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.

Otto Kelland’s Model Dories and the Digital Archives Initiative

Otto Kelland was a truly unique individual in Newfoundland. During his long life he had several careers from being a prison superintendant to being an instructor at Marine Institute. During his life Kelland made hundreds of wooden boat models. They are beautifuly hand-crafted and represented the type of watercraft used by fishermen in Newfoundland. The collection of boat models made by Otto Kelland and owned by Marine Institute made an ideal object to be digitalized. In particular the collection of dories was an ideal group to be digitized. They were housed in one cabinet and accompanied by hand-written documents describing each model. The Digital Archives Initiative (DAI) is a “gateway to the learning and research-based cultural resources held by Memorial University of Newfoundland and partnering organizations.” The DAI hosts a variety of collections which together reinforce the importance, past and present, of Newfoundland and Labrador's history and culture. I will give an oral presentation of the project followed by a demonstration of the Otto Kelland Dories exhibit on the Digital Archives Initiative (DAI) at Memorial University of Newfoundland. I will be happy to answer questions following my presentation.

Change in degree of coherence of partially coherent electromagnetic beams propagating through atmospheric turbulence

We study the change in the degree of coherence of partially coherent electromagnetic beam (so called electromagnetic Gaussian Schell-model beam). It is shown analytically that with a fixed set of source parameters and under a particular atmospheric turbulence model, an electromagnetic Gaussian Schell-model beam propagating through atmospheric turbulence reaches its maximum value of coherence after the beam propagates a particular distance, and the effective width of the spectral degree of coherence also has its maximum value. This phenomenon is independent of the used turbulence model. The results are illustrated by numerical curves. (c) 2006 Elsevier B.V. All rights reserved.

Formal languages, part theory, and change

A general definition of interpreted formal language is presented. The notion “is a part of" is formally developed and models of the resulting part theory are used as universes of discourse of the formal languages. It is shown that certain Boolean algebras are models of part theory.

With this development, the structure imposed upon the universe of discourse by a formal language is characterized by a group of automorphisms of the model of part theory. If the model of part theory is thought of as a static world, the automorphisms become the changes which take place in the world. Using this formalism, we discuss a notion of abstraction and the concept of definability. A Galois connection between the groups characterizing formal languages and a language-like closure over the groups is determined.

It is shown that a set theory can be developed within models of part theory such that certain strong formal languages can be said to determine their own set theory. This development is such that for a given formal language whose universe of discourse is a model of part theory, a set theory can be imbedded as a submodel of part theory so that the formal language has parts which are sets as its discursive entities.

Structure-change-dependent transmittance of PtOx thin film in super-resolution near-field structure: Diffraction effect analysis

To study working mechanism of super-resolution near-field structure (super-RENS) optical disk from a far-field optics view is very necessary because of the actual far-field writing/readout process in the optical disk system. A Gaussian diffraction model based on Fresnel-Kirchhoff diffraction theory of PtOx-type super-RENS has been set up in this Letter. The relationship between micro-structural deformation (change of bubble structure and refractive index profile) with far-field optical response of PtOx thin film has been studied with it in detail. The simulation results are in good agreement with the experimental results reported in literatures with a designed configuration. These results may provide more quantitative information for better understanding of the working mechanism of metal-oxide-type super-RENS. (c) 2007 Elsevier B.V. All rights reserved.

Laser pulse induced bumps in chalcogenide phase change films

Formation of bumps in chalcogenide phase change thin films during the laser writing process is theoretically and experimentally investigated. The process involves basically fast heating and quenching stages. Circular bumps are formed after cooling, and the shape and size of the bumps depend on various parameters such as temperatures, laser power, beam size, laser pulse duration, etc. In extreme cases, holes are formed at the apex of the bumps. To understand the bumps and their formation is of great interest for data storage. In the present work, a theoretical model is established for the formation process, and the geometric characters of the formed bumps can be analytically and quantitatively evaluated from various parameters involved in the formation. Simulations based on the analytic solution are carried out taking Ag8In14Sb55Te23 as an example. The results are verified with experimental observations of the bumps. (C) 2008 American Institute of Physics.

Self-Organized Criticality, Plasticity and Sensorimotor Coupling. Explorations with a Neurorobotic Model in a Behavioural Preference Task

During the last two decades, analysis of 1/f noise in cognitive science has led to a considerable progress in the way we understand the organization of our mental life. However, there is still a lack of specific models providing explanations of how 1/f noise is generated in coupled brain-body-environment systems, since existing models and experiments typically target either externally observable behaviour or isolated neuronal systems but do not address the interplay between neuronal mechanisms and sensorimotor dynamics. We present a conceptual model of a minimal neurorobotic agent solving a behavioural task that makes it possible to relate mechanistic (neurodynamic) and behavioural levels of description. The model consists of a simulated robot controlled by a network of Kuramoto oscillators with homeostatic plasticity and the ability to develop behavioural preferences mediated by sensorimotor patterns. With only three oscillators, this simple model displays self-organized criticality in the form of robust 1/f noise and a wide multifractal spectrum. We show that the emergence of self-organized criticality and 1/f noise in our model is the result of three simultaneous conditions: a) non-linear interaction dynamics capable of generating stable collective patterns, b) internal plastic mechanisms modulating the sensorimotor flows, and c) strong sensorimotor coupling with the environment that induces transient metastable neurodynamic regimes. We carry out a number of experiments to show that both synaptic plasticity and strong sensorimotor coupling play a necessary role, as constituents of self-organized criticality, in the generation of 1/f noise. The experiments also shown to be useful to test the robustness of 1/f scaling comparing the results of different techniques. We finally discuss the role of conceptual models as mediators between nomothetic and mechanistic models and how they can inform future experimental research where self-organized critically includes sensorimotor coupling among the essential interaction-dominant process giving rise to 1/f noise.

A narrativa na e sobre a clínica na atenção primária: uma reflexão sobre o modo pensar e agir dirigido ao diálogo, à integralidade e ao cuidado em saúde

A incorporação do sujeito que adoece e suas expectativas de cuidado é um apelo que acompanha as propostas de mudança da prática clínica no campo da APS. Esta perspectiva implica em um novo modo de ver o processo de adoecimento que procura romper com o reducionismo biomédico onde a clínica e sua ação são, praticamente, independentes do discurso do paciente. Este trabalho usou a narrativa, aplicada como uma ferramenta conceitual e prática na clínica na APS, para investigar as possibilidades de ampliar o universo discursivo e interpretativo, isto é, a competência narrativa do médico, para além de um modelo biomédico restritivo. Foi realizada uma busca, não sistemática, na literatura médica e de ciências sociais procurando identificar os aspectos conceituais, significados e perspectivas que podem ser assumidos para substantivar a narrativa como um conceito/idéia e suas possíveis interfaces e aplicações na clínica. Esta apropriação da narrativa instrumentalizou a observação participante nos módulos do Programa Médico de Família de Niterói, assim como a realização e análise dos resultados de entrevistas semi-estruturadas com seus médicos. Observou-se que a formação da identidade e da legitimidade profissionais do médico de família é dirigida, principalmente, pelo arranjo organizacional promovido pelo modelo de atenção e não pelo desenvolvimento de um saber que o diferencie e qualifique. Identificou-se que as capacidades dialógicas desenvolvidas nas experiências com a clínica na APS eram compreendidas e assumidas pelos médicos como habilidades pessoais e/ou como aspectos morais. Percebeu-se que este modo de pensar dá margem a uma tensão, externada por um discurso ambíguo e fragmentado, entre a proximidade, o vínculo e o diálogo com o paciente e a estruturação do saber e da prática clínica. A limitação dos médicos em incorporar novos saberes a partir de suas vivências, associada à forma como a racionalidade biomédica dirige a clínica, se constituem como obstáculos epistemológicos e práticos para a ampliação da competência narrativa e interpretativa médica. Estas são condições que dificultam o desenvolvimento de um estilo de pensamento médico que reflita, desenvolva e integre o saber prático e os saberes não biomédicos como algo legítimo, sistematizável, avaliável e reprodutível no âmbito da clínica.

Estimates of body sizes at maturation and at sex change, and the spawning seasonality and sex ratio of the endemic Hawaiian grouper (Hyporthodus quernus, F. Epinephelidae)

A case study of the reproductive biology of the endemic Hawaiian grouper or hapu’upu’u (Hyporthodus quernus) is presented as a model for comprehensive future studies of economically important epinephelid groupers. Specimens were collected throughout multiple years (1978–81, 1992–93, and 2005–08) from most reefs and banks of the Northwestern Hawaiian Islands. The absence of small males, presence of atretic oocytes and brown bodies in testes of mature males, and both developed ovarian and testicular tissues in the gonads of five transitional fish provided evidence of protogynous hermaphroditism. No small mature males were collected, indicating that Hawaiian grouper are monandrous (all males are sex-changed females). Complementary microscopic criteria also were used to assign reproductive stage and estimate median body sizes (L50) at female sexual maturity and at adult sex change from female to male. The L50 at maturation and at sex change was 580 ±8 (95% confidence interval [CI]) mm total length (TL) and 895 ±20 mm TL, respectively. The adult sex ratio was strongly female biased (6:1). Spawning seasonality was described by using gonadosomatic indices. Females began ripening in the fall and remained ripe through April. A February–June main spawning period that followed peak ripening was deduced from the proportion of females whose ovaries contained hydrated oocytes, postovulatory follicles, or both. Testes weights were not affected by season; average testes weight was only about 0.2% of body weight—an order of magnitude smaller than that for ovaries that peaked at 1–3% of body weight. The species’ reproductive life history is discussed in relation to its management.

Interdecadal change in growth of sablefish (Anoplopoma fimbria) in the northeast Pacific Ocean

Errors in growth estimates can affect drastically the spawner-perrecruit threshold used to recommend quotas for commercial fish catches. Growth parameters for sablefish (Anoplopoma fimbria) in Alaska have not been updated for stock assessment purposes for more than 20 years, although aging of sablefish has continued. In this study, length-stratified data (1981–93 data from the annual longline survey conducted cooperatively by the Fisheries Agency of Japan and the Alaska Fisheries Science Center of the National Marine Fisheries Service) were updated and corrected for discovered sampling bias. In addition, more recent, randomly collected samples (1996–2004 data from the annual longline survey conducted by the Alaska Fisheries Science Center) were analyzed and new length-at-age and weight-at-age parameters were estimated. Results were similar between this analysis with length-at-age data from 1981 to 2004 and analysis with updated longline survey data through 2010; therefore, we used our initial results from analysis done with data through 2004. We found that, because of a stratified sampling scheme, growth estimates of sablefish were overestimated with the older data (1981–93), and growth parameters used in the Alaskan sablefish assessment model were, thus, too large. In addition, a comparison of the bias-corrected 1981–93 data and the 1996–2004 data showed that, in more recent years, sablefish grew larger and growth differed among regions. The updated growth information improves the fit of the data to the sablefish stock assessment model with biologically reasonable results. These findings indicate that when the updated growth data (1996–2004) are used in the existing sablefish assessment model, estimates of fishing mortality increase slightly and estimates of female spawning biomass decrease slightly. This study provides evidence of the importance of periodically revisiting biological parameter estimates, especially as data accumulate, because the addition of more recent data often will be more biologically realistic. In addition, it exemplifies the importance of correcting biases from sampling that may contribute to erroneous parameter estimates.

Sex-change rules, stock dynamics, and the performance of spawning-per-recruit measures in protogynous stocks

Predicting and under-standing the dynamics of a population requires knowledge of vital rates such as survival, growth, and reproduction. However, these variables are influenced by individual behavior, and when managing exploited populations, it is now generally realized that knowledge of a species’ behavior and life history strategies is required. However, predicting and understanding a response to novel conditions—such as increased fishing-induced mortality, changes in environmental conditions, or specific management strategies—also require knowing the endogenous or exogenous cues that induce phenotypic changes and knowing whether these behaviors and life history patterns are plastic. Although a wide variety of patterns of sex change have been observed in the wild, it is not known how the specific sex-change rule and cues that induce sex change affect stock dynamics. Using an individual based model, we examined the effect of the sex-change rule on the predicted stock dynamics, the effect of mating group size, and the performance of traditional spawning-per-recruit (SPR) measures in a protogynous stock. We considered four different patterns of sex change in which the probability of sex change is determined by 1) the absolute size of the individual, 2) the relative length of individuals at the mating site, 3) the frequency of smaller individuals at the mating site, and 4) expected reproductive success. All four pat-terns of sex change have distinct stock dynamics. Although each sex-change rule leads to the prediction that the stock will be sensitive to the size-selective fishing pattern and may crash if too many reproductive size classes are fished, the performance of traditional spawning-per-recruit measures, the fishing pattern that leads to the greatest yield, and the effect of mating group size all differ distinctly for the four sex-change rules. These results indicate that the management of individual species requires knowledge of whether sex change occurs, as well as an understanding of the endogenous or exogenous cues that induce sex change.

Toward a Model for Fisheries Social Impact Assessment

This paper presents a model for Fisheries Social Impact Assessment (SIA) that lays the groundwork for development of fisheries-focused, quantitative social assessments with a clear conceptual model. The usefulness of current fisheries SIA’s has been called into question by some as incompatible with approaches taken by fisheries biologists and economists when assessing potential effects of management actions. Our model’s approach is closer to the economists’ and biologists’ assessments and is therefore more useful for Fishery Management Council members. The paper was developed by anthropologists initially brought together in 2004 for an SIA Modeling Workshop by the National Marine Fisheries Service, NOAA. Opinions and conclusions expressed or implied are solely those of the authors and do not necessarily reflect the views or policy of the National Marine Fisheries Service, NOAA.

Implications of using On-Farm Flood Flow Capture to recharge groundwater and mitigate flood risks along the Kings River, CA

Two large hydrologic issues face the Kings Basin, severe and chronic overdraft of about 0.16M ac-ft annually, and flood risks along the Kings River and the downstream San Joaquin River. Since 1983, these floods have caused over $1B in damage in today’s dollars. Capturing flood flows of sufficient volume could help address these two pressing issues which are relevant to many regions of the Central Valley and will only be exacerbated with climate change. However, the Kings River has high variability associated with flow magnitudes which suggests that standard engineering approaches and acquisition of sufficient acreage through purchase and easements to capture and recharge flood waters would not be cost effective. An alternative approach investigated in this study, termed On-Farm Flood Flow Capture, involved leveraging large areas of private farmland to capture flood flows for both direct and in lieu recharge. This study investigated the technical and logistical feasibility of best management practices (BMPs) associated with On-Farm Flood Flow Capture. The investigation was conducted near Helm, CA, about 20 miles west of Fresno, CA. The experimental design identified a coordinated plan to determine infiltration rates for different soil series and different crops; develop a water budget for water applied throughout the program and estimate direct and in lieu recharge; provide a preliminary assessment of potential water quality impacts; assess logistical issues associated with implementation; and provide an economic summary of the program. At check locations, we measured average infiltration rates of 4.2 in/d for all fields and noted that infiltration rates decreased asymptotically over time to about 2 – 2.5 in/d. Rates did not differ significantly between the different crops and soils tested, but were found to be about an order of magnitude higher in one field. At a 2.5 in/d infiltration rate, 100 acres are required to infiltrate 10 CFS of captured flood flows. Water quality of applied flood flows from the Kings River had concentrations of COC (constituents of concern; i.e. nitrate, electrical conductivity or EC, phosphate, ammonium, total dissolved solids or TDS) one order of magnitude or more lower than for pumped groundwater at Terranova Ranch and similarly for a broader survey of regional groundwater. Applied flood flows flushed the root zone and upper vadose zone of nitrate and salts, leading to much lower EC and nitrate concentrations to a depth of 8 feet when compared to fields in which more limited flood flows were applied or for which drip irrigation with groundwater was the sole water source. In demonstrating this technology on the farm, approximately 3,100 ac-ft was diverted, primarily from April through mid-July, with about 70% towards in lieu and 30% towards direct recharge. Substantial flood flow volumes were applied to alfalfa, wine grapes and pistachio fields. A subset of those fields, primarily wine grapes and pistachios, were used primarily to demonstrate direct recharge. For those fields about 50 – 75% of water applied was calculated going to direct recharge. Data from the check studies suggests more flood flows could have been applied and infiltrated, effectively driving up the amount of water towards direct recharge. Costs to capture flood flows for in lieu and direct recharge for this project were low compared to recharge costs for other nearby systems and in comparison to irrigating with groundwater. Moreover, the potentially high flood capture capacity of this project suggests significant flood avoidance costs savings to downstream communities along the Kings and San Joaquin Rivers. Our analyses for Terranova Ranch suggest that allocating 25% or more flood flow water towards in lieu recharge and the rest toward direct recharge will result in an economically sustainable recharge approach paid through savings from reduced groundwater pumping. Two important issues need further consideration. First, these practices are likely to leach legacy salts and nitrates from the unsaturated zone into groundwater. We develop a conceptual model of EC movement through the unsaturated zone and estimated through mass balance calculations that approximately 10 kilograms per square meter of salts will be flushed into the groundwater through displacing 12 cubic meters per square meter of unsaturated zone pore water. This flux would increase groundwater salinity but an equivalent amount of water added subsequently is predicted as needed to return to current groundwater salinity levels. All subsequent flood flow capture and recharge is expected to further decrease groundwater salinity levels. Second, the project identified important farm-scale logistical issues including irrigator training; developing cropping plans to integrate farming and recharge activities; upgrading conveyance; and quantifying results. Regional logistical issues also exist related to conveyance, integration with agricultural management, economics, required acreage and Operation and Maintenance (O&M).

Hydrodynamic interaction of two unsteady model microorganisms.

The study of pair-wise interactions between swimming microorganisms is fundamental to the understanding of the rheological and transport properties of semi-dilute suspensions. In this paper, the hydrodynamic interaction of two ciliated microorganisms is investigated numerically using a boundary-element method, and the microorganisms are modeled as spherical squirmers that swim by time-dependent surface deformations. The results show that the inclusion of the unsteady terms in the ciliary propulsion model has a large impact on the trajectories of the interacting cells, and causes a significant change in scattering angles with potential important consequences on the diffusion properties of semi-dilute suspensions. Furthermore, the analysis of the shear stress acting on the surface of the microorganisms revealed that the duration and the intensity of the near-field interaction are significantly modified by the presence of unsteadiness. This observation may account for the hydrodynamic nature of randomness in some biological reactions, and supersedes the distinction between intrinsic randomness and hydrodynamic interactions, adding a further element to the understanding and modeling of interacting microorganisms.

Material model of lung parenchyma based on living precision-cut lung slice testing.

We describe a novel constitutive model of lung parenchyma, which can be used for continuum mechanics based predictive simulations. To develop this model, we experimentally determined the nonlinear material behavior of rat lung parenchyma. This was achieved via uni-axial tension tests on living precision-cut rat lung slices. The resulting force-displacement curves were then used as inputs for an inverse analysis. The Levenberg-Marquardt algorithm was utilized to optimize the material parameters of combinations and recombinations of established strain-energy density functions (SEFs). Comparing the best-fits of the tested SEFs we found Wpar = 4.1 kPa(I1-3)2 + 20.7 kPa(I1 - 3)3 + 4.1 kPa(-2 ln J + J2 - 1) to be the optimal constitutive model. This SEF consists of three summands: the first can be interpreted as the contribution of the elastin fibers and the ground substance, the second as the contribution of the collagen fibers while the third controls the volumetric change. The presented approach will help to model the behavior of the pulmonary parenchyma and to quantify the strains and stresses during ventilation.