Split digraphs

We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences. The first degree sequence characterization is an extension of the concept of splittance to directed graphs, while the second characterization says a digraph is split if and only if its degree sequence satisfies one of the Fulkerson inequalities (which determine when an integer-pair sequence is digraphic) with equality.Comment: 14 pages, 2 figures; Accepted author manuscript (AAM) versio

Lineaments in basement terrane of the Peninsular Ranges, Southern California

The author has identified the following significant results. ERTS and Skylab images reveal a number of prominent lineaments in the basement terrane of the Peninsular Ranges, Southern California. The major, well-known, active, northwest trending, right-slip faults are well displayed; northeast and west to west-northwest trending lineaments are also present. Study of large-scale airphotos followed by field investigations have shown that several of these lineaments represent previously unmapped faults. Pitches of striations on shear surfaces of the northeast and west trending faults indicate oblique slip movement; data are insufficient to determine the net-slip. These faults are restricted to the pre-tertiary basement terrane and are truncated by the major northwest trending faults. They may have been formed in response to an earlier stress system. All lineaments observed in the space photography are not due to faulting, and additional detailed geologic investigations are required to determine the nature of the unstudied lineaments, and the history and net-slip of fault-controlled lineaments

Pseudocolor transformation of ERTS imagery

One of the photographic techniques which shows great promise as an aid in interpreting ERTS imagery is pseudocolor transformation. It is a process where each shade of gray in an original black-and-white image is seen as a different color in the transformation. The well known ERTS-1 MSS image of the Monterey Bay-San Francisco area was transformed using a technique which requires only two intermediate separations. Possible faults were delineated on an overlay of the transformation before referring to geologic maps. The results were quite remarkable in that all large active or recently active faults shown on the latest geologic map of California were interpreted from the image for all, or much, of their length. Perhaps the most interesting result was the Reliz fault. The fault is shown as covered; however, a lineation corresponding to the position of the fault is visible on the image. The usefulness of ERTS image in identifying recently active faults is demonstrable. Although the faults are also visible in the unenhanced image, they are clearly accentuated and more easily mapped on the pseudocolor transformation

Fault tectonics and earthquake hazards in the Peninsular Ranges, Southern California

The author has identified the following significant results. ERTS and Skylab images reveal a number of prominent lineaments in the basement terrane of the Peninsular Ranges, Southern California. The major, well-known, active, northwest trending, right-slip faults are well displayed, but northeast and west to west-northwest trending lineaments are also present. Study of large-scale airphotos followed by field investigations have shown that several of these lineaments represent previously unmapped faults. Pitches of striations on shear surfaces of the northeast and west trending faults indicate oblique-slip movement; data are insufficient to determine the net-slip. These faults are restricted to the pre-Tertiary basement terrane and are truncated by the major northwest trending faults; therefore, they may have formed in response to an earlier stress system. Future work should be directed toward determining whether the northeast and west trending faults are related to the presently active stress system or to an older inactive system, because this question relates to the earthquake risk in the vicinity of these faults

Fault tectonics and earthquake hazards in parts of southern California

The author has identified the following significant results. Four previously unknown faults were discovered in basement terrane of the Peninsular Ranges. These have been named the San Ysidro Creek fault, Thing Valley fault, Canyon City fault, and Warren Canyon fault. In addition fault gouge and breccia were recognized along the San Diego River fault. Study of features on Skylab imagery and review of geologic and seismic data suggest that the risk of a damaging earthquake is greater along the northwestern portion of the Elsinore fault than along the southeastern portion. Physiographic indicators of active faulting along the Garlock fault identifiable in Skylab imagery include scarps, linear ridges, shutter ridges, faceted ridges, linear valleys, undrained depressions and offset drainage. The following previously unrecognized fault segments are postulated for the Salton Trough Area: (1) An extension of a previously known fault in the San Andreas fault set located southeast of the Salton Sea; (2) An extension of the active San Jacinto fault zone along a tonal change in cultivated fields across Mexicali Valley ( the tonal change may represent different soil conditions along opposite sides of a fault). For the Skylab and LANDSAT images studied, pseudocolor transformations offer no advantages over the original images in the recognition of faults in Skylab and LANDSAT images. Alluvial deposits of different ages, a marble unit and iron oxide gossans of the Mojave Mining District are more readily differentiated on images prepared from ratios of individual bands of the S-192 multispectral scanner data. The San Andreas fault was also made more distinct in the 8/2 and 9/2 band ratios by enhancement of vegetation differences on opposite sides of the fault. Preliminary analysis indicates a significant earth resources potential for the discrimination of soil and rock types, including mineral alteration zones. This application should be actively pursued

Analysis of pseudocolor transformations of ERTS-1 images of Southern California area

The author has identified the following significant results. Representative faults and lineaments, natural features on the Mojave Desert, and cultural features of the southern California area were studied on ERTS-1 images. The relative appearances of the features were compared on a band 4 and 5 subtraction image, its pseudocolor transformation, and pseudocolor images of bands 4, 5, and 7. Selected features were also evaluated in a test given students at the University of California, Los Angeles. Observations and the test revealed no significant improvement in the ability to detect and locate faults and lineaments on the pseudocolor transformations. With the exception of dry lake surfaces, no enhancement of the features studied was observed on the bands 4 and 5 subtraction images. Geologic and geographic features characterized by minor tonal differences on relatively flat surfaces were enhanced on some of the pseudocolor images

Algorithm and Complexity for a Network Assortativity Measure

We show that finding a graph realization with the minimum Randi\'c index for a given degree sequence is solvable in polynomial time by formulating the problem as a minimum weight perfect b-matching problem. However, the realization found via this reduction is not guaranteed to be connected. Approximating the minimum weight b-matching problem subject to a connectivity constraint is shown to be NP-Hard. For instances in which the optimal solution to the minimum Randi\'c index problem is not connected, we describe a heuristic to connect the graph using pairwise edge exchanges that preserves the degree sequence. In our computational experiments, the heuristic performs well and the Randi\'c index of the realization after our heuristic is within 3% of the unconstrained optimal value on average. Although we focus on minimizing the Randi\'c index, our results extend to maximizing the Randi\'c index as well. Applications of the Randi\'c index to synchronization of neuronal networks controlling respiration in mammals and to normalizing cortical thickness networks in diagnosing individuals with dementia are provided.Comment: Added additional section on application

Modeling Vocal Fold Motion with a New Hydrodynamic Semi-Continuum Model

Vocal fold (VF) motion is a fundamental process in voice production, and is also a challenging problem for direct numerical computation because the VF dynamics depend on nonlinear coupling of air flow with the response of elastic channels (VF), which undergo opening and closing, and induce internal flow separation. A traditional modeling approach makes use of steady flow approximation or Bernoulli's law which is known to be invalid during VF opening. We present a new hydrodynamic semi-continuum system for VF motion. The airflow is modeled by a quasi-one dimensional continuum aerodynamic system, and the VF by a classical lumped two mass system. The reduced flow system contains the Bernoulli's law as a special case, and is derivable from the two dimensional compressible Navier-Stokes equations. Since we do not make steady flow approximation, we are able to capture transients and rapid changes of solutions, e.g. the double pressure peaks at opening and closing stages of VF motion consistent with experimental data. We demonstrate numerically that our system is robust, and models in-vivo VF oscillation more physically. It is also much simpler than a full two-dimensional Navier-Stokes system.Comment: 27 pages,6 figure