Regarding the benefit of zero-dimensional noise

Baker and Meese (2012) (B&M) provided an empirically driven criticism of the use of two-dimensional (2D) pixel noise in equivalent noise (EN) experiments. Their main objection was that in addition to injecting variability into the contrast detecting mechanisms, 2D noise also invokes gain control processes from a widely tuned contrast gain pool (e.g., Foley, 1994). B&M also developed a zero-dimensional (0D) noise paradigm in which all of the variance is concentrated in the mechanisms involved in the detection process. They showed that this form of noise conformed much more closely to expectations than did a 2D variant.

Strong shift equivalence, algebraic K-theory, and isolating zero-dimensional dynamics on manifolds

We study the relations of shift equivalence and strong shift equivalence for matrices over a ring $\mathcal{R}$, and establish a connection between these relations and algebraic K-theory. We utilize this connection to obtain results in two areas where the shift and strong shift equivalence relations play an important role: the study of finite group extensions of shifts of finite type, and the Generalized Spectral Conjectures of Boyle and Handelman for nonnegative matrices over subrings of the real numbers. We show the refinement of the shift equivalence class of a matrix $A$ over a ring $\mathcal{R}$ by strong shift equivalence classes over the ring is classified by a quotient $NK_{1}(\mathcal{R}) / E(A,\mathcal{R})$ of the algebraic K-group $NK_{1}(\calR)$. We use the K-theory of non-commutative localizations to show that in certain cases the subgroup $E(A,\mathcal{R})$ must vanish, including the case $A$ is invertible over $\mathcal{R}$. We use the K-theory connection to clarify the structure of algebraic invariants for finite group extensions of shifts of finite type. In particular, we give a strong negative answer to a question of Parry, who asked whether the dynamical zeta function determines up to finitely many topological conjugacy classes the extensions by $G$ of a fixed mixing shift of finite type. We apply the K-theory connection to prove the equivalence of a strong and weak form of the Generalized Spectral Conjecture of Boyle and Handelman for primitive matrices over subrings of $\mathbb{R}$. We construct explicit matrices whose class in the algebraic K-group $NK_{1}(\mathcal{R})$ is non-zero for certain rings $\mathcal{R}$ motivated by applications. We study the possible dynamics of the restriction of a homeomorphism of a compact manifold to an isolated zero-dimensional set. We prove that for $n \ge 3$ every compact zero-dimensional system can arise as an isolated invariant set for a homeomorphism of a compact $n$-manifold. In dimension two, we provide obstructions and examples.

Criterion of Normality of the Completely Regular Topology of Separate Continuity

2000 Mathematics Subject Classification: 54C10, 54D15, 54G12.

Shape-Dependent Confinement in Ultrasmall Zero-, One-, and Two-Dimensional PbS Nanostructures

Spatial dimensionality affects the degree of confinement when an electron-hole pair is squeezed from one or more dimensions approaching the bulk exciton Bohr radius (alpha(B)) limit. The etectron-hole interaction in zero-dimensional (0D) dots, one-dimensional (1D) rods/wires, and two-dimensional (2D) wells/sheets should be enhanced by the increase in confinement dimensions in the order 0D > 1D > 2D. We report the controlled synthesis of PbS nanomateriats with 0D, 1D, and 2D forms retaining at least one dimension in the strongly confined regime far below alpha(B) (similar to 10 nm for PbS) and provide evidence through varying the exciton-phonon coupling strength that the degree of confinement is systematically weakened by the loss of confinement dimension. Geometry variations show distinguishable far-field optical polarizations, which could find useful applications in polarization-sensitive devices.

Bayesian variable selection in structured high-dimensional covariate spaces with applications in genomics

We consider the problem of variable selection in regression modeling in high-dimensional spaces where there is known structure among the covariates. This is an unconventional variable selection problem for two reasons: (1) The dimension of the covariate space is comparable, and often much larger, than the number of subjects in the study, and (2) the covariate space is highly structured, and in some cases it is desirable to incorporate this structural information in to the model building process. We approach this problem through the Bayesian variable selection framework, where we assume that the covariates lie on an undirected graph and formulate an Ising prior on the model space for incorporating structural information. Certain computational and statistical problems arise that are unique to such high-dimensional, structured settings, the most interesting being the phenomenon of phase transitions. We propose theoretical and computational schemes to mitigate these problems. We illustrate our methods on two different graph structures: the linear chain and the regular graph of degree k. Finally, we use our methods to study a specific application in genomics: the modeling of transcription factor binding sites in DNA sequences. © 2010 American Statistical Association.

BM+-tree: A hyperplane-based index method for high-dimensional metric spaces

In this paper, we propose a novel high-dimensional index method, the BM+-tree, to support efficient processing of similarity search queries in high-dimensional spaces. The main idea of the proposed index is to improve data partitioning efficiency in a high-dimensional space by using a rotary binary hyperplane, which further partitions a subspace and can also take advantage of the twin node concept used in the M+-tree. Compared with the key dimension concept in the M+-tree, the binary hyperplane is more effective in data filtering. High space utilization is achieved by dynamically performing data reallocation between twin nodes. In addition, a post processing step is used after index building to ensure effective filtration. Experimental results using two types of real data sets illustrate a significantly improved filtering efficiency.

Low-dimensional hydrogen-bonded structures in the 1:1 and 1:2 proton-transfer compounds of 4,5-dichlorophthalic acid with the aliphatic Lewis bases triethylamine, diethylamine, n-butylamine and piperidine

The structures of proton-transfer compounds of 4,5-dichlorophthalic acid (DCPA) with the aliphatic Lewis bases triethylamine, diethylamine, n-butylamine and piperidine, namely triethylaminium 2-carboxy-4,5-dichlorobenzoate C~6~H~16~N^+^ C~8~H~3~Cl~2~O~4~^-^ (I), diethylaminium 2-carboxy-4,5-dichlorobenzoate C~4~H~12~N^+^ C~8~H~3~Cl~2~O~4~^-^ (II), bis(n-butylaminium) 4,5-dichlorophthalate monohydrate 2(C~4~H~12~N^+^) C~8~H~2~Cl~2~O~4~^2-^ . H~2~O (III) and bis(piperidinium) 4,5-dichlorophthalate monohydrate 2(C~5~H~12~N^+^) C~8~H~2~Cl~2~O~4~^2-^ . H~2~O (IV)have been determined at 200 K. All compounds have hydrogen-bonding associations giving in (I) discrete cation-anion units, linear chains in (II) while (III) and (IV) both have two-dimensional structures. In (I) a discrete cation-anion unit is formed through an asymmetric R2/1(4) N+-H...O,O' hydrogen-bonding association whereas in (II), one-dimensional chains are formed through linear N-H...O associations by both aminium H donors. In compounds (III) and (IV) the primary N-H...O linked cation-anion units are extended into a two-dimensional sheet structure via amide N-H...O(carboxyl) and ...O(carbonyl) interactions. In the 1:1 salts [(I) and (II)], the hydrogen 4,5-dichlorophthalate anions are essentially planar with short intramolecular carboxylic acid O-H...O(carboxyl) hydrogen bonds [O...O, 2.4223(14) and 2.388(2)A respectively]. This work provides a further example of the uncommon zero-dimensional hydrogen-bonded DCPA-Lewis base salt and the one-dimensional chain structure type, while even with the hydrate structures of the 1:2 salts with the primary and secondary amines, the low dimensionality generally associated with 1:1 DCPA salts is also found.

Synthesis, structure and optical properties of different dimensional organic-inorganic perovskites

By varying the substituent position of aminomethyl on pyridine ring in acid solution, different dimensional lead bromide frameworks ranging from zero-dimension and one-dimension to two-dimension were obtained. 2-(Aminomethyl)pyridine (2-AMP) or 3-(aminomethyl)pyridine (3-AMP) and PbBr2 construct hybrid perovskites, of which (H(2)2-AMP)PbBr4 (1) exhibits two-dimensional perovskite sheets with special hydrogen bonds and (H(2)3-AMP)PbBr6 (2) shows an uncommon zero-dimensional inorganic framework with isolated octahedra. The characteristic exciton peaks in absorption spectra are located at 431 nm for compound 1 and at 428 nm for compound 2. (H(2)4-AMP)PbBr4 (3) with one-dimensional zigzag edge-sharing octahedral PbBr(4)(2-)chains can be obtained using 4-(aminomethyl)pyridine (4-AMP) as organic component under the same experimental conditions as those for 2-AMP and 3-AMP.

High-Speed Semiconductor Lasers based on Low-Dimensional Active Materials for Optical Telecommunication

The scope of this work is the fundamental growth, tailoring and characterization of self-organized indium arsenide quantum dots (QDs) and their exploitation as active region for diode lasers emitting in the 1.55 µm range. This wavelength regime is especially interesting for long-haul telecommunications as optical fibers made from silica glass have the lowest optical absorption. Molecular Beam Epitaxy is utilized as fabrication technique for the quantum dots and laser structures. The results presented in this thesis depict the first experimental work for which this reactor was used at the University of Kassel. Most research in the field of self-organized quantum dots has been conducted in the InAs/GaAs material system. It can be seen as the model system of self-organized quantum dots, but is not suitable for the targeted emission wavelength. Light emission from this system at 1.55 µm is hard to accomplish. To stay as close as possible to existing processing technology, the In(AlGa)As/InP (100) material system is deployed. Depending on the epitaxial growth technique and growth parameters this system has the drawback of producing a wide range of nano species besides quantum dots. Best known are the elongated quantum dashes (QDash). Such structures are preferentially formed, if InAs is deposited on InP. This is related to the low lattice-mismatch of 3.2 %, which is less than half of the value in the InAs/GaAs system. The task of creating round-shaped and uniform QDs is rendered more complex considering exchange effects of arsenic and phosphorus as well as anisotropic effects on the surface that do not need to be dealt with in the InAs/GaAs case. While QDash structures haven been studied fundamentally as well as in laser structures, they do not represent the theoretical ideal case of a zero-dimensional material. Creating round-shaped quantum dots on the InP(100) substrate remains a challenging task. Details of the self-organization process are still unknown and the formation of the QDs is not fully understood yet. In the course of the experimental work a novel growth concept was discovered and analyzed that eases the fabrication of QDs. It is based on different crystal growth and ad-atom diffusion processes under supply of different modifications of the arsenic atmosphere in the MBE reactor. The reactor is equipped with special valved cracking effusion cells for arsenic and phosphorus. It represents an all-solid source configuration that does not rely on toxic gas supply. The cracking effusion cell are able to create different species of arsenic and phosphorus. This constitutes the basis of the growth concept. With this method round-shaped QD ensembles with superior optical properties and record-low photoluminescence linewidth were achieved. By systematically varying the growth parameters and working out a detailed analysis of the experimental data a range of parameter values, for which the formation of QDs is favored, was found. A qualitative explanation of the formation characteristics based on the surface migration of In ad-atoms is developed. Such tailored QDs are finally implemented as active region in a self-designed diode laser structure. A basic characterization of the static and temperature-dependent properties was carried out. The QD lasers exceed a reference quantum well laser in terms of inversion conditions and temperature-dependent characteristics. Pulsed output powers of several hundred milli watt were measured at room temperature. In particular, the lasers feature a high modal gain that even allowed cw-emission at room temperature of a processed ridge wave guide device as short as 340 µm with output powers of 17 mW. Modulation experiments performed at the Israel Institute of Technology (Technion) showed a complex behavior of the QDs in the laser cavity. Despite the fact that the laser structure is not fully optimized for a high-speed device, data transmission capabilities of 15 Gb/s combined with low noise were achieved. To the best of the author`s knowledge, this renders the lasers the fastest QD devices operating at 1.55 µm. The thesis starts with an introductory chapter that pronounces the advantages of optical fiber communication in general. Chapter 2 will introduce the fundamental knowledge that is necessary to understand the importance of the active region`s dimensions for the performance of a diode laser. The novel growth concept and its experimental analysis are presented in chapter 3. Chapter 4 finally contains the work on diode lasers.

Exploring Bit-Difference for Approximate KNN Search in High-dimensional Databases

In this paper, we develop a novel index structure to support efficient approximate k-nearest neighbor (KNN) query in high-dimensional databases. In high-dimensional spaces, the computational cost of the distance (e.g., Euclidean distance) between two points contributes a dominant portion of the overall query response time for memory processing. To reduce the distance computation, we first propose a structure (BID) using BIt-Difference to answer approximate KNN query. The BID employs one bit to represent each feature vector of point and the number of bit-difference is used to prune the further points. To facilitate real dataset which is typically skewed, we enhance the BID mechanism with clustering, cluster adapted bitcoder and dimensional weight, named the BID⁺. Extensive experiments are conducted to show that our proposed method yields significant performance advantages over the existing index structures on both real life and synthetic high-dimensional datasets.

Coupling an aerosol box model with one-dimensional flow: a tool for understanding observations of new particle formation events

Field observations of new particle formation and the subsequent particle growth are typically only possible at a fixed measurement location, and hence do not follow the temporal evolution of an air parcel in a Lagrangian sense. Standard analysis for determining formation and growth rates requires that the time-dependent formation rate and growth rate of the particles are spatially invariant; air parcel advection means that the observed temporal evolution of the particle size distribution at a fixed measurement location may not represent the true evolution if there are spatial variations in the formation and growth rates. Here we present a zero-dimensional aerosol box model coupled with one-dimensional atmospheric flow to describe the impact of advection on the evolution of simulated new particle formation events. Wind speed, particle formation rates and growth rates are input parameters that can vary as a function of time and location, using wind speed to connect location to time. The output simulates measurements at a fixed location; formation and growth rates of the particle mode can then be calculated from the simulated observations at a stationary point for different scenarios and be compared with the ‘true’ input parameters. Hence, we can investigate how spatial variations in the formation and growth rates of new particles would appear in observations of particle number size distributions at a fixed measurement site. We show that the particle size distribution and growth rate at a fixed location is dependent on the formation and growth parameters upwind, even if local conditions do not vary. We also show that different input parameters used may result in very similar simulated measurements. Erroneous interpretation of observations in terms of particle formation and growth rates, and the time span and areal extent of new particle formation, is possible if the spatial effects are not accounted for.

Ein, zwei Punkte zu Nichtkommutativer Geometrie und Quantenfeldtheorie auf diskreten Räumen

Über viele Jahre hinweg wurden wieder und wieder Argumente angeführt, die diskreten Räumen gegenüber kontinuierlichen Räumen eine fundamentalere Rolle zusprechen. Unser Zugangzur diskreten Welt wird durch neuere Überlegungen der Nichtkommutativen Geometrie (NKG) bestimmt. Seit ca. 15Jahren gibt es Anstrengungen und auch Fortschritte, Physikmit Hilfe von Nichtkommutativer Geometrie besser zuverstehen. Nur eine von vielen Möglichkeiten ist dieReformulierung des Standardmodells derElementarteilchenphysik. Unter anderem gelingt es, auch denHiggs-Mechanismus geometrisch zu beschreiben. Das Higgs-Feld wird in der NKG in Form eines Zusammenhangs auf einer zweielementigen Menge beschrieben. In der Arbeit werden verschiedene Ziele erreicht:Quantisierung einer nulldimensionalen ,,Raum-Zeit'', konsistente Diskretisierungf'ur Modelle im nichtkommutativen Rahmen.Yang-Mills-Theorien auf einem Punkt mit deformiertemHiggs-Potenzial. Erweiterung auf eine ,,echte''Zwei-Punkte-Raum-Zeit, Abzählen von Feynman-Graphen in einer nulldimensionalen Theorie, Feynman-Regeln. Eine besondere Rolle werden Termini, die in derQuantenfeldtheorie ihren Ursprung haben, gewidmet. In diesemRahmen werden Begriffe frei von Komplikationen diskutiert,die durch etwaige Divergenzen oder Schwierigkeitentechnischer Natur verursacht werden könnten.Eichfixierungen, Geistbeiträge, Slavnov-Taylor-Identität undRenormierung. Iteratives Lösungsverfahren derDyson-Schwinger-Gleichung mit Computeralgebra-Unterstützung,die Renormierungsprozedur berücksichtigt.

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.

Semantic oscillations : encoding context and structure in complex valued holographic vectors

In computational linguistics, information retrieval and applied cognition, words and concepts are often represented as vectors in high dimensional spaces computed from a corpus of text. These high dimensional spaces are often referred to as Semantic Spaces. We describe a novel and efficient approach to computing these semantic spaces via the use of complex valued vector representations. We report on the practical implementation of the proposed method and some associated experiments. We also briefly discuss how the proposed system relates to previous theoretical work in Information Retrieval and Quantum Mechanics and how the notions of probability, logic and geometry are integrated within a single Hilbert space representation. In this sense the proposed system has more general application and gives rise to a variety of opportunities for future research.

rac-cis-Cyclohexaane-1,2-dicarboxylic acid-isoquinoline (1/1)

In the structure of the title molecular adduct C8H12O4 . C9H7N, the two species are interlinked through a carboxylic acid-isoquinoline O-H...N hydrogen bond, these molecular pairs then inter-associate through the second acid group of the cis-cyclohexane-1,2-dicarboxylic acids, forming a classic centrosymmetric cyclic head-to-head carboxylic acid--carboxyl O---H...O hydrogen-bonding association [graph set R^2^~2~(8)], giving a zero-dimensional structure.