916 research outputs found
Spectral Dynamics of the Velocity Gradient Field in Restricted Flows
We study the velocity gradients of the fundamental Eulerian equation,
, which shows up in different contexts
dictated by the different modeling of 's. To this end we utilize a basic
description for the spectral dynamics of , expressed in terms of the
(possibly complex) eigenvalues, , which are shown to
be governed by the Ricatti-like equation .
We address the question of the time regularity of four prototype models
associated with different forcing . 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 -dimensional restricted Euler equations we obtain global
invariants, interesting for their own sake, which enable us to precisely
characterize the local topology at breakdown time, extending previous studies
in the -dimensional case. Finally, as a forth model we introduce the
-dimensional restricted Euler-Poisson (REP)system, identifying a set of
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, , with a fixed
being the inverse Rossby number. We ask whether the action of dispersive
rotational forcing alone, , 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, critical threshold, which
is quantified in terms of the initial vorticity, ,
and the initial spectral gap associated with the initial velocity
gradient, . Specifically, global regularity of the rotational Euler equation is
ensured if and only if . 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 resoundingâyesâ. 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 EVâRNA 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 âtraditionalâ 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
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