Formal methods in the foundations of science

The intent of this study is to provide formal apparatus which facilitates the investigation of problems in the methodology of science. The introduction contains several examples of such problems and motivates the subsequent formalism.

A general definition of a formal language is presented, and this definition is used to characterize an individual’s view of the world around him. A notion of empirical observation is developed which is independent of language. The interplay of formal language and observation is taken as the central theme. The process of science is conceived as the finding of that formal language that best expresses the available experimental evidence.

To characterize the manner in which a formal language imposes structure on its universe of discourse, the fundamental concepts of elements and states of a formal language are introduced. Using these, the notion of a basis for a formal language is developed as a collection of minimal states distinguishable within the language. The relation of these concepts to those of model theory is discussed.

An a priori probability defined on sets of observations is postulated as a reflection of an individual’s ontology. This probability, in conjunction with a formal language and a basis for that language, induces a subjective probability describing an individual’s conceptual view of admissible configurations of the universe. As a function of this subjective probability, and consequently of language, a measure of the informativeness of empirical observations is introduced and is shown to be intuitively plausible – particularly in the case of scientific experimentation.

The developed formalism is then systematically applied to the general problems presented in the introduction. The relationship of scientific theories to empirical observations is discussed and the need for certain tacit, unstatable knowledge is shown to be necessary to fully comprehend the meaning of realistic theories. The idea that many common concepts can be specified only by drawing on knowledge obtained from an infinite number of observations is presented, and the problems of reductionism are examined in this context.

A definition of when one formal language can be considered to be more expressive than another is presented, and the change in the informativeness of an observation as language changes is investigated. In this regard it is shown that the information inherent in an observation may decrease for a more expressive language.

The general problem of induction and its relation to the scientific method are discussed. Two hypotheses concerning an individual’s selection of an optimal language for a particular domain of discourse are presented and specific examples from the introduction are examined.

Joule-Thomson coefficients of propane and n-butane

Experimental Joule-Thomson measurements were made on gaseous propane at temperatures from 100 to 280˚F and at pressures from 8 to 66 psia. Joule-Thomson measurements were also made on gaseous n-butane at temperatures from 100 to 280˚ and at pressures from 8 to 42 psia. For propane, the values of these measurements ranged from 0.07986˚F/psi at 280˚F and 8.01 psia to 0.19685˚F/psi at 100˚F and 66.15 psia. For n-butane, the values ranged from 0.11031˚F/psi at 280˚F and 9.36 psia to 0.30141˚F/psi at 100˚F and 41.02 psia. The experimental values have a maximum error of 1.5 percent.

For n-butane, the measurements of this study did not agree with previous Joule-Thomson measurements made in the Laboratory in 1935. The application of a thermal-transfer correction to the previous experimental measurements would cause the two sets of data to agree. Calculated values of the Joule-Thomson coefficient from other types of p-v-t data did agree with the present measurements for n-butane.

The apparatus used to measure the experimental Joule-Thomson coefficients had a radial-flow porous thimble and was operated at pressure changes between 2.3 and 8.6 psi. The major difference between this and other Joule-Thomson apparatus was its larger weight rates of flow (up to 6 pounds per hour) at atmospheric pressure. The flow rate was shown to have an appreciable effect on non-isenthalpic Joule-Thomson measurements.

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Investigations into electronic stopping regime sputtering of uranium tetrafluoride

Yields were measured for ²³⁵U sputtered from UF₄ by ¹⁶O, ¹⁹F, and ³⁵Cl over the energy range ~.12 to 1.5 MeV/ amu sing a charge equilibrated beam in the stripped beam arrangement for all the incident ions and in the transmission arrangement for ¹⁹F and ³⁵Cl. In addition, yields were measured for ¹⁹F incident in a wide range of discrete charge states. The angular dependence of all the measured yields were consistent with cosʋ. The stripped beam and transmission data were well fit by the form (Az²eqln(BƐ)/Ɛ)⁴ (where Ɛ was the ion energy in MeV/amu and z_eq(Ɛ) was taken from Zeigler(80). The fitted values of B for the various sets of data were consistent with a constant B₀, equal to 36.3 ± 2.7, independent of incident ion. The fitted values of A show no consistent variation with incident ion although a difference can be noted between the stripped beam and transmission values, the transmission values being higher.

The incident charge data were well fit by the assumptions that the sputtering yield depended locally on a power of the incident ion charge and that the sputtering from the surface is exponentially correlated to conditions in the bulk. The equilibrated sputtering yields derived from these data are in agreement with the stripped beam yields.

In addition, to aid in the understanding of these data, the data of Hakansson(80,81a,81b) were examined and contrasted with the UF₄ results. The thermal models of Seiberling(80) and Watson(81) were discussed and compared to the data.

A generalized Hausdorff dimension for functions and sets

Let E be a compact subset of the n-dimensional unit cube, 1_n, and let C be a collection of convex bodies, all of positive n-dimensional Lebesgue measure, such that C contains bodies with arbitrarily small measure. The dimension of E with respect to the covering class C is defined to be the number

d_C(E) = sup(β:H_{β, C}(E) > 0),

where H_{β, C} is the outer measure

inf(Ʃm(C_i)^β:UC_i Ↄ E, C_i ϵ C) .

Only the one and two-dimensional cases are studied. Moreover, the covering classes considered are those consisting of intervals and rectangles, parallel to the coordinate axes, and those closed under translations. A covering class is identified with a set of points in the left-open portion, 1’_n, of 1_n, whose closure intersects 1_n - 1’_n. For n = 2, the outer measure H_{β, C} is adopted in place of the usual:

Inf(Ʃ(diam. (C_i))^β: UC_i Ↄ E, C_i ϵ C),

for the purpose of studying the influence of the shape of the covering sets on the dimension d_C(E).

If E is a closed set in 1₁, let M(E) be the class of all non-decreasing functions μ(x), supported on E with μ(x) = 0, x ≤ 0 and μ(x) = 1, x ≥ 1. Define for each μ ϵ M(E),

d_C(μ) = lim/c → inf/0 log ∆μ(c)/log c , (c ϵ C)

where ∆μ(c) = v/x (μ(x+c) – μ(x)). It is shown that

d_C(E) = sup (d_C(μ):μ ϵ M(E)).

This notion of dimension is extended to a certain class Ӻ of sub-additive functions, and the problem of studying the behavior of d_C(E) as a function of the covering class C is reduced to the study of d_C(f) where f ϵ Ӻ. Specifically, the set of points in 1₁,

(*) {d_B(F), d_C(f)): f ϵ Ӻ}

is characterized by a comparison of the relative positions of the points of B and C. A region of the form (*) is always closed and doubly-starred with respect to the points (0, 0) and (1, 1). Conversely, given any closed region in 1₂, doubly-starred with respect to (0, 0) and (1, 1), there are covering classes B and C such that (*) is exactly that region. All of the results are shown to apply to the dimension of closed sets E. Similar results can be obtained when a finite number of covering classes are considered.

In two dimensions, the notion of dimension is extended to the class M, of functions f(x, y), non-decreasing in x and y, supported on 1₂ with f(x, y) = 0 for x · y = 0 and f(1, 1) = 1, by the formula

d_C(f) = lim/s · t → inf/0 log ∆f(s, t)/log s · t , (s, t) ϵ C

where

∆f(s, t) = V/x, y (f(x+s, y+t) – f(x+s, y) – f(x, y+t) + f(x, t)).

A characterization of the equivalence d_C1(f) = d_C2(f) for all f ϵ M, is given by comparison of the gaps in the sets of products s · t and quotients s/t, (s, t) ϵ C_i (I = 1, 2).

Two and Three Finger Caging of Polygons and Polyhedra

Multi-finger caging offers a rigorous and robust approach to robot grasping. This thesis provides several novel algorithms for caging polygons and polyhedra in two and three dimensions. Caging refers to a robotic grasp that does not necessarily immobilize an object, but prevents it from escaping to infinity. The first algorithm considers caging a polygon in two dimensions using two point fingers. The second algorithm extends the first to three dimensions. The third algorithm considers caging a convex polygon in two dimensions using three point fingers, and considers robustness of this cage to variations in the relative positions of the fingers.

This thesis describes an algorithm for finding all two-finger cage formations of planar polygonal objects based on a contact-space formulation. It shows that two-finger cages have several useful properties in contact space. First, the critical points of the cage representation in the hand’s configuration space appear as critical points of the inter-finger distance function in contact space. Second, these critical points can be graphically characterized directly on the object’s boundary. Third, contact space admits a natural rectangular decomposition such that all critical points lie on the rectangle boundaries, and the sublevel sets of contact space and free space are topologically equivalent. These properties lead to a caging graph that can be readily constructed in contact space. Starting from a desired immobilizing grasp of a polygonal object, the caging graph is searched for the minimal, intermediate, and maximal caging regions surrounding the immobilizing grasp. An example constructed from real-world data illustrates and validates the method.

A second algorithm is developed for finding caging formations of a 3D polyhedron for two point fingers using a lower dimensional contact-space formulation. Results from the two-dimensional algorithm are extended to three dimension. Critical points of the inter-finger distance function are shown to be identical to the critical points of the cage. A decomposition of contact space into 4D regions having useful properties is demonstrated. A geometric analysis of the critical points of the inter-finger distance function results in a catalog of grasps in which the cages change topology, leading to a simple test to classify critical points. With these properties established, the search algorithm from the two-dimensional case may be applied to the three-dimensional problem. An implemented example demonstrates the method.

This thesis also presents a study of cages of convex polygonal objects using three point fingers. It considers a three-parameter model of the relative position of the fingers, which gives complete generality for three point fingers in the plane. It analyzes robustness of caging grasps to variations in the relative position of the fingers without breaking the cage. Using a simple decomposition of free space around the polygon, we present an algorithm which gives all caging placements of the fingers and a characterization of the robustness of these cages.

A Poética de Adélia Prado: espaço de articulação entre língua portuguesa e língua literária

A tese estuda a obra poética de Adélia Prado sob o ponto de vista da Estilística. Mostra que a metáfora é o recurso mais afeito a construir a língua literária e, no caso da poetisa, modelá-la em português. O estudo atesta que a linguagem conotativa da poetisa alcança os três níveis da língua e promove o inesperado e o distante da expressão comum. Afirma a importância da polifonia e da intertextualidade , além da excelência do discurso indireto livre na criação literária, não só da poetisa, mas de todo uso da língua portuguesa como ferramenta de expressão poética, principalmente se a intenção do autor é criar o discurso surrealista. A pesquisa mostra que há, na obra, um grande número de poemas em que predomina a linguagem religiosa católica. Ocorre a expressão da alma feminina , marcada com orgulho pela poetisa. A autora cria prosodemas, inaugura neologismos ,aproveitando todos os processos de criação vocabular. Assim, a obra se notabiliza pelo aproveitamento da sonoridade das palavras, pela escolha lexical inédita, por uma estrutura frasal apositiva, evocativa, sucinta e nominal, não escravizada às regras do registro culto como padrão literário. A tese reconhece que a autora lida eficientemente com as classes de palavras, com a construção nominal e com uma estruturação sintática peculiar, em que sobressai a oração adjetiva com função de sujeito, apesar de conter verbo: a oração adjetiva subjetivada. A essência da pesquisa são os conjuntos metafóricos, verdadeiros modelos universais, que permitem reconhecer a possível existência de uma língua literária em português. No mesmo contexto, focaliza um grupo de poemas chamados de telegráficos, curtos e de teor filosófico. Tal qualidade metafórica mostra a importância da poetisa Adélia Prado para a articulação da língua literária em língua portuguesa

Normal structures and automorphism groups of t-designs

Combinatorial configurations known as t-designs are studied. These are pairs ˂B, ∏˃, where each element of B is a k-subset of ∏, and each t-design occurs in exactly λ elements of B, for some fixed integers k and λ. A theory of internal structure of t-designs is developed, and it is shown that any t-design can be decomposed in a natural fashion into a sequence of “simple” subdesigns. The theory is quite similar to the analysis of a group with respect to its normal subgroups, quotient groups, and homomorphisms. The analogous concepts of normal subdesigns, quotient designs, and design homomorphisms are all defined and used.

This structure theory is then applied to the class of t-designs whose automorphism groups are transitive on sets of t points. It is shown that if G is a permutation group transitive on sets of t letters and ф is any set of letters, then images of ф under G form a t-design whose parameters may be calculated from the group G. Such groups are discussed, especially for the case t = 2, and the normal structure of such designs is considered. Theorem 2.2.12 gives necessary and sufficient conditions for a t-design to be simple, purely in terms of the automorphism group of the design. Some constructions are given.

Finally, 2-designs with k = 3 and λ = 2 are considered in detail. These designs are first considered in general, with examples illustrating some of the configurations which can arise. Then an attempt is made to classify all such designs with an automorphism group transitive on pairs of points. Many cases are eliminated of reduced to combinations of Steiner triple systems. In the remaining cases, the simple designs are determined to consist of one infinite class and one exceptional case.

On statistical treatment of the results of parallel trails with special reference to fishery research

Parallel trials form a most important part of the technique of scientific experimentation. Such trials may be divided into two; categories. In the first the results are comparable measurements of one kind or another. In the second the data consist of records of the number of times a certain 'event' has occurred in the two sets of trials compared. Only trials of the second category are dealt with here. In this paper all the reliable methods of testing for significance the results of parallel trials of a certain type with special reference to fishery research are described fully. Some sections relate to exact, others to approximate tests. The only advantage in the use of the latter lies in the fact that they are often the more expeditious. Apart from this it is always preferable to use exact methods.

Feature Selection for Speech Emotion Recognition in Spanish and Basque: On the Use of Machine Learning to Improve Human-Computer Interaction

Study of emotions in human-computer interaction is a growing research area. This paper shows an attempt to select the most significant features for emotion recognition in spoken Basque and Spanish Languages using different methods for feature selection. RekEmozio database was used as the experimental data set. Several Machine Learning paradigms were used for the emotion classification task. Experiments were executed in three phases, using different sets of features as classification variables in each phase. Moreover, feature subset selection was applied at each phase in order to seek for the most relevant feature subset. The three phases approach was selected to check the validity of the proposed approach. Achieved results show that an instance-based learning algorithm using feature subset selection techniques based on evolutionary algorithms is the best Machine Learning paradigm in automatic emotion recognition, with all different feature sets, obtaining a mean of 80,05% emotion recognition rate in Basque and a 74,82% in Spanish. In order to check the goodness of the proposed process, a greedy searching approach (FSS-Forward) has been applied and a comparison between them is provided. Based on achieved results, a set of most relevant non-speaker dependent features is proposed for both languages and new perspectives are suggested.

The brine and gas content of sea ice with attention to low salinities and high temperatures

Based on the well known sea ice phase diagram, equations are derived for determining the brine and gas content of sea Ice for high temperatures (range 0 to -2 °C) and low salinities. The presently widely used equations of Cox and Weeks (1982) are valid only for temperatures below -2°C. Fresh-water ice is used as a boundary condition for the equations. The relative salt concentrations in brine are_assumed to be the same as in normal (or standard) seawater. Two sets of equations are presented: 1) accurate formulae based on UNESCO standard sea water equations, and 2) approximate formulae based on general properties of weak solutions. The approximate formulae are not essentially different from the classical system which basically assumes the freezing point to be a linear function of fractional salt content. The agreement between the two approaches is excellent and the approximate system is good enough for most applications.

Influence of Extracellular Matrix Components on the Expression of Integrins and Regeneration of Adult Retinal Ganglion Cells

Purpose Retinal ganglion cells (RGCs) are exposed to injury in a variety of optic nerve diseases including glaucoma. However, not all cells respond in the same way to damage and the capacity of individual RGCs to survive or regenerate is variable. In order to elucidate factors that may be important for RGC survival and regeneration we have focussed on the extracellular matrix (ECM) and RGC integrin expression. Our specific questions were: (1) Do adult RGCs express particular sets of integrins in vitro and in vivo? (2) Can the nature of the ECM influence the expression of different integrins? (3) Can the nature of the ECM affect the survival of the cells and the length or branching complexity of their neurites? Methods Primary RGC cultures from adult rat retina were placed on glass coverslips treated with different substrates: Poly-L-Lysine (PL), or PL plus laminin (L), collagen I (CI), collagen IV (CIV) or fibronectin (F). After 10 days in culture, we performed double immunostaining with an antibody against beta III-Tubulin to identify the RGCs, and antibodies against the integrin subunits: alpha V, alpha 1, alpha 3, alpha 5, beta 1 or beta 3. The number of adhering and surviving cells, the number and length of the neurites and the expression of the integrin subunits on the different substrates were analysed. Results PL and L were associated with the greatest survival of RGCs while CI provided the least favourable conditions. The type of substrate affected the number and length of neurites. L stimulated the longest growth. We found at least three different types of RGCs in terms of their capacity to regenerate and extend neurites. The different combinations of integrins expressed by the cells growing on different substrata suggest that RGCs expressed predominantly alpha 1 beta 1 or alpha 3 beta 1 on L, alpha 1 beta 1 on CI and CIV, and alpha 5 beta 3 on F. The activity of the integrins was demonstrated by the phosphorylation of focal adhesion kinase (FAK). Conclusions Adult rat RGCs can survive and grow in the presence of different ECM tested. Further studies should be done to elucidate the different molecular characteristics of the RGCs subtypes in order to understand the possible different sensitivity of different RGCs to damage in diseases like glaucoma in which not all RGCs die at the same time.

Population parameters of small pelagic fishes caught off Tawi-Tawi, Philippines

Growth and mortality parameters, exploitation rates and annual recruitment patterns were estimated from monthly length-frequency samples for Sardinella longiceps, S. fimbriata, S. Albella, Decapterus macrosoma, Dipterygonatus balteatus, Rastrelliger faughni and Encrasicolina heteroloba. These results provide the first sets of stock parameter estimates for these species off Tawi-Tawi, Philippines. The growth parameters derived were found comparable with previous estimates available for the same species from other localities. Recruitment was noted to be year-round and bimodal. Estimates of fishing mortality and exploitation rate were found to be presently above appropriate levels.

Length-weight relationships of Cuban marine fishes

A total of 140 sets of parameters (a and b) of the length-weight relationships (LWR) of the form W=aL super(b) are presented for fishes caught in Cuban waters. These parameters cover 94 species of fish belonging to 43 families. Most of the parameters were compiled from 107 sets of published and unpublished studies. Twenty-five sets of parameters were from personal communications through colleagues in Cuba, while the remaining eight sets were estimated by the authors from unpublished data.

Vital statistics of marine fishes of Vanuatu

Vital statistics are presented for 38 marine species of Vanuatu based on previous studies conducted in the area, with parameters describing growth (6 species, 13 sets of parameters), mortality (estimates of M for 6 species), length-weight relationship (32 species), and reproduction (length at first maturity for 26 species, months of reproduction for 18 species). The species covered belong mainly to the family Lutjanidae.

Growth, mortality and recruitment of Nile perch Lates niloticus (L. Centropomidae) in the Nyanza Gulf of Lake Victoria: an evaluation update

A reassessment of the estimates of growth, mortality and recruitment patterns of Nile Perch, Lates niloticus was made based on data from commercial landings collected during the Catch Assessment Survey Programme. Two sets of length frequency data, one each from beach seining and hook and line fisheries, were analyzed. Values of L8 = 169 and 230 (cm TL) and K= 0.18 yr-1 and 0.195 yr-1 were obtained. The total mortality estimates from the catch curve analysis were Z = 0.72 yr-1 and 0.94 yr-1, respectively, with a natural mortality M of about 0.35 for a mean environmental temperature of 27oC. The highest peak for recruitment was in November, December and January with a minor one in June, indicating recruitment of two cohorts per year. These results are discussed and compared to previously available information on L. niloticus in Lake Victoria.