Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications WORKSHOP ON DATA ASSIMILATION IN THE SCIENCES: FOCUS ON GEOPHYSICAL AND NEUROSCIENCE APPLICATIONS March 23- 26, 2015, Fudan University, Shanghai, China http://ccsb.fudan.edu.cn/wdas2015/ Workshop on Data Assimilation in the Sciences:Focus on Geophysical and Neuroscience Applications 1 Workshop on Data Assimilation in the Sciences:Focus on Geophysical and Neuroscience Applications Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Sponsored by Centre for Computational Systems Biology, Fudan University Shanghai Centre for Mathematical Sciences Organized by Centre for Computational Systems Biology, Fudan University Shanghai Centre for Mathematical Sciences Supported by School of Mathematical Sciences, Fudan University Workshop on Data Assimilation in the Sciences:Focus on Geophysical and Neuroscience Applications LOCAL ORGANIZING COMMITTEE General Chairs: Andrew Stuart, Warwick University, UK Henry Abarbanel, University of California, USA Jianfeng Feng, Fudan University, P.R. China & Warwick University, UK Co-chairs: Wenlian Lu, Fudan University, P.R. China Secretary: Qianyi Zhang, Fudan University, P.R. China Haiqing Wang, Fudan University, P.R. China Workshop on Data Assimilation in the Sciences:Focus on Geophysical and Neuroscience Applications CONTENTS I. TECHNICAL PROGRAM …………………………………………… 1 March 23 ………………………………………………………………… 1 March 24 ………………………………………………………………… 2 March 25 ………………………………………………………………… 3 March 26 ………………………………………………………………… 4 II. CONFERENCE INFORMATION R E G IS T R AT IO N ……………………………………5 ………………………………………………………5 AC C O M M OD AT IO N …… …… …… ………… …… ……… ………… … 5 VENUE …………………………………………………………………5 RECEPTION BANQUET ………………………………………………5 MEALS ………………………………………………………………5 TRANSPORTATION ……………………………………………….……6 CONTACTS ………………………………………………..…………..…………8 III. ABSTRACT …………………………………………………….………9 IV. OVERVIEW OF CCSB ……………………………………………………26 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications I. TECHNICAL PROGRAM March 23, Monday (Room 1801, East Guanghua Building, Fudan University) Morning Session Panel(9:00–12:00) Chair: Henry Abarbanel 9:00-9:30 Open Speech Henry Abarbanel (University of California, San Diego) 9:30-10:30 Title: Data Assimilation: A coupling of Measures Perspective Sebastian Reich (University of Potsdam) 10:30-11:00 Conference Photograph & Coffee Break 11:00-12:00 Title: A Low-order Coupled Chemistry Meteorology Model for Testing Advanced Data Assimilation Schemes Marc Bocquet ( École des Ponts ParisTech ) Afternoon Session (14:00-17:30) Chair: Andrew Stuart 14:00-15:00 Title: Sampling Hazards in Data Inference David Cai(New York University & Shanghai Jiao Tong University) 15:00-15:30 Coffee Break 15:30-16:30 Title: Data Based Modelling: Inferring Direct Directed Interactions from Time Series Bjoern Schelter (University of Aberdeen) 16:30-17:30 Title: Ensemble Bayesian Filtering in Oceanography: Successes and Remaining Challenges Ibrahim Hoteit (King Abdullah University of Science and Technology) 1 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications March 24, Tuesday (Room 1801, East Guanghua Building, Fudan University) Morning Session (9:00-11:30) Chair: Henk Nijmeijer 9:00-10:00 Title: Bayesian Inference for Markov Processes with Application to Biochemical Network Dynamics Darren Wilkinson (Newcastle University) 10:00-10:30 Coffee Break 10:30-11:30 Title: From Computational Neuronal Network to Functional MRI: A Prospective of Data Assimilation Wenlian Lu (Fudan University) Afternoon Session (14:00-17:30) Chair: Darren Wilkinson 14:00-15:00 Title: Synchronization in Networks of Diffusively (Time-delayed) Coupled Semi-passive Systems: Does the Electronic Brain Synchronize? Henk Nijmeijer (Eindhoven University of Technology) 15:00-15:30 Coffee Break 15:30-16:30 16:30-17:30 Title: Intelligent Sensing, Data Analysis, and Health Monitoring for Engineered and Biological Systems Liming W. Salvino (US Office of Naval Research Global) Title: Data Processing and Data Driven Modelling in Mental Disorders Jianfeng Feng (Fudan University & Warwick University) 2 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications March 25, Wednesday (Room 2001, East Guanghua Building, Fudan University) Morning Session (9:00-11:30) Chair: Yuguo Yu 9:00-10:00 Title: In Silico Neuroscience: Emergent Structural and Functional Properties of a Neocortical Microcircuit Sean Hill (École Polytechnique Fédérale de Lausanne) 10:00-10:30 Coffee Break 10:30-11:30 Title: Implicit Sampling for Data Assimilation Xuemin Tu (University of Kanas) Afternoon Session (14:00-17:30) Chair: Sean Hill 14:00-15:00 Title: Reconstructing Brain Energy Map and Conserved Energy Budget Rules in Brain Gray Matter and White Matter Across Species Yuguo Yu (Fudan University) 15:00-15:30 Coffee Break 15:30-16:30 Title: On Ensemble and Particle Filters for Large-scale Data Assimilation Roland Potthast (Deutscher Wetterdienst and Reading University) 16:30-17:30 Title: Filtering Partially Observed Chaotic Deterministic Dynamical Systems Andrew Stuart (Warwick University) 3 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications March 26, Thursday (Room 2001, East Guanghua Building, Fudan University) Morning Session (9:00-11:45) Chair: Jianfeng Feng 9:00-10:00 Title: Defining Optimization Problems for Climate Study Nozomi Sugiura (Japan Agency for Marine-Earth Science and Technology ) 10:00-10:30 Coffee Break 10:30-11:30 11:30-11:45 Title: TBA Henry Abarbanel (University of California) Close Talk Andrew Stuart (Warwick University) 4 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications II. CONFERENCE INFORMATION REGISTRATION Could all participants please register at the earliest opportunity. The registration desk will be open at the Lobby of Crowne Plaza Shanghai Fudan, 199 Handan Road (Near: Guoquan Road), on Sunday March 22nd from 13:30 – 17:30. There will also be an opportunity to register at Room 1801, East Guanghua Building, Fudan University, on Monday March 23rd from 08:30-09:00. Your conference materials await collection at the Conference Registration Desk. ACCOMMODATION Accommodation will be arranged at Crowne Plaza Shanghai Fudan. It is located near the main campus of Fudan University, which holds the conference venue. VENUE From March 23rd to March 24th, our conference will take place at Room 1801, East Guanghua Building, which is located in the Handan Campus of Fudan University, 220 Handan Road, Shanghai, P.R.China. From March 25th to March 26th, our conference will take place at Room 2001, East Guanghua Building, Fudan University. RECEPTION BANQUET The reception banquet will take place in the Chancellors Club on the 19th floor of Crowne Plaza Shanghai Fudan, on Sunday March 22nd from 18:00 – 20:00. MEALS Lunches and Dinners from March 23rd to 26th will be provided to all participants on the third floor of Danyuan Restaurant. Breakfast will be available in the hotel where you are staying. 5 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications TRANSPORTATION HOW TO REACH THE VENUE From Airport To Fudan University (Handan Campus): Hongqiao Airport: 1. Taxi to Fudan University costs roughly RMB 90. 2. Take a Metro Line 10 to Jiangwan Stadium Stop (江湾体育场站), which costs RMB 7, and then walk (approximately 15 minutes to the Centre). Pudong International Airport: 1. Taxi to Fudan University costs roughly RMB 160. 2. Shuttle Bus Line 4 (机场四线) to Wu Jiao Chang Stop (五角场) , which costs RMB 20, and then walk (approximately 15 minutes to the Centre). From Train Station To Fudan University (Handan Campus): Shanghai Railway Station: 1. Get out from the South Exit of the Railway Station and then take a taxi to Fudan University, which costs roughly RMB 30. 2. Get out from the North Exit of the Railway Station and then take a No. 942 Bus to Fudan University Stop (复旦大学). Shanghai South Railway Station: Take a Metro Line 3 to Chifeng Road Stop (赤峰路) and then transfer to No. 139 or 854 or 942 or 991 Bus to Fudan University Stop (复旦大学). Hongqiao Railway Station: Take a Metro Line 10 to Jiangwan Stadium Stop (江湾体育场站), which costs RMB 7, and then walk (approximately 15 minutes to the Centre). 6 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Please show the following poster to the taxi driver, if you arrive at Shanghai and intend to take a taxi at the airport or at the railway station to Crowne Plaza Shanghai Fudan. Please take me to: Crowne Plaza Shanghai Fudan Address: 199 Handan Road (Near: Guoquan Road), Shanghai Contact: 86-21- 55529999 请把我送到: 上海复旦皇冠假日酒店 地址:上海市邯郸路 199 号(国权路口) 联系电话: 86-21-55529999 Map of Fudan 7 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications CONTACTS Wenlian Lu, Professor Centre for Computational Systems Biology, School of Mathematical Sciences, Fudan University, Shanghai 200433, China Contact Phone Number: +86-21-5566-5141 Email: [email protected] Qianyi Zhang, Secretary Centre for Computational Systems Biology, Fudan University, Shanghai 200433, China Contact Phone Number: +86-21-5566-5546 ext. 8001 Email: [email protected] 8 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Data Assimilation: A coupling of Measures Perspective Sebastian Reich University of Potsdam, Germany [email protected] Reliable forecasting requires the fusion of scientific modeling with available data. When dynamkical phenomena are to be forecasted, this task leads to sequential data assimilation problems which are best tackled from a Bayesian perspective. Bayes' formula provides the centerpiece for Bayesian data assimilation and Bayesian learning in general. However, beyond its conceptional simplicity and beauty, Bayes' formula is hardly ever directly applicable and this is true in particular when Bayes' formula needs to be interfaced with complex scientific models. In this context it is better to talk of simulating Bayes' formula. Bayes' formula can be simulated in the setting of sequential Monte Carlo methods and general Markov chain Monte Carlo methods. However, those methods suffer from the curse of dimensionality. In my talk, I will approach Bayes' formula from the perspective of coupling probability measures and optimal transportation. This approach (i) naturally puts the popular ensemble Kalman filters into context and suggests natural extensions to non-Gaussian data assimilation problems, (ii) allows for the implementation of sequential Monte Carlo methods in high dimensions using the concept of localisation, and (iii) can be combined with quasi-Monte Carlo sampling approaches. 9 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications A Low-order Coupled Chemistry Meteorology Model for Testing Advanced Data Assimilation Schemes Marc Bocquet , Jean-Matthieu Haussaire CEREA joint laboratory Ecole des Ponts ParisTech and EdF R&D, Université Paris-Est, France. [email protected] In this talk I will illustrate the interest of developing a low-order model to test the performance of advanced data assimilation schemes, as well as their feasibility to higher dimensional models. We have recently introduced a low-order model based on the coupling of the chaotic Lorenz-95 model which simulates winds along a mid-latitude circle, with the transport of a tracer species advected by this wind field. It has been used to test advanced data assimilation methods with an online model that couples meteorology and tracer transport. In the present study, the tracer subsystem of the model is replaced with a reduced photochemistry module meant to emulate reactive air pollution. This coupled chemistry meteorology model, the L95-GRS model, mimics continental and transcontinental transport and photochemistry of ozone, volatile organic compounds and nitrogen dioxides. The L95-GRS is specially useful in testing advanced data assimilation schemes, such as the iterative ensemble Kalman smoother (IEnKS) that combines the best of ensemble and variational methods. The model provides useful insights prior to any implementation of the data assimilation method on larger models. For instance, online and offline data assimilation strategies based on the ensemble Kalman filter or the IEnKS can easily be compared with it. It allows to document the impact of species concentration observations on the wind estimation. The model also illustrates a long standing issue in atmospheric chemistry forecasting: the impact of the wind chaotic dynamics and of the chemical species non-chaotic but highly nonlinear dynamics on the selected data assimilation approach. 10 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Sampling Hazards in Data Inference David Cai New York University & Shanghai Jiao Tong University, P.R. China [email protected] Erroneous inferences can arise in data processing due to sampling hazards. Their resolutions often require one to go deeper to understand underlying dynamical mechanisms. Two illustrative examples will be presented. The first example is potential inference hazards in the application of Grange causality (GC). An effective strategy of overcoming GC sampling issues will be described. In particular, the detailed underlying mechanism for its successful application in the reconstruction of the network topology of nonlinear neuronal networks will be discussed. The second example will illustrate in detail how a large scale computational modeling of the primary visual cortex (V1) has helped to resolve uncertainties about cortical mechanisms inferred from optical imaging of the spatiotemporal dynamics of V1. 11 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Data Based Modelling: Inferring Direct Directed Interactions from Time Series Bjoern Schelter University of Aberdeen, UK [email protected] Recent years have seen a large increase in the availability of data. In fact, increasing amounts of data play a key role in every aspect of our lives, including but not restricted to physics, such as for the Large Hadron Collider (CERN) and the Square Kilometre Array (South Africa), biology, e.g. genomic data, medicine, e.g. functional magnetic resonance imaging or electroencephalography, and data mining in the social sciences or digital economies. Dealing with these data sets efficiently determines the success of the projects, treatments, assessments, and analyses. This necessity to better understand and analyse data has led to an outburst of research into advanced methods of data analysis. The inference of networks underlying complex systems is of utmost importance. Especially when dealing with complex data sets the algorithms for network inference have to fulfil certain fundamental requirements: (i) they need to deal with truly multivariate data, i.e. they must distinguish between direct and indirect influences, (ii) they have to account for various concurrent noise sources, (iii) they need to addresses both linear and non-linear systems, (iv) provide results for each sampling point, (v) and estimate the strengths of the directed interactions. Finally, (vi) they need to provide a rigorous statistical framework to allow their evaluation and (vii) be numerically efficient. A multitude of algorithms has been developed to address these extremely challenging requirements, but until now only very few can address them simultaneously. This is partly due to the fact that a rigorous mathematical framework, i.e. a theory of a suitable highly versatile class of mathematical models to comprise all of these features, is challenging. In this lecture, the challenges will be introduced and means to address these will be discussed. Various methods will be compared and their abilities and limitations will be discussed. This results in a comprehensive overview of techniques that exists to tackle one of the key challenges of data based modelling: The detection of direct directed interactions from time series. 12 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Ensemble Bayesian Filtering in Oceanography: Successes and Remaining Challenges Ibrahim Hoteit King Abdullah University of Science and Technology, Saudi Arabia [email protected] Ensemble Kalman filters (EnKFs) have made long way since they have been introduced for ocean data assimilation in the last decade, reaching performances comparable to 4DVAR while offering computational flexibility and providing, even crudely, estimates of uncertainties. In the first part of my talk I will present the EnKFs and 4DVAR from a Bayesian formulation point of view, arguing that both are different solutions for the same problem. I will present experiments results comparing an EnKF and 4DVAR for predicting the evolution of the loop current in the Gulf of Mexico. The second part of the talk will discuss the remaining challenges of the EnKFs, focusing on the prior (or background) limitations and the Gaussian-based analysis step. I will present an adaptive EnKF-Variational scheme that we have introduced to mitigate the EnKF prior limitations and discuss its relation with the hybrid EnKF-3DVAR schemes. I will also discuss recent developments for deriving efficient non-Gaussian update schemes based on the Particle and Gaussian-Mixture filters, or a hybrid scheme of these that we recently proposed. 13 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Bayesian Inference for Markov Processes with Application to Biochemical Network Dynamics Darren Wilkinson Newcastle University, UK [email protected] A number of interesting statistical applications require the estimation of parameters underlying a nonlinear multivariate continuous time Markov process model, using partial and noisy discrete time observations of the system state. Bayesian inference for this problem is difficult due to the fact that the discrete time transition density of the Markov process is typically intractable and computationally intensive to approximate. It turns out to be possible to develop particle MCMC algorithms which are exact, provided that one can simulate exact realisations of the process forwards in time. Such algorithms, often termed "likelihood free" or "plug-and-play" are very attractive, as they allow separation of the problem of model development and simulation implementation from the development of inferential algorithms. Such techniques break down in the case of perfect observation or high-dimensional data, but more efficient algorithms can be developed if one is prepared to deviate from the likelihood free paradigm. The methods will be illustrated using examples from population dynamics and stochastic biochemical network dynamics. 14 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications From Computational Neuronal Network to Functional MRI: A Prospective of Data Assimilation Wenlian Lu Fudan University, P.R. China [email protected] Functional MRI, known as BOLD signals, are indirect measurements of the neural activities and so less capable to identify the variants of the neural system, in terms of neurotransmitter receptors. An integration of fMRI analysis and computational neuronal network model may enlighten the relationship between the characteristic identified by fMRI study and the variants of the underlying neuronal network. To conduct inference from BOLD signals to neuronal network model, data assimilation might present an efficient method towards understanding the neurophysiological basis of fMRI data. 15 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Synchronization in Networks of Diffusively (Time-delayed) Coupled Semi-passive Systems: Does the Electronic Brain Synchronize? Henk Nijmeijer Eindhoven University of Technology, Netherlands [email protected] The talk consists of three parts. In the first part of the talk we will discuss synchronization in a network of semi-passive systems, i.e. systems that remain bounded if no external activation occurs. The coupling is allowed to contain time-delay and thus mimics the fact that in many physical and biological systems interaction does take some time. The results are illustrated with numerical simulations. In the second part we review shortly some basic mathematical properties that are valid for all existing models of neuronal cells-at least as regarding their electrical activity. We show that under fairly general conditions a network of neuronal cells will exhibit synchronization provided their coupling structure is sufficiently strong. This result, though often accepted, can be proven using the concept of semi-passivity. Next, experimental results regarding an electronic realization of a network of neuronal Hindmarsh-Rose systems are presented. Some of these results illustrate the aforementioned theory, whereas additional experiments deal with (partial) synchronization of time-delayed coupled neuronal systems and induce a conjecture regarding scaling in network synchronization under time-delayed coupling. In the third and final part we review how one can derive sufficient conditions for time-delayed coupled network synchronization on basis of such results for possible smaller and simpler networks. [1] E.Steur, I.Tyukin, H.Nijmeijer, 'Semi-passivity and synchronization of diffusively coupled neuronal oscillators', Physica D 238, pp.2119-2128, (2009). [2] E.Steur, H.Nijmeijer, Synchronization in networks of diffusively time-delay coupled (semi-) passive systems, IEEE Transactions on Circuits and Systems, vol 58 (8), 2011. [3] P.J.Neefs, E.Steur, H.Nijmeijer, Network complexity and synchronous behavior-an experimental approach, Intern Journal of Neural Systems, vol.20, pp.233-247, 2010. [4] E.Steur, W.Michiels, H.Huijberts and H.Nijmeijer, ‘Networks of diffusively time-delayed coupled systems: Conditions for synchronization and its relation to the network topolgy’, Physica D, 277, pp.22-37, 2014. 16 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Intelligent Sensing, Data Analysis, and Health Monitoring for Engineered and Biological Systems Liming W. Salvino US Office of Naval Research Global Embassy of the United States of America, Singapore [email protected] The ability to turn data into information, knowledge, and innovative products often separates success from failure. This presentation provides an overview of structural health monitoring (SHM) technologies and illustrates how SHM can be greatly improved by creating better data analytical methods through an adaptive data analysis approach. SHM is a multidisciplinary science and engineering field with many applications, including those in bio-medical sciences. Understanding data representing nonlinear and non-stationary systems is the key for a successful future SHM implementation applied to intelligent engineered and biological systems. This presentation also gives an overview of the Office of Naval Research Global (ONRG) and its international program tools. ONRG strives to find innovative research, enable technology awareness, and enhance communication and international collaborations. A few ongoing and future international and interdisciplinary collaboration programs for developing SHM technologies and data science will be discussed. 17 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Data Processing and Data Driven Modelling in Mental Disorders Jianfeng Feng Fudan University, P.R. China & Warwick University, UK [email protected] With the accumulated huge data at different scales ranging from whole genome to different behaviours , we are facing challenging problems both in processing and modelling. In the talk, we will first review some of our recent progresses in dealing with genomic, whole brain images, and symptoms for autistic patients and schizophrenia patients. With the largest image data in these disorders, we are able to isolate the key altered areas and hence help us to search for the roots of these disorders. Using modelling approaches, we intend to explore the mechanisms of these disorders and we will illustrate the current difficulties we have. 18 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications In Silico Neuroscience: Emergent Structural and Functional Properties of a Neocortical Microcircuit Sean Hill École Polytechnique Fédérale de Lausane, Switzerland [email protected] The Blue Brain Project consortium has developed a predictive, algorithmic reconstruction strategy that integrates sparse experimental data to derive principles of brain structure and function. A first draft detailed anatomical and physiological map of a prototypical neocortical microcircuit will be presented. This approach integrates knowledge and data from the literature and from experimental neuroscience including single and multi-cell electrophysiology, morphological reconstruction, gene expression, ion channel kinetics and in vitro network experiments using multi-electrode arrays. The resulting model microcircuit is 0.28 mm3 in volume and contains 31,000 neurons belonging to 55 morphological neuron types and 207 morpho-electrical sub-types distributed across 6 layers. The model predicts: the number of neurons of each type per layer (the neurome) with around 7.5 million intrinsic and 27 million extrinsic connections forming around 40 and 141 million synapses, respectively (the connectome); the detailed anatomy and physiology of 2,258 unique synaptic pathways between neurons of different morphological types, 31,628 unique pathways between neurons of different morpho-electrical types, 600 intra- laminar and 1,658 inter-laminar pathways; and the complete map of intrinsic synapses for all neurons (their synaptomes). In silico simulations of the reconstructed microcircuit provide novel, simple and standardized measures of microcircuit behaviour and the computational role of any component of the microcircuit. 19 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Implicit Sampling for Data Assimilation Xuemin Tu The University of Kanas, USA [email protected],[email protected] Applications of filtering and data assimilation arise in engineering, geosciences, weather forecasting, and many other areas where one has to make estimations or predictions based on uncertain models supplemented by a stream of data with noise. For nonlinear problems, filtering can be very expensive since the number of the particles required can grow catastrophically. We will present a particle-based nonlinear filtering scheme. This algorithm is based on implicit sampling, a new sampling technique related to chainless Monte Carlo method. This sampling strategy generates a particle (sample) beam which is focused towards on the high probability region of the target pdf and the focusing makes the number of particles required manageable even if the state dimension is large. Several examples will be given. 20 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Reconstructing Brain Energy Map and Conserved Energy Budget Rules in Brain Gray Matter and White Matter Across Species Yuguo Yu Fudan University, P.R. China [email protected] The human brain is organized on multiple scale network connections and function-dependent regions for low-level sensory information processing to high-order cognitive functions. How is the metabolic energy distributed within the brain supporting those activities is not known well. Are there any economic principles and computational rules underlying brain energy distribution in normal/abnormal brains? In this study, we first calculated energy consumptions in all the known brain components (signaling and non-signaling) of brain cells (including GABAergic interneurons, glutamate-based excitatory neurons, glia cells) in gray matter and white matter based on existing physiological parameters of cells, spiking activities and synaptic transmissions. We then confirmed these brain energy budget calculations with functional MRI and 13C MRS measurements. We next calculated the cell density distribution based on cluster analysis of the BigBrain data (a reconstruction of 7404 cell-stained histological Sections with cellular resolution of 20 micrometer, from a donated 65-years old healthy woman brain, (2013, Science “BigBrain: An Ultrahigh-Resolution 3D Human Brain Model”). Then, we feed the energy budget calculations of individual neurons and glia into brain cell density map, formulating a 3-D brain energy map with energy calculations in unit of either glucose in micromole/min/gram or ATP/min/gram in order to compare with PET measurement of actual brain. The quantitative comparison demonstrated a perfect match, indicating a successful first reconstruction of brain energy map fully consistent with PET glucose imaging measurement. The results suggest: 1) the brain energy changes are mainly controlled by a key factor, i.e., the mean firing rate. Resting human brain might have an averaged firing rate ~1-1.5 Hz, as expected from previous experimental evidences (~1 Hz for the human brain). 2) The brain energy distribution statistics are majorly determined by the densities of neuronal and glia cell distributions. 3) Bottom-up energy budget calculations can capture the major energy consumption sources, which include contributions from housekeeping, resting potential, action potentials, synaptic potentials for neurons and glia in both gray matter and white matter. 4) Brain signaling processes consume over 62% of gray matter and 25% of white matter energy; all cortical glia cells consume about 11% of gray matter energy; all the GABAergic neurons consume 20% of whole energy for neuronal populations. Most importantly, these percentage rules are same for both the human brain and rat, suggesting general rules conserved across species for brain energy budget from mammals, primates to humans. 21 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications On Ensemble and Particle Filters for Large-scale Data Assimilation Roland Potthast Deutscher Wetterdienst, Germany & Reading University, UK [email protected] In almost all operational centres for numerical weather prediction around the world ensemble data assimilation techniques are of rapidly growing importance. Ensemble techniques allow to describe and forecast uncertainty of the analysis, but they also improve the assimilation result itself, by allowing estimates of the covariance or, more general, the prior and posterior probability distribution of atmospheric states. In our talk, we will first give a survey about recent activities of the German Meteorological Service DWD, who is working towards the use of an Ensemble Kalman Filter both for its new global ICON model as well as for the convective scale high-resolution model COSMO-DE. To be more precise, for the global model a hybrid variational ensemble Kalman filter (VarEnKF) is under development. We survey the setup of its Ensemble Kalman Filter component, which is based on the LETKF of Hunt, with a range of further features such as relaxation to prior perturbations or random perturbations. Then, for the kilometer scale ensemble data assimilation (KENDA) for the 2.8km/2.2km resolution COSMO-DE model we des-cribe the ensemble Kalman filter which is being tuned for operational use and show recent results which demonstrate that it is clearly superior to the current nudging scheme. We will also point to very encouraging results on the performance of the COSMO-DE-EPS when initial conditions for its 40-member ensemble are taken from KENDA. In collaborations with several universities and the DWD-funded Hans Ertel Centre on Weather Research (HErZ), research groups employ the ensemble Kalman filter of KENDA as a basis for further research on the assimilation of particular observation systems, such as radar reflectivities, MODE-S data or SEVIRI radiances. We give a brief survey about the state of these projects. In the third part of the talk, we present recent work on the further development of the ensemble data assimilation towards a particle filter for large-scale atmospheric systems, which keeps the advantages of the LETKF, but overcomes some of its limitations. We describe a Localized Markov Chain Particle Filter (LMCPF), present its mathematical foundation and show some tests for simple systems. The implementation of the LMCPF in the KENDA framework of DWD is ongoing work. 22 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Filtering Partially Observed Chaotic Deterministic Dynamical Systems Andrew Stuart Warwick University, UK [email protected] This talk is concerned with determining the state of a chaotic dynamical system, for which the initial condition is only known probabilisticlly, given partial and noisy observations. In particular it is of interest to study this problem in the limit of a large number of such observations, over a long time interval. A key question is to determine which observations are sufficient in order to accurately recover the signal, and thereby overcome the lack of predictiability caused by sensitive dependence on initial conditions. A canonical application is the development of probabilistic weather forecasts. The evolution of many physical systems can be successfully modelled by a deterministic dynamical system for which, however, the initial conditions may contain uncertainty. In the presence of chaos this can lead to undesirable growth of uncertainty over time. However, when noisy observations of the system are present these may be used to compensate for the uncertainty in the initial state. This scenario is naturally modelled by viewing the initial state as given by a probability distribution, and to then condition this probability distribution on the noisy observations, thereby reducing uncertainty. This reduced uncertainty on the initial condition results in reduced uncertainty on the system state at later times. Filtering refers to the situation where the conditional distribution on the system state is updated sequentially, at the time of each observation. The objective of the work described in this talk is to study the asymptotic behaviour of this filtering distribution for large time, a question which relates to the issue of predictability in noisily observed chaotic dynamical systems. In order to study this problem concretely, we will focus on a wide class of dissipative differential equations with quadratic energy-conserving nonlinearity, including the Lorenz 63 and Lorenz 96 models, as well as the Navier-Stokes equation on a 2D torus. The talk will combine ideas from control theory (nonlinear observer), dynamical systems (synchronization) and probability (optimal filter and Galerkin orthogonality) to provide concrete results for this wide class of models. Furthermore, we will consider continuous time limits of the algorithms which give rise to various interesting stochastic partial differential equations (SPDEs). The techniques used to prove our results will build upon two algorithms that are widely used in the numerical weather prediction community, namely the 3DVAR and Ensemble Kalman Filter (EnKF) methods. 23 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications The synchronization techniques which underlie this work are developed in [1] and prototypical results concerning nonlinear observers may be found in [2]. The probabilistic results in this talk, which build on the work in [1,2], may be found in [3]. Further background in the 3DVAR and EnKF methods, as well as derivation of their continuous time SPDE limits, may be found in [4,5,6]. The book [7] provides a pedagogical introduction to this material. [1] K. Hayden, E. Olsen and E.S. Titi, “Discrete data assimilation in the Lorenz and 2D Navier?“Stokes equations.'' Physica D 240(2011) 1416-1425. [2] T. Tarn and Y. Rasis, “Observers for nonlinear stochastic systems''. IEEE Transactions on Automatic Control 21(1976) 441--448. [3] D. Sanz-Alonso and A.M.Stuart, “Long-time asymptotics of the filtering distribution for partially observed chaotic deterministic dynamical systems.'' http://arxiv.org/abs/1411.6510 [4] K.J.H. Law, A. Shukla and A.M. Stuart, “Analysis of the 3DVAR filter for the partially observed Lorenz '63 model.'' Discrete and Continuous Dynamical Systems A, 34(2014), 1061-1078. http://arxiv.org/abs/1212.4923 [5] D. Bloemker, K.J.H. Law, A.M. Stuart and K. Zygalalkis.”Accuracy and stability of the continuous-time 3DVAR filter for the Navier-Stokes equation”. Nonlinearity 26(2013), 2193-2219. http://arxiv.org/abs/1210.1594 [6] D.T.B. Kelly and K.J.H. Law and A.M. Stuart. “Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time”. Nonlinearity 27(2014), 2579-2603. http://arxiv.org/abs/1310.3167 [7] K.J.H. Law, A.M.Stuart and K. Zygalalkis, “Data Assimilation: A Mathematical Introduction.” In preparation, 2015. 24 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications Defining Optimization Problems for Climate Study Nozomi Sugiura Japan Agency for Marine-Earth Science and Technology, Japan [email protected] To make climate data assimilation problems tractable, we usually change the optimization problem into a regularized form. The regularization is realized by attracting rapid modes to a reference model field. Also, I will discuss about how to formulate an effective cost function for climate study. 25 Workshop on Data Assimilation in the Sciences: Focus on Geophysical and Neuroscience Applications IV. OVERVIEW OF CCSB The Centre for Computational Systems Biology (CCSB) of Fudan University was founded in March 2008. Our center focuses its research on Computational Neuroscience/Biology and Cellular Biology. The director of the centre is Professor Jianfeng Feng, also professor and head of the Laboratory of Computational Biology in Warwick University, United Kingdom. The Centre now has around thirty+ research members, an administrative assistant, two research assistants, and twenty+ Ph.D. students. The Centre is divided into three Research Groups, Cellular Biology, Computational Neuroscience, and Computational Biology. The members of the centre have various academic backgrounds, ranging from applied mathematics to statistics, from biology physics to molecular biology, and to neuroscience. We have published papers in Nature (6), Science (7), Mol. Psychiatry (1) Curr. Biol. (3), PNAS (5), Mol. Sys. Biol. (1), J. Neurosci. (4), PRL (5), PLoS Comp. Biol. (7) and others. The Centre is currently in a growing phase. We welcome applications from colleagues interested in joining us. 26
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