Baltasar Trancón y Widemann

Characterising flow patterns in soils by feature extraction and multiple consensus clustering

Abstract The quality of surface water and groundwater is closely related to flow paths in the vadose zone. Therefore, dye tracer studies are often carried out to visualise flow patterns in soils. These experiments provide images of stained soil profiles and their evaluation demands knowledge in hydrology as well as in image analysis and statistics. The classical analysis consists of image classification in stained and non-stained parts and calculation of the dye coverage (i.e. the proportion of staining). The variation of this quantity with depth is interpreted to identify dominant flow types. While some feature extraction from images of dye-stained profiles is necessary, restricting the analysis to the dye coverage alone might miss important information. In our study we propose to use several index functions to extract different (ideally complementary) features. We associate each image row with a feature vector (i.e. a certain number of image function values) and use these features to cluster the image rows to identify similar image areas. Because images of stained profiles might have different reasonable clusterings, we calculate multiple consensus clusterings. Experts can explore these different solutions and base their interpretation of predominant flow type on quantitative (objective) criteria.

Paisley: pattern matching à la carte

Professional development of software dealing with structured models requires more systematic approach and semantic foundations than standard practice in general-purpose programming languages affords. One remedy is to move to domain-specific environments. Here, instead, we present a tool for the implementation of pattern matching as fundamental means of automated data extraction from complex models in a general-purpose programming language. The interface is simple but, thanks to elaborate and rigorous design, is also light-weight, portable, non-invasive, type-safe, modular and extensible. It is compatible with object-oriented data abstraction and has full support for nondeterminism by backtracking. The tool comes as a library consisting of two levels: elementary pattern constructs (generic, highly reusable) and pattern bindings for particular data models (specific, fairly reusable, user-definable). Applications use the library code in a small number of idiomatic ways, making pattern-matching code declarative in style (yet retaining richer host-language semantics), easily writable, readable and maintainable. Library and idiom together form a tightly embedded domain-specific language; no extension of the host language is required. The current implementation is in Java, but assumes only standard object-oriented features, and can hence be ported to other mainstream languages.

Applications of Algebra and Coalgebra in Scientific Modelling

In computer science, the algebra-coalgebra duality serves as a formal framework for connecting the perspectives of state-based and behavior-based models. In other sciences such as ecology, these perspectives are seemingly harder to reconcile. We explore modelling paradigms, in the sense of philosophy of science, as an intermediate step in translating the (co)algebraic framework from computer science into applications in ecology. We illustrate the application potential of this approach with a simple model from theoretical ecology: the logistic map. Several versions of algebraic models with progressively more sophisticated carriers and operations are introduced and finally contrasted with a corresponding coalgebraic model. We illustrate two modelling paradigms with these examples. Only one of these has traditionally been used in ecology. The second one, which is based on a coalgebraic dualisation, offers new modelling perspectives in ecology and environmental science.

The shepard tone and higher-order multi-rate synchronous data-flow programming in Sig

The total functional real-time data-flow programming language Sig features a core layer with elegant denotational semantics, in terms of Mealy stream transducers and coiterative causal stream functions, that is convenient for domain experts in the primary application domains, such as scientific modeling and digital music and event arts. The core suffices for the implementation of many basic signal processing components. For the expression of more sophisticated computations, a second layer of Sig provides additional features, namely higher-order functional programming and multi-rate synchronicity, reducible by transformational semantics to the core layer. Here we describe the design of the upper layer of Sig and demonstrate its usage with the Shepard Tone, a well-known sound synthesis problem and model of psycho-acoustically paradoxical perception of relative musical pitch.

Foundations of Total Functional Data-Flow Programming

The field of declarative stream programming (discrete time, clocked synchronous, modular, data-centric) is divided between the data-flow graph paradigm favored by domain experts, and the functional reactive paradigm favored by academics. In this paper, we describe the foundations of a framework for unifying functional and data-flow styles that differs from FRP proper in significant ways: It is based on set theory to match the expectations of domain experts, and the two paradigms are reduced symmetrically to a low-level middle ground, with strongly compositional semantics. The design of the framework is derived from mathematical first principles, in particular coalgebraic coinduction and a standard relational model of stateful computation. The abstract syntax and semantics introduced here constitute the full core of a novel stream programming language.

Distributive-law semantics for cellular automata and agent-based models

We present an effort to give formal semantics to the popular but theoretically rather unreflected scientific modelling paradigm of agent- or individual-based models. To this end, we give a generic formalization of two-dimensional cellular automata with flexible topology as the abstract basis of such models. The semantic approach of structural operational semantics a la Turi and Plotkin [7], based on bialgebras and distributive laws, leads in this case to a natural separation of the concerns of spatial structure, temporal behavior and local interaction. We give a generic distributive law for local behavior of automata and prove the equivalence to a more traditional, array-based formalization.

On-Line Synchronous Total Purely Functional Data-Flow Programming on the Java Virtual Machine with Sig

Sig is the prototype of a purely declarative programming language and system for the processing of discrete, clocked synchronous, potentially real-time data streams. It aspires to combine good static safety, scalability and platform independence, with semantics that are precise, concise and suitable for domain experts. Its semantical and operational core has been formalized. Here we discuss the general strategy for making Sig programs executable, and describe the current state of a prototype compiler. The compiler is implemented in Java and targets the JVM. By careful cooperation with the JVM just-in-time compiler, it provides immediate executability in a simple and quickly extensible runtime environment, with code performance suitable for moderate real-time applications such as interactive audio synthesis.

Image analysis for soil dye tracer infiltration studies

Flow processes in soils are closely related to groundwater quality often affected by human activities. Because hydrological models usually lack explanatory power, direct visualization of flow paths in dye tracer infiltration studies has become a standard tool in soil hydrology. These experiments provide images of dye-stained paths in soils and help evaluating the vulnerability or understanding the general hydrological functioning of a given site. Extracting relevant information demands expertise in hydrology as well as in image analysis and statistics. To our knowledge, no agreed and effective method to analyze large collections of such images exists in the soil hydrology community. In this paper we propose a general framework consisting of index functions and visual tools to support the expert in his/her evaluation of dye tracer infiltration images.

Laminar Data Flow: On the Role of Slicing in Functional Data-Flow Programming

We use the concept of laminar flow, as opposed to turbulent flow, as a metaphor for the decomposition of well-behaved purely functional data-flow programs into largely independent parts, necessitated by aspects with different execution constraints. In the context of the total functional data-flow language Sig, we identify three distinct but methodologically related implementation challenges, namely multi-rate scheduling, declarative initialization, and conditional execution, and demonstrate how they can be solved orthogonally, by decomposition using the standard program transformation technique, slicing.

[Demo abstract] Sound and soundness: practical total functional data-flow programming

The field of declarative data-stream programming (discrete time, clocked synchronous, compositional, data-centric) is divided between the visual data-flow graph paradigm favored by domain experts, the functional reactive paradigm favored by academics, and the synchronous paradigm favored by developers of low-level systems. Each approach has its particular theoretical and practical merits and target audience. The programming language Sig has been designed to unify the underlying paradigms in a novel way. The natural expressivity of visual approaches is combined with the support for concise pattern-based symbolic computation of functional programming, and the rigorous, elementary semantical foundation of synchronous approaches. Here we demonstrate the current state of implementation of the Sig system by means of example programs that realize typical components of digital sound synthesis.