299 research outputs found
Numerical Bifurcation Analysis of PDEs From Lattice Boltzmann Model Simulations: a Parsimonious Machine Learning Approach
We address a three-tier data-driven approach for the numerical solution of the inverse problem in Partial Differential Equations (PDEs) and for their numerical bifurcation analysis from spatio-temporal data produced by Lattice Boltzmann model simulations using machine learning. In the first step, we exploit manifold learning and in particular parsimonious Diffusion Maps using leave-one-out cross-validation (LOOCV) to both identify the intrinsic dimension of the manifold where the emergent dynamics evolve and for feature selection over the parameter space. In the second step, based on the selected features, we learn the right-hand-side of the effective PDEs using two machine learning schemes, namely shallow Feedforward Neural Networks (FNNs) with two hidden layers and single-layer Random Projection Networks (RPNNs), which basis functions are constructed using an appropriate random sampling approach. Finally, based on the learned black-box PDE model, we construct the corresponding bifurcation diagram, thus exploiting the numerical bifurcation analysis toolkit. For our illustrations, we implemented the proposed method to perform numerical bifurcation analysis of the 1D FitzHugh-Nagumo PDEs from data generated by D1Q3 Lattice Boltzmann simulations. The proposed method was quite effective in terms of numerical accuracy regarding the construction of the coarse-scale bifurcation diagram. Furthermore, the proposed RPNN scheme was ∼ 20 to 30 times less costly regarding the training phase than the traditional shallow FNNs, thus arising as a promising alternative to deep learning for the data-driven numerical solution of the inverse problem for high-dimensional PDEs
ISOMAP and machine learning algorithms for the construction of embedded functional connectivity networks of anatomically separated brain regions fromresting state fMRI data of patients with Schizophrenia
We construct Functional Connectivity Networks (FCN) from resting state fMRI (rsfMRI) recordings towards the classification of brain activity between healthy and schizophrenic subjects using a publicly available dataset (the COBRE dataset) of 145 subjects (74 healthy controls and 71 schizophrenic subjects). First, we match the anatomy of the brain of each individual to the Desikan- Killiany brain atlas. Then, we use the conventional approach of correlating the parcellated time series to construct FCN and ISOMAP, a nonlinear manifold learning algorithm to produce low-dimensional embeddings of the correlation matrices. For the classification analysis, we computed five key local graph-theoretic measures of the FCN and used the LASSO and Random Forest (RF) algorithms for feature selection. For the classification we used standard linear Support Vector Machines. The classification performance is tested by a double cross-validation scheme [consisting of an outer and an inner loop of “Leave one out” cross-validation (LOOCV)]. The standard cross-correlation methodology produced a classification rate of 73.1%, while ISOMAP resulted in 79.3%, thus providing a simpler model with a smaller number of features as chosen from LASSO and RF, namely the participation coefficient of the right thalamus and the strength of the right lingual gyrus
Universality of ac-conduction in anisotropic disordered systems: An effective medium approximation study
Anisotropic disordered system are studied in this work within the random
barrier model. In such systems the transition probabilities in different
directions have different probability density functions. The
frequency-dependent conductivity at low temperatures is obtained using an
effective medium approximation. It is shown that the isotropic universal
ac-conduction law, , is recovered if properly scaled
conductivity () and frequency () variables are used.Comment: 5 pages, no figures, final form (with corrected equations
Avoiding catastrophic failure in correlated networks of networks
Networks in nature do not act in isolation but instead exchange information,
and depend on each other to function properly. An incipient theory of Networks
of Networks have shown that connected random networks may very easily result in
abrupt failures. This theoretical finding bares an intrinsic paradox: If
natural systems organize in interconnected networks, how can they be so stable?
Here we provide a solution to this conundrum, showing that the stability of a
system of networks relies on the relation between the internal structure of a
network and its pattern of connections to other networks. Specifically, we
demonstrate that if network inter-connections are provided by hubs of the
network and if there is a moderate degree of convergence of inter-network
connection the systems of network are stable and robust to failure. We test
this theoretical prediction in two independent experiments of functional brain
networks (in task- and resting states) which show that brain networks are
connected with a topology that maximizes stability according to the theory.Comment: 40 pages, 7 figure
Spectral statistics of random geometric graphs
We use random matrix theory to study the spectrum of random geometric graphs,
a fundamental model of spatial networks. Considering ensembles of random
geometric graphs we look at short range correlations in the level spacings of
the spectrum via the nearest neighbour and next nearest neighbour spacing
distribution and long range correlations via the spectral rigidity Delta_3
statistic. These correlations in the level spacings give information about
localisation of eigenvectors, level of community structure and the level of
randomness within the networks. We find a parameter dependent transition
between Poisson and Gaussian orthogonal ensemble statistics. That is the
spectral statistics of spatial random geometric graphs fits the universality of
random matrix theory found in other models such as Erdos-Renyi, Barabasi-Albert
and Watts-Strogatz random graph.Comment: 19 pages, 6 figures. Substantially updated from previous versio
Modularity map of the network of human cell differentiation
Cell differentiation in multicellular organisms is a complex process whose
mechanism can be understood by a reductionist approach, in which the individual
processes that control the generation of different cell types are identified.
Alternatively, a large scale approach in search of different organizational
features of the growth stages promises to reveal its modular global structure
with the goal of discovering previously unknown relations between cell types.
Here we sort and analyze a large set of scattered data to construct the network
of human cell differentiation (NHCD) based on cell types (nodes) and
differentiation steps (links) from the fertilized egg to a crying baby. We
discover a dynamical law of critical branching, which reveals a fractal
regularity in the modular organization of the network, and allows us to observe
the network at different scales. The emerging picture clearly identifies
clusters of cell types following a hierarchical organization, ranging from
sub-modules to super-modules of specialized tissues and organs on varying
scales. This discovery will allow one to treat the development of a particular
cell function in the context of the complex network of human development as a
whole. Our results point to an integrated large-scale view of the network of
cell types systematically revealing ties between previously unrelated domains
in organ functions.Comment: 32 pages, 7 figure
Anisotropic thermally activated diffusion in percolation systems
We present a study of static and frequency-dependent diffusion with
anisotropic thermally activated transition rates in a two-dimensional bond
percolation system. The approach accounts for temperature effects on diffusion
coefficients in disordered anisotropic systems. Static diffusion shows an
Arrhenius behavior for low temperatures with an activation energy given by the
highest energy barrier of the system. From the frequency-dependent diffusion
coefficients we calculate a characteristic frequency ,
related to the time needed to overcome a characteristic barrier. We find
that follows an Arrhenius behavior with different activation
energies in each direction.Comment: 5 pages, 4 figure
Walks on Apollonian networks
We carry out comparative studies of random walks on deterministic Apollonian
networks (DANs) and random Apollonian networks (RANs). We perform computer
simulations for the mean first passage time, the average return time, the
mean-square displacement, and the network coverage for unrestricted random
walk. The diffusions both on DANs and RANs are proved to be sublinear. The
search efficiency for walks with various strategies and the influence of the
topology of underlying networks on the dynamics of walks are discussed.
Contrary to one's intuition, it is shown that the self-avoiding random walk,
which has been verified as an optimal strategy for searching on scale-free and
small-world networks, is not the best strategy for the DAN in the thermodynamic
limit.Comment: 5 pages, 4 figure
Electrocatalytic hydrogen production by dinuclear cobalt(ii) compounds containing redox-active diamidate ligands: a combined experimental and theoretical study
The chiral dicobalt(II) complex [CoII2(μ2-L)2] (1) (H2L = N2,N6-di(quinolin-8-yl)pyridine-2,6-dicarboxamide) and its tert-butyl analogue [CoII2(μ2-LBu)2] (2) were synthesized and structurally characterized. Addition of one equivalent of AgSbF6 to the dichloromethane solution of 1 and 2 resulted in the isolation of the mixed-valent dicobalt(III,II) species [CoIIICoII(μ2-L)2]SbF6 (3) and [CoIIICoII(μ2-LBu)2]SbF6 (4). Homovalent 1 and 2 exhibited catalytic activity towards proton reduction in the presence of acetic acid (AcOH) as the substrate. The complexes are stable in solution while their catalytic turnover frequency is estimated at 10 and 34.6 h−1 molcat−1 for 1 and 2, respectively. Calculations reveal one-electron reduction of 1 is ligand-based, preserving the dicobalt(II) core and activating the ligand toward protonation at the quinoline group. This creates a vacant coordination site that is subsequently protonated to generate the catalytically ubiquitous Co(III) hydride. The dinuclear structure persists throughout where the distal Co(II) ion modulates the reactivity of the adjacent metal site by promoting ligand redox activity through spin state switching
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