Mathematical Abstraction, Conceptual Variation and Identity

One of the key features of modern mathematics is the adoption of the abstract method. Our goal in this paper is to propose an explication of that method that is rooted in the history of the subject

Mathematical Abstraction, Conceptual Variation and Identity

One of the key features of modern mathematics is the adoption of the abstract method. Our goal in this paper is to propose an explication of that method that is rooted in the history of the subject

Proving Abstractions of Dynamical Systems through Numerical Simulations

A key question that arises in rigorous analysis of cyberphysical systems under attack involves establishing whether or not the attacked system deviates significantly from the ideal allowed behavior. This is the problem of deciding whether or not the ideal system is an abstraction of the attacked system. A quantitative variation of this question can capture how much the attacked system deviates from the ideal. Thus, algorithms for deciding abstraction relations can help measure the effect of attacks on cyberphysical systems and to develop attack detection strategies. In this paper, we present a decision procedure for proving that one nonlinear dynamical system is a quantitative abstraction of another. Directly computing the reach sets of these nonlinear systems are undecidable in general and reach set over-approximations do not give a direct way for proving abstraction. Our procedure uses (possibly inaccurate) numerical simulations and a model annotation to compute tight approximations of the observable behaviors of the system and then uses these approximations to decide on abstraction. We show that the procedure is sound and that it is guaranteed to terminate under reasonable robustness assumptions

Coping with speaker-related variation via abstract phonemic categories

Listeners can cope with considerable variation in the way that different speakers talk. We argue here that they can do so because of a process of phonological abstraction in the speech-recognition system. We review evidence that listeners adjust the bounds of phonemic categories after only very limited exposure to a deviant realisation of a given phoneme. This learning can be talker-specific and is stable over time; further, the learning generalizes to previously unheard words containing the deviant phoneme. Together these results suggest that the learning involves adjustment of prelexical phonemic representations which mediate between the speech signal and the mental lexicon during word recognition. We argue that such an abstraction process is inconsistent with claims made by some recent models of language processing that the mental lexicon consists solely of multiple detailed traces of acoustic episodes. Simulations with a purely episodic model without functional prelexical abstraction confirm that such a model cannot account for the evidence on lexical generalization of perceptual learning. We conclude that abstract phonemic categories form a necessary part of lexical access, and that the ability to store talker-specific knowledge about those categories provides listeners with the means to deal with cross-talker variation

Defining user perception of distributed multimedia quality

This article presents the results of a study that explored the human side of the multimedia experience. We propose a model that assesses quality variation from three distinct levels: the network, the media and the content levels; and from two views: the technical and the user perspective. By facilitating parameter variation at each of the quality levels and from each of the perspectives, we were able to examine their impact on user quality perception. Results show that a significant reduction in frame rate does not proportionally reduce the user's understanding of the presentation independent of technical parameters, that multimedia content type significantly impacts user information assimilation, user level of enjoyment, and user perception of quality, and that the device display type impacts user information assimilation and user perception of quality. Finally, to ensure the transfer of information, low-level abstraction (network-level) parameters, such as delay and jitter, should be adapted; to maintain the user's level of enjoyment, high-level abstraction quality parameters (content-level), such as the appropriate use of display screens, should be adapted

OntoCAT - an integrated programming toolkit for common ontology application tasks

OntoCAT provides high level abstraction for interacting with ontology resources including local ontology files in standard OWL and OBO formats (via OWL API) and public ontology repositories: EBI Ontology Lookup Service (OLS) and NCBO BioPortal. Each resource is wrapped behind easy to learn Java, Bioconductor/R and REST web service commands enabling reuse and integration of ontology software efforts despite variation in technologies

Empiricism without Magic: Transformational Abstraction in Deep Convolutional Neural Networks

In artificial intelligence, recent research has demonstrated the remarkable potential of Deep Convolutional Neural Networks (DCNNs), which seem to exceed state-of-the-art performance in new domains weekly, especially on the sorts of very difficult perceptual discrimination tasks that skeptics thought would remain beyond the reach of artificial intelligence. However, it has proven difficult to explain why DCNNs perform so well. In philosophy of mind, empiricists have long suggested that complex cognition is based on information derived from sensory experience, often appealing to a faculty of abstraction. Rationalists have frequently complained, however, that empiricists never adequately explained how this faculty of abstraction actually works. In this paper, I tie these two questions together, to the mutual benefit of both disciplines. I argue that the architectural features that distinguish DCNNs from earlier neural networks allow them to implement a form of hierarchical processing that I call “transformational abstraction”. Transformational abstraction iteratively converts sensory-based representations of category exemplars into new formats that are increasingly tolerant to “nuisance variation” in input. Reflecting upon the way that DCNNs leverage a combination of linear and non-linear processing to efficiently accomplish this feat allows us to understand how the brain is capable of bi-directional travel between exemplars and abstractions, addressing longstanding problems in empiricist philosophy of mind. I end by considering the prospects for future research on DCNNs, arguing that rather than simply implementing 80s connectionism with more brute-force computation, transformational abstraction counts as a qualitatively distinct form of processing ripe with philosophical and psychological significance, because it is significantly better suited to depict the generic mechanism responsible for this important kind of psychological processing in the brain

Measuring Data Abstraction Quality in Multiresolution Visualizations

Data abstraction techniques are widely used in multiresolution visualization systems to reduce visual clutter and facilitate analysis from overview to detail. However, analysts are usually unaware of how well the abstracted data represent the original dataset, which can impact the reliability of results gleaned from the abstractions. In this thesis, we define three types of data abstraction quality measures for computing the degree to which the abstraction conveys the original dataset: the Histogram Difference Measure, the Nearest Neighbor Measure and Statistical Measure. They have been integrated within XmdvTool, a public-domain multiresolution visualization system for multivariate data analysis that supports sampling as well as clustering to simplify data. Several interactive operations are provided, including adjusting the data abstraction level, changing selected regions, and setting the acceptable data abstraction quality level. Conducting these operations, analysts can select an optimal data abstraction level. We did an evaluation to check how well the data abstraction measures conform to the data abstraction quality perceived by users. We adjusted the data abstraction measures based on the results of the evaluation. We also experimented on the measures with different distance methods and different computing mechanisms, in order to find the optimal variation from many variations of each type of measure. Finally, we developed two case studies to demonstrate how analysts can compare different abstraction methods using the measures to see how well relative data density and outliers are maintained, and then select an abstraction method that meets the requirement of their analytic tasks

Climate change and water abstraction impacts on the long-term variability of water levels in Lake Bracciano (Central Italy): A Random Forest approach

Abstract Study Region Lake Bracciano has been historically used as a strategic water reservoir for the city of Rome (Italy) since ancient times. However, following the severe water crisis of 2017, water abstraction has been completely stopped. Study Focus The relative impact of the various drivers of change (climatological and management) on fluctuations in lake water level is not yet clear. To quantify this impact, we applied the Random Forest (RF) machine learning approach, taking advantage of a century of observations. New Hydrological Insights for the Region Since the late 1990s the monthly variation in lake water levels has doubled, as has variation in monthly abstraction. Increased variation in annual cumulated precipitation and a rise in mean air temperature have also been observed. The RF machine learning approach made it possible to confirm the marginal role of temperature, the increasing role of abstraction during the last two decades (from 24 % to 39 %), and the key role played by the increased precipitation variability. These results highlight the notable prediction and inference capabilities of RF in a complex and partially unknown hydrological context. We conclude by discussing the limits of this approach, which are mainly associated with its capacity to generates scenarios compared to physical based models