Reconfiguration on sparse graphs

A vertex-subset graph problem Q defines which subsets of the vertices of an input graph are feasible solutions. A reconfiguration variant of a vertex-subset problem asks, given two feasible solutions S and T of size k, whether it is possible to transform S into T by a sequence of vertex additions and deletions such that each intermediate set is also a feasible solution of size bounded by k. We study reconfiguration variants of two classical vertex-subset problems, namely Independent Set and Dominating Set. We denote the former by ISR and the latter by DSR. Both ISR and DSR are PSPACE-complete on graphs of bounded bandwidth and W[1]-hard parameterized by k on general graphs. We show that ISR is fixed-parameter tractable parameterized by k when the input graph is of bounded degeneracy or nowhere-dense. As a corollary, we answer positively an open question concerning the parameterized complexity of the problem on graphs of bounded treewidth. Moreover, our techniques generalize recent results showing that ISR is fixed-parameter tractable on planar graphs and graphs of bounded degree. For DSR, we show the problem fixed-parameter tractable parameterized by k when the input graph does not contain large bicliques, a class of graphs which includes graphs of bounded degeneracy and nowhere-dense graphs

A unified framework for approximation in inverse problems for distributed parameter systems

A theoretical framework is presented that can be used to treat approximation techniques for very general classes of parameter estimation problems involving distributed systems that are either first or second order in time. Using the approach developed, one can obtain both convergence and stability (continuous dependence of parameter estimates with respect to the observations) under very weak regularity and compactness assumptions on the set of admissible parameters. This unified theory can be used for many problems found in the recent literature and in many cases offers significant improvements to existing results

Formation of Hot Planets by a combination of planet scattering, tidal circularization, and Kozai mechanism

We have investigated the formation of close-in extrasolar giant planets through a coupling effect of mutual scattering, Kozai mechanism, and tidal circularization, by orbital integrations. We have carried out orbital integrations of three planets with Jupiter-mass, directly including the effect of tidal circularization. We have found that in about 30% runs close-in planets are formed, which is much higher than suggested by previous studies. We have found that Kozai mechanism by outer planets is responsible for the formation of close-in planets. During the three-planet orbital crossing, the Kozai excitation is repeated and the eccentricity is often increased secularly to values close enough to unity for tidal circularization to transform the inner planet to a close-in planet. Since a moderate eccentricity can remain for the close-in planet, this mechanism may account for the observed close-in planets with moderate eccentricities and without nearby secondary planets. Since these planets also remain a broad range of orbital inclinations (even retrograde ones), the contribution of this process would be clarified by more observations of Rossiter-McLaughlin effects for transiting planets.Comment: 15 pages, 16 figures, Accepted for publication in Ap

Nutritional characteristics of moon dust for soil microorganisms

Approximately 46% of the lunar sample (10084,151), 125.42 mg, was solubilized in 680 ml 0.01 M salicylic acid. Atomic absorption spectroscopic analysis of the solubilized lunar sample showed the following amount of metal ions: Ca, 3.1; Mg, 4.0; K, 0.09; Na, 0.67; Fe, 7.3; Mn, 1.6; Cu, Ni, Cr, less than 0.1 each. All are in ppm. Salicylic acid used to solubilize the lunar sample was highly inhibitory to the growth of mixed soil microbes. However, the mineral part of the lunar extract stimulated the growth. For optimal growth of the soil microbes the following nutrients must be added to the moon extract; sources of carbon, nitrogen, sulfur, phosphorus, and magnesium in addition to water

Mediation of Supersymmetry Breaking via Anti-Generation Fields

In the context of the weakly coupled heterotic string, we propose a new model of mediating supersymmetry breaking. The breakdown of supersymmetry in the hidden sector is transmitted to anti-generation fields via gravitational interactions. Subsequent transmission of the breaking to the MSSM sector occurs via gauge interactions. It is shown that the mass spectra of superparticles are phenomenologically viable.Comment: 8pages, LaTeX, 1 figure, final version to appear in Prog. Theor. Phys. Vol.103, No.6 (2000

Degree-constrained Subgraph Reconfiguration is in P

The degree-constrained subgraph problem asks for a subgraph of a given graph such that the degree of each vertex is within some specified bounds. We study the following reconfiguration variant of this problem: Given two solutions to a degree-constrained subgraph instance, can we transform one solution into the other by adding and removing individual edges, such that each intermediate subgraph satisfies the degree constraints and contains at least a certain minimum number of edges? This problem is a generalization of the matching reconfiguration problem, which is known to be in P. We show that even in the more general setting the reconfiguration problem is in P.Comment: Full version of the paper published at Mathematical Foundations of Computer Science (MFCS) 201

Asynchronous vibration problem of centrifugal compressor

An unstable asynchronous vibration problem in a high pressure centrifugal compressor and the remedial actions against it are described. Asynchronous vibration of the compressor took place when the discharge pressure (Pd) was increased, after the rotor was already at full speed. The typical spectral data of the shaft vibration indicate that as the pressure Pd increases, pre-unstable vibration appears and becomes larger, and large unstable asynchronous vibration occurs suddenly (Pd = 5.49MPa). A computer program was used which calculated the logarithmic decrement and the damped natural frequency of the rotor bearing systems. The analysis of the log-decrement is concluded to be effective in preventing unstable vibration in both the design stage and remedial actions