Dissipativity characterization of a class of oscillators and networks of oscillators

This paper uses dissipativity theory to provide the system-theoretic description of a basic oscillation mechanism. Elementary input-output tools are then used to prove the existence and stability of limit cycles in these "oscillators". The main benefit of the proposed approach is that it is well suited for the analysis and design of interconnections, thus providing a valuable mathematical tool for the study of networks of coupled oscillators.

Synthesis using electrospinning and stabilization of single layer macroporous films and fibrous networks of poly(vinyl alcohol)

We demonstrated in this paper an electrospinning technique could be employed to prepare the single layer macroporous films and fibrous networks of poly(vinyl alcohol) (PVA). A crucial element using electrospinning on the development of these electrospun structures was to shorten the distance of from the needle tip to the collector (L), which resulted in the bond of the wet fibers deposited on the collector at the junctions. The morphologies and average pore size of electrospun structures of PVA were mainly predominated by L and the time of collecting wet fibers on the collector. In addition, experimental results showed that an increase of the PVA concentration or a decrease of the applied voltage could also diminish slightly the average pore size of electrospun productions. Furthermore, a 60 degrees C absolute ethanol soak to PVA electrospun production led them to be able to stabilize in water for 1 month against disintegration. Differential scanning calorimetry (DSC) demonstrated that the 60 degrees C ethanol soak enhanced the degree of crystallinity of PVA production. The structural characteristic of macroporous films and networks in combination with their easy processability suggests potential utility in issue engineering applications.

Multiple Dynamic Processes Contribute to the Complex Steady Shear Behavior of Cross-Linked Supramolecular Networks of Semidilute Entangled Polymer Solutions.

Molecular theories of shear thickening and shear thinning in associative polymer networks are typically united in that they involve a single kinetic parameter that describes the network -- a relaxation time that is related to the lifetime of the associative bonds. Here we report the steady-shear behavior of two structurally identical metallo-supramolecular polymer networks, for which single-relaxation parameter models break down in dramatic fashion. The networks are formed by the addition of reversible cross-linkers to semidilute entangled solutions of PVP in DMSO, and they differ only in the lifetime of the reversible cross-links. Shear thickening is observed for cross-linkers that have a slower dissociation rate (17 s(-1)), while shear thinning is observed for samples that have a faster dissociation rate (ca. 1400 s(-1)). The difference in the steady shear behavior of the unentangled vs. entangled regime reveals an unexpected, additional competing relaxation, ascribed to topological disentanglement in the semidilute entangled regime that contributes to the rheological properties.

Graphs of relations and Hilbert series

We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by $n$ generators and $\frac {n(n-1)}{2}$ relations for $n \leq 7$. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated to each color are pairwise 2-isomorphic.

Constructing networks of continuous-time velocity-based models

A conventional local model (LM) network consists of a set of affine local models blended together using appropriate weighting functions. Such networks have poor interpretability since the dynamics of the blended network are only weakly related to the underlying local models. In contrast, velocity-based LM networks employ strictly linear local models to provide a transparent framework for nonlinear modelling in which the global dynamics are a simple linear combination of the local model dynamics. A novel approach for constructing continuous-time velocity-based networks from plant data is presented. Key issues including continuous-time parameter estimation, correct realisation of the velocity-based local models and avoidance of the input derivative are all addressed. Application results are reported for the highly nonlinear simulated continuous stirred tank reactor process.

Identifying Critical Financial Networks of the DJIA: Toward a Network-Based Index

The purpose of this article is twofold. First, we introduce a novel definition of financial networks obtained from time series data from the stock market. Second, we demonstrate that these networks can be used as an index with the property to reflect critical states of the market, respectively, crashes sufficiently. Our work aims to advocate a network-based analysis in the context of the stock market, because such a collective phenomenon can not only be economically described by networks but also analyzed as demonstrated in this article. (C) 2010 Wiley Periodicals, Inc. Complexity 16: 24-33, 2010

Finite dimensional semigroup quadratic algebras with the minimal number of relations

A quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp.

Interfacing cellular networks of S. cerevisiae and E. coli: Connecting dynamic and genetic information

Background: In recent years, various types of cellular networks have penetrated biology and are nowadays used omnipresently for studying eukaryote and prokaryote organisms. Still, the relation and the biological overlap among phenomenological and inferential gene networks, e.g., between the protein interaction network and the gene regulatory network inferred from large-scale transcriptomic data, is largely unexplored.

Results: We provide in this study an in-depth analysis of the structural, functional and chromosomal relationship between a protein-protein network, a transcriptional regulatory network and an inferred gene regulatory network, for S. cerevisiae and E. coli. Further, we study global and local aspects of these networks and their biological information overlap by comparing, e.g., the functional co-occurrence of Gene Ontology terms by exploiting the available interaction structure among the genes.

Conclusions: Although the individual networks represent different levels of cellular interactions with global structural and functional dissimilarities, we observe crucial functions of their network interfaces for the assembly of protein complexes, proteolysis, transcription, translation, metabolic and regulatory interactions. Overall, our results shed light on the integrability of these networks and their interfacing biological processes.

A Note on Networks of Collaboration in Multimarket Oligopolies

In this note, we extend the Goyal and Joshi’s model of collaboration networks in oligopoly to multi-market situations. We examine the incentive of firms to form links and the architectures of the resulting equilibrium networks in this setting. We then present some results on efficient networks.