On the probability that the determinant of an nxn matrix over a finite field vanishe

An expression is derived for the probability that the determinant of an n x n matrix over a finite field vanishes; from this it is deduced that for a fixed field this probability tends to 1 as n tends to.

Periodic Rayleigh waves of finite amplitude on an isotropic solid

Existence of a periodic progressive wave solution to the nonlinear boundary value problem for Rayleigh surface waves of finite amplitude is demonstrated using an extension of the method of strained coordinates. The solution, obtained as a second-order perturbation of the linearized monochromatic Rayleigh wave solution, contains harmonics of all orders of the fundamental frequency. It is shown that the higher harmonic content of the wave increases with amplitude, but the slope of the waveform remains finite so long as the amplitude is less than a critical value.

Analysis of a finite composite plate with smooth rigid pin

A continuum method of analysis is presented in this paper for the problem of a smooth rigid pin in a finite composite plate subjected to uniaxial loading. The pin could be of interference, push or clearance fit. The plate is idealized to an orthotropic sheet. As the load on the plate is progressively increased, the contact along the pin-hole interface is partial above certain load levels in all three types of fit. In misfit pins (interference or clearance), such situations result in mixed boundary value problems with moving boundaries and in all of them the arc of contact and the stress and displacement fields vary nonlinearly with the applied load. In infinite domains similar problems were analysed earlier by ‘inverse formulation’ and, now, the same approach is selected for finite plates. Finite outer domains introduce analytical complexities in the satisfaction of boundary conditions. These problems are circumvented by adopting a method in which the successive integrals of boundary error functions are equated to zero. Numerical results are presented which bring out the effects of the rectangular geometry and the orthotropic property of the plate. The present solutions are the first step towards the development of special finite elements for fastener joints.

Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups

The extension of Hehl's Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.

Algebraic and geometric intersection numbers for free groups

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups Coincides With the geometric intersection number for the sphere complex of the connected sum of copies of S-2 x S-1. (C) 2009 Elsevier B.V. All rights reserved.

Contributions to the Theory of Finite-State Based Grammars

This dissertation is a theoretical study of finite-state based grammars used in natural language processing. The study is concerned with certain varieties of finite-state intersection grammars (FSIG) whose parsers define regular relations between surface strings and annotated surface strings. The study focuses on the following three aspects of FSIGs: (i) Computational complexity of grammars under limiting parameters In the study, the computational complexity in practical natural language processing is approached through performance-motivated parameters on structural complexity. Each parameter splits some grammars in the Chomsky hierarchy into an infinite set of subset approximations. When the approximations are regular, they seem to fall into the logarithmic-time hierarchyand the dot-depth hierarchy of star-free regular languages. This theoretical result is important and possibly relevant to grammar induction. (ii) Linguistically applicable structural representations Related to the linguistically applicable representations of syntactic entities, the study contains new bracketing schemes that cope with dependency links, left- and right branching, crossing dependencies and spurious ambiguity. New grammar representations that resemble the Chomsky-Schützenberger representation of context-free languages are presented in the study, and they include, in particular, representations for mildly context-sensitive non-projective dependency grammars whose performance-motivated approximations are linear time parseable. (iii) Compilation and simplification of linguistic constraints Efficient compilation methods for certain regular operations such as generalized restriction are presented. These include an elegant algorithm that has already been adopted as the approach in a proprietary finite-state tool. In addition to the compilation methods, an approach to on-the-fly simplifications of finite-state representations for parse forests is sketched. These findings are tightly coupled with each other under the theme of locality. I argue that the findings help us to develop better, linguistically oriented formalisms for finite-state parsing and to develop more efficient parsers for natural language processing. Avainsanat: syntactic parsing, finite-state automata, dependency grammar, first-order logic, linguistic performance, star-free regular approximations, mildly context-sensitive grammars

Non-finite constructions in Old English : with special reference to syntactic borrowing from Latin

My dissertation is a corpus-based study of non-finite constructions in Old English (OE). It revisits the question of Latin influence on the OE syntax, offering a new evaluation of syntactic interference between Latin and OE, and, more generally, of the contact situation in the OE period, drawing on methods used in studying grammaticalization and language contact. I address three non-finite constructions: absolute participial construction, accusative-and-infinitive construction, and nominative-and-infinitive construction, exemplified respectively in present-day English as - She looked like a pixie sometimes, her eyes darting here and there, forever watchful (BNC CCM 98); - My first acquaintance with her was when I heard her sing (BNC CFY 2215); - Charles the Bald was said to resemble his grandfather physically (BNC HPT 175). This study compares data from translated texts against the background of original OE writings, establishing dependencies and differences between the two. Although the contrastive analysis of source and target texts is one of the major methods employed in the study, translation and translation strategies as such are only my secondary foci. The emphasis is rather on what source/target comparison can tell us about the OE non-finite syntax and the typological differences between Latin and OE in this domain, and on whether contact-induced change can originate in translation. In terms of theoretical framework, I have adopted functional-typological approach, which rests on the principles of iconicity and event integration, and to the best of my knowledge, has not been applied systematically to OE non-finite constructions. Therefore one more aim of the dissertation is to test this framework and to see how OE fits into the cross-linguistic picture of non-finites. My research corpus consists of two samples: 1) written OE closely dependent on the Latin originals, based on editions of two gloss texts, five translations, and Latin originals of these texts, representing four text types: hymns, religious regulations, homily/life narrative, and biblical narrative (180,622 words); and 2) written OE as far independent from Latin as possible, based on a selection from the York-Toronto-Helsinki Parsed Corpus of Old English Prose (YCOE) and representing five text types: laws, charters, correspondence, chronicle narrative, and homily/life narrative (274,757 words).

Analysis of laminated shells with laminated stiffeners using rectangular shell finite elements

A finite element analysis of laminated shells reinforced with laminated stiffeners is described in this paper. A rectangular laminated anisotropic shallow thin shell finite element of 48 d.o.f. is used in conjunction with a laminated anisotropic curved beam and shell stiffening finite element having 16 d.o.f. Compatibility between the shell and the stiffener is maintained all along their junction line. Some problems of symmetrically stiff ened isotropic plates and shells have been solved to evaluate the performance of the present method. Behaviour of an eccentrically stiffened laminated cantilever cylindrical shell has been predicted to show the ability of the present program. General shells amenable to rectangular meshes can also be solved in a similar manner.

Virtual versus classroom language teaching : A comparative study of the learning outcomes and student responses between two English reading comprehension groups

A 26-hour English reading comprehension course was taught to two groups of second year Finnish Pharmacy students: a virtual group (33 students) and a teacher-taught group (25 students). The aims of the teaching experiment were to find out: 1.What has to be taken into account when teaching English reading comprehension to students of pharmacy via the Internet and using TopClass? 2. How will the learning outcomes of the virtual group and the control group differ? 3. How will the students and the Department of Pharmacy respond to the different and new method, i.e. the virtual teaching method? 4. Will it be possible to test English reading comprehension learning material using the groupware tool TopClass? The virtual exercises were written within the Internet authoring environment, TopClass. The virtual group was given the reading material and grammar booklet on paper, but they did the reading comprehension tasks (written by the teacher), autonomously via the Internet. The control group was taught by the same teacher in 12 2-hour sessions, while the virtual group could work independently within the given six weeks. Both groups studied the same material: ten pharmaceutical articles with reading comprehension tasks as well as grammar and vocabulary exercises. Both groups took the same final test. Students in both groups were asked to evaluate the course using a 1 to 5 rating scale and they were also asked to assess their respective courses verbally. A detailed analysis of the different aspects of the student evaluation is given. Conclusions: 1.The virtual students learned pharmaceutical English relatively well but not significantly better than the classroom students 2. The overall student satisfaction in the virtual pharmacy English reading comprehension group was found to be higher than that in the teacher-taught control group. 3. Virtual learning is easier for linguistically more able students; less able students need more time with the teacher. 4. The sample in this study is rather small, but it is a pioneering study. 5. The Department of Pharmacy in the University of Helsinki wishes to incorporate virtual English reading comprehension teaching in its curriculum. 6. The sophisticated and versatile TopClass system is relatively easy for a traditional teacher and quite easy for the students to learn. It can be used e.g. for automatic checking of routine answers and document transfer, which both lighten the workloads of both parties. It is especially convenient for teaching reading comprehension. Key words: English reading comprehension, teacher-taught class, virtual class, attitudes of students, learning outcomes

Overfitting Bayesian mixture models with an unknown number of components

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of standard Markov Chain Monte Carlo (MCMC) sampling techniques, and the related label switching problem. An overfitting approach is used to estimate the number of components in a finite mixture model via a Zmix algorithm. Zmix provides a bridge between multidimensional samplers and test based estimation methods, whereby priors are chosen to encourage extra groups to have weights approaching zero. MCMC sampling is made possible by the implementation of prior parallel tempering, an extension of parallel tempering. Zmix can accurately estimate the number of components, posterior parameter estimates and allocation probabilities given a sufficiently large sample size. The results will reflect uncertainty in the final model and will report the range of possible candidate models and their respective estimated probabilities from a single run. Label switching is resolved with a computationally light-weight method, Zswitch, developed for overfitted mixtures by exploiting the intuitiveness of allocation-based relabelling algorithms and the precision of label-invariant loss functions. Four simulation studies are included to illustrate Zmix and Zswitch, as well as three case studies from the literature. All methods are available as part of the R package Zmix, which can currently be applied to univariate Gaussian mixture models.

A study of the use of the Edinburgh postnatal depression scale with parent groups outside the postpartum period

The Edinburgh Postnatal Depression Scale (EPDS) was sent by post to 206 mothers and 201 fathers of toddlers (aged between 19 and 22 months). At the same time these parents also completed subscales of the Crown—Crisp Experiential Index (CCEI). The responses were used to assess the feasibility of postal completion of the EPDS and its acceptability to parents outside the postpartum year, particularly fathers for whom there have been no previous reports of its use. On a small sub-group, the sensitivity, specificity and predictive values of the measures were assessed using the Present. State Examination. Answers to the depression subscale of the CCEI to the EPDS and to the Present State Examination were compared to assess validity. Completion of the postally-administered EPDS was satisfactory, though some difficulties were experienced in a second postal administration to a subsample. The scale was completed without obvious error or omission and this, combined with positive comments from parents, suggests the acceptability of the scale to both mothers and fathers. The mean scores were higher for mothers than for fathers, but the pattern of distribution was similar with a marked positive skew and a distinct decline in scores above 10. Because the subsample of parents interviewed was small the calculation of sensitivity and specificity has to be treated with caution. However, the results for mothers suggest that the EPDS has satisfactory validity for this group and one superior to the depression subscale of the CCEI. Among the fathers interviewed there were insufficient cases to enable calculation of sensitivity and specificity. Other results were encouraging, however, and suggest the merit of further studies of the application and validity of the EPDS with fathers.

Analysis of laminated shells of revolution with laminated stiffeners using a doubly curved quadrilateral finite element

A finite element analysis of laminated shells of revolution reinforced with laminated stifieners is described here-in. A doubly curved quadrilateral laminated anisotropic shell of revolution finite element of 48 d.o.f. is used in conjunction with two stiffener elements of 16 d.o.f. namely: (i) A laminated anisotropic parallel circle stiffener element (PCSE); (ii) A laminated anisotropic meridional stiffener element (MSE). These stifiener elements are formulated under line member assumptions as degenerate cases of the quadrilateral shell element to achieve compatibility all along the shell-stifiener junction lines. The solutions to the problem of a stiffened cantilever cylindrical shell are used to check the correctness of the present program while it's capability is shown through the prediction of the behavior of an eccentrically stiffened laminated hyperboloidal shell.

Evolution of sex ratios in social hymenoptera: consequences of finite brood size

Evolutionarily stable sex ratios are determined for social hymenoptera under local mate competition (LMC) and when the brood size is finite. LMC is modelled by the parameter d. Of the reproductive progeny from a single foundress nest, a fraction d disperses (outbreeding), while (1-d) mate amongst themselves (sibmating). When the brood size is finite, d is taken to be the probability of an offspring dispersing, and similarly, r, the proportion of male offspring, the probability of a haploid egg being laid. Under the joint influence of these two stochastic processes, there is a nonzero probability that some females remain unmated in the nest. As a result, the optimal proportion of males (corresponding to the evolutionarily stable strategy, ESS) is higher than that obtained when the brood size is infinite. When the queen controls the sex ration, the ESS becomes more female biased under increased inbreeding (lower d), However, the ESS under worker control shows an unexpected pattern, including an increase in the proportion of males with increased inbreeding. This effect is traced to the complex interaction between inbreeding and local mate competition.

Fatigued driving : prevalence, risk factors and groups, and the law

Fatigue and sleepiness are major causes of road traffic accidents. However, precise data is often lacking because a validated and reliable device for detecting the level of sleepiness (cf. the breathalyzer for alcohol levels) does not exist, nor does criteria for the unambiguous detection of fatigue/sleepiness as a contributing factor in accident causation. Therefore, identification of risk factors and groups might not always be easy. Furthermore, it is extremely difficult to incorporate fatigue in operationalized terms into either traffic or criminal law. The main aims of this thesis were to estimate the prevalence of fatigue problems while driving among the Finnish driving population, to explore how VALT multidisciplinary investigation teams, Finnish police, and courts recognize (and prosecute) fatigue in traffic, to identify risk factors and groups, and finally to explore the application of the Finnish Road Traffic Act (RTA), which explicitly forbids driving while tired in Article 63. Several different sources of data were used: a computerized database and the original folders of multidisciplinary teams investigating fatal accidents (VALT), the driver records database (AKE), prosecutor and court decisions, a survey of young male military conscripts, and a survey of a representative sample of the Finnish active driving population. The results show that 8-15% of fatal accidents during 1991-2001 were fatigue related, that every fifth Finnish driver has fallen asleep while driving at some point during his/her driving career, and that the Finnish police and courts punish on average one driver per day on the basis of fatigued driving (based on the data from the years 2004-2005). The main finding regarding risk factors and risk groups is that during the summer months, especially in the afternoon, the risk of falling asleep while driving is increased. Furthermore, the results indicate that those with a higher risk of falling asleep while driving are men in general, but especially young male drivers including military conscripts and the elderly during the afternoon hours and the summer in particular; professional drivers breaking the rules about duty and rest hours; and drivers with a tendency to fall asleep easily. A time-of-day pattern of sleep-related incidents was repeatedly found. It was found that VALT teams can be considered relatively reliable when assessing the role of fatigue and sleepiness in accident causation; thus, similar experts might be valuable in the court process as expert witnesses when fatigue or sleepiness are suspected to have a role in an accident’s origins. However, the application of Article 63 of the RTA that forbids, among other things, fatigued driving will continue to be an issue that deserves further attention. This should be done in the context of a needed attitude change towards driving while in a state of extreme tiredness (e.g., after being awake for more than 24 hours), which produces performance deterioration comparable to illegal intoxication (BAC around 0.1%). Regarding the well-known interactive effect of increased sleepiness and even small alcohol levels, the relatively high proportion (up to 14.5%) of Finnish drivers owning and using a breathalyzer raises some concern. This concern exists because these drivers are obviously more focused on not breaking the “magic” line of 0.05% BAC than being concerned about driving impairment, which might be much worse than they realize because of the interactive effects of increased sleepiness and even low alcohol consumption. In conclusion, there is no doubt that fatigue and sleepiness problems while driving are common among the Finnish driving population. While we wait for the invention of reliable devices for fatigue/sleepiness detection, we should invest more effort in raising public awareness about the dangerousness of fatigued driving and educate drivers about how to recognize and deal with fatigue and sleepiness when they ultimately occur.