On the maximum cardinality search lower bound for treewidth

The Maximum Cardinality Search (MCS) algorithm visits the vertices of a graph in some order, such that at each step, an unvisited vertex that has the largest number of visited neighbours becomes visited. A maximum cardinality search ordering (MCS-ordering) of a graph is an ordering of the vertices that can be generated by the MCS algorithm. The visited degree of a vertex v in an MCS-ordering is the number of neighbours of v that are before v in the ordering. The visited degree of an MCS-ordering ψ of G is the maximum visited degree over all vertices v in ψ. The maximum visited degree over all MCS-orderings of graph G is called its maximum visited degree. Lucena [A new lower bound for tree-width using maximum cardinality search, SIAM J. Discrete Math. 16 (2003) 345-353] showed that the treewidth of a graph G is at least its maximum visited degree.We show that the maximum visited degree is of size O(logn) for planar graphs, and give examples of planar graphs G with maximum visited degree k with O(k!) vertices, for all k∈N. Given a graph G, it is NP-complete to determine if its maximum visited degree is at least k, for any fixed k?7. Also, this problem does not have a polynomial time approximation algorithm with constant ratio, unless P=NP. Variants of the problem are also shown to be NP-complete.In this paper, we also propose some heuristics for the problem, and report on an experimental analysis of them. Several tiebreakers for the MCS algorithm are proposed and evaluated. We also give heuristics that give upper bounds on the value of the maximum visited degree of a graph, which appear to give results close to optimal on many graphs from real life applications.     

Ultrashort-pulse dual-wavelength source for digital holographic two-wavelength contouring

Digital holographic shape measurements using femtosecond laser pulses are reported. For contouring of very fast moving objects, the simultaneous generation of at least two spectrally separated ultrashort pulses is required. To deliver this particular spectral signature at high pulse energies, a chirped-pulse Ti:sapphire laser amplifier was modified to emit two spectrally separated pulses with energies above 1 μJ each. The wavelength separation of these pulses was adjustable within the 50 nm gain bandwidth, cutting out two distinct wavelength peaks by a variable double-slit assembly in a prism sequence. A Michelson-type interferometer was employed to perform the two-wavelength contouring. The phases of the holograms and the phase differences are calculated numerically, which allow us to deduce the contour lines of the topology of the object. The suitability of the light source for digital holography is demonstrated with contouring of stationary objects and the potential for high-speed applications is indicated. PACS 42.40.-i; 42.60.By     

Physics, mind, society: Back and forth

The life course of the physicist and biologist George Feher may be seen as an epitome of science of the second half of the 20th century and the beginning of the 21st century. Feher, a native of Slovakia, barely escaped Nazism and communism and became a scientist in the USA. The Nazi concentration camps and the communist gulags have become a symbol of the 20th century. This symbol stands here to pose a question: How the two totalitarian systems, fraught with irrationality, may have arisen and thrived in parallel with an unprecedented expansion of science, the paragon of rationalism? The question has become even more urgent in the 21st century. The Ground Zero, an empty spot left after the collapse of the twin towers of the World Trade Center on 11 September 2001, has become the symbol of the entrance of humankind into the new millennium. We can do much, but we understand too little about who we are and what we are doing — this is a message that the two symbols convey about the precarious stage of our evolution. The second message concerns the role of artifacts, specifically scientific instruments, in the advancement of science. Human cultural evolution has been steadily progressing, in a form of a ratchet, only because artifacts have been continually evolving. Contrary to the common Popperian wisdom, the demarcation in science may not consist in the amenability to theoretical falsification, but rather in the amenability to instrumental grasping. Scientific instruments have empowered humans for impressive feats of manipulation with Nature and themselves. Knowledge arising in the course of autonomous evolution of artifacts may surpass the horizon of human understanding and grasping. New knowledge may still be power, but no longer the power of humans. We may need a revision of some fundamental ideas of European thought. Our understanding of the human mind may entirely reshape our comprehension of the nature of physical knowledge, and vice versa.     

Spray thermometry using thermographic phosphors

In this study a novel technique for 2D spray temperature measurement is presented. For this purpose the thermographic phosphor (TP) Mg₄GeO_5.5F:Mn was dispersed in n-dodecane and atomised using a conventional semi solid-cone nozzle. The thermographic phosphor was excited electronically by a frequency tripled Nd:YAG laser (355 nm). An ICCD-camera in combination with an image doubler detected the subsequently emitted phosphorescence at both peak emission wavelengths located at 633 nm and 659 nm, respectively. Utilising suitable calibration measurements, the local spray temperature was determined by evaluating the intensity ratio of both emission wavelengths. To the knowledge of the authors this is the first approach of spray temperature measurement exploiting the temperature dependent intensity ratio of thermographic phosphors. PACS 07.20.Dt; 32.50.+d     

Joint detection of a given number of reference fragments in a quasi-periodic sequence and its partition into segments containing series of identical fragments

The problem of joint a posteriori detection of reference fragments in a quasi-periodic sequence and its partition into segments containing series of recurring fragments from the reference tuple is solved. It is assumed that (i) an ordered reference tuple of sequences to be detected is given, (ii) the number of desired fragments is known, (iii) the index of the sequence term corresponding to the beginning of a fragment is a deterministic (not random) value, and (iv) a sequence distorted by an additive uncorrelated Gaussian noise is available for observation. It is established that the problem consists in testing a set of hypotheses about the mean of a random Gaussian vector. The cardinality of the set grows exponentially as the vector dimension (i.e., the sequence length) increases. An efficient a posteriori algorithm producing a maximum-likelihood optimal solution to the problem is substantiated. Time and space complexity bounds related to the parameters of the problem are derived. The results of numerical simulation are presented.     

Phasing of three vircators simulated in terms of coupled van der Pol oscillators

Phase synchronization in a system of three virtual-cathode microwave oscillators (vircators) simulated by coupled van der Pol oscillators is studied. The phasing dynamics of the vircators is visualized with the phase portraits of the system in the triangular coordinates. Different phasing conditions are found.     

Wide-range regulation of polyaniline conduction by interphase doping of a polyaniline film

The not-sufficient-enough conductance of semioxidized protonated polyaniline (PANI) is usually attributed to the presence of ordered quasi-metallic domains surrounded by a poorly conducting amorphous phase. The paper presents experimental results testifying to the existence, in semioxidized PANI, of multilevel redox heterogeneity that crucially effects the conductance magnitude in view of specific topology at which higher-oxidized (conducting) domains are surrounded by less oxidized (poorly conducting) domains and because the PANI conduction is extremely sensitive to the oxidation degree. It is shown experimentally that the interphase doping with metals and degenerate semiconductors of a semioxidized salt of PANI and poly(2-acrylamide-2-methyl-1-propanesulfonic acid) (PAMPSA) with a 1: 2 ratio between PANI and PAMPSA raises the PANI-PAMPSA conductivity by 3–8 orders of magnitude due to the formation near the interface of thin layers whose conductance depends on the work function of the material in contact with PANI-PAMPSA and in extreme cases substantially exceeds the conductance of gold and copper at room temperature.     

Conformational characteristics of polycaproamide in dimethylacetamide containing lithium chloride

The viscosity behavior, index of refraction, and density of dilute polycaproamide solutions in DMAc containing lithium chloride have been studied. On the basis of temperature dependences of the index of refraction and the density of solutions, the θ-condition of polycaproamide solutions in DMAc containing 2.5% lithium chloride is estimated as 21.3°C. From intrinsic viscosity [η] measurements, the coefficients of swelling of a polymer coil, the mean-square distance between chain ends, and other parameters of macromolecules in solution are calculated.