A General Reduction Theorem with Applications to Pathwidth and the Complexity of MAX 2-CSP

We prove a general reduction theorem which allows us to extend bounds for certain graph parameters on cubic graphs to bounds for general graphs taking into account the individual vertex degrees. As applications, we give an algorithm for Max 2 -CSP whose complexity matches the algorithm of Scott and Sorkin in the case of d -regular graphs, d=5 , but is otherwise faster. It also improves on the previously fastest known algorithm in terms of the average degree, given by Golovnev and Kutzkov. Also from the general theorem, we derive a bound for the pathwidth of a general graph which equals that of Fomin et al. and Gaspers for graphs of degree at most 6 , but is smaller otherwise, and use this to give an improved exponential-space algorithm for Max 2 -CSP. Finally we use the general result to give a faster algorithm for Max 2 -CSP on claw-free graphs

Polynomial kernelization for removing induced claws and diamonds

A graph is called (claw,diamond)-free if it contains neither a claw (a $K_{1,3}$) nor a diamond (a $K_4$ with an edge removed) as an induced subgraph. Equivalently, (claw,diamond)-free graphs can be characterized as line graphs of triangle-free graphs, or as linear dominoes, i.e., graphs in which every vertex is in at most two maximal cliques and every edge is in exactly one maximal clique. In this paper we consider the parameterized complexity of the (claw,diamond)-free Edge Deletion problem, where given a graph $G$ and a parameter $k$, the question is whether one can remove at most $k$ edges from $G$ to obtain a (claw,diamond)-free graph. Our main result is that this problem admits a polynomial kernel. We complement this finding by proving that, even on instances with maximum degree $6$, the problem is NP-complete and cannot be solved in time $2^{o(k)}\cdot |V(G)|^{O(1)}$ unless the Exponential Time Hypothesis fai

Coal mine ventilation air methane combustion in a catalytic reverse flow reactor: Influence of emission humidity

The role of the humidity content on the performance of catalytic reverse flow reactors (RFRs) for the abatement of methane emissions from coal mines is studied in this manuscript. It has been demonstrated that this technique is very useful for the abatement, and even upgrading, of these emissions. However, the effect of humidity on the reactor performance has not been addressed yet, in spite of being well known that water is an inhibitor in catalytic combustion. Experimental studies in a lab-scale isothermal fixed bed reactor demonstrated that water decreases the activity of a palladium on alumina catalyst for the combustion of methane, but this inhibition is entirely reversible, results fitting well to a Langmuir–Hinshelwood kinetic model. Then, the influence of water was studied in a bench-scale RFR operating at near adiabatic conditions at different switching times (100–600 s) and methane feed concentrations (2700–7200 ppm). Finally, a mathematical model for the reverse flow reactor, including the kinetic model with water inhibition, has been validated using the experimental results. This model is of key importance for designing this type of reactors for the treatment of mine ventilation emissions

On Directed Feedback Vertex Set parameterized by treewidth

We study the Directed Feedback Vertex Set problem parameterized by the treewidth of the input graph. We prove that unless the Exponential Time Hypothesis fails, the problem cannot be solved in time $2^{o(t\log t)}\cdot n^{\mathcal{O}(1)}$ on general directed graphs, where $t$ is the treewidth of the underlying undirected graph. This is matched by a dynamic programming algorithm with running time $2^{\mathcal{O}(t\log t)}\cdot n^{\mathcal{O}(1)}$. On the other hand, we show that if the input digraph is planar, then the running time can be improved to $2^{\mathcal{O}(t)}\cdot n^{\mathcal{O}(1)}$.Comment: 20

The Firefighter Problem: A Structural Analysis

We consider the complexity of the firefighter problem where b>=1 firefighters are available at each time step. This problem is proved NP-complete even on trees of degree at most three and budget one (Finbow et al.,2007) and on trees of bounded degree b+3 for any fixed budget b>=2 (Bazgan et al.,2012). In this paper, we provide further insight into the complexity landscape of the problem by showing that the pathwidth and the maximum degree of the input graph govern its complexity. More precisely, we first prove that the problem is NP-complete even on trees of pathwidth at most three for any fixed budget b>=1. We then show that the problem turns out to be fixed parameter-tractable with respect to the combined parameter "pathwidth" and "maximum degree" of the input graph

Exploring Graphs with Time Constraints by Unreliable Collections of Mobile Robots

A graph environment must be explored by a collection of mobile robots. Some of the robots, a priori unknown, may turn out to be unreliable. The graph is weighted and each node is assigned a deadline. The exploration is successful if each node of the graph is visited before its deadline by a reliable robot. The edge weight corresponds to the time needed by a robot to traverse the edge. Given the number of robots which may crash, is it possible to design an algorithm, which will always guarantee the exploration, independently of the choice of the subset of unreliable robots by the adversary? We find the optimal time, during which the graph may be explored. Our approach permits to find the maximal number of robots, which may turn out to be unreliable, and the graph is still guaranteed to be explored. We concentrate on line graphs and rings, for which we give positive results. We start with the case of the collections involving only reliable robots. We give algorithms finding optimal times needed for exploration when the robots are assigned to fixed initial positions as well as when such starting positions may be determined by the algorithm. We extend our consideration to the case when some number of robots may be unreliable. Our most surprising result is that solving the line exploration problem with robots at given positions, which may involve crash-faulty ones, is NP-hard. The same problem has polynomial solutions for a ring and for the case when the initial robots' positions on the line are arbitrary. The exploration problem is shown to be NP-hard for star graphs, even when the team consists of only two reliable robots

The loop structure and the RNA helicase p72/DDX17 influence the processing efficiency of the mice miR-132

miRNAs are small RNAs that are key regulators of gene expression in eukaryotic organisms. The processing of miRNAs is regulated by structural characteristics of the RNA and is also tightly controlled by auxiliary protein factors. Among them, RNA binding proteins play crucial roles to facilitate or inhibit miRNA maturation and can be controlled in a cell, tissue and species-specific manners or in response to environmental stimuli. In this study we dissect the molecular mechanism that promotes the overexpression of miR-132 in mice over its related, co-transcribed and co-regulated miRNA, miR-212. We have shown that the loop structure of miR-132 is a key determinant for its efficient processing in cells. We have also identified a range of RNA binding proteins that recognize the loop of miR-132 and influence both miR-132 and miR-212 processing. The DEAD box helicase p72/DDX17 was identified as a factor that facilitates the specific processing of miR-132

Traumatic brain injury and NADPH oxidase: A deep relationship

Traumatic brain injury (TBI) represents one of the major causes of mortality and disability in the world. TBI is characterized by primary damage resulting from the mechanical forces applied to the head as a direct result of the trauma and by the subsequent secondary injury due to a complex cascade of biochemical events that eventually lead to neuronal cell death. Oxidative stress plays a pivotal role in the genesis of the delayed harmful effects contributing to permanent damage. NADPH oxidases (Nox), ubiquitary membrane multisubunit enzymes whose unique function is the production of reactive oxygen species (ROS), have been shown to be a major source of ROS in the brain and to be involved in several neurological diseases. Emerging evidence demonstrates that Nox is upregulated after TBI, suggesting Nox critical role in the onset and development of this pathology. In this review, we summarize the current evidence about the role of Nox enzymes in the pathophysiology of TBI

Experimental observation of nonlinear Thomson scattering

A century ago, J. J. Thomson showed that the scattering of low-intensity light by electrons was a linear process (i.e., the scattered light frequency was identical to that of the incident light) and that light's magnetic field played no role. Today, with the recent invention of ultra-high-peak-power lasers it is now possible to create a sufficient photon density to study Thomson scattering in the relativistic regime. With increasing light intensity, electrons quiver during the scattering process with increasing velocity, approaching the speed of light when the laser intensity approaches 10^18 W/cm^2. In this limit, the effect of light's magnetic field on electron motion should become comparable to that of its electric field, and the electron mass should increase because of the relativistic correction. Consequently, electrons in such high fields are predicted to quiver nonlinearly, moving in figure-eight patterns, rather than in straight lines, and thus to radiate photons at harmonics of the frequency of the incident laser light, with each harmonic having its own unique angular distribution. In this letter, we report the first ever direct experimental confirmation of these predictions, a topic that has previously been referred to as nonlinear Thomson scattering. Extension of these results to coherent relativistic harmonic generation may eventually lead to novel table-top x-ray sources.Comment: including 4 figure