Information-Preserving Markov Aggregation

We present a sufficient condition for a non-injective function of a Markov chain to be a second-order Markov chain with the same entropy rate as the original chain. This permits an information-preserving state space reduction by merging states or, equivalently, lossless compression of a Markov source on a sample-by-sample basis. The cardinality of the reduced state space is bounded from below by the node degrees of the transition graph associated with the original Markov chain. We also present an algorithm listing all possible information-preserving state space reductions, for a given transition graph. We illustrate our results by applying the algorithm to a bi-gram letter model of an English text.Comment: 7 pages, 3 figures, 2 table

Multiphase Thermohaline Convection in the Earth's Crust: I. A New Finite Element - Finite Volume Solution Technique Combined With a New Equation of State for NaCl-H2O

We present a new finite element - finite volume (FEFV) method combined with a realistic equation of state for NaCl-H2O to model fluid convection driven by temperature and salinity gradients. This method can deal with the nonlinear variations in fluid properties, separation of a saline fluid into a high-density, high-salinity brine phase and low-density, low-salinity vapor phase well above the critical point of pure H2O, and geometrically complex geological structures. Similar to the well-known implicit pressure explicit saturation formulation, this approach decouples the governing equations. We formulate a fluid pressure equation that is solved using an implicit finite element method. We derive the fluid velocities from the updated pressure field and employ them in a higher-order, mass conserving finite volume formulation to solve hyperbolic parts of the conservation laws. The parabolic parts are solved by finite element methods. This FEFV method provides for geometric flexibility and numerical efficiency. The equation of state for NaCl-H2O is valid from 0 to 750°C, 0 to 4000bar, and 0-100 wt.% NaCl. This allows the simulation of thermohaline convection in high-temperature and high-pressure environments, such as continental or oceanic hydrothermal systems where phase separation is commo

Multiphase Thermohaline Convection in the Earth's Crust: II. Benchmarking and Application of a Finite Element - Finite Volume Solution Technique with a NaCl-H2O Equation of State

We present the benchmarking of a new finite element - finite volume (FEFV) solution technique capable of modeling transient multiphase thermohaline convection for geological realistic p-T-X conditions. The algorithm embeds a new and accurate equation of state for the NaCl-H2O system. Benchmarks are carried out to compare the numerical results for the various component-processes of multiphase thermohaline convection. They include simulations of (i) convection driven by temperature and/or concentration gradients in a single-phase fluid (i.e., the Elder problem, thermal convection at different Rayleigh numbers, and a free thermohaline convection example), (ii) multiphase flow (i.e., the Buckley-Leverett problem), and (iii) energy transport in a pure H2O fluid at liquid, vapor, supercritical, and two-phase conditions (i.e., comparison to the U.S. Geological Survey Code HYDROTHERM). The results produced with the new FEFV technique are in good agreement with the reference solutions. We further present the application of the FEFV technique to the simulation of thermohaline convection of a 400°C hot and 10 wt.% saline fluid rising from 4km depth. During the buoyant rise, the fluid boils and separates into a high-density, high-salinity liquid phase and a low-density, low-salinity vapor phas

Synaptic boutons sizes are tuned to best fit their physiological performances

To truly appreciate the myriad of events which relate synaptic function and vesicle dynamics, simulations should be done in a spatially realistic environment. This holds true in particular in order to explain as well the rather astonishing motor patterns which we observed within in vivo recordings which underlie peristaltic contractionsas well as the shape of the EPSPs at different forms of long-term stimulation, presented both here, at a well characterized synapse, the neuromuscular junction (NMJ) of the Drosophila larva (c.f. Figure 1). To this end, we have employed a reductionist approach and generated three dimensional models of single presynaptic boutons at the Drosophila larval NMJ. Vesicle dynamics are described by diffusion-like partial differential equations which are solved numerically on unstructured grids using the uG platform. In our model we varied parameters such as bouton-size, vesicle output probability (Po), stimulation frequency and number of synapses, to observe how altering these parameters effected bouton function. Hence we demonstrate that the morphologic and physiologic specialization maybe a convergent evolutionary adaptation to regulate the trade off between sustained, low output, and short term, high output, synaptic signals. There seems to be a biologically meaningful explanation for the co-existence of the two different bouton types as previously observed at the NMJ (characterized especially by the relation between size and Po), the assigning of two different tasks with respect to short- and long-time behaviour could allow for an optimized interplay of different synapse types. We can present astonishing similar results of experimental and simulation data which could be gained in particular without any data fitting, however based only on biophysical values which could be taken from different experimental results. As a side product, we demonstrate how advanced methods from numerical mathematics could help in future to resolve also other difficult experimental neurobiological issues

Synaptic bouton sizes are tuned to best fit their physiological performances : poster presentation from Twentieth Annual Computational Neuroscience Meeting: CNS*2011, Stockholm, Sweden, 23 - 28 July 2011

Poster presentation from Twentieth Annual Computational Neuroscience Meeting: CNS*2011 Stockholm, Sweden. 23-28 July 2011. To truly appreciate the myriad of events which relate synaptic function and vesicle dynamics, simulations should be done in a spatially realistic environment. This holds true in particular in order to explain the rather astonishing motor patterns presented here which we observed within in vivo recordings which underlie peristaltic contractions at a well characterized synapse, the neuromuscular junction (NMJ) of the Drosophila larva. To this end, we have employed a reductionist approach and generated three dimensional models of single presynaptic boutons at the Drosophila larval NMJ. Vesicle dynamics are described by diffusion-like partial differential equations which are solved numerically on unstructured grids using the uG platform. In our model we varied parameters such as bouton-size, vesicle output probability (Po), stimulation frequency and number of synapses, to observe how altering these parameters effected bouton function. Hence we demonstrate that the morphologic and physiologic specialization maybe a convergent evolutionary adaptation to regulate the trade off between sustained, low output, and short term, high output, synaptic signals. There seems to be a biologically meaningful explanation for the co-existence of the two different bouton types as previously observed at the NMJ (characterized especially by the relation between size and Po),the assigning of two different tasks with respect to short- and long-time behaviour could allow for an optimized interplay of different synapse types. As a side product, we demonstrate how advanced methods from numerical mathematics could help in future to resolve also other difficult experimental neurobiological issues

Directed invasion of cancer cell spheroids inside 3D collagen matrices oriented by microfluidic flow in experiment and simulation

Invasion is strongly influenced by the mechanical properties of the extracellular matrix. Here, we use microfluidics to align fibers of a collagen matrix and study the influence of fiber orientation on invasion from a cancer cell spheroid. The microfluidic setup allows for highly oriented collagen fibers of tangential and radial orientation with respect to the spheroid, which can be described by finite element simulations. In invasion experiments, we observe a strong bias of invasion towards radial as compared to tangential fiber orientation. Simulations of the invasive behavior with a Brownian diffusion model suggest complete blockage of migration perpendicularly to fibers allowing for migration exclusively along fibers. This slows invasion toward areas with tangentially oriented fibers down, but does not prevent it

A General Framework for Equivariant Neural Networks on Reductive Lie Groups

Reductive Lie Groups, such as the orthogonal groups, the Lorentz group, or the unitary groups, play essential roles across scientific fields as diverse as high energy physics, quantum mechanics, quantum chromodynamics, molecular dynamics, computer vision, and imaging. In this paper, we present a general Equivariant Neural Network architecture capable of respecting the symmetries of the finite-dimensional representations of any reductive Lie Group G. Our approach generalizes the successful ACE and MACE architectures for atomistic point clouds to any data equivariant to a reductive Lie group action. We also introduce the lie-nn software library, which provides all the necessary tools to develop and implement such general G-equivariant neural networks. It implements routines for the reduction of generic tensor products of representations into irreducible representations, making it easy to apply our architecture to a wide range of problems and groups. The generality and performance of our approach are demonstrated by applying it to the tasks of top quark decay tagging (Lorentz group) and shape recognition (orthogonal group)

Analgosedation for less-invasive surfactant administration: Variations in practice

BACKGROUND Less-invasive surfactant administration (LISA) is widely used for surfactant delivery to spontaneously breathing preterm infants on nasal CPAP. However, the use of analgesia and/or sedation for the LISA procedure remains controversial. METHODS We conducted a cross-sectional survey of all tertiary neonatal intensive care units (NICUs) in Austria, Germany, and Switzerland to assess current practices of analgosedation for LISA in preterm infants. RESULTS Eighty-eight of 172 (51.2%) NICUs responded to the survey, of which 83 (94.3%) perform LISA. Analgosedation for LISA is used in 60 (72.3%) NICUs. Twenty-eight of those (46.7%) have unit protocols to guide analgosedation while 32 (53.3%) administer medication at the discretion of the attending physician. Ketamine (45.0% of NICUs), propofol (41.7%), fentanyl (21.7%), morphine (20.0%), and midazolam (20.0%) were most frequently used for analgosedation for LISA. Nine (10.7%) NICUs reported the use of pain or distress scores during LISA. CONCLUSION LISA is well established among tertiary NICUs in the German-speaking countries. However, there are considerable variations regarding the use of analgosedation. More evidence is required to guide clinicians seeking to safely and effectively deliver surfactant via a thin catheter to spontaneously breathing preterm infants

Difficulties in diagnosis of SARS-CoV-2 myocarditis in an adolescent

OBJECTIVES We present an adolescent with cardiogenic shock due to ventricular tachycardia 2 weeks after SARS-CoV-2 infection. Acute myocarditis or myocardial dysfunction is associated with SARS-CoV-2 infection, but diagnosis may be difficult, even including endomyocardial biopsy. CASE REPORT A 15-year-old healthy adolescent was admitted to our hospital 2 weeks after SARS-CoV-2 infection with cardiogenic shock due to ventricular tachycardia. After cardioversion, antiarrhythmic treatment, ventilation, and inotropic support, the severely reduced myocardial function recovered completely within 2 weeks. Cardiac magnetic resonance imaging and cardiac catheterisation including right ventricular endomyocardial biopsy revealed an increased number of CD68+ macrophages in the myocardium, but nested (RT-) polymerase chain reaction (PCR) investigations revealed no viral or bacterial DNA/RNA. DISCUSSION SARS-CoV-2 infection may be associated with myocarditis leading to life-threatening arrhythmia and severe myocardial systolic and diastolic dysfunction, which may be short lasting and completely recover. Although former SARS-Cov-2 infection might suggest SARS-CoV-2-associated myocarditis, definite histological diagnosis including nested PCR investigations remains difficult