Spectral Dynamics of the Velocity Gradient Field in Restricted Flows

We study the velocity gradients of the fundamental Eulerian equation, $\partial_t u +u\cdot \nabla u=F$, which shows up in different contexts dictated by the different modeling of $F$'s. To this end we utilize a basic description for the spectral dynamics of $\nabla u$, expressed in terms of the (possibly complex) eigenvalues, $\lambda=\lambda(\nabla u)$, which are shown to be governed by the Ricatti-like equation $\lambda_t+u\cdot \nabla\lambda+\lambda^2=$. We address the question of the time regularity of four prototype models associated with different forcing $F$. Using the spectral dynamics as our essential tool in these investigations, we obtain a simple form of a critical threshold for the linear damping model and we identify the 2D vanishing viscosity limit for the viscous irrotational dusty medium model. Moreover, for the $n$-dimensional restricted Euler equations we obtain $[n/2]+1$ global invariants, interesting for their own sake, which enable us to precisely characterize the local topology at breakdown time, extending previous studies in the $n=3$-dimensional case. Finally, as a forth model we introduce the $n$-dimensional restricted Euler-Poisson (REP)system, identifying a set of $[n/2]$ global invariants, which in turn yield (i) sufficient conditions for finite time breakdown, and (ii) characterization of a large class of 2-dimensional initial configurations leading to global smooth solutions. Consequently, the 2D restricted Euler-Poisson equations are shown to admit a critical threshold

Mammalian BEX, WEX and GASP genes: Coding and non-coding chimaerism sustained by gene conversion events

BACKGROUND: The identification of sequence innovations in the genomes of mammals facilitates understanding of human gene function, as well as sheds light on the molecular mechanisms which underlie these changes. Although gene duplication plays a major role in genome evolution, studies regarding concerted evolution events among gene family members have been limited in scope and restricted to protein-coding regions, where high sequence similarity is easily detectable. RESULTS: We describe a mammalian-specific expansion of more than 20 rapidly-evolving genes on human chromosome Xq22.1. Many of these are highly divergent in their protein-coding regions yet contain a conserved sequence motif in their 5' UTRs which appears to have been maintained by multiple events of concerted evolution. These events have led to the generation of chimaeric genes, each with a 5' UTR and a protein-coding region that possess independent evolutionary histories. We suggest that concerted evolution has occurred via gene conversion independently in different mammalian lineages, and these events have resulted in elevated G+C levels in the encompassing genomic regions. These concerted evolution events occurred within and between genes from three separate protein families ('brain-expressed X-linked' [BEX], WWbp5-like X-linked [WEX] and G-protein-coupled receptor-associated sorting protein [GASP]), which often are expressed in mammalian brains and associated with receptor mediated signalling and apoptosis. CONCLUSION: Despite high protein-coding divergence among mammalian-specific genes, we identified a DNA motif common to these genes' 5' UTR exons. The motif has undergone concerted evolution events independently of its neighbouring protein-coding regions, leading to formation of evolutionary chimaeric genes. These findings have implications for the identification of non protein-coding regulatory elements and their lineage-specific evolution in mammals

Rotation Prevents Finite-Time Breakdown

We consider a two-dimensional convection model augmented with the rotational Coriolis forcing, $U_t + U\cdot\nabla_x U = 2k U^\perp$, with a fixed $2k$ being the inverse Rossby number. We ask whether the action of dispersive rotational forcing alone, $U^\perp$, prevents the generic finite time breakdown of the free nonlinear convection. The answer provided in this work is a conditional yes. Namely, we show that the rotating Euler equations admit global smooth solutions for a subset of generic initial configurations. With other configurations, however, finite time breakdown of solutions may and actually does occur. Thus, global regularity depends on whether the initial configuration crosses an intrinsic, ${\mathcal O}(1)$ critical threshold, which is quantified in terms of the initial vorticity, $\omega_0=\nabla \times U_0$, and the initial spectral gap associated with the $2\times 2$ initial velocity gradient, $\eta_0:=\lambda_2(0)-\lambda_1(0), \lambda_j(0)= \lambda_j(\nabla U_0)$. Specifically, global regularity of the rotational Euler equation is ensured if and only if $4k \omega_0(\alpha) +\eta^2_0(\alpha) <4k^2, \forall \alpha \in \R^2$ . We also prove that the velocity field remains smooth if and only if it is periodic. We observe yet another remarkable periodic behavior exhibited by the {\em gradient} of the velocity field. The spectral dynamics of the Eulerian formulation reveals that the vorticity and the eigenvalues (and hence the divergence) of the flow evolve with their own path-dependent period. We conclude with a kinetic formulation of the rotating Euler equation

Increased earthquake rate prior to mainshocks

According to the Omori-Utsu law, the rate of aftershocks after a mainshock decays as a power law with an exponent close to 1. This well-established law was intensively used in the past to study and model the statistical properties of earthquakes. Moreover, according to the so-called inverse Omori law, the rate of earthquakes should also increase prior to a mainshock -- this law has received much less attention due to its large uncertainty. Here, we mainly study the inverse Omori law based on a highly detailed Southern California earthquake catalog, which is complete for magnitudes larger than M>0.3. First, we develop a technique to identify mainshocks, foreshocks, and aftershocks. We then find, based on a statistical procedure we developed, that the rate of earthquakes is higher a few days prior to a mainshock. We find that this increase is much smaller for a catalog with a magnitude threshold of m over 2.5 and for the Epidemic-Type Aftershocks Sequence (ETAS) model catalogs, even when used with a small magnitude threshold. We also analyze the rate of aftershocks after mainshocks and find that the Omori-Utsu law does not hold for many individual mainshocks and that it may be valid only statistically when considering many mainshocks together. Yet, the analysis of the ETAS model based on the Omori-Utsu law exhibits similar behavior as that of the real catalogs, indicating the validity of this law.Comment: 19 pages, 7 figure

Ribonucleic artefacts: are some extracellular RNA discoveries driven by cell culture medium components?

In a recently published study, Anna Krichevsky and colleagues raise the important question ofwhether results of in vitro extracellular RNA (exRNA) studies, including extracellular vesicle (EV)investigations, are confounded by the presence of RNA in cell culture medium components suchas foetal bovine serum (FBS). The answer, according to their data, is a resounding“yes”. Even afterlengthy ultracentrifugation to remove bovine EVs from FBS, the majority of exRNA in FBSremained. Although technical factors may affect the degree of depletion, residual EVs andexRNA in FBS could influence the conclusions of in vitro studies: certainly, for secreted RNA,and possibly also for cell-associated RNA. In this commentary, we critically examine some of theliterature in this field, including a recent study from some of the authors of this piece, in light ofthe Wei et al. study and explore how cell culture-derived RNAs may affect what we think we knowabout EV RNAs. These findings hold particular consequence as the field moves towards a deeperunderstanding of EV–RNA associations and potential functions

Towards Transcervical Ultrasound Image Guidance for Transoral Robotic Surgery

Purpose: Trans-oral robotic surgery (TORS) using the da Vinci surgical robot is a new minimally-invasive surgery method to treat oropharyngeal tumors, but it is a challenging operation. Augmented reality (AR) based on intra-operative ultrasound (US) has the potential to enhance the visualization of the anatomy and cancerous tumors to provide additional tools for decision-making in surgery. Methods: We propose and carry out preliminary evaluations of a US-guided AR system for TORS, with the transducer placed on the neck for a transcervical view. Firstly, we perform a novel MRI-transcervical 3D US registration study. Secondly, we develop a US-robot calibration method with an optical tracker and an AR system to display the anatomy mesh model in the real-time endoscope images inside the surgeon console. Results: Our AR system reaches a mean projection error of 26.81 and 27.85 pixels for the projection from the US to stereo cameras in a water bath experiment. The average target registration error for MRI to 3D US is 8.90 mm for the 3D US transducer and 5.85 mm for freehand 3D US, and the average distance between the vessel centerlines is 2.32 mm. Conclusion: We demonstrate the first proof-of-concept transcervical US-guided AR system for TORS and the feasibility of trans-cervical 3D US-MRI registration. Our results show that trans-cervical 3D US is a promising technique for TORS image guidance.Comment: 12 pages, 8 figures. Accepted by Information Processing for Computer Assisted Interventions (IPCAI 2023

Identification of a Cytotoxic Form of Dimeric Interleukin-2 in Murine Tissues

Interleukin-2 (IL-2) is a multi-faceted cytokine, known for promoting proliferation, survival, and cell death depending on the cell type and state. For example, IL-2 facilitates cell death only in activated T cells when antigen and IL-2 are abundant. The availability of IL-2 clearly impacts this process. Our laboratory recently demonstrated that IL-2 is retained in blood vessels by heparan sulfate, and that biologically active IL-2 is released from vessel tissue by heparanase. We now demonstrate that heparanase digestion also releases a dimeric form of IL-2 that is highly cytotoxic to cells expressing the IL-2 receptor. These cells include “traditional” IL-2 receptor-bearing cells such as lymphocytes, as well as those less well known for IL-2 receptor expression, such as epithelial and smooth muscle cells. The morphologic changes and rapid cell death induced by dimeric IL-2 imply that cell death is mediated by disruption of membrane permeability and subsequent necrosis. These findings suggest that IL-2 has a direct and unexpectedly broad influence on cellular homeostatic mechanisms in both immune and non-immune systems