Singular Structures Research Articles

Reference-less complex wavefields characterization with a high-resolution wavefront sensor

Wavefront sensing is a widely used non-interferometric, single-shot, and quantitative technique providing the spatial-phase of a beam. The phase is obtained by integrating the measured wavefront gradient. Complex and random wavefields intrinsically contain a high density of singular phase structures (optical vortices) associated with non-conservative gradients making this integration step especially delicate. Here, using a high-resolution wavefront sensor, we demonstrate experimentally a systematic approach for achieving the complete and quantitative reconstruction of complex wavefronts. Based on Stokes' theorem, we propose an image segmentation algorithm to provide an accurate determination of the charge and location of optical vortices. This technique is expected to benefit to several fields requiring complex media characterization.

Experimental Evaluation of Dynamic Rock Scour Protection in Morphodynamic Environments for Offshore Wind Jackets

Bottom-fixed offshore wind turbines are generally built on continental-shelf sections that are morphodynamically active due to their shallow depths and severe wave and current conditions. Such sites are commonly protected against scour to prevent the loss of structural stability. Scour protection can be designed using static or dynamic solutions. Designing dynamic protection requires experimental validation, especially for singular or unconventional structures. This article presents an experimental method for the laboratory analysis of scour protection for jacket foundations placed at morphodynamically active sites. The test campaign was conducted within the project East Anglia ONE (UK) as part of the asset owner studies and aimed to evaluate operation and maintenance (O&M) aspects, independent of the contractor’s original design assessments. The physical experiments explored morphodynamic changes on the sea bottom and their importance to scour protection, as well as the importance of the history of the wave loads to the deformation of the rock scour protection. This was explored by repeating different cumulative tests, including a succession of randomly ordered sea states (Return Period (RP) 1-10-20-50 years). The experimental results show that the deformation of the rock sour protection was the greatest when the most energetic sea states occurred at the beginning of the experimental test campaign. The maximum deformation was at 5D50 when the first test was also the most energetic, while it was at 3D50 when not included as the first test, yielding a 40% reduction in the scour protection deformation.

Projection-Based cascaded U-Net model for MR image reconstruction

Background and ObjectiveBackground and Objective: Recent studies in deep learning reveal that the U-Net stands out among the diverse set of deep models as an effective network structure, especially for imaging inverse problems. Initially, the U-Net model was developed to solve segmentation problems for biomedical images while using an annotated dataset. In this paper, we will study a novel application of the U-Net structure for the important inverse problem of MRI reconstruction. Deep networks are particularly efficient for the speed-up of the MR image reconstruction process by decreasing the data acquisition time, and they can significantly reduce the aliasing artifacts caused by the undersampling in the k-space. Our aim is to develop a novel and efficient cascaded U-Net framework for reconstructing MR images from undersampled k-space data. The new framework should have improved reconstruction performance when compared to competing methodologies. MethodsIn this paper, a novel cascaded framework utilizing the U-Net as a sub-block is being proposed. The introduced U-Net cascade structure is applied to the magnetic resonance image reconstruction problem. The connection between the cascaded U-Nets is realized in the form of a recently developed projection-based updated data consistency layer. The novel structure is implemented in the PyTorch environment, which is one of the standards for deep learning implementations. The recently created fastMRI dataset which forms an important benchmark for MRI reconstruction is used for training and testing purposes. ResultsWe present simulation results comparing the novel method with a variety of competitive deep networks. The new cascaded U-Net structures PSNR performance stands on average 1.28 dB higher than the baseline U-Net. The improvement, when compared to the standard CNN, is on average 3.32 dB. ConclusionsThe proposed cascaded U-Net configuration results in an improved reconstruction performance when compared to the CNN, the cascaded CNN, and also the singular U-Net structures, where the singular U-Net forms the baseline reconstruction method from the fastMRI package. The use of the projection-based updated data consistency layer also leads to improved quantitative (including SSIM, PSNR, and NMSE results) and qualitative results when compared to the use of the conventional data consistency layer.

Hydrodynamic decay of decorated quantum vortex rings

The decay of quantum vortex rings in counterflow regimes, visualized in Helium II with the help of solid hydrogen particles trapped to their cores, has been a puzzling issue within the usual description of superfluid vortex dynamics, grounded on the hypothesis that a vortex filament is, effectively, an extended massless object subject to a canceling superposition of Magnus and mutual friction forces. We discuss, from a general energy-budget point of view, a phenomenological solution of this problem, which relies on viscous and quantum dissipation mechanisms, the later associated to the backreaction of vortex singular structures on the surrounding two-component fluid mixture.

On the Breakdown of Regular Solutions with Finite Energy for 3D Degenerate Compressible Navier–Stokes Equations

In this paper, the three-dimensional (3D) isentropic compressible Navier–Stokes equations with degenerate viscosities (ICND) is considered in both the whole space and the periodic domain. First, for the corresponding Cauchy problem, when shear and bulk viscosity coefficients are both given as a constant multiple of the density’s power ( $$\rho ^\delta $$ with $$0<\delta <1$$ ), based on some elaborate analysis of this system’s intrinsic singular structures, we show that the $$L^\infty $$ norm of the deformation tensor D(u) and the $$L^6$$ norm of $$\nabla \rho ^{\delta -1}$$ control the possible breakdown of regular solutions with far field vacuum. This conclusion means that if a solution with far field vacuum of the ICND system is initially regular and loses its regularity at some later time, then the formation of singularity must be caused by losing the bound of D(u) or $$\nabla \rho ^{\delta -1}$$ as the critical time approaches. Second, when $$0<\delta \le 1$$ , under the additional assumption that the shear and second viscosities (respectively $$\mu (\rho )$$ and $$\lambda (\rho )$$ ) satisfy the BD relation $$\lambda (\rho )=2(\mu '(\rho )\rho -\mu (\rho ))$$ , if we consider the corresponding problem in some periodic domain and the initial density is away from the vacuum, it can be proved that the possible breakdown of classical solutions can be controlled only by the $$L^\infty $$ norm of D(u). It is worth pointing out that, except the conclusions mentioned above, another purpose of the current paper is to show how to understand the intrinsic singular structures of the fluid system considered now, and then how to develop the corresponding nonlinear energy estimates in the specially designed energy space with singular weights for the unique regular solution with finite energy.

The core structure of a laboratory-made dust devil-like vortex and its condensed matter analogs

We consider the defect core structures of topological line defects characterized by a winding number k=1. In the experimental part of the work, we illustrate a simple and robust method of creating a laboratory-scale air-flow vortex, simulating a dust devil. We stabilized an escaped-type non-singular vortex-type configuration in the small-scale confined convective system with a converging inflow with imposed shear but lack of horizontal vorticity. Furthermore, we show that analogous defect core structures could be stabilized in simple condensed matter systems. In particular, different liquid crystalline phases represent an ideal testing ground to study different topological defects due to their unique combination of fluidity, softness, optical anisotropy, and rich diversity of defect configurations. In the theoretical and numerical study, we focused on the most common static k=1 line defect core structures in vector and nematic ordering. Namely, these two cases exhibit two different symmetries and can consequently exhibit qualitatively different defect core structures. We discuss conditions stabilizing either singular or non-singular core structures.

Mind the Gap: Mitochondria and the Endoplasmic Reticulum in Neurodegenerative Diseases.

The way organelles are viewed by cell biologists is quickly changing. For many years, these cellular entities were thought to be unique and singular structures that performed specific roles. However, in recent decades, researchers have discovered that organelles are dynamic and form physical contacts. In addition, organelle interactions modulate several vital biological functions, and the dysregulation of these contacts is involved in cell dysfunction and different pathologies, including neurodegenerative diseases. Mitochondria–ER contact sites (MERCS) are among the most extensively studied and understood juxtapositioned interorganelle structures. In this review, we summarise the major biological and ultrastructural dysfunctions of MERCS in neurodegeneration, with a particular focus on Alzheimer’s disease as well as Parkinson’s disease, amyotrophic lateral sclerosis and frontotemporal dementia. We also propose an updated version of the MERCS hypothesis in Alzheimer’s disease based on new findings. Finally, we discuss the possibility of MERCS being used as possible drug targets to halt cell death and neurodegeneration.

Simulated generation of noncanonical polarization singularities based on power-exponent-phase vortices

In this article, we proposed the simulated noncanonical polarization singularities structures using light beams carrying power-exponent-phase vortex. The distribution patterns of the polarization states of such structures exhibit differently from the canonical ones. Our work enriched polarized singular optical field structures, and broadened understanding of such light fields.

Reproducible Orientation Relationships Developed from Phase Transformations—Role of Interfaces

The orientation relationship (OR) between phases related by a phase transformation is often reproducible. This study interprets and predicts the reproducible ORs with a two-stage approach. The initial OR formed at the nucleation stage tends to allow a periodic structure of a preferred state to form in the interface. A matching correspondence of either a one-to-one or n-to-m nature can be specified in the periodic structure. An initial OR will become the final reproducible OR if there is no misfit. Otherwise, a reproducible OR developed at the growth stage tends to permit a singular dislocation structure to form in an interface where the preferred state must be sustained locally. The actual change in the OR is subject to the given material system and the phase-transformation condition. Various singular dislocation structures and their constraints on the ORs are analyzed, with thermodynamics and kinetics applied conceptually. The resulting ORs can be specified by following one or more Δg parallelism rules. A set of workable steps is provided to facilitate the interpretation of observed reproducible ORs. Some unsolved problems are identified, which call for further studies that can quantitatively combine the thermodynamics, kinetics and crystallography of phase transformations.

On nodal and generalized singular structures of Laplacian eigenfunctions and applications to inverse scattering problems

In this paper, we present some novel and intriguing findings on the geometric structures of Laplacian eigenfunctions and their deep relationship to the quantitative behaviours of the eigenfunctions in two dimensions. We introduce a new notion of generalized singular lines of the Laplacian eigenfunctions, and carefully study these singular lines and the nodal lines. The studies reveal that the intersecting angle between two of those lines is closely related to the vanishing order of the eigenfunction at the intersecting point. We establish an accurate and comprehensive quantitative characterisation of the relationship. Roughly speaking, the vanishing order is generically infinite if the intersecting angle is irrational, and the vanishing order is finite if the intersecting angle is rational. In fact, in the latter case, the vanishing order is the degree of the rationality. The theoretical findings are original and of significant interest in spectral theory. Moreover, they are applied directly to some physical problems of great importance, including the inverse obstacle scattering problem and the inverse diffraction grating problem. It is shown in a certain polygonal setup that one can recover the support of the unknown scatterer as well as the surface impedance parameter by finitely many far-field patterns. Indeed, at most two far-field patterns are sufficient for some important applications. Unique identifiability by finitely many far-field patterns remains to be a highly challenging fundamental mathematical problem in the inverse scattering theory.

Halogenated derivatives of cytidine: Structural analysis and binding affinity

Cytidine is a well-known inhibitor of DNA methyltransferase (MTN) enzyme for preventing cancer cells growth. Based on therapeutic benefits, it could be considered as a “lead compound” to be optimized through structural modification for arising better binding affinity in this case. Halogenated derivatives of cytidine were investigated in this work to examine structural and biological features employing in silico approach. To this aim, geometries of the original cytidine and four of its halogenated derivatives were minimized to prepare ligands for interacting with MTN enzyme target in molecular docking simulations. The results for singular ligand structures introduced I-cytidine as an optimized lead compound for contributing to proper interactions with MTN enzyme; the trend was confirmed by molecular docking simulations. As a final remark, I-cytidine could be considered as better ligand for complexation with the MTN enzyme in comparison with the original cytidine.

Relaxation by nonlinear diffusion enhancement in a two-dimensional cross-diffusion model for urban crime propagation

We consider a class of macroscopic models for the spatio-temporal evolution of urban crime, as originally going back to Ref. 29 [M. B. Short, M. R. D’Orsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior, Math. Models Methods Appl. Sci. 18 (2008) 1249–1267]. The focus here is on the question of how far a certain porous medium enhancement in the random diffusion of criminal agents may exert visible relaxation effects. It is shown that sufficient regularity of the non-negative source terms in the system and a sufficiently strong nonlinear enhancement ensure that a corresponding Neumann-type initial–boundary value problem, posed in a smoothly bounded planar convex domain, admits locally bounded solutions for a wide class of arbitrary initial data. Furthermore, this solution is globally bounded under mild additional conditions on the source terms. These results are supplemented by numerical evidence which illustrates smoothing effects in solutions with sharply structured initial data in the presence of such porous medium-type diffusion and support the existence of singular structures in the linear diffusion case, which is the type of diffusion proposed in Ref. 29.

Structure of the putative long tail fiber receptor-binding tip of a novel temperate bacteriophage from the Antarctic bacterium Bizionia argentinensis JUB59

Tailed bacteriophages are one of the most widespread biological entities on Earth. Their singular structures, such as spikes or fibers are of special interest given their potential use in a wide range of biotechnological applications. In particular, the long fibers present at the termini of the T4 phage tail have been studied in detail and are important for host recognition and adsorption. Although significant progress has been made in elucidating structural mechanisms of model phages, the high-resolution structural description of the vast population of marine phages is still unexplored. In this context, we present here the crystal structure of C24, a putative receptor-binding tip-like protein from Bizionia argentinensis JUB59, a psychrotolerant bacterium isolated from the marine surface waters of Potter Cove, Antarctica. The structure resembles the receptor-binding tip from the bacteriophage T4 long tail fiber yet showing marked differences in its domain organization, size, sequence identity and metal binding nature. We confirmed the viral origin of C24 by induction experiments using mitomycin C. Our results reveal the presence of a novel uncharacterized prophage in the genome of B. argentinensis JUB59, whose morphology is compatible with the order Caudovirales and that carries the nucleotide sequence of C24 in its genome. This work provides valuable information to expand our current knowledge on the viral machinery prevalent in the oceans.

The Lord of the NanoRings: Cyclodextrins and the battle against SARS-CoV-2.

A handful of singular structures and laws can be observed in nature. They are not always evident but, once discovered, it seems obvious how to take advantage of them. In chemistry, the discovery of reproducible patterns stimulates the imagination to develop new functional materials and technological or medical applications. Two clear examples are helical structures at different levels in biological polymers as well as ring and spherical structures of different size and composition. Rings are intuitively observed as holes able to thread elongated structures. A large number of real and fictional stories have rings as inanimate protagonists. The design, development or just discovering of a special ring has often been taken as a symbol of power or success. Several examples are the Piscatory Ring wore by the Pope of the Catholic Church, the NBA Championship ring and the One Ring created by the Dark Lord Sauron in the epic story The Lord of the Rings. In this work, we reveal the power of another extremely powerful kind of rings to fight against the pandemic which is currently affecting the whole world. These rings are as small as ~1nm of diameter and so versatile that they are able to participate in the attack of viruses, and specifically SARS-CoV-2, in a large range of different ways. This includes the encapsulation and transport of specific drugs, as adjuvants to stabilize proteins, vaccines or other molecules involved in the infection, as cholesterol trappers to destabilize the virus envelope, as carriers for RNA therapies, as direct antiviral drugs and even to rescue blood coagulation upon heparin treatment. "One ring to rule them all. One ring to find them. One ring to bring them all and in the darkness bind them." J. R. R. Tolkien.

Open Loop Amplitudes and Causality to All Orders and Powers from the Loop-Tree Duality.

Multiloop scattering amplitudes describing the quantum fluctuations at high-energy scattering processes are the main bottleneck in perturbative quantum field theory. The loop-tree duality is a novel method aimed at overcoming this bottleneck by opening the loop amplitudes into trees and combining them at integrand level with the real-emission matrix elements. In this Letter, we generalize the loop-tree duality to all orders in the perturbative expansion by using the complex Lorentz-covariant prescription of the original one-loop formulation. We introduce a series of mutiloop topologies with arbitrary internal configurations and derive very compact and factorizable expressions of their open-to-trees representation in the loop-tree duality formalism. Furthermore, these expressions are entirely independent at integrand level of the initial assignments of momentum flows in the Feynman representation and remarkably free of noncausal singularities. These properties, that we conjecture to hold to other topologies at all orders, provide integrand representations of scattering amplitudes that exhibit manifest causal singular structures and better numerical stability than in other representations.

Multivariate analysis of covariance with potentially singular covariance matrices and non-normal responses

In applied research, it is often sensible to account for one or several covariates when testing for differences between multivariate means of several groups. However, the “classical” parametric multivariate analysis of covariance (MANCOVA) tests (e.g., Wilks’ Lambda) are based on quite restrictive assumptions (homoscedasticity and normality of the errors), which might be difficult to justify. Furthermore, existing potential remedies (e.g., heteroskedasticity-robust approaches) become inappropriate in cases where the covariance matrices are singular or close to singular. Nevertheless, such scenarios are frequently encountered in the life sciences and other fields, when, for example, in the context of standardized assessments, a summary performance measure as well as its corresponding subscales are analyzed. Moreover, computational issues may also lead to singular covariance structures. In the present manuscript, we consider a general MANCOVA model, allowing for potentially heteroskedastic and even singular covariance matrices as well as non-normal errors. We combine heteroskedasticity-consistent covariance matrix estimation methods with our proposed modified MANCOVA ANOVA-type statistic (MANCATS) and apply two different bootstrap approaches. We provide the proofs of the asymptotic validity of the respective testing procedures as well as the results from an extensive simulation study, which indicate that especially the parametric bootstrap version of the MANCATS outperforms its competitors in most small-sample scenarios, both in terms of type I error rates and power. These considerations are further illustrated and substantiated by examining real-life data from standardized achievement tests. Yet, for large sample sizes, Wald-type approaches are an attractive alternative option. Moreover, the choice between Wald-type and MANCATS-based tests might depend on the particular setting (e.g., the covariance structure, or the alternative under consideration).

A boundary element-based automatic domain partitioning approach for semi-structured quad mesh generation

In this paper, a boundary element-based approach is proposed for partitioning a planar domain automatically into a set of 4-sided regions, which is suitable for semi-structured quad mesh generation. The basic idea is to generate a smooth cross-field via solving PDEs with the boundary element method and then partition the input domain by extracting singular structures of the cross-field. Firstly, a cross is configured at each boundary vertex of the input domain. Then, two Laplacian equations are selected as the governing equation to smoothly propagate the crosses defined on the boundary into the interior of the domain. To obtain an accurate cross-field, the boundary element method is used to solve the governing equations. Then the singular vertices are identified by analyzing the structure of the cross-field, and the streamlines emanating from these points are traced and simplified as segmentation curves to partition the domain. Finally, to demonstrate the efficiency and effectiveness of the proposed approach, some quad mesh generation examples and comparison with previous approaches are presented.

Adaptively weighted nonlocal means and TV minimization for speckle reduction in SAR images

Speckle noise reduction is an important issue in synthetic aperture radar (SAR) imaging. Because SAR images are distinct in being complex valued and susceptible to corruption owing to multiplicative fluctuations, specialized methods for speckle reduction are needed. Techniques based on nonlocal means perform denoising by exploiting the natural redundancy of patterns within an image. They calculate a weighted average of pixels whose neighborhoods are close to one another, where this significantly reduces noise while preserving most image content. While this method performs well on flat areas and textures, its results are excessively smooth in low-contrast areas, and leave residual noise around edges and singular structures. Another variational denoising method uses total variation (TV) minimization to restore regular images but is prone to excessively smooth textures, the staircasing effect, and contrast losses. Our proposed model is intended for the logarithmic domain of SAR data, and combines the above two methods by minimizing an adaptive TV using a nonlocal data fidelity term. In the variational functionals developed here, weighted parameters of nonlocal regularization are adaptively tuned based on local heterogeneity information and noise in the images. A fast iterative shrinkage/thresholding algorithm (FISTA) is then used to solve the optimization problem. The results of experiments on real SAR images verify the effectiveness of the proposed method in terms of speckle reduction.

Regional economic resilience of resource‐based cities and influential factors during economic crises in China

AbstractResource‐based cities (RBCs) whose economies depend primarily on exploiting and processing natural resources usually have rigid, singular, and low‐end industrial structures, which often cripples their ability to cope with external disturbances such as international resource price fluctuations and economic downturns. This paper quantitatively analyzes the economic resilience of RBCs in China in terms of resistance and recoverability during the Asian financial crisis and the global financial crisis. Furthermore, it identifies the main factors affecting resilience. There are four main findings: First, RBCs were quickly and negatively impacted by the Asian financial crisis, which suggests that economic resistance was generally low during this period. In the recovery period, while the rate of recovery was slow at the beginning, economic recoverability improved after 2002. Economic resistance and recoverability were found to have a strong negative correlation. Second, at the beginning of the global financial crisis, the economic resistance of RBCs was generally high. However, after 2012, the number of cities that were severely affected by the economic crisis increased rapidly. Third, economic resistance varied across different types of RBCs. Coal‐based and forestry‐based cities had lower economic resistance, while oil &amp; gas‐based cities were more resistant. RBCs in the Eastern region generally had low economic resistance, while the economic resilience of recessionary cities was also low. Finally, while factors affecting the economic resilience varied across the two economic cycles, we found that economic development, labor conditions and, most of all, the industrial structure had a statistically significant negative effect on economic resilience.

Morphology and evolutionary significance of phosphatic otoliths within the inner ears of cartilaginous fishes (Chondrichthyes)

BackgroundChondrichthyans represent a monophyletic group of crown group gnathostomes and are central to our understanding of vertebrate evolution. Like all vertebrates, cartilaginous fishes evolved concretions of material within their inner ears to aid with equilibrium and balance detection. Up to now, these materials have been identified as calcium carbonate-bearing otoconia, which are small bio-crystals consisting of an inorganic mineral and a protein, or otoconial masses (aggregations of otoconia bound by an organic matrix), being significantly different in morphology compared to the singular, polycrystalline otolith structures of bony fishes, which are solidified bio-crystals forming stony masses. Reinvestigation of the morphological and chemical properties of these chondrichthyan otoconia revises our understanding of otolith composition and has implications on the evolution of these characters in both the gnathostome crown group, and cartilaginous fishes in particular.ResultsDissections of Amblyraja radiata, Potamotrygon leopoldi, and Scyliorhinus canicula revealed three pairs of singular polycrystalline otolith structures with a well-defined morphology within their inner ears, as observed in bony fishes. IR spectroscopy identified the material to be composed of carbonate/collagen-bearing apatite in all taxa. These findings contradict previous hypotheses suggesting these otoconial structures were composed of calcium carbonate in chondrichthyans. A phylogenetic mapping using 37 chondrichthyan taxa further showed that the acquisition of phosphatic otolith structures might be widespread within cartilaginous fishes.ConclusionsDifferences in the size and shape of otoliths between taxa indicate a taxonomic signal within elasmobranchs. Otoliths made of carbonate/collagen-bearing apatite are reported for the first time in chondrichthyans. The intrinsic pathways to form singular, polycrystalline otoliths may represent the plesiomorphic condition for vertebrates but needs further testing. Likewise, the phosphatic composition of otoliths in early vertebrates such as cyclostomes and elasmobranchs is probably closely related to the lack of bony tissue in these groups, supporting a close relationship between skeletal tissue mineralization patterns and chemical otolith composition, underlined by physiological constraints.