A general lower bound for collaborative tree exploration

We consider collaborative graph exploration with a set of $k$ agents. All agents start at a common vertex of an initially unknown graph and need to collectively visit all other vertices. We assume agents are deterministic, vertices are distinguishable, moves are simultaneous, and we allow agents to communicate globally. For this setting, we give the first non-trivial lower bounds that bridge the gap between small ($k \leq \sqrt n$) and large ($k \geq n$) teams of agents. Remarkably, our bounds tightly connect to existing results in both domains. First, we significantly extend a lower bound of $\Omega(\log k / \log\log k)$ by Dynia et al. on the competitive ratio of a collaborative tree exploration strategy to the range $k \leq n \log^c n$ for any $c \in \mathbb{N}$. Second, we provide a tight lower bound on the number of agents needed for any competitive exploration algorithm. In particular, we show that any collaborative tree exploration algorithm with $k = Dn^{1+o(1)}$ agents has a competitive ratio of $\omega(1)$, while Dereniowski et al. gave an algorithm with $k = Dn^{1+\varepsilon}$ agents and competitive ratio $O(1)$, for any $\varepsilon > 0$ and with $D$ denoting the diameter of the graph. Lastly, we show that, for any exploration algorithm using $k = n$ agents, there exist trees of arbitrarily large height $D$ that require $\Omega(D^2)$ rounds, and we provide a simple algorithm that matches this bound for all trees

Divergence Measure Between Chaotic Attractors

We propose a measure of divergence of probability distributions for quantifying the dissimilarity of two chaotic attractors. This measure is defined in terms of a generalized entropy. We illustrate our procedure by considering the effect of additive noise in the well known H\'enon attractor. Comparison of two H\'enon attractors for slighly different parameter values, has shown that the divergence has complex scaling structure. Finally, we show how our approach allows to detect non-stationary events in a time series.Comment: 9 pages, 6 figure

Time series irreversibility: a visibility graph approach

We propose a method to measure real-valued time series irreversibility which combines two differ- ent tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally effi- cient, does not require any ad hoc symbolization process, and naturally takes into account multiple scales. We find that the method correctly distinguishes between reversible and irreversible station- ary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic pro- cesses (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identifiy the irreversible nature of the series.Comment: submitted for publicatio

Anonymous Graph Exploration with Binoculars

International audienceWe investigate the exploration of networks by a mobile agent. It is long known that, without global information about the graph, it is not possible to make the agent halts after the exploration except if the graph is a tree. We therefore endow the agent with binoculars, a sensing device that can show the local structure of the environment at a constant distance of the agent current location.We show that, with binoculars, it is possible to explore and halt in a large class of non-tree networks. We give a complete characterization of the class of networks that can be explored using binoculars using standard notions of discrete topology. This class is much larger than the class of trees: it contains in particular chordal graphs, plane triangulations and triangulations of the projective plane. Our characterization is constructive, we present an Exploration algorithm that is universal; this algorithm explores any network explorable with binoculars, and never halts in non-explorable networks

Significance of cutoff in meandering river dynamics

The occurrence of cutoff events, although sporadic, is a key component in the complex dynamics of meandering rivers. In the present work, we show that cutoff has a twofold role: (1) It removes older meanders, limiting the planform geometrical complexity (geometrical role), and (2) it generates an intermittent noise that is able to influence the spatiotemporal dynamics of the whole river (dynamical role). The geometrical role limits the spatial evolution of the meanders, sporadically eliminating portions of the river planimetry. In this way it stabilizes the mean river geometry around a statistically steady state. The dynamical role is due to the propagation of a noise wave that is triggered by cutoff events. Because of the spatial memory component which is present in the meandering dynamics, such waves propagate all along the river, thus affecting its meandering dynamic

Violacein Induces Death of Resistant Leukaemia Cells via Kinome Reprogramming, Endoplasmic Reticulum Stress and Golgi Apparatus Collapse

It is now generally recognised that different modes of programmed cell death (PCD) are intimately linked to the cancerous process. However, the mechanism of PCD involved in cancer chemoprevention is much less clear and may be different between types of chemopreventive agents and tumour cell types involved. Therefore, from a pharmacological view, it is crucial during the earlier steps of drug development to define the cellular specificity of the candidate as well as its capacity to bypass dysfunctional tumoral signalling pathways providing insensitivity to death stimuli. Studying the cytotoxic effects of violacein, an antibiotic dihydro-indolone synthesised by an Amazon river Chromobacterium, we observed that death induced in CD34(+)/c-Kit(+)/P-glycoprotein(+)/MRP1(+) TF1 leukaemia progenitor cells is not mediated by apoptosis and/or autophagy, since biomarkers of both types of cell death were not significantly affected by this compound. To clarify the working mechanism of violacein, we performed kinome profiling using peptide arrays to yield comprehensive descriptions of cellular kinase activities. Pro-death activity of violacein is actually carried out by inhibition of calpain and DAPK1 and activation of PKA, AKT and PDK, followed by structural changes caused by endoplasmic reticulum stress and Golgi apparatus collapse, leading to cellular demise. Our results demonstrate that violacein induces kinome reprogramming, overcoming death signaling dysfunctions of intrinsically resistant human leukaemia cells.TopInstitute pharma (The Netherlands)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Dutch Cancer SocietyErasmus MC Univ Med Ctr, Dept Gastroenterol & Hepatol, Rotterdam, NetherlandsUniv Amsterdam, Acad Med Ctr, Ctr Expt & Mol Med, NL-1105 AZ Amsterdam, NetherlandsUniv Estadual Campinas, Brazil UNICAMP, Dept Biochem, Inst Biol, São Paulo, BrazilFed Univ São Paulo UNIFESP, Dept Biochem, São Paulo, BrazilFed Univ São Paulo UNIFESP, Dept Cell Biol, São Paulo, BrazilUniv Grande Rio UNIGRANRIO, Heath Sci Sch, Multidisciplinary Lab Dent Res, Rio de Janeiro, BrazilNatl Inst Metrol Qual & Technol Inmetro, Biotechnol Lab, Bioengn Sect, Rio de Janeiro, BrazilUniv Campinas UNICAMP, Inst Chem, Biol Chem Lab, Rio de Janeiro, BrazilUniv Groningen, Univ Med Ctr Groningen, Dept Pediat Oncol, Beatrix Childrens Hosp, Groningen, NetherlandsFed Univ São Paulo UNIFESP, Dept Biochem, São Paulo, BrazilFed Univ São Paulo UNIFESP, Dept Cell Biol, São Paulo, BrazilDutch Cancer Society: EMCR 2010-4737Web of Scienc