1,291 research outputs found
Balance of interactions determines optimal survival in multi-species communities
We consider a multi-species community modelled as a complex network of
populations, where the links are given by a random asymmetric matrix J, with
fraction 1-C of zero entries, where C reflects the over-all connectivity of the
system. The non-zero elements of J are drawn from a gaussian distribution with
mean 'mu' and standard deviation . The signs of the elements J reflect the
nature of density-dependent interactions, such as predatory-prey, mutualism or
competition, and their magnitudes reflect the strength of the interaction. In
this study we try to uncover the broad features of the interspecies
interactions that determine the global robustness of this network, as indicated
by the average number of active nodes (i.e. non-extinct species) in the
network, and the total population, reflecting the biomass yield. We find that
the network transitions from a completely extinct system to one where all nodes
are active, as the mean interaction strength goes from negative to positive. We
also find that the total population, displays distinct non-monotonic scaling
behaviour with respect to the product 'mu'C, implying that survival is
dependent not merely on the number of links, but rather on the combination of
the sparseness of the connectivity matrix and the net interaction strength.
Moreover, the total population levels are optimal when the network has
intermediate net positive connection strengths. At the local level we observe
marked qualitative changes in dynamical patterns, ranging from anti-phase
clusters of period 2 cycles and chaotic bands, to fixed points, under the
variation of mean 'mu' of the interaction strengths. Lastly, we propose an
effective low dimensional map to capture the behavior of the entire network,
and this provides a broad understanding of the interplay of the local dynamical
patterns and the global robustness trends in the network.Comment: 19 Pages(single column), 9 Figures, Submitte
Noise Enhanced Activity in a Complex Network
We consider the influence of local noise on a generalized network of
populations having positive and negative feedbacks. The population dynamics at
the nodes is nonlinear, typically chaotic, and allows cessation of activity if
the population falls below a threshold value. We investigate the global
stability of this large interactive system, as indicated by the average number
of nodal populations that manage to remain active. Our central result is that
the probability of obtaining active nodes in this network is significantly
enhanced under fluctuations. Further, we find a sharp transition in the number
of active nodes as noise strength is varied, along with clearly evident scaling
behaviour near the critical noise strength. Lastly, we also observe noise
induced temporal coherence in the active sub-network, namely, there is an
enhancement in synchrony among the nodes at an intermediate noise strength.Comment: 7 pages, 11 figure
Recovery time after localized perturbations in complex dynamical networks
Maintaining the synchronous motion of dynamical systems interacting on complex networks is often critical to their functionality. However, real-world networked dynamical systems operating synchronously are prone to random perturbations driving the system to arbitrary states within the corresponding basin of attraction, thereby leading to epochs of desynchronized dynamics with a priori unknown durations. Thus, it is highly relevant to have an estimate of the duration of such transient phases before the system returns to synchrony, following a random perturbation to the dynamical state of any particular node of the network. We address this issue here by proposing the framework of single-node recovery time (SNRT) which provides an estimate of the relative time scales underlying the transient dynamics of the nodes of a network during its restoration to synchrony. We utilize this in differentiating the particularly slow nodes of the network from the relatively fast nodes, thus identifying the critical nodes which when perturbed lead to significantly enlarged recovery time of the system before resuming synchronized operation. Further, we reveal explicit relationships between the SNRT values of a network, and its global relaxation time when starting all the nodes from random initial conditions. Earlier work on relaxation time generally focused on investigating its dependence on macroscopic topological properties of the respective network. However, we employ the proposed concept for deducing microscopic relationships between topological features of nodes and their respective SNRT values. The framework of SNRT is further extended to a measure of resilience of the different nodes of a networked dynamical system. We demonstrate the potential of SNRT in networks of Rössler oscillators on paradigmatic topologies and a model of the power grid of the United Kingdom with second-order Kuramoto-type nodal dynamics illustrating the conceivable practical applicability of the proposed concept.Bundesministerium für Bildung und Forschunghttps://doi.org/10.13039/501100002347Deutsche Forschungsgemeinschafthttps://doi.org/10.13039/501100001659Peer Reviewe
Neural networks embrace learned diversity
Diversity conveys advantages in nature, yet homogeneous neurons typically
comprise the layers of artificial neural networks. Here we construct neural
networks from neurons that learn their own activation functions, quickly
diversify, and subsequently outperform their homogeneous counterparts.
Sub-networks instantiate the neurons, which meta-learn especially efficient
sets of nonlinear responses. Such learned diversity provides examples of
dynamical systems selecting diversity over uniformity and elucidates the role
of diversity in natural and artificial systems.Comment: 6 pages, 6 figure
GENCODE: reference annotation for the human and mouse genomes in 2023.
GENCODE produces high quality gene and transcript annotation for the human and mouse genomes. All GENCODE annotation is supported by experimental data and serves as a reference for genome biology and clinical genomics. The GENCODE consortium generates targeted experimental data, develops bioinformatic tools and carries out analyses that, along with externally produced data and methods, support the identification and annotation of transcript structures and the determination of their function. Here, we present an update on the annotation of human and mouse genes, including developments in the tools, data, analyses and major collaborations which underpin this progress. For example, we report the creation of a set of non-canonical ORFs identified in GENCODE transcripts, the LRGASP collaboration to assess the use of long transcriptomic data to build transcript models, the progress in collaborations with RefSeq and UniProt to increase convergence in the annotation of human and mouse protein-coding genes, the propagation of GENCODE across the human pan-genome and the development of new tools to support annotation of regulatory features by GENCODE. Our annotation is accessible via Ensembl, the UCSC Genome Browser and https://www.gencodegenes.org
Optimasi Portofolio Resiko Menggunakan Model Markowitz MVO Dikaitkan dengan Keterbatasan Manusia dalam Memprediksi Masa Depan dalam Perspektif Al-Qur`an
Risk portfolio on modern finance has become increasingly technical, requiring the use of sophisticated mathematical tools in both research and practice. Since companies cannot insure themselves completely against risk, as human incompetence in predicting the future precisely that written in Al-Quran surah Luqman verse 34, they have to manage it to yield an optimal portfolio. The objective here is to minimize the variance among all portfolios, or alternatively, to maximize expected return among all portfolios that has at least a certain expected return. Furthermore, this study focuses on optimizing risk portfolio so called Markowitz MVO (Mean-Variance Optimization). Some theoretical frameworks for analysis are arithmetic mean, geometric mean, variance, covariance, linear programming, and quadratic programming. Moreover, finding a minimum variance portfolio produces a convex quadratic programming, that is minimizing the objective function ðð¥with constraintsð ð 𥠥 ðandð´ð¥ = ð. The outcome of this research is the solution of optimal risk portofolio in some investments that could be finished smoothly using MATLAB R2007b software together with its graphic analysis
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