual Quantum State and in the Vacuum

In this paper we consider the question of the degree to which negative and positive energy are intertwined. We examine in more detail a previously studied quantum state of the massless minimally coupled scalar field, which we call a ``Helfer state''. This is a state in which the energy density can be made arbitrarily negative over an arbitrarily large region of space, but only at one instant in time. In the Helfer state, the negative energy density is accompanied by rapidly time-varying energy fluxes. It is the latter feature which allows the quantum inequalities, bounds which restrict the magnitude and duration of negative energy, to hold for this class of states. An observer who initially passes through the negative energy region will quickly encounter fluxes of positive energy which subsequently enter the region. We examine in detail the correlation between the energy density and flux in the Helfer state in terms of their expectation values. We then study the correlation function between energy density and flux in the Minkowski vacuum state, for a massless minimally coupled scalar field in both two and four dimensions. In this latter analysis we examine correlation functions rather than expectation values. Remarkably, we see qualitatively similar behavior to that in the Helfer state. More specifically, an initial negative energy vacuum fluctuation in some region of space is correlated with a subsequent flux fluctuation of positive energy into the region. We speculate that the mechanism which ensures that the quantum inequalities hold in the Helfer state, as well as in other quantum states associated with negative energy, is, at least in some sense, already ``encoded'' in the fluctuations of the vacuum.Comment: 21 pages, 7 figures; published version with typos corrected and one added referenc

Implementing a Shared Dataspace Language on a Message-Based Multiprocessor

The term shared dataspace refers to the general class of models and languages in which the principal means of communication is a common, content-addressable data structure called a dataspace. This paper reports on progress we have made toward the development of prototype implementation of a shared dataspace language, Swarm, on a hypercube multiprocessor. The paper includes an informal overview of the Swarm language, describes the design organization of a transaction processing system which forms the kernels of a Swam implementation, and explains the algorithms implementing a subset of Swarm embedded in the language C

Epileptic high-frequency network activity in a model of non-lesional temporal lobe epilepsy

High-frequency cortical activity, particularly in the 250–600 Hz (fast ripple) band, has been implicated in playing a crucial role in epileptogenesis and seizure generation. Fast ripples are highly specific for the seizure initiation zone. However, evidence for the association of fast ripples with epileptic foci depends on animal models and human cases with substantial lesions in the form of hippocampal sclerosis, which suggests that neuronal loss may be required for fast ripples. In the present work, we tested whether cell loss is a necessary prerequisite for the generation of fast ripples, using a non-lesional model of temporal lobe epilepsy that lacks hippocampal sclerosis. The model is induced by unilateral intrahippocampal injection of tetanus toxin. Recordings from the hippocampi of freely-moving epileptic rats revealed high-frequency activity (4100 Hz), including fast ripples. High-frequency activity was present both during interictal discharges and seizure onset. Interictal fast ripples proved a significantly more reliable marker of the primary epileptogenic zone than the presence of either interictal discharges or ripples (100–250 Hz). These results suggest that fast ripple activity should be considered for its potential value in the pre-surgical workup of non-lesional temporal lobe epilepsy

Quantum kernels to learn the phases of quantum matter

Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical order parameter explicitly. Here we exploit quantum kernels instead. They are naturally related to the fidelity, and thus it is possible to interpret the learning process with the help of quantum information tools. In particular, we use a support vector machine (with a quantum kernel) to predict and characterize second-order quantum phase transitions. We explain and understand the process of learning when the fidelity per site (rather than the fidelity) is used. The general theory is tested in the Ising chain in transverse field. We show that for small-sized systems, the algorithm gives accurate results, even when trained away from criticality. Besides, for larger sizes we confirm the success of the technique by extracting the correct critical exponent ¿. Finally, we present two algorithms, one based on fidelity and one based on the fidelity per site, to classify the phases of matter in a quantum processor

Development Of The Extraction Method Of Inactive Forms Of Pectin Substances From Fruits To Easy-digestible Active Form During The Obtaining Of Nanofood

The aim of the work is development of a unique method for deep processing of fruits and vegetables with a high content of sparingly soluble pectin substances, which makes it possible to remove pectic substances from inactive form and transform them into an easily digestible active form when obtaining natural semi-finished products and food products in nanosized form. To achieve the aim, a complex effect on the raw material of steam-thermal treatment or cryogenic shock freezing and fine-dispersed grinding is used as an innovation.A new method for obtaining finely dispersed additives and health products from fruits and vegetables with a high content of biologically active substances (BAS) and prebiotic substances is developed, which is based on a complex effect on raw materials of processes of steam-thermal or cryogenic treatment of raw materials and fine-dispersed grinding, which is accompanied by destruction, mechanochemistry, non-enzymatic catalysis. It is found that when these processes are activated, pectic substances are activated, more complete extraction from raw materials (4.5 ... 7.3 times) from a latent form and transformation into a soluble form. The mechanism of these processes is disclosed, recommendations for the creation of recreational nanoproducts are developed. It is shown that, in parallel, non-enzymatic catalysis (up to 70%) of hardly soluble pectic substances in individual monomers takes place, that is, transformation into a soluble, easily digestible form.The increase and seizures of latent forms of biologically active substances in finely dispersed frozen and heat-treated purees from fruit compared with fresh raw materials is established. The increase is respectively 1.5 ... 4.0 times and 1.5 ... 3.0 times. The quality of the obtained new types of fine mashed potatoes exceeds the known analogs for BAS content and technological characteristics. New types of purees are in a nanoscale, easily digestible form.With the use of new types of finely dispersed additives, a wide range of products for health-improving nutrition has been developed with a record content of natural BASs (new types of nano-lipids, nanosorb products, milk-vegetable cocktails, fillings for confectionery and extruded products, curd desserts, bakery products, snacks - falafel, creams, etc.)

Dynamical mechanism of atrial fibrillation: a topological approach

While spiral wave breakup has been implicated in the emergence of atrial fibrillation, its role in maintaining this complex type of cardiac arrhythmia is less clear. We used the Karma model of cardiac excitation to investigate the dynamical mechanisms that sustain atrial fibrillation once it has been established. The results of our numerical study show that spatiotemporally chaotic dynamics in this regime can be described as a dynamical equilibrium between topologically distinct types of transitions that increase or decrease the number of wavelets, in general agreement with the multiple wavelets hypothesis. Surprisingly, we found that the process of continuous excitation waves breaking up into discontinuous pieces plays no role whatsoever in maintaining spatiotemporal complexity. Instead this complexity is maintained as a dynamical balance between wave coalescence -- a unique, previously unidentified, topological process that increases the number of wavelets -- and wave collapse -- a different topological process that decreases their number.Comment: 15 pages, 14 figure

The averaged null energy condition and difference inequalities in quantum field theory

Recently, Larry Ford and Tom Roman have discovered that in a flat cylindrical space, although the stress-energy tensor itself fails to satisfy the averaged null energy condition (ANEC) along the (non-achronal) null geodesics, when the ``Casimir-vacuum" contribution is subtracted from the stress-energy the resulting tensor does satisfy the ANEC inequality. Ford and Roman name this class of constraints on the quantum stress-energy tensor ``difference inequalities." Here I give a proof of the difference inequality for a minimally coupled massless scalar field in an arbitrary two-dimensional spacetime, using the same techniques as those we relied on to prove ANEC in an earlier paper with Robert Wald. I begin with an overview of averaged energy conditions in quantum field theory.Comment: 20 page

Bacterial Peptidoglycan as a Driver of Chronic Brain Inflammation

Peptidoglycan (PGN) is a cell wall component of both Gram-positive and Gram-negative bacteria. Signature fragments of PGN are proinflammatory through engagement of pattern recognition receptors (PRR) on resident tissue cells and circulating leukocytes. Despite its abundance in the gut microbiota, there is limited recognition that PGN could contribute to chronic neuroinflammation. This review highlights current insights into the roles of PGN as a determinant of brain inflammation, notably in multiple sclerosis (MS) and its experimental autoimmune encephalomyelitis (EAE) models. Recent studies demonstrate PGN in blood of healthy adult humans. PGN amplifies autoimmune pathology via activation of innate immune cells. Novel uptake routes through (altered) gut mucosa by myeloid leukocyte subsets promote PGN transport to the brain