Interactive Composition Operators An Alternative Approach for Selecting Linear Embedding Parameters.

In most graphics and visualization applications, the effects of the mapping parameters on the output domain are multidimensional, non-linear and discontinuous. The complexity of such mapping often makes it difficult for a user to manually explore and manipulate the design parameter space to produce the desired output. Computer assistance is therefore useful in setting the mapping parameter values to generate desired outputs. Existing systems rely on exploring the entire input parameter space, which can be time and resource-intensive, particularly if the number of input parameters is large. We introduce a new approach to handling a large number of mapping parameters more efficiently. The basis for our approach is the identification of a small and effective set of highlevel parameters that can be associated directly with the characteristics of the outputs. Users will have a better understanding of this small set of high-level parameters and can easily modify their values interactively to produce the desired outputs. We demonstrate this technique in manipulating mapping parameters for a non-photorealistic volume rendering application.

The Dual Analysis framework is a powerful enabling technology for the exploration of high dimensional quantitative data by treating data dimensions as first-class objects that can be explored in tandem with data values. In this article, we extend the Dual Analysis framework through the joint treatment of quantitative (numerical) and qualitative (categorical) dimensions. Computing common measures for all dimensions allows us to visualize both quantitative and qualitative dimensions in the same view. This enables a natural joint treatment of mixed data during interactive visual exploration and analysis. Several measures of variation for nominal qualitative data can also be applied to ordinal qualitative and quantitative data. For example, instead of measuring variability from a mean or median, other measures assess inter-data variation or average variation from a mode. In this work, we demonstrate how these measures can be integrated into the Dual Analysis framework to explore and generate hypotheses about high-dimensional mixed data. A medical case study using clinical routine data of patients suffering from Cerebral Small Vessel Disease (CSVD), conducted with a senior neurologist and a medical student, shows that a joint Dual Analysis approach for quantitative and qualitative data can rapidly lead to new insights based on which new hypotheses may be generated.

This thesis will be of particular interest to anyone integrating Charge-Coupled Devices (CCDs) into any precision scientific imaging instrument, especially so in space. The first part of the thesis concerns optimization of a CCD camera as a whole. CCDs for the WaSP imager at the Hale telescope are characterized using a minimal amount of data using just a flat-field illumination source. By measuring performance over the entire parameter space of (clock and bias) inputs and analyzing the multidimensional output (linearity, dynamic range, read noise etc), optimal operating conditions can be selected quickly (and possibly automatically). With ever growing sizes of detector arrays such as the recently launched Gaia mission, the upcoming Euclid mission and ground-based cameras such as the LSST (189 CCDs), the task of streamlining detector optimization will be increasingly important. In the second (larger) part, the optimization of Charge Transfer Efficiency (CTE) is explored in particular. In modern CCDs, CTE is caused by lattice defects in the bulk silicon and is significantly worsened by radiation exposure, which is unavoidable in space. As shown in the literature, just a year of exposure to high energy solar proton radiation at low earth orbit can result in CTE reducing to 0.9999 for a signal level of 10,000e- — problematic for most precision astronomical measurements. Here, CTE degrading traps are fully explored in an undamaged CCD to new levels of accuracy. Several unique species are identified, and their population statistics are analyzed by both wafer and sub-pixel location. Subsequently, easily applied CTE measurement techniques are presented, yielding results with new levels of accuracy, concluding in the presentation of a new trap mitigating readout clocking scheme. This scheme can be readily applied to any CCD employing a parallel transfer gate without readout speed penalty. It is proposed that the results herein may be used to construct a simple model to predict CTE given a temperature, readout timing and signal level. This model could then be used to automatically optimize CTE for any CCD, given only its trap parameter statistics.

Low-distortion embeddings of infinite metric spaces into the real line

The analysis of multidimensional functions is important in many engineering disciplines, and poses a major problem as the number of dimensions increases. Previous visualization approaches focus on representing three or fewer dimensions at a time. This paper presents a new focus+context visualization that provides an integrated overview of an entire multidimensional function space, with uniform treatment of all dimensions. The overview is displayed with respect to a user-controlled polar focal point in the function's parameter space. Function value patterns are viewed along rays that emanate from the focal point in all directions in the parameter space, and represented radially around the focal point in the visualization. Data near the focal point receives proportionally more screen space than distant data. This approach scales smoothly from two dimensions to 10-20, with a 1000 pixel range on each dimension.

Embedding methods have emerged as a valuable class of approaches for distilling essential information from complex high-dimensional data into more accessible lower-dimensional spaces. Applications of embedding methods to biological data have demonstrated that gene embeddings can effectively capture physical, structural, and functional relationships between genes. However, this utility has been primarily realized by using gene embeddings for downstream machine-learning tasks. Much less has been done to examine the embeddings directly, especially analyses of gene sets in embedding spaces. Here, we propose an Algorithm for Network Data Embedding and Similarity (ANDES), a novel best-match approach that can be used with existing gene embeddings to compare gene sets while reconciling gene set diversity. This intuitive method has important downstream implications for improving the utility of embedding spaces for various tasks. Specifically, we show how ANDES, when applied to different gene embeddings encoding protein-protein interactions, can be used as a novel overrepresentation- and rank-based gene set enrichment analysis method that achieves state-of-the-art performance. Additionally, ANDES can use multiorganism joint gene embeddings to facilitate functional knowledge transfer across organisms, allowing for phenotype mapping across model systems. Our flexible, straightforward best-match methodology can be extended to other embedding spaces with diverse community structures between set elements.

We establish a pseudoisotopy result for embedding spaces in the line of that of Weiss and Williams for diffeomorphism groups. In other words, for $P\subset M$ a codimension at least three embedding, we describe the difference in a range of homotopical degrees between the spaces of block and ordinary embeddings of $P$ into $M$ as a certain infinite loop space involving the relative algebraic $K$-theory of the pair $(M,M-P)$. This range of degrees is the so-called concordance embedding stable range, which, by recent developments of Goodwillie-Krannich-Kupers, is far beyond that of the aforementioned theorem of Weiss-Williams. We use this result to obtain split fibre sequences in the concordance embedding stable range, with explicit, analysable base and fibre, which determine the homotopy type of spaces of long knots of codimension at least 3. This leads to explicit computations of homotopy groups, including torsion information, in that range. In doing so, we carry out an extensive analysis of certain geometric involutions in algebraic $K$-theory that may be of independent interest.

A design method for control systems with uncertain parameters is presented. The method utilizes a generalized sensitivity approach which separates the parameter space into regions which produce a system response that satisfies given design criteria and regions which do not. Nonparametric statistics and confidence limits for the binomial distribution are used to determine degree of parameter sensitivity and to locate regions in the parameter space which maximize the probability of producing a desirable system response. In an example it is shown that a given parameter may have to be known to a lesser degree of uncertainty to be able to specify a satisfactory design.

In this work, the numerical solution of the Einstein-Maxwell equations of a rotating disc of charged dust and the extended application of its solution results are presented. The formation of the field equations for the rotating charged fluid are discussed. The boundary conditions, which provide the disc character, are derived subsequently from the field equations. Combining the field equations and the boundary conditions yields an equation system describing a rotating disc of charged dust, which is in turn solved by the numerical approach of the pseudo-spectral method. Further discussion of the improvement on the calculation speed, such as the analytical mesh-refinement is also included. The outcome raw potential data of the equation system is processed into more straightforward and intuitive physical quantities, which can further be utilised to analyse the gyromagnetic character of the system. Furthermore, the ergosphere surface can be obtained by analysing the raw data using the bisection method. All the results are summarised in the final chapters of this work. The discussion covers the whole parameter space: from the classical limit to the black hole limit, and from the non-charged limit to the electrical counter-poised limit. A detailed discussion of the gyromagnetic factor and different methods of its acquisition are compared. The configuration of the ergosphere surface is presented, as observed from both the near-source and far-field perspectives. A complete survey from the point at which the ergosphere starts appearing is discussed, covering the whole parameter space. Possible further development of this work is also discussed in the final chapter.

Constraining the many biological parameters that govern cortical dynamics is computationally and conceptually difficult because of the curse of dimensionality. This paper addresses these challenges by proposing (1) a novel data-informed mean-field (MF) approach to efficiently map the parameter space of network models; and (2) an organizing principle for studying parameter space that enables the extraction biologically meaningful relations from this high-dimensional data. We illustrate these ideas using a large-scale network model of the Macaque primary visual cortex. Of the 10-20 model parameters, we identify 7 that are especially poorly constrained, and use the MF algorithm in (1) to discover the firing rate contours in this 7D parameter cube. Defining a “biologically plausible” region to consist of parameters that exhibit spontaneous Excitatory and Inhibitory firing rates compatible with experimental values, we find that this region is a slightly thickened codimension-1 submanifold. An implication of this finding is that while plausible regimes depend sensitively on parameters, they are also robust and flexible provided one compensates appropriately when parameters are varied. Our organizing principle for conceptualizing parameter dependence is to focus on certain 2D parameter planes that govern lateral inhibition: Intersecting these planes with the biologically plausible region leads to very simple geometric structures which, when suitably scaled, have a universal character independent of where the intersections are taken. In addition to elucidating the geometry of the plausible region, this invariance suggests useful approximate scaling relations. Our study offers, for the first time, a complete characterization of the set of all biologically plausible parameters for a detailed cortical model, which has been out of reach due to the high dimensionality of parameter space.

The 21 cm hyperfine structure transition of neutral hydrogen promises to open a window into the first billion years of the Universe (z > 6). With the exception of rare lines of sight towards exceptionally distant and luminous galaxies, this period of the universe's history remains largely unexplored. During this time the 21 cm transition is expected to be detectable as a 10--100 mK perturbation in the thermal Cosmic Microwave Background (CMB) spectrum. Due to the large field of view of low frequency radio telescopes (typically composed of dipole antennas) and the fact that the line of sight distance can be inferred from the measured frequency of the transition, the ultimate goal of 21 cm cosmology is to produce three dimensional tomographic maps of the 21 cm brightness temperature. In this way, the formation of the first stars and galaxies will be revealed through their influence on the neutral gas around them. This thesis saw the construction of the Owens Valley Radio Observatory Long Wavelength Array (OVRO-LWA), a new low frequency (27--85 MHz) radio telescope located near Bishop, California. Composed of 288 crossed-dipole antennas, the OVRO-LWA is capable of imaging the entire visible hemisphere in a single 13 s snapshot image with 8 arcmin angular resolution. The primary challenges faced by efforts to detect the highly redshifted 21 cm transition are seeing past the blinding glow of foreground radio emission that is five orders of magnitude brighter than the cosmological emission, and calibrating the instrument to a level where it's possible to make the separation between foreground emission and the 21 cm signal. In this thesis I will present foundational work using the OVRO-LWA to place upper limits on spatial fluctuations of the 21 cm transition during the Cosmic Dawn---the period of first star formation. In this thesis I present the highest angular resolution maps of the full sky below 100 MHz, and generated with a new widefield imaging technique that is specialized for drift scanning interferometers. These sky maps are a 10-fold improvement in angular resolution over existing maps at comparable frequencies, and are publicly available now for use in modeling and subtracting the contamination of foreground emission in 21 cm experiments. Using a 28 hr integration with the OVRO-LWA, I place to-date the most constraining upper limits on the amplitude of the 21 cm spatial power spectrum at the Cosmic Dawn, and the first limits at z > 18. Although the current constraints Δ212 ≲ (104mK)2 do not meaningfully restrict the parameter space of models of early star formation, they do inform the design and calibrations necessary for future measurements to push towards a detection of the high-redshift 21 cm transition. In making this measurement I demonstrate the application of a new foreground filter that accounts for the full covariance of the foreground emission, and provide an updated measurement of the foreground angular covariance. Finally, I interpret the limiting factors in this measurement and determine the instrumental calibration and characterization requirements the OVRO-LWA will need to achieve in order to make a detection of the 21 cm power spectrum of the Cosmic Dawn.

High dimensional data is a phenomenon in real-world data mining applications. Text data is a typical example. In text mining, a text document is viewed as a vector of terms whose dimension is equal to the total number of unique terms in a data set, which is usually in thousands. High dimensional data occurs in business as well. In retails, for example, to effectively manage supplier relationship, suppliers are often categorized according to their business behaviors (Zhang, Huang, Qian, Xu, & Jing, 2006). The supplier’s behavior data is high dimensional, which contains thousands of attributes to describe the supplier’s behaviors, including product items, ordered amounts, order frequencies, product quality and so forth. One more example is DNA microarray data. Clustering high-dimensional data requires special treatment (Swanson, 1990; Jain, Murty, & Flynn, 1999; Cai, He, & Han, 2005; Kontaki, Papadopoulos & Manolopoulos., 2007), although various methods for clustering are available (Jain & Dubes, 1988). One type of clustering methods for high dimensional data is referred to as subspace clustering, aiming at finding clusters from subspaces instead of the entire data space. In a subspace clustering, each cluster is a set of objects identified by a subset of dimensions and different clusters are represented in different subsets of dimensions. Soft subspace clustering considers that different dimensions make different contributions to the identification of objects in a cluster. It represents the importance of a dimension as a weight that can be treated as the degree of the dimension in contribution to the cluster. Soft subspace clustering can find the cluster memberships of objects and identify the subspace of each cluster in the same clustering process.

Recently emerging approaches to high-throughput phenotyping have become important tools in unraveling the biological basis of agronomically and medically important phenotypes. These experiments produce very large sets of either low or high-dimensional data. Finding clusters in the entire space of high-dimensional data (HDD) is a challenging task, because the relative distances between any two objects converge to zero with increasing dimensionality. Additionally, real data may not be mathematically well behaved. Finally, many clusters are expected on biological grounds to be "natural" -- that is, to have irregular, overlapping boundaries in different subsets of the dimensions. More precisely, the natural clusters of the data could differ in shape, size, density, and dimensionality; and they might not be disjoint. In principle, clustering such data could be done by dimension reduction methods. However, these methods convert many dimensions to a smaller set of dimensions that make the clustering results difficult to interpret and may also lead to a significant loss of information. Another possible approach is to find subspaces (subsets of dimensions) in the entire data space of the HDD. However, the existing subspace methods don't discover natural clusters. Therefore, in this dissertation I propose a novel data preprocessing method, demonstrating that a group of phenotypes are interdependent, and propose a novel density-based subspace clustering algorithm for high-dimensional data, called Dynamic Locally Density Adaptive Scalable Subspace Clustering (DynaDASC). This algorithm is relatively locally density adaptive, scalable, dynamic, and nonmetric in nature, and discovers natural clusters.

Purpose. Increasing the efficiency of scientific research and solving applied problems in the field of fire safety by introducing a computational computer experiment – the method of multi-criteria synthesis to reduce the time, material and labor costs for the experiment and provide correct systemic interpretation of test results. Methods. To solve the problems of fire safety, the method of multi-criteria synthesis was applied. It makes it possi-ble to predict the behavior of the system, taking into account the stochasticity of its parameters and the choice of rational characteristics that provide the required output parameters. The search for the optimal set of parameters of a technical object involves the determination of the calculated values of the criteria by the values of the calculated points, which are located in the multidimensional space of variable parameters. In this case, the space of parameters is transformed into the space of criteria, taking into ac-count the accepted restrictions. Findings. The article provides examples of the application of the method of multi-criteria synthesis in solving problems of ensuring fire safety. The formulation of a fire retardant and fire extinguishing composition based on synthetic phosphates of bivalent and trivalent ammonium metals, being highly effective in impact on peat and wood, was determined. The using of an optimization-simulation approach made it possible to predict the time of extinguishing a fire in a tank and to select the optimal parameters of extinguishing by supply of low expansion foam directly into the fuel layer. On the basis of multi-criteria computer synthesis, the concentration of the modifying additive in the set of diamond segments and the cutting conditions for the tool during emergency rescue operations was determined. The way of assessing the aggregate territorial risk by the method of statistical modeling was developed which created a framework for risk management, including legal, economic regulation and compulsory insurance. Application field of research. The presented research results are aimed at improving the fire safety of various objects.

In this paper we introduce a new framework for geometric modeling that combines implicit and parametric surface representations with volumetric warpings. The framework is based on dynamic, adaptive simplicial decompositions of the embedding space and conforming piecewise diffeomorphisms.