The Use of the Relative Interior in Integration with Nonconvex Data

Introducing an appropriate inclusion between approximate minima associated with two nonconvex functions, we derive explicit relations between the closed convex hulls of these functions. The formula we obtain goes beyond the so-called epi-pointed property of functions which is usually concerned with such a topic.

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.

(Table 2) Chemical composition of upper and lower surfaces of Fe-Mn nodules from the Eastern Subequatorial Pacific

Materials of polygon exploration during Cruise 41 of R/V Dmitry Mendeleev showed that diagenetic and sedimentary-diagenetic nodules close in morphology, texture, and composition vary greatly in size and productivity. Local variations in productivity of this nodule type in pelagic areas of the Pacific Ocean are closely connected with thickness of underlying clayey-radiolarian oozes.

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.

Translations on Soviet geodesy, 1925-1940.

JPRS: R-105-N/31; R-107-N/31; R-107-N/72; R-113-N/1; R-104-N/25; R-104-N/2; R-105-N/25; R-105-N/24.

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.