141 research outputs found
Generating directed networks with prescribed Laplacian spectra
Complex real-world phenomena are often modeled as dynamical systems on
networks. In many cases of interest, the spectrum of the underlying graph
Laplacian sets the system stability and ultimately shapes the matter or
information flow. This motivates devising suitable strategies, with rigorous
mathematical foundation, to generate Laplacian that possess prescribed spectra.
In this paper, we show that a weighted Laplacians can be constructed so as to
exactly realize a desired complex spectrum. The method configures as a non
trivial generalization of existing recipes which assume the spectra to be real.
Applications of the proposed technique to (i) a network of Stuart-Landau
oscillators and (ii) to the Kuramoto model are discussed. Synchronization can
be enforced by assuming a properly engineered, signed and weighted, adjacency
matrix to rule the pattern of pairing interactions
Spectral control for ecological stability
A system made up of N interacting species is considered. Self-reaction terms
are assumed of the logistic type. Pairwise interactions take place among
species according to different modalities, thus yielding a complex asymmetric
disordered graph. A mathematical procedure is introduced and tested to
stabilise the ecosystem via an {\it ad hoc} rewiring of the underlying
couplings. The method implements minimal modifications to the spectrum of the
Jacobian matrix which sets the stability of the fixed point and traces these
changes back to species-species interactions. Resilience of the equilibrium
state appear to be favoured by predator-prey interactions
Robust Distributed Fusion with Labeled Random Finite Sets
This paper considers the problem of the distributed fusion of multi-object
posteriors in the labeled random finite set filtering framework, using
Generalized Covariance Intersection (GCI) method. Our analysis shows that GCI
fusion with labeled multi-object densities strongly relies on label
consistencies between local multi-object posteriors at different sensor nodes,
and hence suffers from a severe performance degradation when perfect label
consistencies are violated. Moreover, we mathematically analyze this phenomenon
from the perspective of Principle of Minimum Discrimination Information and the
so called yes-object probability. Inspired by the analysis, we propose a novel
and general solution for the distributed fusion with labeled multi-object
densities that is robust to label inconsistencies between sensors.
Specifically, the labeled multi-object posteriors are firstly marginalized to
their unlabeled posteriors which are then fused using GCI method. We also
introduce a principled method to construct the labeled fused density and
produce tracks formally. Based on the developed theoretical framework, we
present tractable algorithms for the family of generalized labeled
multi-Bernoulli (GLMB) filters including -GLMB, marginalized
-GLMB and labeled multi-Bernoulli filters. The robustness and
efficiency of the proposed distributed fusion algorithm are demonstrated in
challenging tracking scenarios via numerical experiments.Comment: 17pages, 23 figure
CMB Observations: improvements of the performance of correlation radiometers by signal modulation and synchronous detection
Observation of the fine structures (anisotropies, polarization, spectral
distortions) of the Cosmic Microwave Background (CMB) is hampered by
instabilities, 1/f noise and asymmetries of the radiometers used to carry on
the measurements. Addition of modulation and synchronous detection allows to
increase the overall stability and the noise rejection of the radiometers used
for CMB studies. In this paper we discuss the advantages this technique has
when we try to detect CMB polarization. The behaviour of a two channel
correlation receiver to which phase modulation and synchronous detection have
been added is examined. Practical formulae for evaluating the improvements are
presented.Comment: 18 pages, 3 figures, New Astronomy accepte
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