Voronoi cells via linear inequality systems

The theory and methods of linear algebra are a useful alternative to those of convex geometry in the framework of Voronoi cells and diagrams, which constitute basic tools of computational geometry. As shown by Voigt and Weis in 2010, the Voronoi cells of a given set of sites T, which provide a tesselation of the space called Voronoi diagram when T is finite, are solution sets of linear inequality systems indexed by T. This paper exploits systematically this fact in order to obtain geometrical information on Voronoi cells from sets associated with T (convex and conical hulls, tangent cones and the characteristic cones of their linear representations). The particular cases of T being a curve, a closed convex set and a discrete set are analyzed in detail. We also include conclusions on Voronoi diagrams of arbitrary sets.

From the Farkas Lemma to the Hahn–Banach Theorem

This paper provides new versions of the Farkas lemma characterizing those inequalities of the form f(x) ≥ 0 which are consequences of a composite convex inequality (S ◦ g)(x) ≤ 0 on a closed convex subset of a given locally convex topological vector space X, where f is a proper lower semicontinuous convex function defined on X, S is an extended sublinear function, and g is a vector-valued S-convex function. In parallel, associated versions of a stable Farkas lemma, considering arbitrary linear perturbations of f, are also given. These new versions of the Farkas lemma, and their corresponding stable forms, are established under the weakest constraint qualification conditions (the so-called closedness conditions), and they are actually equivalent to each other, as well as equivalent to an extended version of the so-called Hahn–Banach–Lagrange theorem, and its stable version, correspondingly. It is shown that any of them implies analytic and algebraic versions of the Hahn–Banach theorem and the Mazur–Orlicz theorem for extended sublinear functions.

Mathematical programming model for heat exchanger design through optimization of partial objectives

Mathematical programming can be used for the optimal design of shell-and-tube heat exchangers (STHEs). This paper proposes a mixed integer non-linear programming (MINLP) model for the design of STHEs, following rigorously the standards of the Tubular Exchanger Manufacturers Association (TEMA). Bell–Delaware Method is used for the shell-side calculations. This approach produces a large and non-convex model that cannot be solved to global optimality with the current state of the art solvers. Notwithstanding, it is proposed to perform a sequential optimization approach of partial objective targets through the division of the problem into sets of related equations that are easier to solve. For each one of these problems a heuristic objective function is selected based on the physical behavior of the problem. The global optimal solution of the original problem cannot be ensured even in the case in which each of the sub-problems is solved to global optimality, but at least a very good solution is always guaranteed. Three cases extracted from the literature were studied. The results showed that in all cases the values obtained using the proposed MINLP model containing multiple objective functions improved the values presented in the literature.

The structure of a PII signaling protein from a halophilic archaeon reveals novel traits and high-salt adaptations

To obtain insights into archaeal nitrogen signaling and haloadaptation of the nitrogen/carbon/energy-signaling protein PII, we determined crystal structures of recombinantly produced GlnK2 from the extreme halophilic archaeon Haloferax mediterranei, complexed with AMP or with the PII effectors ADP or ATP, at respective resolutions of 1.49 Å, 1.45 Å, and 2.60 Å. A unique trait of these structures was a three-tongued crown protruding from the trimer body convex side, formed by an 11-residue, N-terminal, highly acidic extension that is absent from structurally studied PII proteins. This extension substantially contributed to the very low pI value, which is a haloadaptive trait of H. mediterranei GlnK2, and participated in hexamer-forming contacts in one crystal. Similar acidic N-extensions are shown here to be common among PII proteins from halophilic organisms. Additional haloadaptive traits prominently represented in H. mediterranei GlnK2 are a very high ratio of small residues to large hydrophobic aliphatic residues, and the highest ratio of polar to nonpolar exposed surface for any structurally characterized PII protein. The presence of a dense hydration layer in the region between the three T-loops might also be a haloadaptation. Other unique findings revealed by the GlnK2 structure that might have functional relevance are: the adoption by its T-loop of a three-turn α-helical conformation, perhaps related to the ability of GlnK2 to directly interact with glutamine synthetase; and the firm binding of AMP, confirmed by biochemical binding studies with ATP, ADP, and AMP, raising the possibility that AMP could be an important PII effector, at least in archaea.

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.

Structural Analysis with ANSYS on Stone Constructions in the Historical Spanish Heritage

According to the importance of rehabilitation and recovery of Architectural Heritage in the live of people, this paper is aimed to strengthen the traditional methods of stone vaults calculation taking advantage of the technological characteristics of the powerful program ANSYS Workbench. As an example of this, it could find out the possible pathologies that could arise during the construction history of the building. To limit this research, the upper vault of the main chapel of the Santiago parish church in Orihuela -Alicante- is selected as a reference which is a Jeronimo Quijano´s important building work in the XVI century in the Renaissance. Moreover, it is an innovative stone masonry vault that consists of 8 double intercrossed arches with each other and braced by severies. During the seventeenth century there was a lantern in the central cap and it is unknown why it was removed. Its construction could justify the original constructive solution with intercrossed arches that freed the center to create a more enlightened and comfortable presbytery. By similarity with other Quijano’s works, it is considered a small lantern drilling the central spherical cap. It is proposed to carry out a comparative study of it with different architectural solutions from the same period and based on several common parameters such as: a vault of square plant with spherical surround, intercrossed arches, a possible lantern, the dimension of the permitted space, similar states of loads and compact limestone masonry. The three solutions are mainly differentiated by their size and the type of lantern and its comparison lets us know which one is the most resistant and stable. The other two building works maintain some connection with the Quijano's professional scope. It has selected the particular case of the Communion chapel of the Basilica in Elche (a large prismatic lantern with a large cylindrical drum that starts from the own arches and an upper hemispherical dome), for its conservation, its proximity to Orihuela and its implementation during the century XVIII. Finally, a significant Dome Spanish Renaissance complete the selection: a cross vault of the Benavides Chapel of the Saint Francisco Convent in Baeza - Jaén-, designed by Andres of Vandelvira in the sixteenth century (a large hemispherical dome that starts from the own arcs). To simplify the calculation and standardize the work that have to be contrasted, all of them were considered with some similar characteristics: 30 cm constant thickness, the intercrossed arches were specifically analyzed and had identical loads, Young's modulus and Poisson's ratio. Regarding the calculation solutions, in general terms, the compressive stresses predominate, influencing on it the joint collaboration of the filling material on the vault, the vault itself, the thick side walls, the buttresses and the top cover weight . In addition, the three solutions are suitable, being the Orihuela one the safest and the Baeza one the riskiest for its large dimensions. Thus, the idea of intercrossed arches with suitable thickness would allow carry out the heaviest lantern and this would confirm it as a Renaissance architectural typology built in stone.

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.

Nd isotope ratios of surface sediments from the Pacific Ocean (Table 2)

The neodymium isotopic composition of the silicate fraction of Holocene pelagic sediments from the North Pacific define two provinces: a central North Pacific province characterized by unradiogenic and remarkably homogeneous end (-10.2 +/- 0.5) and a narrow circum-Pacific marginal province characterized by more radiogenic and variable end (-4.2 +/- 3.8). The silicate fraction in the central North Pacific is exclusively eolian; based on prevailing wind patterns, meteorological data, and neodymium isotopic data, the only significant sediment source is Chinese loess. Leaching experiments on Chinese loess confirm that leachable Nd is isotopically indistinguishable from bulk and residual silicate Nd. Silicates in the circum-North Pacific marginal province comprise eolian loess, volcanic ash, and hemipelagic sediments derived from volcanic arcs. A compilation of Pacific seawater and Mn nodule epsilon-Nd data shows no clear spatial variation except for a general decrease from surface to deep waters from -3 to -4 and slightly lower epsilon-Nd in bottom waters along the western North Pacific due to the incursion of Antarctic Bottom Water. The relative homogeneity of bottom water epsilon-Nd, which contrasts sharply with the distinctive variation in sediment epsilon-Nd, plus the large difference between the average end of bottom waters and the central North Pacific eolian silicates (-4 vs. -10), suggests that any contribution of REE to seawater from eolian materials is insignificant. Furthermore, leaching of REE from eolian particles as they sink though the water column must be insignificant because Nd in shallow waters is more radiogenic than Nd in deeper waters. That there is no contrast in the Nd isotopic composition of bottom waters that overlie the central and marginal sediment provinces suggests that the ash and hemipelagic sediments derived from Pacific rim volcanic arcs also contribute minimal REE to seawater. The elimination of eolian, ash, and hemipelagic sediments leaves only near-shore riverine particulates as a possibly significant particulate source of REE to seawater.