An approximate Hahn–Banach theorem for positively homogeneous functions

This note provides an approximate version of the Hahn–Banach theorem for non-necessarily convex extended-real valued positively homogeneous functions of degree one. Given p : X → R∪{+∞} such a function defined on the real vector space X, and a linear function defined on a subspace V of X and dominated by p (i.e. (x) ≤ p(x) for all x ∈ V), we say that can approximately be p-extended to X, if is the pointwise limit of a net of linear functions on V, every one of which can be extended to a linear function defined on X and dominated by p. The main result of this note proves that can approximately be p-extended to X if and only if is dominated by p∗∗, the pointwise supremum over the family of all the linear functions on X which are dominated by p.

Global behavior of the Douglas–Rachford method for a nonconvex feasibility problem

In recent times the Douglas–Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to explain this observed success and is mainly concerned with questions of local convergence. In this paper we analyze global behavior of the method for finding a point in the intersection of a half-space and a potentially non-convex set which is assumed to satisfy a well-quasi-ordering property or a property weaker than compactness. In particular, the special case in which the second set is finite is covered by our framework and provides a prototypical setting for combinatorial optimization problems.

Tectonic geomorphology assessment of the Ken River catchment near Panna, Madhya Pradesh, India

This thesis focuses on tectonic geomorphology and the response of the Ken River catchment to postulated tectonic forcing along a NE-striking monocline fold in the Panna region, Madhya Pradesh, India. Peninsular India is underlain by three northeast-trending paleotopographic ridges of Precambrian Indian basement, bounded by crustal-scale faults. Of particular interest is the Pokhara lineament, a crustal scale fault that defines the eastern edge of the Faizabad ridge, a paleotopographic high cored by the Archean Bundelkhand craton. The Pokhara lineament coincides with the monocline structure developed in the Proterozoic Vindhyan Supergroup rocks along the Bundelkhand cratonic margin. A peculiar, deeply incised meander-like feature, preserved along the Ken River where it flows through the monocline, may be intimately related to the tectonic regime of this system. This thesis examines 41 longitudinal stream profiles across the length of the monocline structure to identify any tectonic signals generated from recent surface uplift above the Pokhara lineament. It also investigates the evolution of the Ken River catchment in response to the generation of the monocline fold. Digital Elevation Models (DEM) from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) were used to delineate a series of tributary watersheds and extract individual stream profiles which were imported into MATLAB for analysis. Regression limits were chosen to define distinct channel segments, and knickpoints were defined at breaks between channel segments where there was a discrete change in the steepness of the channel profile. The longitudinal channel profiles exhibit the characteristics of a fluvial system in transient state. There is a significant downstream increase in normalized steepness index in the channel profiles, as well as a general increase in concavity downstream, with some channels exhibiting convex, over-steepened segments. Normalized steepness indices and uppermost knickpoint elevations are on average much higher in streams along the southwest segment of the monocline compared to streams along the northeast segment. Most channel profiles have two to three knickpoints, predominantly exhibiting slope-break morphology. These data have important implications for recent surface uplift above the Pokhara lineament. Furthermore, geomorphic features preserved along the Ken River suggest that it is an antecedent river. The incised meander-like feature appears to be the abandoned river valley of a former Ken River course that was captured during the evolution of the landscape by what is the present day Ken River.

FPGA implementation of a multi-population PBIL algorithm

Evolutionary-based algorithms play an important role in finding solutions to many problems that are not solved by classical methods, and particularly so for those cases where solutions lie within extreme non-convex multidimensional spaces. The intrinsic parallel structure of evolutionary algorithms are amenable to the simultaneous testing of multiple solutions; this has proved essential to the circumvention of local optima, and such robustness comes with high computational overhead, though custom digital processor use may reduce this cost. This paper presents a new implementation of an old, and almost forgotten, evolutionary algorithm: the population-based incremental learning method. We show that the structure of this algorithm is well suited to implementation within programmable logic, as compared with contemporary genetic algorithms. Further, the inherent concurrency of our FPGA implementation facilitates the integration and testing of micro-populations.

Petrophysical measurement of ODP Leg 122 and 123 samples (Tables 1, 2)

The capillary-pressure characteristics of 22 samples of lithified post-Paleozoic Indian-Ocean carbonates were compared to published data from older carbonate rocks (lower Paleozoic Hunton Group of Texas and Oklahoma). The Indian-Ocean samples are considerably more porous than are the Paleozoic samples, yet all of the Indian-Ocean samples fit readily into a descriptive petrofacies scheme previously established for the Hunton Group. The Indian-Ocean samples may be assigned to four petrophysical facies (petrofacies) based on the shapes of their capillary-pressure curves, their pore-throat-size distributions, their estimated recovery efficiency values (for nonwetting fluids), and the visual characteristics of their pore systems, as observed with a scanning-electron microscope. Petrofacies assignments for the Indian-Ocean samples are as follows. Petrofacies I includes six samples collected from the coarse basal portions of event deposits (primarily turbidites). These samples have large throats, leptokurtic throat-size distributions, low- to moderate recovery efficiency values, concave cumulative-intrusion capillary-pressure curves, and high porosity values. Petrofacies II includes two sedimentologically dissimilar samples that have medium-size throats, platykurtic throat-size distributions, moderate- to-high recovery efficiency values, gently sloping cumulative-intrusion capillary-pressure curves, and high porosity values. Petrofacies III includes two polymictic sandstones and a skeletal packstone that have small throats, polymodal throat-size distributions, moderate recovery efficiency values, gently sloping cumulative-intrusion capillary-pressure curves, and high porosity values. Petrofacies IV includes 11 samples, mostly recrystallized neritic carbonates, that have small throats, leptokurtic throat-size distributions, high recovery efficiency values, convex cumulative-intrusion capillary-pressure curves, and low porosity values. Comparison of petrofacies assignment to core-, thin-section-, and smear-slide data, and to inferred depositional setting, suggests that pore systems in most samples from Holes 765C and 766A result from primary depositional features, whereas pore systems in samples from Hole 761C and one sample from Hole 765C have been strongly influenced by diagenetic processes. For Hole 761C, prediction of petrophysical parameters should be most successful if based on diagenetic facies patterns. By contrast, the distribution of favorable reservoir facies and of permeability barriers in less highly altered rocks collected from Holes 765C and 766A is related to depositional patterns. Recovery efficiency is inversely related to both porosity and median throat size for the present data set. This relationship is similar to that observed for carbonates of the lower Paleozoic Hunton Group and the Ordovician Ellenburger dolomite, but opposite of that observed for some other ancient carbonates. The coarse deposits of the massive basal units of turbidites are petrophysically distinct and form a coherent petrophysical group (Petrofacies I) with substantial reservoir potential. Two samples assigned to Petrofacies I have extremely large throats (median throat size at least 4 ?m, and at least six times that of any other sample) and therefore high permeability values. These two samples come from thin, coarse turbidites that lack or have poorly developed fine divisions and are interpreted to have been deposited on channeled suprafan lobes in a proximal mid-fan setting. The restriction of extremely high permeability values to a single depositional facies suggests that careful facies mapping of deep-sea fans in a deliberate search for such coarse turbidites could dramatically enhance the success of exploration for aquifers or hydrocarbon reservoirs. Such reservoirs should have substantial vertical heterogeneity. They should have high lateral permeability values but low vertical permeability values, and reservoir sections should include numerous thin units having widely differing petrophysical characteristics.

On Managing Stochastic Decentralized Projects

Thesis (Ph.D.)--University of Washington, 2016-06

Geometry and Optimization of Relative Arbitrage

Thesis (Ph.D.)--University of Washington, 2016-06

Orientation of the genetic variance-covariance matrix and the fitness surface for multiple male sexually selected traits

Stabilizing selection has been predicted to change genetic variances and covariances so that the orientation of the genetic variance-covariance matrix (G) becomes aligned with the orientation of the fitness surface, but it is less clear how directional selection may change G. Here we develop statistical approaches to the comparison of G with vectors of linear and nonlinear selection. We apply these approaches to a set of male sexually selected cuticular hydrocarbons (CHCs) of Drosophila serrata. Even though male CHCs displayed substantial additive genetic variance, more than 99% of the genetic variance was orientated 74.9degrees away from the vector of linear sexual selection, suggesting that open-ended female preferences may greatly reduce genetic variation in male display traits. Although the orientation of G and the fitness surface were found to differ significantly, the similarity present in eigenstructure was a consequence of traits under weak linear selection and strong nonlinear ( convex) selection. Associating the eigenstructure of G with vectors of linear and nonlinear selection may provide a way of determining what long-term changes in G may be generated by the processes of natural and sexual selection.

Contrasting mutual sexual selection on homologous signal traits in Drosophila serrata

The nature of male mating preferences, and how they differ from female mating preferences in species with conventional sex roles, has received little attention in sexual selection studies. We estimated the form and strength of sexual selection as a consequence of male and female mating preferences in a laboratory-based population of Drosophila serrata. The differences between sexual selection on male and female signal traits (cuticular hydrocarbons [CHCs]) were evaluated within a formal framework of linear and nonlinear selection gradients. Females tended to exert linear sexual selection on male CHCs, whereas males preferred intermediate female CHC phenotypes leading to convex (stabilizing) selection gradients. Possible mechanisms determining the nonlinear nature of sexual selection on female CHCs are proposed.

Experimental evidence for multivariate stabilizing sexual selection

Stabilizing selection is a fundamental concept in evolutionary biology. In the presence of a single intermediate optimum phenotype (fitness peak) on the fitness surface, stabilizing selection should cause the population to evolve toward such a peak. This prediction has seldom been tested, particularly for suites of correlated traits. The lack of tests for an evolutionary match between population means and adaptive peaks may be due, at least in part, to problems associated with empirically detecting multivariate stabilizing selection and with testing whether population means are at the peak of multivariate fitness surfaces. Here we show how canonical analysis of the fitness surface, combined with the estimation of confidence regions for stationary points on quadratic response surfaces, may be used to define multivariate stabilizing selection on a suite of traits and to establish whether natural populations reside on the multivariate peak. We manufactured artificial advertisement calls of the male cricket Teleogryllus commodus and played them back to females in laboratory phonotaxis trials to estimate the linear and nonlinear sexual selection that female phonotactic choice imposes on male call structure. Significant nonlinear selection on the major axes of the fitness surface was convex in nature and displayed an intermediate optimum, indicating multivariate stabilizing selection. The mean phenotypes of four independent samples of males, from the same population as the females used in phonotaxis trials, were within the 95% confidence region for the fitness peak. These experiments indicate that stabilizing sexual selection may play an important role in the evolution of male call properties in natural populations of T. commodus.

First record from Australia of the Cretaceous fern genus Tempskya and the description of a new species, T judithae

Silicified fragments of false-trunks of the fern, Tempskya judithae sp. nov., are described from lower Cretaceous (latest Albian) sediments near Winton, central-western Queensland. The species is characterised by a three-layered sclerenchymatous cortex and a two-layered pith of sclerenchyma cells. In possessing these characters, T judithae is more similar to T readii than to other species of Tempskya. However, the Australian species differs from T readii in the abaxial shape of the petiole xylem trace (concave in T judithae, convex in T readii) and in symmetry attributes of the leaf-bases within the false-trunk (random in T judithae and radially symmetrical in T readii). T judithae is the first record of Tempskya from Australia and the second from Gondwana; the known distribution range of the genus embraces a broad area in mid-high latitudinal regions of Laurasia and the Gondwana record now comprises Australia and Argentina. Ecological signals of plant fossil assemblages recorded from the Australian sediments are in accord with flood plain habitats and a temperate climatic regime. (c) 2004 Elsevier B.V. All rights reserved.

Spatial and ontogenetic variation in growth of nursery-bound juvenile lemon sharks, Negaprion brevirostris: a comparison of two age-assigning techniques

We compared growth rates of the lemon shark, Negaprion brevirostris, from Bimini, Bahamas and the Marquesas Keys (MK), Florida using data obtained in a multi-year annual census. We marked new neonate and juvenile sharks with unique electronic identity tags in Bimini and in the MK we tagged neonate and juvenile sharks. Sharks were tagged with tiny, subcutaneous transponders, a type of tagging thought to cause little, if any disruption to normal growth patterns when compared to conventional external tagging. Within the first 2 years of this project, no age data were recorded for sharks caught for the first time in Bimini. Therefore, we applied and tested two methods of age analysis: ( 1) a modified 'minimum convex polygon' method and ( 2) a new age-assigning method, the 'cut-off technique'. The cut-off technique proved to be the more suitable one, enabling us to identify the age of 134 of the 642 previously unknown aged sharks. This maximised the usable growth data included in our analysis. Annual absolute growth rates of juvenile, nursery-bound lemon sharks were almost constant for the two Bimini nurseries and can be best described by a simple linear model ( growth data was only available for age-0 sharks in the MK). Annual absolute growth for age-0 sharks was much greater in the MK than in either the North Sound (NS) and Shark Land (SL) at Bimini. Growth of SL sharks was significantly faster during the first 2 years of life than of the sharks in the NS population. However, in MK, only growth in the first year was considered to be reliably estimated due to low recapture rates. Analyses indicated no significant differences in growth rates between males and females for any area.

Field observations of instantaneous water slopes and horizontal pressure gradients in the swash-zone

Field observations of instantaneous water surface slopes in the swash zone are presented. For free-surface flows with a hydrostatic pressure distribution the surface slope is equivalent to the horizontal pressure gradient. Observations were made using a novel technique which in its simplest form consists of a horizontal stringline extending seaward from the beach face. Visual observation, still photography or video photography is then sufficient to determine the surface slope where the free-surface cuts the line or between reference points in the image. The method resolves the mean surface gradient over a cross-shore distance of 5 m or more to within +/- 0.001, or 1/20th -1/100th of typical beach gradients. In addition, at selected points and at any instant in time during the swash cycle, the water surface slope can be determined exactly to be dipping either seaward or landward. Close to the location of bore collapse landward dipping water surface slopes of order 0.05-0.1 occur over a very small region (order 0.5 m) at the blunt or convex leading edge of the swash. In the middle and upper swash the water surface slope at this leading edge is usually very close to horizontal or slightly seaward. Behind the leading edge, the water surface slope was observed to be very close to horizontal or dipping seaward at all times throughout the swash uprush. During the backwash the water surface slope was observed to be always dipping seaward, approaching the beach slope, and remained seaward until a new uprush edge or incident bore passed any particular cross-shore location of interest. The observations strongly Suggest that the swash boundary layer is subject to an adverse pressure gradient during uprush and a favourable pressure gradient during the backwash. Furthermore, assuming Euler's equations are a good approximation in the swash, the observations also show that the total fluid acceleration is negative (offshore) for almost the whole of the uprush and for the entire backwash. The observations are contrary to recent work suggesting significant shoreward directed accelerations and pressure gradients occur in the swash (i.e., delta u/delta t > 0 similar to delta p/delta x < 0), but consistent with analytical and numerical solutions for swash uprush and backwash. The results have important implications for sediment transport modelling in the swash zone.

In situ observation of bainite growth during isothermal holding

The mechanism of bainite growth has been investigated using in situ transmission electron microscopy observations. It was found that, in a number of alloys studied, a bainitic embryo is made of basic transformation units. These units are either a group of stacking faults or, in two dimensions, a series of parallelograms of different sizes. Thickening/widening of the bainite embryo takes place through shear along the stacking fault planes or twining planes. The bainite embryo is elongated by the formation of new transformation units at both tips of the bainite plate. The three-dimensional morphology of bainite is a convex tens-like lath. It is believed that the bainite embryo grows by shearing, which is controlled by the diffusion of solute atoms during the transformation. As the growth rate is much lower than that of martensite, it is therefore detectable. (c) 2006 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Stability for parametric implicit vector equilibrium problems

In this paper, we consider a class of parametric implicit vector equilibrium problems in Hausdorff topological vector spaces where a mapping f and a set K are perturbed by parameters is an element of and lambda respectively. We establish sufficient conditions for the upper semicontinuity and lower semicontinuity of the solution set mapping S : Lambda(1) x A(2) -> 2(X) for such parametric implicit vector equilibrium problems. (c) 2005 Elsevier Ltd. All rights reserved.