A Complexity Dichotomy for the Coloring of Sparse Graphs

Galluccio, Goddyn, and Hell proved in 2001 that in any minor‐closed class of graphs, graphs with large enough girth have a homomorphism to any given odd cycle. In this paper, we study the computational aspects of this problem. Let be a monotone class of graphs containing all planar graphs, and closed under clique‐sum of order at most two. Examples of such class include minor‐closed classes containing all planar graphs, and such that all minimal obstructions are 3‐connected. We prove that for any k and g, either every graph of girth at least g in has a homomorphism to , or deciding whether a graph of girth g in has a homomorphism to is NP‐complete. We also show that the same dichotomy occurs when considering 3‐Colorability or acyclic 3‐Colorability of graphs under various notions of density that are related to a question of Havel (On a conjecture of Grünbaum, J Combin Theory Ser B 7 (1969), 184–186) and a conjecture of Steinberg (The state of the three color problem, Quo Vadis, Graph theory?, Ann Discrete Math 55 (1993), 211–248) about the 3‐Colorability of sparse planar graphs.     

Characters, fields, Schur indices and divisibility

Let G be a finite nilpotent group. Suppose that G ₀ is a subgroup of G and that ${\psi}$ is an irreducible character of G ₀. Consider the set S whose elements are the natural numbers $${\rm m}_{\bf Q}(\chi)[{\bf Q}(\chi) : {\bf Q}]$$ as ${\chi}$ runs through the irreducible characters of G which contain ${\psi}$ as a summand when restricted to G ₀. Here m _Q (χ) is, as usual, the rational Schur index of ${\chi}$ , and ${[{\bf Q}(\chi) : {\bf Q}]}$ is the degree of the extension of the field of values of the character as an extension of the rationals. We prove that then the minimum element of S divides all the other elements of S. The result is not true when G is an arbitrary finite group. We also consider some variations of this result.     

Implicit Sampling, with Application to Data Assimilation

There are many computational tasks, in which it is necessary to sample a given probability density function (or pdf for short), i.e., to use a computer to construct a sequence of independent random vectors x i (i = 1, 2, ··· ), whose histogram converges to the given pdf. This can be difficult because the sample space can be huge, and more importantly, because the portion of the space, where the density is significant, can be very small, so that one may miss it by an ill-designed sampling scheme. Indeed, Markovchain Monte Carlo, the most widely used sampling scheme, can be thought of as a search algorithm, where one starts at an arbitrary point and one advances step-by-step towards the high probability region of the space. This can be expensive, in particular because one is typically interested in independent samples, while the chain has a memory. The authors present an alternative, in which samples are found by solving an algebraic equation with a random right-hand side rather than by following a chain; each sample is independent of the previous samples. The construction in the context of numerical integration is explained, and then it is applied to data assimilation.     

GigaManP2P: an overlay network for distributed QoS management and resilient routing

Management of long‐distance, high‐speed optical backbones spanning multiple administrative domains requires new solutions for challenging tasks. In particular, it is not trivial to negotiate, monitor and continuously enforce the required quality of service (QoS) for applications that span multiple domains. This paper proposes GigaManP2P: a novel peer‐to‐peer (P2P) management architecture for high‐speed QoS‐aware backbones. GigaManP2P peers provide management services in a ubiquitous fashion through modules that interface with both the communication infrastructure and network users. In particular, we describe management services for on inter‐domain QoS monitoring and resilient routing. After detecting a QoS constraint violation trend, a proactive rerouting strategy is triggered based on redundant virtual circuits, allowing both full and partial rerouting. The P2P overlay implementation is the basis for allowing transparent communication across autonomous systems. Experimental results showing the overhead of the P2P infrastructure in comparison to raw Simple Network Management Protocol, and the performance of the rerouting strategy, are presented. Copyright © 2011 John Wiley & Sons, Ltd.     

PDE-based enhancement of color images in RGB space

A novel method for color image enhancement is proposed as an extension of the scalar-diffusion-shock-filter coupling model, where noisy and blurred images are denoised and sharpened. The proposed model is based on using the single vectors of the gradient magnitude and the second derivatives as a manner to relate different color components of the image. This model can be viewed as a generalization of the Bettahar-Stambouli filter to multivalued images. The proposed algorithm is more efficient than the mentioned filter and some previous works at color images denoising and deblurring without creating false colors.     

An efficient parallel architecture for ray-tracing

Real time rendering of three-dimensional scenes in high photorealistic details is a hard task, such as in the ray tracing rendering algorithm. In general, the performance achieved by a sequential software-based implementation of ray tracing is far from satisfactory. However, parallel implementations of ray tracing have been enabling reasonable real time performance, as the algorithm is embarrassingly parallel. Thus, a custom parallel design in hardware is likely to achieve an even higher performance. In this paper, we propose a hardware parallel architecture capable of dealing with the main desirable features of ray tracing, such as shadows and reflection effects, imposing low area cost and a promising rendering performance. Such architecture, called GridRT, is based on the Uniform Grid acceleration structure and is intended to deliver massive parallelism through parallel ray-triangle intersection tests as well as parallel processing of many rays. A hardware implementation of the proposed architecture is presented, together with some performance results and resources requirements. The rendering is reduced by 80% using a grid configuration of eight processing elements.     

One-pot synthesis of block copolymers in supercritical carbon dioxide: a simple versatile route to nanostructured microparticles

We present a one-pot synthesis for well-defined nanostructured polymeric microparticles formed from block copolymers that could easily be adapted to commercial scale. We have utilized reversible addition-fragmentation chain transfer (RAFT) polymerization to prepare block copolymers in a dispersion polymerization in supercritical carbon dioxide, an efficient process which uses no additional solvents and hence is environmentally acceptable. We demonstrate that a wide range of monomer types, including methacrylates, acrylamides, and styrenics, can be utilized leading to block copolymer materials that are amphiphilic (e.g., poly(methyl methacrylate)-b-poly(N,N-dimethylacrylamide)) and/or mechanically diverse (e.g., poly(methyl methacrylate)-b-poly(N,N-dimethylaminoethylmethacrylate)). Interrogation of the internal structure of the microparticles reveals an array of nanoscale morphologies, including multilayered, curved cylindrical, and spherical domains. Surprisingly, control can also be exerted by changing the chemical nature of the constituent blocks and it is clear that selective CO(2) sorption must strongly influence the block copolymer phase behavior, resulting in kinetically trapped morphologies that are different from those conventionally observed for block copolymer thin films formed in absence of CO(2).     

Mapping the Energy Distribution of SERRS Hot Spots from Anti-Stokes to Stokes Intensity Ratios

The anomalies in the anti-Stokes to Stokes intensity ratios in single-molecule surface-enhanced resonance Raman scattering were investigated. Brilliant green and crystal violet dyes were the molecular probes, and the experiments were carried out on an electrochemically activated Ag surface. The results allowed new insights into the origin of these anomalies and led to a new method to confirm the single-molecule regime in surface-enhanced Raman scattering. Moreover, a methodology to estimate the distribution of resonance energies that contributed to the imbalance in the anti-Stokes to Stokes intensity ratios at the electromagnetic hot spots was proposed. This method allowed the local plasmonic resonance energies on the metallic surface to be spatially mapped.     

Density induced transition in a school of fish

Collective behaviour has been studied in various fields of science. As an example, we may consider the patterns observed in living systems, whose aggregates form organized groups such as flocks of birds, herds of mammals and schools of fish. These aggregates may be formed as a consequence of an external stimulus or due to the local interaction among nearby specimens. As an example of the latter case one may think about a school of fish, where each individual bases its behaviour on its perception of the position and velocity of its nearest neighbours. As a result of these interactions, global collective behaviour may emerge, originating and maintaining the cohesion of the aggregate. In this work, we model the collective movement of a school of fish using an agent-based model which follows biologically motivated behavioural rules previously proposed. The distributions of nearest neighbour distance and relative orientations between neighbouring fishes are measured and the results are found to be in good agreement with previous experimental measurements.     

Copper-free asymmetric allylic alkylation using grignard reagents on bifunctional allylic bromides

A series of substrates containing a vinylic bromide were employed in a copper-free methodology using bidendate NHC ligands. The desired compounds are generally obtained with good enantioselectivity and good regioselectivity. Importantly the copper-catalyzed system afforded a lower enantioselectivity value. The catalytic products could be transformed into a broad scope of new 1,1-disubstituted olefins in a single step transformation without erosion of the enantioselectivity.