Two-parameter nonsmooth grazing bifurcations of limit cycles: classification and open problems

This paper proposes a strategy for the classification of codimension-two grazing bifurcations of limit cycles in piecewise smooth systems of ordinary differential equations. Such nonsmooth transitions (C-bifurcations) occur when the cycle interacts with a discontinuity boundary of phase space in a non-generic way. Several such codimension-one events have recently been identified, causing for example period-adding or sudden onset of chaos. Here, the focus is on codimension-two grazings that are local in the sense that the dynamics can be fully described by an appropriate Poincaré map from a neighbourhood of the grazing point (or points) of the critical cycle to itself. It is proposed that codimension-two grazing bifurcations can be divided into three distinct types: either the grazing point is degenerate, or the the grazing cycle is itself degenerate (e.g. non-hyperbolic) or we have the simultaneous occurrence of two grazing events. A careful distinction is drawn between their occurrence in systems with discontinuous states, discontinuous vector fields, or that have discontinuity in some derivative of the vector field. Examples of each kind of bifurcation are presented, mostly derived from mechanical applications. For each example, where possible, principal bifurcation curves characteristic to the codimension-two scenario are presented and general features of the dynamics discussed. Many avenues for future research are opened.

A Match in Time Saves Nine: Deterministic Online Matching With Delays

We consider the problem of online Min-cost Perfect Matching with Delays (MPMD) introduced by Emek et al. (STOC 2016). In this problem, an even number of requests appear in a metric space at different times and the goal of an online algorithm is to match them in pairs. In contrast to traditional online matching problems, in MPMD all requests appear online and an algorithm can match any pair of requests, but such decision may be delayed (e.g., to find a better match). The cost is the sum of matching distances and the introduced delays. We present the first deterministic online algorithm for this problem. Its competitive ratio is $O(m^{\log_2 5.5})$ $= O(m^{2.46})$, where $2 m$ is the number of requests. This is polynomial in the number of metric space points if all requests are given at different points. In particular, the bound does not depend on other parameters of the metric, such as its aspect ratio. Unlike previous (randomized) solutions for the MPMD problem, our algorithm does not need to know the metric space in advance

A physics-based machine learning technique rapidly reconstructs the wall-shear stress and pressure fields in coronary arteries

With the global rise of cardiovascular disease including atherosclerosis, there is a high demand or accurate diagnostic tools that can be used during a short consultation. In view of pathology, abnormal blood flow patterns have been demonstrated to be strong predictors of atherosclerotic lesion incidence, location, progression, and rupture. Prediction of patient-specific blood flow patterns can hence enable fast clinical diagnosis. However, the current state of art for the technique is by employing 3D-imaging-based Computational Fluid Dynamics (CFD). The high computational cost renders these methods impractical. In this work, we present a novel method to expedite the reconstruction of 3D pressure and shear stress fields using a combination of a reduced-order CFD modelling technique together with non-linear regression tools from the Machine Learning (ML) paradigm. Specifically, we develop a proof-of-concept automated pipeline that uses randomised perturbations of an atherosclerotic pig coronary artery to produce a large dataset of unique mesh geometries with variable blood flow. A total of 1407 geometries were generated from seven reference arteries and were used to simulate blood flow using the CFD solver Abaqus. This CFD dataset was then post-processed using the mesh-domain common-base Proper Orthogonal Decomposition (cPOD) method to obtain Eigen functions and principal coefficients, the latter of which is a product of the individual mesh flow solutions with the POD Eigenvectors. Being a data-reduction method, the POD enables the data to be represented using only the ten most significant modes, which captures cumulatively greater than 95% of variance of flow features due to mesh variations. Next, the node coordinate data of the meshes were embedded in a two-dimensional coordinate system using the t-distributed Stochastic Neighbor Embedding (t-SNE) algorithm. The reduced dataset for t-SNE coordinates and corresponding vector of POD coefficients were then used to train a Random Forest Regressor (RFR) model. The same methodology was applied to both the volumetric pressure solution and the wall shear stress. The predicted pattern of blood pressure, and shear stress in unseen arterial geometries were compared with the ground truth CFD solutions on 'unseen' meshes. The new method was able to reliably reproduce the 3D coronary artery haemodynamics in less than 10 seconds

A physics-based machine learning technique rapidly reconstructs the wall-shear stress and pressure fields in coronary arteries

With the global rise of cardiovascular disease including atherosclerosis, there is a high demand for accurate diagnostic tools that can be used during a short consultation. In view of pathology, abnormal blood flow patterns have been demonstrated to be strong predictors of atherosclerotic lesion incidence, location, progression, and rupture. Prediction of patient-specific blood flow patterns can hence enable fast clinical diagnosis. However, the current state of art for the technique is by employing 3D-imaging-based Computational Fluid Dynamics (CFD). The high computational cost renders these methods impractical. In this work, we present a novel method to expedite the reconstruction of 3D pressure and shear stress fields using a combination of a reduced-order CFD modelling technique together with non-linear regression tools from the Machine Learning (ML) paradigm. Specifically, we develop a proof-of-concept automated pipeline that uses randomised perturbations of an atherosclerotic pig coronary artery to produce a large dataset of unique mesh geometries with variable blood flow. A total of 1,407 geometries were generated from seven reference arteries and were used to simulate blood flow using the CFD solver Abaqus. This CFD dataset was then post-processed using the mesh-domain common-base Proper Orthogonal Decomposition (cPOD) method to obtain Eigen functions and principal coefficients, the latter of which is a product of the individual mesh flow solutions with the POD Eigenvectors. Being a data-reduction method, the POD enables the data to be represented using only the ten most significant modes, which captures cumulatively greater than 95% of variance of flow features due to mesh variations. Next, the node coordinate data of the meshes were embedded in a two-dimensional coordinate system using the t-distributed Stochastic Neighbor Embedding ((Formula presented.) -SNE) algorithm. The reduced dataset for (Formula presented.) -SNE coordinates and corresponding vector of POD coefficients were then used to train a Random Forest Regressor (RFR) model. The same methodology was applied to both the volumetric pressure solution and the wall shear stress. The predicted pattern of blood pressure, and shear stress in unseen arterial geometries were compared with the ground truth CFD solutions on “unseen” meshes. The new method was able to reliably reproduce the 3D coronary artery haemodynamics in less than 10 s

Long Wavelength Anomalous Diffusion Mode in the 2D XY Dipole Magnet

In 2D XY ferromagnet the dipole force induces a strong interaction between spin-waves in the long-wavelength limit. The major effect of this interaction is the transformation of a propagating spin-wave into a diffusion mode. We study the anomalous dynamics of such diffusion modes. We find that the Janssen-De Dominics functional, which governs this dynamics, approaches the non-Gaussian fixed-point. A spin-wave propagates by an anomalous anisotropic diffusion with the dispersion relation: $i\omega{\sim}k_{y}^{\Delta_y}$ and $i\omega{\sim}k_{x}^{\Delta_x}$, where ${\Delta_y}=47/27$ and ${\Delta_x}=47/36$. The low-frequency response to the external magnetic field is found.Comment: 34 pages, RevTeX, 2 .ps figures, the third figure is available upon reques

A quantitative approach for measuring the reservoir of latent HIV-1 proviruses.

A stable latent reservoir for HIV-1 in resting CD4+ T cells is the principal barrier to a cure1-3. Curative strategies that target the reservoir are being tested4,5 and require accurate, scalable reservoir assays. The reservoir was defined with quantitative viral outgrowth assays for cells that release infectious virus after one round of T cell activation1. However, these quantitative outgrowth assays and newer assays for cells that produce viral RNA after activation6 may underestimate the reservoir size because one round of activation does not induce all proviruses7. Many studies rely on simple assays based on polymerase chain reaction to detect proviral DNA regardless of transcriptional status, but the clinical relevance of these assays is unclear, as the vast majority of proviruses are defective7-9. Here we describe a more accurate method of measuring the HIV-1 reservoir that separately quantifies intact and defective proviruses. We show that the dynamics of cells that carry intact and defective proviruses are different in vitro and in vivo. These findings have implications for targeting the intact proviruses that are a barrier to curing HIV infection

Deletion of the gabra2 gene results in hypersensitivity to the acute effects of ethanol but does not alter ethanol self administration

Human genetic studies have suggested that polymorphisms of the GABRA2 gene encoding the GABA(A) α2-subunit are associated with ethanol dependence. Variations in this gene also convey sensitivity to the subjective effects of ethanol, indicating a role in mediating ethanol-related behaviours. We therefore investigated the consequences of deleting the α2-subunit on the ataxic and rewarding properties of ethanol in mice. Ataxic and sedative effects of ethanol were explored in GABA(A) α2-subunit wildtype (WT) and knockout (KO) mice using a Rotarod apparatus, wire hang and the duration of loss of righting reflex. Following training, KO mice showed shorter latencies to fall than WT littermates under ethanol (2 g/kg i.p.) in both Rotarod and wire hang tests. After administration of ethanol (3.5 g/kg i.p.), KO mice took longer to regain the righting reflex than WT mice. To ensure the acute effects are not due to the gabra2 deletion affecting pharmacokinetics, blood ethanol concentrations were measured at 20 minute intervals after acute administration (2 g/kg i.p.), and did not differ between genotypes. To investigate ethanol's rewarding properties, WT and KO mice were trained to lever press to receive increasing concentrations of ethanol on an FR4 schedule of reinforcement. Both WT and KO mice self-administered ethanol at similar rates, with no differences in the numbers of reinforcers earned. These data indicate a protective role for α2-subunits, against the acute sedative and ataxic effects of ethanol. However, no change was observed in ethanol self administration, suggesting the rewarding effects of ethanol remain unchange

Design and development of a prototype electrotherapy device

This article describes a complete prototype system that can be used in electrotherapy treatments, that is, in medical treatments involving electric currents. The system is composed of two main blocks: the master and the slave. The Master block, whose main component is a CPU, controls the user interface. The Slave block, which is composed of a microcontroller and a wave generator, produces the appropriated voltages and currents compatible with the desired treatment. The whole system is powered by a 12 V power supply and the output signal voltage ranges between -100 V and 100 V. Despite the prototype being able of performing all the electrotherapy treatments in the low-medium frequency ranges, it was tested in aesthetic mesotherapy, namely in anticellulite, located anticellulite, antistretch, and antiflaccidity. In these treatments, the output signal is composed of an overlap of two frequencies: the first one is selected in the range of 1.2 kHz - 1.8 kHz and the second in the range of 0.07 Hz - 2 Hz. The system was tested in a clinical environment with real patients. It showed good results both in effectiveness of treatments and in terms of pain suffered by the patients.(undefined

The association of vitamin D deficiency with non-alcoholic fatty liver disease

OBJECTIVE: Vitamin D deficiency has been related to diabetes, hypertension, hyperlipidemia and peripheral vascular disease. In this study, we aimed to investigate the role of vitamin D status in non-alcoholic fatty liver disease. METHODS: We included 211 consecutive subjects to examine the presence of non-alcoholic fatty liver disease. Of these subjects, 57 did not have non-alcoholic fatty liver disease and 154 had non-alcoholic fatty liver disease. RESULTS: The non-alcoholic fatty liver disease group had significantly higher fasting blood glucose (p = 0.005), uric acid (p = 0.001), aspartate aminotransferase (

A novel class of microRNA-recognition elements that function only within open reading frames.

MicroRNAs (miRNAs) are well known to target 3' untranslated regions (3' UTRs) in mRNAs, thereby silencing gene expression at the post-transcriptional level. Multiple reports have also indicated the ability of miRNAs to target protein-coding sequences (CDS); however, miRNAs have been generally believed to function through similar mechanisms regardless of the locations of their sites of action. Here, we report a class of miRNA-recognition elements (MREs) that function exclusively in CDS regions. Through functional and mechanistic characterization of these 'unusual' MREs, we demonstrate that CDS-targeted miRNAs require extensive base-pairing at the 3' side rather than the 5' seed; cause gene silencing in an Argonaute-dependent but GW182-independent manner; and repress translation by inducing transient ribosome stalling instead of mRNA destabilization. These findings reveal distinct mechanisms and functional consequences of miRNAs that target CDS versus the 3' UTR and suggest that CDS-targeted miRNAs may use a translational quality-control-related mechanism to regulate translation in mammalian cells