Complex singularities and PDEs

In this paper we give a review on the computational methods used to characterize the complex singularities developed by some relevant PDEs. We begin by reviewing the singularity tracking method based on the analysis of the Fourier spectrum. We then introduce other methods generally used to detect the hidden singularities. In particular we show some applications of the Pad\'e approximation, of the Kida method, and of Borel-Polya method. We apply these techniques to the study of the singularity formation of some nonlinear dispersive and dissipative one dimensional PDE of the 2D Prandtl equation, of the 2D KP equation, and to Navier-Stokes equation for high Reynolds number incompressible flows in the case of interaction with rigid boundaries

Comparative electrochemical behavior of Prussian blue analogues as a host electrode for rare earth element recovery

In this paper, electrodeposited films belonging to the Prussian Blue Analogues (PBAs) family, namely, nickel-hexacyanoferrate (NiHCF) and copper-hexacyanoferrate (CuHCF), were employed as a host material for rare earth elements (REE), and the reported insertion/release study reveals a recovery capability for such valuable metals. The ion insertion/release was accomplished by adopting an electrochemically-driven process. A reversible intercalation was observed while considering both heavy and ligth rare earth elements. The amount of REEs inserted/released over the process and its kinetic evolution during the process were also studied by a chemometric approach. For CuHCF, it was seen that the intercalation of heavy rare earth elements occurs easily respect to the light ones, suggesting a possible selectivity among these ions

Cardiovascular autonomic function and MCI in Parkinson's disease

Introduction: dysautonomic dysfunction and cognitive impairment represent the most disabling non-motor features of Parkinson's Disease (PD). Recent evidences suggest the association between Orthostatic Hypotension (OH) and PD-Dementia. However, little is known on the interactions between cardiovascular dysautonomia and Mild Cognitive Impairment (MCI). We aimed to evaluate the association between cardiovascular dysautonomia and MCI in patients with PD. Methods: non-demented PD patients belonging to the PACOS cohort underwent a comprehensive instrumental neurovegetative assessment including the study of both parasympathetic and sympathetic function (30:15 ratio, Expiratory-Inspiratory ratio [E-I] and presence of Orthostatic Hypotension [OH]). Diagnosis of MCI was made according to the MDS criteria level II. Results: we enrolled 185 PD patients of whom 102 (55.1%) were men, mean age was 64.6 ± 9.7 years, mean disease duration of 5.6 ± 5.5 years with a mean UPDRS-ME score of 31.7 ± 10.9. MCI was diagnosed in 79 (42.7%) patients. OH was recorded in 52 (28.1%) patients, altered 30:15 ratio was recorded in 39 (24.1%) patients and an altered E-I ratio was found in 24 (19.1%) patients. Presence of MCI was associated with an altered 30:15 ratio (adjOR 2.83; 95%CI 1.25–6.40) but not with an altered E-I ratio, while OH was associated only with the amnestic MCI subgroup (OR 2.43; 95% CI 1.05–5.06). Conclusion: in our study sample, MCI was mainly associated with parasympathetic dysfunction in PD

Complex singularity analysis for vortex layer flows

We study the evolution of a 2D vortex layer at high Reynolds number. Vortex layer flows are characterized by intense vorticity concentrated around a curve. In addition to their intrinsic interest, vortex layers are relevant configurations because they are regularizations of vortex sheets. In this paper, we consider vortex layers whose thickness is proportional to the square-root of the viscosity. We investigate the typical roll-up process, showing that crucial phases in the initial flow evolution are the formation of stagnation points and recirculation regions. Stretching and folding characterizes the following stage of the dynamics, and we relate these events to the growth of the palinstrophy. The formation of an inner vorticity core, with vorticity intensity growing to infinity for larger Reynolds number, is the final phase of the dynamics. We display the inner core's self-similar structure, with the scale factor depending on the Reynolds number. We reveal the presence of complex singularities in the solutions of Navier-Stokes equations; these singularities approach the real axis with increasing Reynolds number. The comparison between these singularities and the Birkhoff-Rott singularity seems to suggest that vortex layers, in the limit, behave differently from vortex sheets

Radiation hardened transistor characteristics for applications at LHC and beyond

The high radiation environment at the LHC will require the use of radiation hardened microelectronics for the readout of inner detectors. Two such technologies are a Harris bulk CMOS process and the DMILL mixed technology process. Transistors have been fabricated in both of these and have been tested before and after irradiation to 10 Mrads, the total dose expected in the innermost silicon microstrip layers. Several processing runs of Harris transistors have been carried out and samples from one have also been irradiated to 100 Mrads. A preamplifier-shaper circuit, to be used for readout of the CMS microstrip tracker, has been tested and the noise performance is compared with individual transistors

Restitution of Holocaust-Era Assets: A Bibliography of Government Documents

This bibliography addresses the issue of assets stolen from or subsequently denied to victims of the Holocaust and their heirs, as represented by the documentation provided by government resources. As such, it accrues the disparate media documenting the issue of Holocaust-era restitution: the details of original looting and restitution actions, as well as actions taken in the last sixty years that have caused it to become a controversial topic in our contemporary society. Forty government documents were located, evaluated for content, and annotated. Formats include Congressional Hearings, Public Law, Military Histories, and records from the Presidential Advisory Committee on Holocaust Assets. An introduction provides context for the documents, which represent how and why assets were stolen, what happened to them following in the aftermath of World War II, and the subsequent barriers to appropriate restitution that led to current lawmaking on Holocaust victims' behalf. This bibliography is meant to be used by researchers with an interest in the looting and restitution of fine art, financial assets, or gold by the Nazi Party, originally taking place between 1933 and 1945

Reply

Previous data showed that PFOs not detected by high-quality transthoracic echocardiography are smaller and associated with small right-to-left shunts (4); therefore, they are far less likely to be associated with embolic stroke features (5)

Cytokine-induced instabilities in a reaction–diffusion-chemotaxis model of Multiple Sclerosis: Bifurcation analysis and well-posedness

In this paper, we develop a model for the evolution of the Multiple Sclerosis pathology that considers the modulatory influence of cytokines on the activation rate of macrophages. Our starting point is the reaction–diffusion-chemotaxis model proposed in 4, and we modify the macrophage activation mechanism. What triggers the immune cells into an active state is still debated in the medical literature. In this paper, we explore the hypothesis, e.g., Lassmann, (2018), that cytokines mediate the activation mechanism. Our primary focus is on the rigorous analysis of instabilities responsible for the formation of demyelinating lesions and on the qualitative properties of the solution. Through a weakly nonlinear analysis, we characterize the chemotaxis-driven Turing instability and construct the stationary patterns that emerge from this instability. Using biologically relevant parameter values, we show that the asymptotic solutions of our model system reproduce the concentric demyelinating rings, confluent plaques, and preactive lesions observed in Balò sclerosis and type III Multiple Sclerosis. Furthermore, we explore the initiation and progression of demyelinated plaques through extensive numerical simulations on two-dimensional domains. Our findings reveal that the alternative scenario proposed here results in a less aggressive pathology characterized by reduced inflammation levels and significantly slower disease progression. Under the appropriate regularity conditions on the initial data, we prove the existence of a unique global solution to our proposed system. This study provides insights into the role of cytokines in the pathogenesis of Multiple Sclerosis, shedding light on the disease's dynamics and offering potential avenues for therapeutic interventions

Folding mechanisms steer the amyloid fibril formation propensity of highly homologous proteins

Significant advances in the understanding of the molecular determinants of fibrillogenesis can be expected from comparative studies of the aggregation propensities of proteins with highly homologous structures but different folding pathways. Here, we fully characterize, by means of stopped-flow, T-jump, CD and DSC experiments, the unfolding mechanisms of three highly homologous proteins, zinc binding Ros87 and Ml153-149 and zinc-lacking Ml452-151. The results indicate that the three proteins significantly differ in terms of stability and (un)folding mechanisms. Particularly, Ros87 and Ml153-149 appear to be much more stable to guanidine denaturation and are characterized by folding mechanisms including the presence of an intermediate. On the other hand, metal lacking Ml452-151 folds according to a classic two-state model. Successively, we have monitored the capabilities of Ros87, Ml452-151 and Ml153-149 to form amyloid fibrils under native conditions. Particularly, we show, by CD, fluorescence, DLS, TEM and SEM experiments, that after 168 hours, amyloid formation of Ros87 has started, while Ml153-149 has formed only amorphous aggregates and Ml452-151 is still monomeric in solution. This study shows how metal binding can influence protein folding pathways and thereby control conformational accessibility to aggregation-prone states, which in turn changes aggregation kinetics, shedding light on the role of metal ions in the development of protein deposition diseases

Quantification of Myocardial Perfusion in Human Subjects Using 82Rb and Wavelet-Based Noise Reduction

Quantification of myocardial perfusion with 82Rb has been difficult to achieve because of the low signal-to-noise ratio of the dynamic data curves. This study evaluated the accuracy of flow estimates after the application of a novel multidimensional wavelet-based noise-reduction protocol. Methods: Myocardial perfusion was estimated using 82Rb and a two-compartment model from dynamic PET scans on 11 healthy volunteers at rest and after hyperemic stress with dipyridamole. Midventricular planes were divided into eight regions of interest, and a wavelet transform protocol was applied to images and time–activity curves. Flow estimates without and with the wavelet approach were compared with those obtained using H215O. Results: Over a wide flow range (0.45–2.75 mL/g/min), flow achieved with the wavelet approach correlated extremely closely with values obtained with H215O (y = 1.03 x -0.12; n = 23 studies, r = 0.94, P < 0.001). If the wavelet noise-reduction technique was not used, the correlation was less strong (y = 1.11 x + 0.24; n = 23 studies, r = 0.79, P < 0.001). In addition, the wavelet approach reduced the regional variation from 75% to 12% and from 62% to 11% (P < 0.001 for each comparison) for resting and stress studies, respectively. Conclusion: The use of a wavelet protocol allows near-optimal noise reduction, markedly enhances the physiologic flow signal within the PET images, and enables accurate measurement of myocardial perfusion with 82Rb in human subjects over a wide range of flows