Statistical Analysis of Twin Populations using Dissimilarity Measurements in Hippocampus Shape Space

By analyzing interpoint comparisons, we obtain significant results describing the relationship in “hippocampus shape space” of clinically depressed, high-risk, and control populations. In particular, our analysis demonstrates that the high-risk population is closer in shape space to the control population than to the clinically depressed population

Machine learning in space forms: Embeddings, classification, and similarity comparisons

We take a non-Euclidean view at three classical machine learning subjects: low-dimensional embedding, classification, and similarity comparisons. We first introduce kinetic Euclidean distance matrices to solve kinetic distance geometry problems. In distance geometry problems (DGPs), the task is to find a geometric representation, that is, an embedding, for a collection of entities consistent with pairwise distance (metric) or similarity (nonmetric) measurements. In kinetic DGPs, the twist is that the points are dynamic. And our goal is to localize them by exploiting the information about their trajectory class. We show that a semidefinite relaxation can reconstruct trajectories from incomplete, noisy, time-varying distance observations. We then introduce another distance-geometric object: hyperbolic distance matrices. Recent works have focused on hyperbolic embedding methods for low-distortion embedding of distance measurements associated with hierarchical data. We derive a semidefinite relaxation to estimate the missing distance measurements and denoise them. Further, we formalize the hyperbolic Procrustes analysis, which uses extraneous information in the form of anchor points, to uniquely identify the embedded points. Next, we address the design of learning algorithms in mixed-curvature spaces. Learning algorithms in low-dimensional mixed-curvature spaces have been limited to certain non-Euclidean neural networks. Here, we study the problem of learning a linear classifier (a perceptron) in product of Euclidean, spherical, and hyperbolic spaces, i.e., space forms. We introduce a notion of linear separation surfaces in Riemannian manifolds and use a metric that renders distances in different space forms compatible with each other and integrates them into one classifier. Lastly, we show how similarity comparisons carry information about the underlying space of geometric graphs. We introduce the ordinal spread of a distance list and relate it to the ordinal capacity of their underlying space, a notion that quantifies the space's ability to host extreme patterns in nonmetric measurements. Then, we use the distribution of random ordinal spread variables as a practical tool to identify the underlying space form

Black box and mechanistic modelling of electronic nose systems

Electronic nose systems have been in existence for around 20 years or more. The ability to mimic the function of the mammalian olfactory system is a very tempting goal. Such devices would offer the possibility of rapid chemical screening of samples. To gain a detailed insight into the operation of such systems it is proposed to carry out a systems modelling analysis. This thesis reports such an analysis using black box and mechanistic models. The nature and construction of electronic nose systems are discussed. The challenges presented by these systems in order to produce a truly electronic nose are analysed as a prelude to systems modelling. These may be summarised as time and environmental dependent behaviour, information extraction and computer data handling. Model building in general is investigated. It is recognised that robust parameter estimation is necessary to build good models of electronic nose systems. A number of optimisation algorithms for parameter estimation are proposed and investigated, these being gradient search, genetic algorithms and the support vector method. It is concluded that the support vector method is most robust, although the genetic algorithm approach shows promise for initial parameter value estimation. A series of investigations are reported that involve the analysis of biomedical samples. These samples are of blood, urine and bacterial cultures. The findings demonstrate that the nature of such samples, such as bacterial content and type, may be accurately identified using an electronic nose system by careful modelling of the system. These findings also highlight the advantages of data set reduction and feature extraction. A mechanistic model embodying the operating principles of carbon black-polymer sensors is developed. This is validated experimentally and is used to investigate the environmental dependencies of electronic nose systems. These findings demonstrate a clear influence of environmental conditions on the behaviour of carbon black-polymer sensors and these should be considered when designing future electronic nose systems. The findings in this thesis demonstrate that careful systems modelling and analysis of electronic nose systems allows a greater understanding of such systems

Language impairment and colour categories

Goldstein (1948) reported multiple cases of failure to categorise colours in patients that he termed amnesic or anomic aphasics. these patients have a particular difficulty in producing perceptual categories in the absence of other aphasic impairments. we hold that neuropsychological evidence supports the view that the task of colour categorisation is logically impossible without labels

Habitat use, movement patterns, and home ranges of coaster brook trout in Nipigon Bay, Lake Superior

Coaster brook trout are one of two salmonine species native to Lake Superior. Abundant and widely distributed in Lake Superior a century ago, they have been reduced to a few remnant stocks due to exploitation and habitat loss. Twenty coaster brook trout, captured from Nipigon Bay, Lake Superior were surgically implanted with radio transmitters and were located from June 1999 to October 2000. Coaster brook trout locations were used to determine the characteristics of utilized lake habitat, identify streams and the critical habitat characteristics within them utilized for spawning, and establish home ranges and movement patterns on a daily and seasonal time scale. A total of 638 locations were obtained during the tracking period with 483 locations within Nipigon Bay and the remaining 155 within tributary streams. Coaster brook trout were located almost exclusively within the shallow nearshore areas of Nipigon Bay with 92% of locations in areas less than 7 m deep (mean depth = 3.4 m), and 94% less than 400 m from shore (mean distance to shore = 116.1 m). Coaster brook trout inhabited deeper areas (ANOVA, F=3.533, p=0.002) with steeper shoreline slopes (ANOVA, F=2.562, p=0.013) during July and August when the water temperature of shallow nearshore areas became higher than their tolerable limit. Following selected individuals for 24 hours revealed coaster brook trout utilized deeper areas during daylight hours and moved to extremely shallow nearshore areas during the night (ANOVA, F=3.187, p=0.02). Home range estimates for individual coaster brook trout using a 95% fixed kernel varied from less than 1 km to 185 sq. km. in size. Home range size was not correlated with the number of locations for the individual (r2=0.046), or fork length (r2=0.009). Tagged coaster brook trout began ascending streams during late summer in both 1999 and 2000. The mean residency time for brook trout in spawning tributary streams in 1999 was 46 days. Spawning occurred in early October with most tagged coaster brook trout returning to Lake Superior by mid-October. Four different streams were used by tagged coaster brook trout, with all brook trout entering streams exhibiting strong spawning site fidelity. Catchment size of spawning streams varied from 8.38 sq. km to 288.04 sq. km, but stream reach characteristics of spawning areas were similar, exhibiting a moderate gradient, riffle-pool complexes, coarse sands and gravels, and groundwater input. These results suggest that coaster brook trout utilize specific areas depending upon the time of year. Protection of these identified areas is critical to maintain these remnant natural stocks