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

Node Labels in Local Decision

The role of unique node identifiers in network computing is well understood as far as symmetry breaking is concerned. However, the unique identifiers also leak information about the computing environment - in particular, they provide some nodes with information related to the size of the network. It was recently proved that in the context of local decision, there are some decision problems such that (1) they cannot be solved without unique identifiers, and (2) unique node identifiers leak a sufficient amount of information such that the problem becomes solvable (PODC 2013). In this work we give study what is the minimal amount of information that we need to leak from the environment to the nodes in order to solve local decision problems. Our key results are related to scalar oracles $f$ that, for any given $n$, provide a multiset $f(n)$ of $n$ labels; then the adversary assigns the labels to the $n$ nodes in the network. This is a direct generalisation of the usual assumption of unique node identifiers. We give a complete characterisation of the weakest oracle that leaks at least as much information as the unique identifiers. Our main result is the following dichotomy: we classify scalar oracles as large and small, depending on their asymptotic behaviour, and show that (1) any large oracle is at least as powerful as the unique identifiers in the context of local decision problems, while (2) for any small oracle there are local decision problems that still benefit from unique identifiers.Comment: Conference version to appear in the proceedings of SIROCCO 201

Combined indocyanine green and quantitative perfusion assessment with hyperspectral imaging during colorectal resections

Anastomotic insufficiencies still represent one of the most severe complications in colorectal surgery. Since tissue perfusion highly affects anastomotic healing, its objective assessment is an unmet clinical need. Indocyanine green-based fluorescence angiography (ICG-FA) and hyperspectral imaging (HSI) have received great interest in recent years but surgeons have to decide between both techniques. For the first time, two data processing pipelines capable of reconstructing an ICG-FA correlating signal from hyperspectral data were developed. Results were technically evaluated and compared to ground truth data obtained during colorectal resections. In 87% of 46 data sets, the reconstructed images resembled the ground truth data. The combined applicability of ICG-FA and HSI within one imaging system might provide supportive and complementary information about tissue vascularization, shorten surgery time, and reduce perioperative mortality

Byzantine Gathering in Networks

This paper investigates an open problem introduced in [14]. Two or more mobile agents start from different nodes of a network and have to accomplish the task of gathering which consists in getting all together at the same node at the same time. An adversary chooses the initial nodes of the agents and assigns a different positive integer (called label) to each of them. Initially, each agent knows its label but does not know the labels of the other agents or their positions relative to its own. Agents move in synchronous rounds and can communicate with each other only when located at the same node. Up to f of the agents are Byzantine. A Byzantine agent can choose an arbitrary port when it moves, can convey arbitrary information to other agents and can change its label in every round, in particular by forging the label of another agent or by creating a completely new one. What is the minimum number M of good agents that guarantees deterministic gathering of all of them, with termination? We provide exact answers to this open problem by considering the case when the agents initially know the size of the network and the case when they do not. In the former case, we prove M=f+1 while in the latter, we prove M=f+2. More precisely, for networks of known size, we design a deterministic algorithm gathering all good agents in any network provided that the number of good agents is at least f+1. For networks of unknown size, we also design a deterministic algorithm ensuring the gathering of all good agents in any network but provided that the number of good agents is at least f+2. Both of our algorithms are optimal in terms of required number of good agents, as each of them perfectly matches the respective lower bound on M shown in [14], which is of f+1 when the size of the network is known and of f+2 when it is unknown

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

Quantum coherent control of highly multipartite continuous-variable entangled states by tailoring parametric interactions

The generation of continuous-variable multipartite entangled states is important for several protocols of quantum information processing and communication, such as one-way quantum computation or controlled dense coding. In this article we theoretically show that multimode optical parametric oscillators can produce a great variety of such states by an appropriate control of the parametric interaction, what we accomplish by tailoring either the spatio-temporal shape of the pump, or the geometry of the nonlinear medium. Specific examples involving currently available optical parametric oscillators are given, hence showing that our ideas are within reach of present technology.Comment: 14 pages, 5 figure

X. couchianus and X. hellerii genome models provide genomic variation insight among Xiphophorus species

4 inter-chromosomal rearrangement events between X. hellerii and X. maculatus. (XLSX 40 kb

Propionyl-L-carnitine corrects metabolic and cardiovascular alterations in diet-induced obese mice and improves liver respiratory chain activity

AIMS: Obesity is a primary contributor to acquired insulin resistance leading to the development of type 2 diabetes and cardiovascular alterations. The carnitine derivate, propionyl-L-carnitine (PLC), plays a key role in energy control. Our aim was to evaluate metabolic and cardiovascular effects of PLC in diet-induced obese mice. METHODS: C57BL/6 mice were fed a high-fat diet for 9 weeks and then divided into two groups, receiving either free- (vehicle-HF) or PLC-supplemented water (200 mg/kg/day) during 4 additional weeks. Standard diet-fed animals were used as lean controls (vehicle-ST). Body weight and food intake were monitored. Glucose and insulin tolerance tests were assessed, as well as the HOMA(IR), the serum lipid profile, the hepatic and muscular mitochondrial activity and the tissue nitric oxide (NO) liberation. Systolic blood pressure, cardiac and endothelial functions were also evaluated. RESULTS: Vehicle-HF displayed a greater increase of body weight compared to vehicle-ST that was completely reversed by PLC treatment without affecting food intake. PLC improved the insulin-resistant state and reversed the increased total cholesterol but not the increase in free fatty acid, triglyceride and HDL/LDL ratio induced by high-fat diet. Vehicle-HF exhibited a reduced cardiac output/body weight ratio, endothelial dysfunction and tissue decrease of NO production, all of them being improved by PLC treatment. Finally, the decrease of hepatic mitochondrial activity by high-fat diet was reversed by PLC. CONCLUSIONS: Oral administration of PLC improves the insulin-resistant state developed by obese animals and decreases the cardiovascular risk associated to this metabolic alteration probably via correction of mitochondrial function