1,254 research outputs found
Characterization of exact lumpability for vector fields on smooth manifolds
We characterize the exact lumpability of smooth vector fields on smooth manifolds. We derive necessary and sufficient conditions for lumpability and express them from four different perspectives, thus simplifying and generalizing various results from the literature that exist for Euclidean spaces. We introduce a partial connection on the pullback bundle that is related to the Bott connection and behaves like a Lie derivative. The lumping conditions are formulated in terms of the differential of the lumping map, its covariant derivative with respect to the connection and their respective kernels. Some examples are discussed to illustrate the theory. © 2016 Published by Elsevier B.V
Lumpability of linear evolution equations in banach spaces
We analyze the lumpability of linear systems on Banach spaces, namely, the possibility of projecting the dynamics by a linear reduction opera-tor onto a smaller state space in which a self-contained dynamical description exists. We obtain conditions for lumpability of dynamics defined by unbounded operators using the theory of strongly continuous semigroups. We also derive results from the dual space point of view using sun dual theory. Furthermore, we connect the theory of lumping to several results from operator factoriza-tion. We indicate several applications to particular systems, including delay differential equations. © 2017, American Institute of Mathematical Sciences. All rights reserved
Spectral plots and the representation and interpretation of biological data
It is basic question in biology and other fields to identify the char-
acteristic properties that on one hand are shared by structures from a
particular realm, like gene regulation, protein-protein interaction or neu- ral
networks or foodwebs, and that on the other hand distinguish them from other
structures. We introduce and apply a general method, based on the spectrum of
the normalized graph Laplacian, that yields repre- sentations, the spectral
plots, that allow us to find and visualize such properties systematically. We
present such visualizations for a wide range of biological networks and compare
them with those for networks derived from theoretical schemes. The differences
that we find are quite striking and suggest that the search for universal
properties of biological networks should be complemented by an understanding of
more specific features of biological organization principles at different
scales.Comment: 15 pages, 7 figure
Chaos synchronization in networks of coupled maps with time-varying topologies
Complexity of dynamical networks can arise not only from the complexity of
the topological structure but also from the time evolution of the topology. In
this paper, we study the synchronous motion of coupled maps in time-varying
complex networks both analytically and numerically. The temporal variation is
rather general and formalized as being driven by a metric dynamical system.
Four network models are discussed in detail in which the interconnections
between vertices vary through time randomly. These models are 1) i.i.d.
sequences of random graphs with fixed wiring probability, 2) groups of graphs
with random switches between the individual graphs, 3) graphs with temporary
random failures of nodes, and 4) the meet-for-dinner model where the vertices
are randomly grouped. We show that the temporal variation and randomness of the
connection topology can enhance synchronizability in many cases; however, there
are also instances where they reduce synchronizability. In analytical terms,
the Hajnal diameter of the coupling matrix sequence is presented as a measure
for the synchronizability of the graph topology. In topological terms, the
decisive criterion for synchronization of coupled chaotic maps is that the
union of the time-varying graphs contains a spanning tree
Mean field approximation of two coupled populations of excitable units
The analysis on stability and bifurcations in the macroscopic dynamics
exhibited by the system of two coupled large populations comprised of
stochastic excitable units each is performed by studying an approximate system,
obtained by replacing each population with the corresponding mean-field model.
In the exact system, one has the units within an ensemble communicating via the
time-delayed linear couplings, whereas the inter-ensemble terms involve the
nonlinear time-delayed interaction mediated by the appropriate global
variables. The aim is to demonstrate that the bifurcations affecting the
stability of the stationary state of the original system, governed by a set of
4N stochastic delay-differential equations for the microscopic dynamics, can
accurately be reproduced by a flow containing just four deterministic
delay-differential equations which describe the evolution of the mean-field
based variables. In particular, the considered issues include determining the
parameter domains where the stationary state is stable, the scenarios for the
onset and the time-delay induced suppression of the collective mode, as well as
the parameter domains admitting bistability between the equilibrium and the
oscillatory state. We show how analytically tractable bifurcations occurring in
the approximate model can be used to identify the characteristic mechanisms by
which the stationary state is destabilized under different system
configurations, like those with symmetrical or asymmetrical inter-population
couplings.Comment: 5 figure
Catalytic Depolymerization of Lignin and Woody Biomass in Supercritical Ethanol:Influence of Reaction Temperature and Feedstock
The one-step ethanolysis approach to upgrade lignin to monomeric aromatics using a CuMgAl mixed oxide catalyst is studied in detail. The influence of reaction temperature (200-420 °C) on the product distribution is investigated. At low temperature (200-250 °C), recondensation is dominant, while char-forming reactions become significant at high reaction temperature (>380 °C). At preferred intermediate temperatures (300-340 °C), char-forming reactions are effectively suppressed by alkylation and Guerbet and esterification reactions. This shifts the reaction toward depolymerization, explaining high monomeric aromatics yield. Carbon-14 dating analysis of the lignin residue revealed that a substantial amount of the carbon in the lignin residue originates from reactions of lignin with ethanol. Recycling tests show that the activity of the regenerated catalyst was strongly decreased due to a loss of basic sites due to hydrolysis of the MgO function and a loss of surface area due to spinel oxide formation of the Cu and Al components. The utility of this one-step approach for upgrading woody biomass was also demonstrated. An important observation is that conversion of the native lignin contained in the lignocellulosic matrix is much easier than the conversion of technical lignin.</p
Discovering universal statistical laws of complex networks
Different network models have been suggested for the topology underlying
complex interactions in natural systems. These models are aimed at replicating
specific statistical features encountered in real-world networks. However, it
is rarely considered to which degree the results obtained for one particular
network class can be extrapolated to real-world networks. We address this issue
by comparing different classical and more recently developed network models
with respect to their generalisation power, which we identify with large
structural variability and absence of constraints imposed by the construction
scheme. After having identified the most variable networks, we address the
issue of which constraints are common to all network classes and are thus
suitable candidates for being generic statistical laws of complex networks. In
fact, we find that generic, not model-related dependencies between different
network characteristics do exist. This allows, for instance, to infer global
features from local ones using regression models trained on networks with high
generalisation power. Our results confirm and extend previous findings
regarding the synchronisation properties of neural networks. Our method seems
especially relevant for large networks, which are difficult to map completely,
like the neural networks in the brain. The structure of such large networks
cannot be fully sampled with the present technology. Our approach provides a
method to estimate global properties of under-sampled networks with good
approximation. Finally, we demonstrate on three different data sets (C.
elegans' neuronal network, R. prowazekii's metabolic network, and a network of
synonyms extracted from Roget's Thesaurus) that real-world networks have
statistical relations compatible with those obtained using regression models
An Alternative Proof of the Characterization of Core Stability for the Assignment Game
Atomic-scale confinement of optical fields
In the presence of matter there is no fundamental limit preventing
confinement of visible light even down to atomic scales. Achieving such
confinement and the corresponding intensity enhancement inevitably requires
simultaneous control over atomic-scale details of material structures and over
the optical modes that such structures support. By means of self-assembly we
have obtained side-by-side aligned gold nanorod dimers with robust
atomically-defined gaps reaching below 0.5 nm. The existence of
atomically-confined light fields in these gaps is demonstrated by observing
extreme Coulomb splitting of corresponding symmetric and anti-symmetric dimer
eigenmodes of more than 800 meV in white-light scattering experiments. Our
results open new perspectives for atomically-resolved spectroscopic imaging,
deeply nonlinear optics, ultra-sensing, cavity optomechanics as well as for the
realization of novel quantum-optical devices
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