scholarly journals Exact description of SIR-Bass epidemics on 1D lattices

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Gadi Fibich ◽  
Samuel Nordmann
Keyword(s):  
Initial Conditions ◽  
Cluster Formation ◽  
A Priori ◽  
Point Sources ◽  
Continuous Models ◽  
Extra Factor ◽  
Sources Of Infection ◽  
New Space ◽  
Spatio Temporal ◽  
Deterministic Description

<p style='text-indent:20px;'>This paper is devoted to the study of a stochastic epidemiological model which is a variant of the SIR model to which we add an extra factor in the transition rate from susceptible to infected accounting for the inflow of infection due to immigration or environmental sources of infection. This factor yields the formation of new clusters of infections, without having to specify a priori and explicitly their date and place of appearance.</p><p style='text-indent:20px;'>We establish an exact deterministic description for such stochastic processes on 1D lattices (finite lines, semi-infinite lines, infinite lines) by showing that the probability of infection at a given point in space and time can be obtained as the solution of a deterministic ODE system on the lattice. Our results allow stochastic initial conditions and arbitrary spatio-temporal heterogeneities on the parameters.</p><p style='text-indent:20px;'>We then apply our results to some concrete situations and obtain useful qualitative results and explicit formulae on the macroscopic dynamics and also the local temporal behavior of each individual. In particular, we provide a fine analysis of some aspects of cluster formation through the study of patient-zero problems and the effects of time-varying point sources.</p><p style='text-indent:20px;'>Finally, we show that the space-discrete model gives rise to new space-continuous models, which are either ODEs or PDEs, depending on the rescaling regime assumed on the parameters.</p>

scholarly journals Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 85
Author(s):  
Andreas Rauh ◽  
Julia Kersten
Keyword(s):  
Linear Systems ◽  
Initial Conditions ◽  
A Priori ◽  
Real Life ◽  
Reachability Analysis ◽  
Interval Methods ◽  
Space Representation ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Similarity Transformations

Continuous-time linear systems with uncertain parameters are widely used for modeling real-life processes. The uncertain parameters, contained in the system and input matrices, can be constant or time-varying. In the latter case, they may represent state dependencies of these matrices. Assuming bounded uncertainties, interval methods become applicable for a verified reachability analysis, for feasibility analysis of feedback controllers, or for the design of robust set-valued state estimators. The evaluation of these system models becomes computationally efficient after a transformation into a cooperative state-space representation, where the dynamics satisfy certain monotonicity properties with respect to the initial conditions. To obtain such representations, similarity transformations are required which are not trivial to find for sufficiently wide a-priori bounds of the uncertain parameters. This paper deals with the derivation and algorithmic comparison of two different transformation techniques for which their applicability to processes with constant and time-varying parameters has to be distinguished. An interval-based reachability analysis of the states of a simple electric step-down converter concludes this paper.

scholarly journals Accelerating simulations using REDCHEM_v0.0 for atmospheric chemistry mechanism reduction

2018 ◽  
Vol 11 (8) ◽  
pp. 3391-3407 ◽  
Author(s):  
Zacharias Marinou Nikolaou ◽  
Jyh-Yuan Chen ◽  
Yiannis Proestos ◽  
Jos Lelieveld ◽  
Rolf Sander
Keyword(s):  
Atmospheric Chemistry ◽  
Transport Model ◽  
A Priori ◽  
Chemical Mechanism ◽  
Climate Modelling ◽  
Mechanism Reduction ◽  
Computational Speed ◽  
Speed Up ◽  
Spatio Temporal ◽  
Skeletal Mechanism

Abstract. Chemical mechanism reduction is common practice in combustion research for accelerating numerical simulations; however, there have been limited applications of this practice in atmospheric chemistry. In this study, we employ a powerful reduction method in order to produce a skeletal mechanism of an atmospheric chemistry code that is commonly used in air quality and climate modelling. The skeletal mechanism is developed using input data from a model scenario. Its performance is then evaluated both a priori against the model scenario results and a posteriori by implementing the skeletal mechanism in a chemistry transport model, namely the Weather Research and Forecasting code with Chemistry. Preliminary results, indicate a substantial increase in computational speed-up for both cases, with a minimal loss of accuracy with regards to the simulated spatio-temporal mixing ratio of the target species, which was selected to be ozone.

scholarly journals Validation of nine years of MOPITT V5 NIR using MOZAIC/IAGOS measurements: biases and long-term stability

2014 ◽  
Vol 7 (11) ◽  
pp. 3783-3799 ◽  
Author(s):  
A. T. J. de Laat ◽  
I. Aben ◽  
M. Deeter ◽  
P. Nédélec ◽  
H. Eskes ◽  
...  
Keyword(s):  
Near Infrared ◽  
Transport Model ◽  
A Priori ◽  
Validation Data ◽  
Chemistry Transport Model ◽  
Large Variability ◽  
Long Term Stability ◽  
Spatio Temporal ◽  
Good Agreement

Abstract. Validation results from a comparison between Measurement Of Pollution In The Troposphere (MOPITT) V5 Near InfraRed (NIR) carbon monoxide (CO) total column measurements and Measurement of Ozone and Water Vapour on Airbus in-service Aircraft (MOZAIC)/In-Service Aircraft for a Global Observing System (IAGOS) aircraft measurements are presented. A good agreement is found between MOPITT and MOZAIC/IAGOS measurements, consistent with results from earlier studies using different validation data and despite large variability in MOPITT CO total columns along the spatial footprint of the MOZAIC/IAGOS measurements. Validation results improve when taking the large spatial footprint of the MOZAIC/IAGOS data into account. No statistically significant drift was detected in the validation results over the period 2002–2010 at global, continental and local (airport) scales. Furthermore, for those situations where MOZAIC/IAGOS measurements differed from the MOPITT a priori, the MOPITT measurements clearly outperformed the MOPITT a priori data, indicating that MOPITT NIR retrievals add value to the MOPITT a priori. Results from a high spatial resolution simulation of the chemistry-transport model MOCAGE (MOdèle de Chimie Atmosphérique à Grande Echelle) showed that the most likely explanation for the large MOPITT variability along the MOZAIC-IAGOS profile flight path is related to spatio-temporal CO variability, which should be kept in mind when using MOZAIC/IAGOS profile measurements for validating satellite nadir observations.

Commercial microwave links instead of rain gauges: fiction or reality?

2014 ◽  
Vol 71 (1) ◽  
pp. 31-37 ◽  
Author(s):  
Martin Fencl ◽  
Jörg Rieckermann ◽  
Petr Sýkora ◽  
David Stránský ◽  
Vojtěch Bareš
Keyword(s):  
Rainfall Variability ◽  
A Priori ◽  
Rain Gauges ◽  
Precipitation Estimates ◽  
Spatio Temporal ◽  
Areal Rainfall ◽  
Quantitative Precipitation Estimates ◽  
Commercial Microwave Links ◽  
Unique Dataset

Commercial microwave links (MWLs) were suggested about a decade ago as a new source for quantitative precipitation estimates (QPEs). Meanwhile, the theory is well understood and rainfall monitoring with MWLs is on its way to being a mature technology, with several well-documented case studies, which investigate QPEs from multiple MWLs on the mesoscale. However, the potential of MWLs to observe microscale rainfall variability, which is important for urban hydrology, has not been investigated yet. In this paper, we assess the potential of MWLs to capture the spatio-temporal rainfall dynamics over small catchments of a few square kilometres. Specifically, we investigate the influence of different MWL topologies on areal rainfall estimation, which is important for experimental design or to a priori check the feasibility of using MWLs. In a dedicated case study in Prague, Czech Republic, we collected a unique dataset of 14 MWL signals with a temporal resolution of a few seconds and compared the QPEs from the MWLs to reference rainfall from multiple rain gauges. Our results show that, although QPEs from most MWLs are probably positively biased, they capture spatio-temporal rainfall variability on the microscale very well. Thus, they have great potential to improve runoff predictions. This is especially beneficial for heavy rainfall, which is usually decisive for urban drainage design.

Estimating local CH4 emissions in the Upper Silesian Coal Basin using inverse modelling

2021 ◽  
Author(s):  
Sebastian Wolff ◽  
Friedemann Reum ◽  
Christoph Kiemle ◽  
Gerhard Ehret ◽  
Mathieu Quatrevalet ◽  
...  
Keyword(s):  
Remote Sensing ◽  
A Priori ◽  
Point Sources ◽  
Airborne Lidar ◽  
Inverse Modelling ◽  
Emission Rates ◽  
Coal Basin ◽  
Upper Silesian Coal Basin ◽  
The Individual ◽  
Modelling Approach

&lt;p&gt;Methane (CH&lt;sub&gt;4&lt;/sub&gt;) is the second most important anthropogenic greenhouse gas (GHG) with respect to radiative forcing. Since pre-industrial times, the globally averaged CH&lt;sub&gt;4&lt;/sub&gt; concentration in the atmosphere has risen by a factor of 2.5. A large fraction of global anthropogenic CH&lt;sub&gt;4&lt;/sub&gt; emissions originates from localized point sources, e.g. coal mine ventilation shafts. International treaties foresee GHG emission reductions, entailing independent monitoring and verification support capacities. Considering the spatially widespread distribution of point sources, remote sensing approaches are favourable, in order to enable rapid survey of larger areas. In this respect, active remote sensing by airborne lidar is promising, such as provided by the integrated-path differential-absorption lidar CHARM-F operated by DLR. Installed onboard the German research aircraft HALO, CHARM-F serves as a demonstrator for future satellite missions, e.g. MERLIN. CHARM-F simultaneously measures weighted vertical column mixing ratios of CO&lt;sub&gt;2&lt;/sub&gt; and CH&lt;sub&gt;4&lt;/sub&gt; below the aircraft. In spring 2018, during the CoMet field campaign, measurements were taken in the Upper Silesian Coal Basin (USCB) in Poland. The USCB is considered to be a European hotspot of CH&lt;sub&gt;4&lt;/sub&gt; emissions, covering an area of approximately 50 km &amp;#215; 50 km. Due to the high number of coal mines and density of ventilation shafts in the USCB, individual CH&lt;sub&gt;4&lt;/sub&gt; exhaust plumes can overlap. This makes simple approaches to determine the emission rates of single shafts, i.e. the cross-sectional flux method, difficult. Therefore, we use an inverse modelling approach to obtain an estimate of the individual emission rates. Specifically, we employ the Weather Research and Forecast Model (WRF) coupled to the CarbonTracker Data Assimilation Shell (CTDAS), an Ensemble Kalman Filter. CTDAS-WRF propagates an ensemble realization of the a priori CH&lt;sub&gt;4&lt;/sub&gt; emissions forward in space and time, samples the simulated CH&lt;sub&gt;4&lt;/sub&gt; concentrations along the measurement&amp;#8217;s flight path, and scales the a priori emission rates to optimally fit the measured values, while remaining tied to the prior. Hereby, we obtain a regularized a posteriori best emission estimate for the individual ventilation shafts. Here, we report on the results of this inverse modelling approach, including individual and aggregated emission estimates, their uncertainties, and to which extent the data are able to constrain individual emitters independently.&lt;/p&gt;

The Road to Chaos by Time-Asymmetric Hebbian Learning in Recurrent Neural Networks

2007 ◽  
Vol 19 (1) ◽  
pp. 80-110 ◽  
Author(s):  
Colin Molter ◽  
Utku Salihoglu ◽  
Hugues Bersini
Keyword(s):  
Supervised Learning ◽  
Hebbian Learning ◽  
Learning Algorithm ◽  
Initial Conditions ◽  
A Priori ◽  
Computational Cost ◽  
Chaotic Regime ◽  
Dynamical Regime ◽  
New Form ◽  
The Impact

This letter aims at studying the impact of iterative Hebbian learning algorithms on the recurrent neural network's underlying dynamics. First, an iterative supervised learning algorithm is discussed. An essential improvement of this algorithm consists of indexing the attractor information items by means of external stimuli rather than by using only initial conditions, as Hopfield originally proposed. Modifying the stimuli mainly results in a change of the entire internal dynamics, leading to an enlargement of the set of attractors and potential memory bags. The impact of the learning on the network's dynamics is the following: the more information to be stored as limit cycle attractors of the neural network, the more chaos prevails as the background dynamical regime of the network. In fact, the background chaos spreads widely and adopts a very unstructured shape similar to white noise. Next, we introduce a new form of supervised learning that is more plausible from a biological point of view: the network has to learn to react to an external stimulus by cycling through a sequence that is no longer specified a priori. Based on its spontaneous dynamics, the network decides “on its own” the dynamical patterns to be associated with the stimuli. Compared with classical supervised learning, huge enhancements in storing capacity and computational cost have been observed. Moreover, this new form of supervised learning, by being more “respectful” of the network intrinsic dynamics, maintains much more structure in the obtained chaos. It is still possible to observe the traces of the learned attractors in the chaotic regime. This complex but still very informative regime is referred to as “frustrated chaos.”

Simulating star-forming regions in spiral galaxies with AMUSE

2019 ◽  
Vol 14 (S351) ◽  
pp. 216-219
Author(s):  
Steven Rieder ◽  
Clare Dobbs ◽  
Thomas Bending
Keyword(s):  
Gas Dynamics ◽  
Molecular Clouds ◽  
Spiral Galaxies ◽  
Initial Conditions ◽  
Cluster Formation ◽  
Star Cluster ◽  
Star Forming ◽  
Star Forming Regions ◽  
Formation And Evolution ◽  
Spiral Arm

AbstractWe present a model for hydrodynamic + N-body simulations of star cluster formation and evolution using AMUSE. Our model includes gas dynamics, star formation in regions of dense gas, stellar evolution and a galactic tidal spiral potential, thus incorporating most of the processes that play a role in the evolution of star clusters.We test our model on initial conditions of two colliding molecular clouds as well as a section of a spiral arm from a previous galaxy simulation.

scholarly journals Better Baltic Sea wave forecasts: improving resolution or introducing ensembles?

Ocean Science ◽  
2018 ◽  
Vol 14 (6) ◽  
pp. 1435-1447
Author(s):  
Torben Schmith ◽  
Jacob Woge Nielsen ◽  
Till Andreas Soya Rasmussen ◽  
Henrik Feddersen
Keyword(s):  
Baltic Sea ◽  
Wave Height ◽  
Spectral Resolution ◽  
Significant Wave Height ◽  
Initial Conditions ◽  
A Priori ◽  
The Baltic Sea ◽  
Significant Wave ◽  
Operational Forecasts ◽  
The Baltic

Abstract. The performance of short-range operational forecasts of significant wave height (SWH) in the Baltic Sea is evaluated. Forecasts produced by a base configuration are intercompared with forecasts from two improved configurations: one with improved horizontal and spectral resolution and one with ensembles representing uncertainties in the physics of the forcing wind field and the initial conditions of this field. Both of the improved forecast classes represent an almost equal increase in computational costs. Therefore, the intercomparison addresses the question of whether more computer resources would be more favorably spent on enhancing the spatial and spectral resolution or, alternatively, on introducing ensembles. The intercomparison is based on comparisons with hourly observations of significant wave height from seven observation sites in the Baltic Sea during the 3-year period from 2015 to 2017. We conclude that for most wave measurement sites, the introduction of ensembles enhances the overall performance of the forecasts, whereas increasing the horizontal and spectral resolution does not. These sites represent offshore conditions, in that they are well exposed from all directions, are a large distance from the nearest coast and in deep water. Therefore, there is the a priori expectation that a detailed shoreline and bathymetry will not have any impact. Only at one site do we find that increasing the horizontal and spectral resolution significantly improves the forecasts. This site is situated in nearshore conditions, close to land and a nearby island, and is therefore shielded from many directions. Consequently, this study concludes that to improve wave forecasts in offshore areas, ensembles should be introduced. For near shore areas, in comparison, the study suggests that additional computational resources should be used to increase the resolution.

scholarly journals A method for estimating Hill function-based dynamic models of gene regulatory networks

2018 ◽  
Vol 5 (2) ◽  
pp. 171226 ◽  
Author(s):  
Faizan Ehsan Elahi ◽  
Ammar Hasan
Keyword(s):  
Gene Regulatory Networks ◽  
Regulatory Networks ◽  
Optimization Problem ◽  
Dynamic Models ◽  
Initial Conditions ◽  
Computational Cost ◽  
Optimization Approach ◽  
Continuous Models ◽  
Gene Regulatory ◽  
The Cost

Gene regulatory networks (GRNs) are quite large and complex. To better understand and analyse GRNs, mathematical models are being employed. Different types of models, such as logical, continuous and stochastic models, can be used to describe GRNs. In this paper, we present a new approach to identify continuous models, because they are more suitable for large number of genes and quantitative analysis. One of the most promising techniques for identifying continuous models of GRNs is based on Hill functions and the generalized profiling method (GPM). The advantage of this approach is low computational cost and insensitivity to initial conditions. In the GPM, a constrained nonlinear optimization problem has to be solved that is usually underdetermined. In this paper, we propose a new optimization approach in which we reformulate the optimization problem such that constraints are embedded implicitly in the cost function. Moreover, we propose to split the unknown parameter in two sets based on the structure of Hill functions. These two sets are estimated separately to resolve the issue of the underdetermined problem. As a case study, we apply the proposed technique on the SOS response in Escherichia coli and compare the results with the existing literature.

scholarly journals Extracting Point Source Spectra / Recovering Extended Object Spectra Using Richardson-Lucy Restoration

2003 ◽  
Vol 209 ◽  
pp. 412-412
Author(s):  
J. R. Walsh ◽  
L. B. Lucy
Keyword(s):  
Point Source ◽  
A Priori ◽  
Central Star ◽  
Spectral Element ◽  
Point Sources ◽  
Source Spectrum ◽  
Extended Source ◽  
Extended Object ◽  
Source Signal ◽  
Source Spectra

Long slit spectra of astronomical objects either contain point sources, characterized by a known Point Spread Function (PSF), which is often wavelength dependent, and extended sources, such as nebulae, whose spatial extent is not a priori known. The analysis of long slit spectra consists in separating the spectrum into either: the point source(s), free of the background (“extraction”); or the extended source(s), free of contaminating point source spectra. Depending on the scientific aim, one or both of these data are of interest, such as the spectrum of the central star of a planetary nebula AND the line and continuum spectrum of the nebula with the star removed. In the simple case of a point source with a background gradient, the spectrum of the point source can be simply extracted by subtracting a background fit by a low order function and summing (perhaps with weights, as in optimal extraction) the point source signal at each spectral element in the cross-dispersion direction. When the background is complex or there are many point sources, there is no guide as to how to fit the extended source spectrum beneath the point sources. Simple methods can give a poor estimate of the spectra of point sources and the spectrum of the background in the vicinity of the stars. The application of image restoration algorithms to the spatial component of long slit spectra offers a potential solution.

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