Searching the space of representations: reasoning through transformations for mathematical problem solving

The role of representation in reasoning has been long and widely regarded as crucial. It has remained one of the fundamental considerations in the design of information-processing systems and, in particular, for computer systems that reason. However, the process of change and choice of representation has struggled to achieve a status as a task for the systems themselves. Instead, it has mostly remained a responsibility for the human designers and programmers. Many mathematical problems have the characteristic of being easy to solve only after a unique choice of representation has been made. In this thesis we examine two classes of problems in discrete mathematics which follow this pattern, in the light of automated and interactive mechanical theorem provers. We present a general notion of structural transformation, which accounts for the changes of representation seen in such problems, and link this notion to the existing Transfer mechanism in the interactive theorem prover Isabelle/HOL. We present our mechanisation in Isabelle/HOL of some specific transformations identified as key in the solutions of the aforementioned mathematical problems. Furthermore, we present some tools that we developed to extend the functionalities of the Transfer mechanism, designed with the specific purpose of searching efficiently the space of representations using our set of transformations. We describe some experiments that we carried out using these tools, and analyse these results in terms of how close the tools lead us to a solution, and how desirable these solutions are. The thorough qualitative analysis we present in this thesis reveals some promise as well as some challenges for the far-reaching problem of representation in reasoning, and the automation of the processes of change and choice of representation

Potential implications of coronary artery calcium testing for guiding aspirin use among asymptomatic individuals with diabetes.

ObjectiveIt is unclear whether coronary artery calcium (CAC) is effective for risk stratifying patients with diabetes in whom treatment decisions are uncertain.Research design and methodsOf 44,052 asymptomatic individuals referred for CAC testing, we studied 2,384 individuals with diabetes. Subjects were followed for a mean of 5.6 ± 2.6 years for the end point of all-cause mortality.ResultsThere were 162 deaths (6.8%) in the population. CAC was a strong predictor of mortality across age-groups (age <50, 50-59, ≥60), sex, and risk factor burden (0 vs. ≥1 additional risk factor). In individuals without a clear indication for aspirin per current guidelines, CAC stratified risk, identifying patients above and below the 10% risk threshold of presumed aspirin benefit.ConclusionsCAC can help risk stratify individuals with diabetes and may aid in selection of patients who may benefit from therapies such as low-dose aspirin for primary prevention

Automating Change of Representation for Proofs in Discrete Mathematics (Extended Version)

Representation determines how we can reason about a specific problem. Sometimes one representation helps us find a proof more easily than others. Most current automated reasoning tools focus on reasoning within one representation. There is, therefore, a need for the development of better tools to mechanise and automate formal and logically sound changes of representation. In this paper we look at examples of representational transformations in discrete mathematics, and show how we have used Isabelle's Transfer tool to automate the use of these transformations in proofs. We give a brief overview of a general theory of transformations that we consider appropriate for thinking about the matter, and we explain how it relates to the Transfer package. We show our progress towards developing a general tactic that incorporates the automatic search for representation within the proving process

Cognitive analysis for representation change

The rep2rep project is developing an AI tool to automatically select an appropriate representation to solve a particular problem for a particular person. A prerequisite of this tool is to understand (i.e., model) how a reader interprets a representation. But interpretations can vary wildly between novices and experts, readers of similar ability, or even the same reader in different tasks. We present a theory and notation (RIST and RISN) for analysing the cognitive features of a representation's interpretation, and introduce a web app to construct RISN models. These models provide information about cognitive properties of representations to guide automated representation selection to support human problem solving

Oruga: an avatar of representational systems theory

Humans use representations flexibly. We draw diagrams, change representations and exploit creative analogies across different domains. We want to harness this kind of power and endow machines with it to make them more compatible with human use. Previously we developed Representational Systems Theory (RST) to study the structure and transformations of representations [1, 2]. In this paper we present Oruga (caterpillar in Spanish; a symbol of transformation), an implementation of various aspects of RST. Oruga consists of a core of data structures corresponding to concepts in RST, a language for communicating with the core, and an engine for producing transformations using a method we call structure transfer. In this paper we present an overview of the core and language of Oruga, with a brief example of the kind of transformation that structure transfer can execute

Reduced functional measure of cardiovascular reserve predicts admission to critical care unit following kidney transplantation

Background: There is currently no effective preoperative assessment for patients undergoing kidney transplantation that is able to identify those at high perioperative risk requiring admission to critical care unit (CCU). We sought to determine if functional measures of cardiovascular reserve, in particular the anaerobic threshold (VO2AT) could identify these patients. Methods: Adult patients were assessed within 4 weeks prior to kidney transplantation in a University hospital with a 37-bed CCU, between April 2010 and June 2012. Cardiopulmonary exercise testing (CPET), echocardiography and arterial applanation tonometry were performed. Results: There were 70 participants (age 41.7614.5 years, 60% male, 91.4% living donor kidney recipients, 23.4% were desensitized). 14 patients (20%) required escalation of care from the ward to CCU following transplantation. Reduced anaerobic threshold (VO2AT) was the most significant predictor, independently (OR = 0.43; 95% CI 0.27–0.68; p,0.001) and in the multivariate logistic regression analysis (adjusted OR = 0.26; 95% CI 0.12–0.59; p = 0.001). The area under the receiveroperating- characteristic curve was 0.93, based on a risk prediction model that incorporated VO2AT, body mass index and desensitization status. Neither echocardiographic nor measures of aortic compliance were significantly associated with CCU admission. Conclusions: To our knowledge, this is the first prospective observational study to demonstrate the usefulness of CPET as a preoperative risk stratification tool for patients undergoing kidney transplantation. The study suggests that VO2AT has the potential to predict perioperative morbidity in kidney transplant recipients

BariSurg trial: Sleeve gastrectomy versus Roux-en-Y gastric bypass in obese patients with BMI 35–60 kg/m2 – a multi-centre randomized patient and observer blind non-inferiority trial

Background: Roux-en-Ygastric bypass (RYGB) and sleeve gastrectomy (SG) rank among the most frequently applied bariatric procedures worldwide due to their positive risk/benefit correlation. A systematic review revealed a similar excess weight loss (EWL) 2 years postoperatively between SG and RYGB. However, there is a lack of randomized controlled multi-centre trials comparing SG and RYGB, not only concerning EWL, but also in terms of remission of obesity-related co-morbidities, gastroesophageal reflux disease (GERD) and quality of life (QoL) in the mid- and long-term. Methods: The BariSurg trial was designed as a multi-centre, randomized controlled patient and observer blind trial. The trial protocol was approved by the corresponding ethics committees of the centres. To demonstrate EWL non-inferiority of SG compared to RYGB, power calculation was performed according to a non-inferiority study design. Morbidity, mortality, remission of obesity-related co-morbidities, GERD course and QoL are major secondary endpoints. 248 patients between 18 and 70 years, with a body mass index (BMI) between 35–60 kg/m2 and indication for bariatric surgery according to the most recent German S3-guidelines will be randomized. The primary and secondary endpoints will be assessed prior to surgery and afterwards at discharge and at the time points 3–6, 12, 24, 36, 48 and 60 months postoperatively. Discussion: With its five year follow-up, the BariSurg-trial will provide further evidence based data concerning the impact of SG and RYGB on EWL, remission of obesity-related co-morbidities, the course of GERD and QoL. Trial registration: The trial protocol has been registered in the German Clinical Trials Register DRKS0000476

LOCALIZACIÓN DE ROEDORES EN PRUEBAS DE CAMPO ABIERTO

ResumenEstudiar el comportamiento de roedores (ratas) es de suma utilidad para detectar diversas afectaciones que éstos puedan presentar así como determinar cambios en sus comportamientos. Una prueba importante realizada es la de campo abierto, la cual consiste en una caja marcada en el fondo en nueve regiones cuadradas, donde se coloca al roedor y se observan diversos comportamientos, lo que permite identificar cambios en los mismos. Para realizar anotaciones es preciso que el investigador observe en repetidas ocasiones un video de la prueba para detectar los comportamientos y registrarlos. Esta es una tarea laboriosa y puede presentar errores. Se propone un sistema basado en visión por computadora que asiste a los investigadores del área de Neurociencias mediante llevar un seguimiento del roedor de las regiones visitadas y contabilizarlas mostrando los resultados, estos se organizan en dos secciones: una que muestra la región actual en la que se encuentra el roedor, y otra en la que muestra la trayectoria seguida. A partir de una toma de video se localiza al roedor por un proceso de segmentación para posteriormente ser ubicado dentro del área de la prueba marcando las regiones visitadas correctamente de acuerdo a la posición calculada del roedor.Palabras Clave: Análisis del comportamiento, prueba de campo abierto, seguimiento. AbstractThe rodent behavior study is very useful for detect various affectations that they may suffer and also determinate changes in their behaviors. One important test is the open field test, which consist in a box marked in the botton in nine square regions, wherein the rodent is placed and then it is observed some behaviors. To make annotations is necessary that the researcher watch many times the video recorded from the test to detect the behaviors and record them. This is an exhaustive task and it may present errors.  We propose a computer vision based system to assist to the researches from the neuroscience area in make a tracking of the rodent in the visited regions and also count the regions, showing the results in two sections: the actual region that is visited, and another one in which the tracking is showed. To do this task, from a video recorded, the rodent is searched by a segmentation process and next it is located in the visited region according to the position of the rodent.Keywords: Behavior analysis, open field test, follow-up