Small-world and scale-free networks are known to be more easily synchronized than regular lattices, which is usually attributed to the smaller network distance between oscillators. Surprisingly, we find that networks with a homogeneous distribution of connectivity are more synchronizable than heterogeneous ones, even though the average network distance is larger. We present numerical computations and analytical estimates on synchronizability of the network in terms of its heterogeneity parameters. Our results suggest that some degree of homogeneity is expected in naturally evolved structures, such as neural networks, where synchronizability is desirable.
An imperative condition for the functioning of a power-grid network is that its power generators remain synchronized. Disturbances can prompt desynchronization, which is a process that has been involved in large power outages. Here we derive a condition under which the desired synchronous state of a power grid is stable, and use this condition to identify tunable parameters of the generators that are determinants of spontaneous synchronization. Our analysis gives rise to an approach to specify parameter assignments that can enhance synchronization of any given network, which we demonstrate for a selection of both test systems and real power grids. Because our results concern spontaneous synchronization, they are relevant both for reducing dependence on conventional control devices, thus offering an additional layer of protection given that most power outages involve equipment or operational errors, and for contributing to the development of "smart grids" that can recover from failures in real time.
Purpose: Histone deacetylase (HDAC) inhibitors have emerged recently as promising anticancer agents. They arrest cells in the cell cycle and induce differentiation and cell death. The antitumor activity of HDAC inhibitors has been linked to their ability to induce gene expression through acetylation of histone and nonhistone proteins. However, it has recently been suggested that HDAC inhibitors may also enhance the activity of other cancer therapeutics, including radiotherapy. The purpose of this study was to evaluate the ability of HDAC inhibitors to radiosensitize human melanoma cells in vitro. Experimental Design: A panel of HDAC inhibitors that included sodium butyrate (NaB), phenylbutyrate, tributyrin, and trichostatin A were tested for their ability to radiosensitize two human melanoma cell lines (A375 and MeWo) using clonogenic cell survival assays. Apoptosis and DNA repair were measured by standard assays. Results: NaB induced hyperacetylation of histone H4 in the two melanoma cell lines and the normal human fibroblasts. NaB radiosensitized both the A375 and MeWo melanoma cell lines, substantially reducing the surviving fraction at 2 Gy (SF2), whereas it had no effect on the normal human fibroblasts. The other HDAC inhibitors, phenylbutyrate, tributyrin, and trichostatin A had significant radiosensitizing effects on both melanoma cell lines tested. NaB modestly enhanced radiation-induced apoptosis that did not correlate with survival but did correlate with functional impairment of DNA repair as determined based on the host cell reactivation assay. Moreover, NaB significantly reduced the expression of the repair-related genes Ku70 and Ku86 and DNA-dependent protein kinase catalytic subunit in melanoma cells at the protein and mRNA levels. Normal human fibroblasts showed no change in DNA repair capacity or levels of DNA repair proteins following NaB treatment. We also examined g-H2AX phosphorylation as a marker of radiation response to NaB and observed that compared with controls, g-H2AX foci persisted long after ionizing exposure in the NaB-treated cells. Conclusions: HDAC inhibitors radiosensitize human tumor cells by affecting their ability to repair the DNA damage induced by ionizing radiation and that g-H2AX phosphorylation can be used as a predictive marker of radioresponse.
We consider the problem of maximizing the synchronizability of oscillator networks by assigning weights and directions to the links of a given interaction topology. We first extend the well-known master stability formalism to the case of non-diagonalizable networks. We then show that, unless some oscillator is connected to all the others, networks of maximum synchronizability are necessarily non-diagonalizable and can always be obtained by imposing unidirectional information flow with normalized input strengths. The extension makes the formalism applicable to all possible network structures, while the maximization results provide insights into hierarchical structures observed in complex networks in which synchronization plays a significant role. [6,7,8]. The effects of these properties on synchronization has particularly attracted the attention of researchers, partly because of the elegant analysis due to Pecora and Carroll [9] which allows us to isolate the contribution of the network structure in terms of the eigenvalues of the coupling matrix.Synchronizability of complex networks of oscillators generally has been shown to improve as the average network distance decreases, with one notable exception: in random scalefree networks, which are characterized by a strong heterogeneity of the connectivity distribution [4], synchronization was shown to become more difficult as the heterogeneity increases [10], even though the average network distance decreases at the same time. Motivated by this counter-intuitive effect, researchers have pursued ways to enhance the synchronizability of scale-free networks by introducing directionality and weight to each link in the network [6,7,11]. A natural question arising in this context is: Given a network of oscillators with a fixed topology of interactions, which assignment of weights and directions maximizes its synchronizability? By maximization, we mean that the synchronized states are stable for the widest possible range of the parameter representing the overall coupling strength.The study of such a question not only provides us with insights into the dynamics of real-world complex networks but also guides us in designing large artificial networks. Metabolic networks-the system of hundreds of interconnected biochemical reactions responsible for the biomass and energy production in a cell-is a prototypic example where the weights and directions of feasible links (metabolic fluxes) are adjusted to optimize fitness, which is likely to account for robustness of synchronized behavior against environmental changes [12]. Other examples range from the enhancement of neuronal synchronization for a given topology of synaptic connections in the brain, to the design of interaction schemes that optimize the performance of computational tasks based on the synchronization of processes in computer networks [13]. The adjustment of flows in power grids and communication patterns in social organizations are additional examples where directional and weighted patterns can be favored because th...
The dynamics of power-grid networks is becoming an increasingly active area of research within the physics and network science communities. The results from such studies are typically insightful and illustrative, but are often based on simplifying assumptions that can be either difficult to assess or not fully justified for realistic applications. Here we perform a comprehensive comparative analysis of three leading models recently used to study synchronization dynamics in power-grid networks-a fundamental problem of practical significance given that frequency synchronization of all power generators in the same interconnection is a necessary condition for a power grid to operate. We show that each of these models can be derived from first principles within a common framework based on the classical model of a generator, thereby clarifying all assumptions involved. This framework allows us to view power grids as complex networks of coupled second-order phase oscillators with both forcing and damping terms. Using simple illustrative examples, test systems, and real power-grid datasets, we study the inherent frequencies of the oscillators as well as their coupling structure, comparing across the different models. We demonstrate, in particular, that if the network structure is not homogeneous, generators with identical parameters need to be modeled as non-identical oscillators in general. We also discuss an approach to estimate the required (dynamical) parameters that are unavailable in typical power-grid datasets, their use for computing the constants of each of the three models, and an open-source MATLAB toolbox that we provide for these computations (available at https://sourceforge.net/projects/pg-sync-models).
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