The Complexity of Order Type Isomorphism

The order type of a point set in $R^d$ maps each $(d{+}1)$-tuple of points to its orientation (e.g., clockwise or counterclockwise in $R^2$). Two point sets $X$ and $Y$ have the same order type if there exists a mapping $f$ from $X$ to $Y$ for which every $(d{+}1)$-tuple $(a_1,a_2,\ldots,a_{d+1})$ of $X$ and the corresponding tuple $(f(a_1),f(a_2),\ldots,f(a_{d+1}))$ in $Y$ have the same orientation. In this paper we investigate the complexity of determining whether two point sets have the same order type. We provide an $O(n^d)$ algorithm for this task, thereby improving upon the $O(n^{\lfloor{3d/2}\rfloor})$ algorithm of Goodman and Pollack (1983). The algorithm uses only order type queries and also works for abstract order types (or acyclic oriented matroids). Our algorithm is optimal, both in the abstract setting and for realizable points sets if the algorithm only uses order type queries.Comment: Preliminary version of paper to appear at ACM-SIAM Symposium on Discrete Algorithms (SODA14

Spherically symmetric solutions of Einstein + non-polynomial gravities

We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to maintain the (first) derivative order of the Einstein equations in Schwarzschild gauge. Generically, the solutions exhibit both horizons and a singularity at the origin, except for one model that forbids spherical symmetry altogether. Extensions to arbitrary dimension with a cosmological constant, Maxwell source and Gauss-Bonnet terms are also considered.Comment: 6 pages, no figures, REVTeX

Illumination and annealing characteristics of two-dimensional electron gas systems in metal-organic vapor-phase epitaxy grown AlGaN/AlN/GaN heterostructures

We studied the persistent photoconductivity (PPC) effect in AlGaN/AlN/GaN heterostructures with two different Al-compositions (x=0.15 and x=0.25). The two-dimensional electron gas formed at the AlN/GaN heterointerface was characterized by Shubnikov-de Haas and Hall measurements. Using optical illumination, we were able to increase the carrier density of the Al0.15Ga0.85N/AlN/GaN sample from 1.6x10^{12} cm^{-2} to 5.9x1012 cm^{-2}, while the electron mobility was enhanced from 9540 cm2/Vs to 21400 cm2/Vs at T = 1.6 K. The persistent photocurrent in both samples exhibited a strong dependence on illumination wavelength, being highest close to the bandgap and decreasing at longer wavelengths. The PPC effect became fairly weak for illumination wavelengths longer than 530 nm and showed a more complex response with an initial negative photoconductivity in the infrared region of the spectrum (>700 nm). The maximum PPC-efficiency for 390 nm illumination was 0.011% and 0.005% for Al0.25Ga0.75N/AlN/GaN and Al0.15Ga0.85N/AlN/GaN samples, respectively. After illumination, the carrier density could be reduced by annealing the sample. Annealing characteristics of the PPC effect were studied in the 20-280 K temperature range. We found that annealing at 280 K was not sufficient for full recovery of the carrier density. In fact, the PPC effect occurs in these samples even at room temperature. Comparing the measurement results of two samples, the Al0.25Ga0.75N/AlN/GaN sample had a larger response to illumination and displayed a smaller recovery with thermal annealing. This result suggests that the energy scales of the defect configuration-coordinate diagrams for these samples are different, depending on their Al-composition.Comment: 27 pages, 8 figure

Spherically symmetric solutions of Einstein + non-polynomial gravities

We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to maintain the (first) derivative order of the Einstein equations in Schwarzschild gauge. Generically, the solutions exhibit both horizons and a singularity at the origin, except for one model that forbids spherical symmetry altogether. Extensions to arbitrary dimension with a cosmological constant, Maxwell source and Gauss-Bonnet terms are also considered

Topologically massive gravity as a Pais-Uhlenbeck oscillator

We give a detailed account of the free field spectrum and the Newtonian limit of the linearized "massive" (Pauli-Fierz), "topologically massive" (Einstein-Hilbert-Chern-Simons) gravity in 2+1 dimensions about a Minkowski spacetime. For a certain ratio of the parameters, the linearized free theory is Jordan-diagonalizable and reduces to a degenerate "Pais-Uhlenbeck" oscillator which, despite being a higher derivative theory, is ghost-free.Comment: 9 pages, no figures, RevTEX4; version 2: a new paragraph and a reference added to the Introduction, a new appendix added to review Pais-Uhlenbeck oscillators; accepted for publication in Class. Quant. Gra

Godel-type Metrics in Various Dimensions II: Inclusion of a Dilaton Field

This is the continuation of an earlier work where Godel-type metrics were defined and used for producing new solutions in various dimensions. Here a simplifying technical assumption is relaxed which, among other things, basically amounts to introducing a dilaton field to the models considered. It is explicitly shown that the conformally transformed Godel-type metrics can be used in solving a rather general class of Einstein-Maxwell-dilaton-3-form field theories in D >= 6 dimensions. All field equations can be reduced to a simple "Maxwell equation" in the relevant (D-1)-dimensional Riemannian background due to a neat construction that relates the matter fields. These tools are then used in obtaining exact solutions to the bosonic parts of various supergravity theories. It is shown that there is a wide range of suitable backgrounds that can be used in producing solutions. For the specific case of (D-1)-dimensional trivially flat Riemannian backgrounds, the D-dimensional generalizations of the well known Majumdar-Papapetrou metrics of general relativity arise naturally.Comment: REVTeX4, 17 pp., no figures, a few clarifying remarks added and grammatical errors correcte

Uzay Kafes Yapıların Ateş Böceği Algoritması Yöntemiyle Optimizasyonu

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2015Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2015Hayvan ve böcek türlerinin sürü/koloni/grup davranışlarını taklit eden sezgisel optimizasyon yöntemleri son yıllarda farklı tasarım problemlerinin çözümünde kullanılmıştır. Ateşböceği algoritması, ateşböceklerinin davranışları ve parıldama yoluyla yaptıkları iletişimleri taklit etmektedir. Bu çalışma ile, ateşböceği algoritması yöntemiyle uzay kafes yapıların optimizasyonu yapılacaktır. Optimizasyon probleminde, deplasman ve gerilme sınırlayıcıları altında minimum ağırlıklı kafes yapıların elde edilmesi amaçlanmaktadır. Ateşböceği algoritması yönteminin performansı; daha önce armoni arama, hibrid parçacık sürü optimizasyonu, hibrid parçacık sürü-karınca koloni optimizasyonu, adaptif armoni arama ve ateşböceği algoritması yöntemleriyle optimize edilmiş olan 25 elemanlı uzay kafes yapı üzerinde test edilmiştir. Yapılan kıyaslamalar ateşböceği algoritmasının en az diğer yöntemler kadar güçlü bir optimizasyon yöntemi olduğunu göstermektedir.Meta-heuristic optimization algorithms simulated the behaviour of flock/colony/group have been used for the solving of different design problems. Firefly algorithm (FFA) is a recently developed meta-heuristic optimization algorithm inspired by social behaviour of fireflies and the phenomenon of bioluminescent communication. The main purpose of this study is to implement a robust FFA algorithm for sizing optimization of spatial truss structures. The objective of the study is to obtain the minimum weight truss design under the displacement and stress constraints. The efficiency of the FFA algorithm implemented in this study is tested on weight minimization problem of 25-bar truss structure. The optimization results are compared with those reported in the literature for other state-of-the-art meta-heuristic optimization methods such as harmony search, hybrid particle swarm optimization, hybrid particle swarm ant colony optimization, self-adaptive harmony search algorithm and firefly algorithm. The comparisons showed that firefly algorithm is as powerful as the other meta-heuristic optimization methods

Uzay Çelik Çerçevelerin Tabu Arama Yöntemiyle Optimum Tasarımı

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2008Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2008Bu çalışmada, uzay çelik çerçevelerin optimum tasarımında tabu arama yöntemi kullanılmıştır. Tabu arama (TA), insan hafızasının çalışma mekanizmasını taklit eden gelişmiş bir arama yöntemidir. TA’dan elde edilen sonuçları kıyaslamak amacıyla uzay çelik çerçevelerin genetik algoritma (GA) yöntemiyle optimum tasarımı için de bir algoritma geliştirilmiştir. Optimum tasarımda çelik çerçevelerin gerilme, deplasman ve kesit sınırlayıcıları altında minimum ağırlıklı olarak boyutlandırılması amaçlanmıştır. Geliştirilen bilgisayar programlarının uygulaması olarak 40 ve 63 elemanlı iki uzay çelik çerçevenin optimum tasarımı yapılmıştır. Bu uygulamaların sonucunda tabu arama ile genetik algoritmaya kıyasla daha ekonomik çerçeve tasarımları elde edilmiştir.In this study, tabu search method was used for optimum design of steel space frames. Tabu search (TS) is a sophisticated search method which imitates working mechanism of human memory. To compare the results of TS method, an algorithm was also developed for optimum design of steel space frames using genetic algorithm (GA). Minimum weight design of steel frames was aimed under the stress, displacement and size constraints. Optimum designs of two steel space frames with 40 and 63 members were performed as application of the developed computer programs. As a result of these applications, it was found that tabu search yielded more economical frame designs than genetic algorithm