Physical Sciences and Mathematics Commons^™

Second-Order Subdifferential Calculus With Applications To Tilt Stability In Optimization, Boris S. Mordukhovich, R T. Rockafellar

Mathematics Research Reports

The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the so-called (full and partial) second-order subdifferentials of extended-real-valued functions, which are dual-type constructions generated by coderivatives of first-order sub differential mappings. We develop an extended second-order subdifferential calculus and analyze the basic second-order qualification condition ensuring the fulfillment of the principal secondorder chain rule for strongly and fully amenable compositions. The calculus results obtained in this way and computing the second-order subdifferentials for piecewise linear-quadratic functions and …

Sensitivity Analysis For Two-Level Value Functions With Applications To Bilevel Programming, S Dempe, Boris S. Mordukhovich, B Zemkoho

Mathematics Research Reports

This paper contributes to a deeper understanding of the link between a now conventional framework in hierarchical optimization spread under the name of the optimistic bilevel problem and its initial more difficult formulation that we call here the original optimistic bilevel optimization problem. It follows from this research that, although the process of deriving necessary optimality conditions for the latter problem is more involved, the conditions themselves do not to a large extent differ from those known for the conventional problem. It has been already well recognized in the literature that for optimality conditions of the usual optimistic bilevel program …

Variational Analysis Of Marginal Functions With Applications To Bilevel Programming, Boris S. Mordukhovich, Nguyen Mau Nam, Hung M. Phan

Mathematics Research Reports

This paper pursues a twofold goal. First to derive new results on generalized differentiation in variational analysis focusing mainly on a broad class of intrinsically nondifferentiable marginal/value functions. Then the results established in this direction apply to deriving necessary optimality conditions for the optimistic version of bilevel programs that occupy a remarkable place in optimization theory and its various applications. We obtain new sets of optimality conditions in both smooth and smooth settings of finite-dimensional and infinite-dimensional spaces.

Depositional Fluxes And Concentrations Of 7Be And 210Pb In Bulk Precipitation And Aerosols At The Interface Of Atlantic And Mediterranean Coasts In Spain, R. L. Lozano, E. G. San Miguel, J. P. Bolívar, M. Baskaran

Environmental Science and Geology Faculty Research Publications

Bulk depositional fluxes of ⁷Be and ²¹⁰Pb in precipitation measured over a period of 16 months (April 2009–July 2010) in Huelva, Spain varied between 5.6 and 186 Bq m⁻² month⁻¹ (annual mean: 834 Bq m⁻² year⁻¹) and 0.8 and 8.1 Bq m⁻² month⁻¹ (annual mean: 59 Bq m⁻² year⁻¹), respectively, with the lowest depositional fluxes occurring during dry summer months. Quantitative evaluation of the precipitation-normalized seasonal depositional fluxes of ⁷Be and ²¹⁰Pb indicates that the enrichment factor in winter is < 1.0 while in 2010 spring, it is significantly higher than 1, possibly indicating input of air from the stratosphere-troposphere exchange (for ⁷Be). The specific activities of …

Magnetic Properties Of Ilmenite‐Hematite Single Crystals From The Ecstall Pluton Near Prince Rupert, British Columbia, Sarah J. Brownlee, Joshua M. Feinberg, Takeshi Kasama, Richard J. Harrison, Gary R. Scott, Paul R. Renne

Environmental Science and Geology Faculty Research Publications

Paleomagnetic studies of the 91 Ma Ecstall pluton and other Cretaceous plutons of British Columbia imply large northward tectonic movements (>2000 km) may have occurred during the tectonic evolution of western North America. However, more recent studies have shown that the eastern edge of the Ecstall pluton experienced considerable mineralogical changes as younger Eocene plutons, such as the ∼58 Ma Quottoon Pluton, were emplaced along its margins. We investigated changes in the rock magnetic properties associated with this reheating event by examining isolated grains of intergrown ilmenite and hematite, the primary paleomagnetic recorder in the Ecstall pluton. Measurements of …

Several Approaches For The Derivation Of Stationary Conditions For Elliptic Mpecs With Upper-Level Control Constraints, M Hintermüller, Boris S. Mordukhovich, T Surowiec

Mathematics Research Reports

The derivation of multiplier-based optimality conditions for elliptic mathematical programs with equilibrium constraints (MPEC) is essential for the characterization of solutions and development of numerical methods. Though much can be said for broad classes of elliptic MPECs in both polyhedric and non-polyhedric settings, the calculation becomes significantly more complicated when additional constraints are imposed on the control. In this paper we develop three derivation methods for constrained MPEC problems: via concepts from variational analysis, via penalization of the control constraints, and via penalization of the lower-level problem with the subsequent regularization of the resulting nonsmoothness. The developed methods and obtained …

Predicted Velocity And Density Structure Of The Exhuming Papua New Guinea Ultrahigh‐Pressure Terrane, Sarah J. Brownlee, Bradley R. Hacker, Matthew Salisbury, Gareth Seward, Timothy A. Little, Suzanne A. Baldwin, Geoffrey A. Abers

Environmental Science and Geology Faculty Research Publications

New electron backscatter diffraction measurements show that the Papua New Guinea (PNG) ultrahigh‐pressure (UHP) terrane is dominated by rocks with weakly oriented quartz and feldspar and less abundant strongly oriented hornblende, clinopyroxene, and mica. Velocities measured at high pressures (600 MPa) show that V_P is 5.8–6.3 km/s for gneiss samples, 6.5–7.7 km/s for amphibolite, and 7.7–8.2 km/s for eclogite and V_S is 3.4–3.9 km/s for gneiss, 4.0–4.4 km/s for amphibolite, and 4.5–4.6 km/s for eclogite. Velocities and anisotropies calculated from mineral crystal preferred orientations (CPOs) are equivalent to within 5% of the measured values. The highest seismic anisotropy …

Directional Subdifferentials And Optimality Conditions, Ivan Ginchev, Boris S. Mordukhovich

Mathematics Research Reports

This paper is devoted to the introduction and development of new dual-space constructions of generalized differentiation in variational analysis, which combine certain features of subdifferentials for nonsmooth functions (resp. normal cones to sets) and directional derivatives (resp. tangents). We derive some basic properties of these constructions and apply them to optimality conditions in problems of unconstrained and constrained optimization.

The Variable Quiescent X-Ray Emission Of The Neutron Star Transient Xte J1701-462, Joel K. Fridriksson, Jeroen Homan, Rudy Wijnands, Edward M. Cackett, Diego Altamirano, Nathalie Degenaar, Edward F. Brown, Mariano Méndez, Tomaso M. Belloni

Physics and Astronomy Faculty Research Publications

We present the results of continued monitoring of the quiescent neutron star low-mass X-ray binary XTE J1701-462 with Chandra and Swift. A new Chandra observation from 2010 October extends our tracking of the neutron star surface temperature from ≃ 800 days to ≃ 1160 days since the end of an exceptionally luminous 19 month outburst. This observation indicates that the neutron star crust may still be slowly cooling toward thermal equilibrium with the core; another observation further into quiescence is needed to verify this. The shape of the overall cooling curve is consistent with that of a broken power law, …

Cross Sections For 14-Ev E-H2 Resonant Collisions: Isotope Effect In Dissociative Electron Attachment, R Celiberto, R. K. Janev, J. M. Wadehra, A Laricchiuta

Physics and Astronomy Faculty Research Publications

The process of dissociative attachment of electrons to molecular hydrogen and its isotopes in the energy range at approximately 14 eV is investigated. The dissociative electron attachment cross sections for all six hydrogen isotopes are calculated over an extended range of electron energies using the local complex potential model with the excited Rydberg 2Σ+g electronic state of H2− acting as the intermediate resonant state. A significant isotope effect in theoretical electron attachment cross sections is observed, in agreement with previous predictions and experimental observations. A two-parameter analytic expression for the cross section is derived from the theory that fits accurately …

Applications Of Variational Analysis To A Generalized Heron Problem, Boris S. Mordukhovich, Nguyen Mau Nam, Juan Salinas Jr

Mathematics Research Reports

This paper is a continuation of our ongoing efforts to solve a number of geometric problems and their extensions by using advanced tools of variational analysis and generalized differentiation. Here we propose and study, from both qualitative and numerical viewpoints, the following optimal location problem as well as its further extensions: on a given nonempty subset of a Banach space, find a point such that the sum of the distances from it to n given nonempty subsets of this space is minimal. This is a generalized version of the classical Heron problem: on a given straight line, find a point …

Quiescent X-Ray Variability From The Neutron Star Transient Aql X-1, E. M. Cackett, J. K. Fridriksson, J. Homan, J. M. Miller, R. Wijnands

Physics and Astronomy Faculty Research Publications

A number of studies have revealed variability from neutron star low-mass X-ray binaries during quiescence. Such variability is not well characterized, or understood, but may be a common property that has been missed due to lack of multiple observations. One such source where variability has been observed is Aql X-1. Here, we analyse 14 Chandra and XMM-Newton observations of Aql X-1 in quiescence, covering a period of approximately 2 yr. There is clear variability between the epochs, with the most striking feature being a flare-like increase in the flux by a factor of 5. Spectral fitting is inconclusive as to …

Constraint Qualifications And Optimality Conditions For Nonconvex Semi-Infinite And Infinite Programs, Boris S. Mordukhovich, T T. A. Nghia

Mathematics Research Reports

The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many of equality and inequality constraints with arbitrary (may not be compact) index sets. These problems reduce to semi-infinite programs in the case of finite-dimensional spaces of decision variables. We extend the classical Mangasarian-Fromovitz and Farkas-Minkowski constraint qualifications to such infinite and semi-infinite programs. The new qualification conditions are used for efficient computing the appropriate normal cones to sets of feasible solutions for these programs by employing advanced …

Statistical Reanalysis Of Jewish Priests’ And Non-Priests’ Haplotypes Using Exact Methods, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

Researchers in an article appearing in Nature used asymptotic (i.e., large sample) chi-square tests in analyzing haplotypes of Y chromosomes using the polymerase chain reaction applied to genomic DNA from male Israeli, North American, and British Jews. The use of classical methods for analyzing extremely sparse contingency tables is frequently done, but with the advent of statistical software capable of conducting exact tests, researchers should certainly cease relying on outdated methods for small sample analyses. A reanalysis was conducted using modern statistical methods. Results and implications for using exact tests are discussed.

Bias In Monte Carlo Simulations Due To Pseudo-Random Number Generator Initial Seed Selection, Jack C. Hill, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

Pseudo-random number generators can bias Monte Carlo simulations of the standard normal probability distribution function with initial seeds selection. Five generator designs were initial-seeded with values from 10000HEX to 1FFFFHEX, estimates of the mean were calculated for each seed, the distribution of mean estimates was determined for each generator and simulation histories were graphed for selected seeds.

Rated Extremal Principles For Finite And Infinite Systems, Hung M. Phan, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here rated extremal principles. These developments are in the core geometric theory of variational analysis. We present their applications to calculus and optimality conditions for problems with infinitely many constraints.

Quantitative Stability Of Linear Infinite Inequality Systems Under Block Perturbations With Applications To Convex Systems, M J. Cánovas, M A. Lopez, Boris S. Mordukhovich, J Parra

Mathematics Research Reports

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is loo(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel-Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn …

Further X-Ray Observations Of Exo 0748-676 In Quiescence: Evidence For A Cooling Neutron Star Crust, N. Degenaar, M. T. Wolff, P. S. Ray, K. S. Wood, J. Homan, W. H. G. Lewin, P. G. Jonker, E. M. Cackett, J. M. Miller, E. F. Brown, R. Wijnands

Physics and Astronomy Faculty Research Publications

In late 2008, the quasi-persistent neutron star X-ray transient and eclipsing binary EXO 0748-676 started a transition from outburst to quiescence, after it actively accreted for more than 24 yr. In a previous work, we discussed Chandra and Swift observations obtained during the first 5 months of this transition. Here, we report on further X-ray observations of EXO 0748-676, extending the quiescent monitoring to 1.6 yr. Chandra and XMM-Newton data reveal quiescent X-ray spectra composed of a soft, thermal component that is well fitted by a neutron star atmosphere model. An additional hard power-law tail is detected that changes non-monotonically …

A Fast X-Ray Disk Wind In The Transient Pulsar Igr J17480-2446 In Terzan 5, Jon M. Miller, Dipankar Maitra, Edward M. Cackett, Sudip Bhattacharyya, Tod E. Strohmayer

Physics and Astronomy Faculty Research Publications

Accretion disk winds are revealed in Chandra gratings spectra of black holes. The winds are hot and highly ionized (typically composed of He-like and H-like charge states) and show modest blueshifts. Similar line spectra are sometimes seen in "dipping" low-mass X-ray binaries (LMXBs), which are likely viewed edge-on; however, that absorption is tied to structures in the outer disk, and blueshifts are not typically observed. Here, we report the detection of blueshifted He-like Fe XXV (3100 ± 400 km s^-1) and H-like Fe XXVI (1000 ± 200 km s^-1) absorption lines in a Chandra/HETG spectrum of …

Complete Characterizations Of Local Weak Sharp Minima With Applications To Semi-Infinite Optimization And Complementarity, Boris S. Mordukhovich, Naihua Xiu, Jinchuan Zhou

Mathematics Research Reports

In this paper we identify a favorable class of nonsmooth functions for which local weak sharp minima can be completely characterized in terms of normal cones and subdifferentials, or tangent cones and subderivatives, or their mixture in finite-dimensional spaces. The results obtained not only significantly extend previous ones in the literature, but also allow us to provide new types of criteria for local weak sharpness. Applications of the developed theory are given to semi-infinite programming and to semi-infinite complementarity problems.

A Distinctive Disk-Jet Coupling In The Seyfert-1 Active Galactic Nucleus Ngc 4051, A. L. King, J. M. Miller, E. M. Cackett, A. C. Fabian, S. Markoff, M. A. Nowak, M. Rupen, K. Gültekin, M. T. Reynolds

Physics and Astronomy Faculty Research Publications

We report on the results of a simultaneous monitoring campaign employing eight Chandra X-ray (0.5-10 keV) and six Very Large Array/Extended Very Large Array (8.4 GHz) radio observations of NGC 4051 over seven months. Evidence for compact jets is observed in the 8.4 GHz radio band; this builds on mounting evidence that jet production may be prevalent even in radio-quiet Seyferts. Assuming comparatively negligible local diffuse emission in the nucleus, the results also demonstrate an inverse correlation of L _radio ∝ L ^-0.72±0.04 _X-ray . If the A configuration is excluded in the case where diffuse emission plays a significant …

Multistate Observations Of The Galactic Black Hole Xte J1752-223: Evidence For An Intermediate Black Hole Spin, R. C. Reis, J. M. Miller, A. C. Fabian, E. M. Cackett, D. Maitra, C. S. Reynolds, M. Rupen, D. T. H. Steeghs, R. Wijnands

Physics and Astronomy Faculty Research Publications

The Galactic black hole candidate XTE J1752-223 was observed during the decay of its 2009 outburst with the Suzaku and XMM-Newton observatories. The observed spectra are consistent with the source being in the ‘intermediate’ and ‘low-hard’ states, respectively. The presence of a strong, relativistic iron emission line is clearly detected in both observations and the line profiles are found to be remarkably consistent and robust to a variety of continuum models. This strongly points to the compact object in XTE J1752-223 being a stellar mass black hole accretor and not a neutron star. Physically motivated and self-consistent reflection models for …

Tangential Extremal Principles For Finite And Infinite Systems Of Sets, Ii: Applications To Semi-Infinite And Multiobjective Optimization, Boris S. Mordukhovich, Hung M. Phan

Mathematics Research Reports

This paper contains selected applications of the new tangential extremal principles and related results developed in [20] to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraints.

Modeling Moisture Fluxes Using Artificial Neural Networks: Can Information Extraction Overcome Data Loss?, A. L. Neal, H. V. Gupta, S. A. Kurc, P. D. Brooks

Environmental Science and Geology Faculty Research Publications

Eddy covariance sites can experience data losses as high as 30 to 45% on an annual basis. Artificial neural networks (ANNs) have been identified as powerful tools for gap filling, but their performance depends on the representativeness of data used to train the model. In this paper, we develop a normalization method, which has similar performance compared to conventional training approaches, but exhibits differences in the timing of fluxes, indicating different and previously unused information in the data record. Specifically, the differences between half-hourly model fluxes, especially during summer months, indicate that the structure of the information content in the …

Reproduction And Genetic Detection Of Veligers In Changing Dreissena Populations In The Great Lakes, Jeffrey L. Ram, Aos S. Karim, Payel Acharya, Pranav Jagtap, Sonal Purohit, Donna R. Kashian

Environmental Science and Geology Faculty Research Publications

Dreissenid bivalves, Dreissena polymorpha (zebra mussel) and Dreissena bugensis (quagga mussel) are biofouling species that invaded the Great Lakes region of North America from source populations in Europe in the 1980s. Initially, D. polymorpha spread faster and farther; however, D. bugensis have recently displaced D. polymorpha in many areas of the Great Lakes and was the first to be found west of the Continental Divide. Early detection of dreissenids is important in anticipating and preventing potentially high economic impacts. To study population dynamics and to enhance detection methods, we assessed “spawnability” using a serotonin bioassay and developed a new, sensitive, …

Cloudaligner: A Fast And Full-Featured Mapreduce Based Tool For Sequence Mapping, Tung Nguyen, Weisong Shi, Douglas Ruden

Wayne State University Associated BioMed Central Scholarship

Abstract

Background

Research in genetics has developed rapidly recently due to the aid of next generation sequencing (NGS). However, massively-parallel NGS produces enormous amounts of data, which leads to storage, compatibility, scalability, and performance issues. The Cloud Computing and MapReduce framework, which utilizes hundreds or thousands of shared computers to map sequencing reads quickly and efficiently to reference genome sequences, appears to be a very promising solution for these issues. Consequently, it has been adopted by many organizations recently, and the initial results are very promising. However, since these are only initial steps toward this trend, the developed software does …

A Supermatrix Analysis Of Genomic, Morphological, And Paleontological Data From Crown Cetacea, Jonathan H. Geisler, Michael R. Mcgowen, Guang Yang, John Gatesy

Wayne State University Associated BioMed Central Scholarship

Abstract

Background

Cetacea (dolphins, porpoises, and whales) is a clade of aquatic species that includes the most massive, deepest diving, and largest brained mammals. Understanding the temporal pattern of diversification in the group as well as the evolution of cetacean anatomy and behavior requires a robust and well-resolved phylogenetic hypothesis. Although a large body of molecular data has accumulated over the past 20 years, DNA sequences of cetaceans have not been directly integrated with the rich, cetacean fossil record to reconcile discrepancies among molecular and morphological characters.

Results

We combined new nuclear DNA sequences, including segments of six genes (~2800 …

Bio::Phylo-Phyloinformatic Analysis Using Perl, Rutger A. Vos, Jason Caravas, Klaas Hartmann, Mark A. Jensen, Chase Miller

Wayne State University Associated BioMed Central Scholarship

Abstract

Background

Phyloinformatic analyses involve large amounts of data and metadata of complex structure. Collecting, processing, analyzing, visualizing and summarizing these data and metadata should be done in steps that can be automated and reproduced. This requires flexible, modular toolkits that can represent, manipulate and persist phylogenetic data and metadata as objects with programmable interfaces.

Results

This paper presents Bio::Phylo, a Perl5 toolkit for phyloinformatic analysis. It implements classes and methods that are compatible with the well-known BioPerl toolkit, but is independent from it (making it easy to install) and features a richer API and a data model that is …

Tangential Extremal Principles For Finite And Infinite Systems Of Sets, I: Basic Theory, Boris S. Mordukhovich, Hung M. Phan

Mathematics Research Reports

In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified under the name of tangential extremal principles, combine primal and dual approaches to the study of variational systems being in fact first extremal principles applied to infinite systems of sets. The first part of the paper concerns the basic theory of tangential extremal principles while the second part presents applications to problems of semi-infinite programming and multiobjective optimization.