Doing and Showing

The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization techniques. I mean the (informal) notion of axiomatic theory according to which a mathematical theory consists of a set of axioms and further theorems deduced from these axioms according to certain rules of logical inference. Thus the usual notion of axiomatic method is inadequate and needs a replacement.Comment: 54 pages, 2 figure

Revisiting noninteracting string partition functions in Rindler space

We revisit non-interacting string partition functions in Rindler space by summing over fields in the spectrum. In field theory, the total partition function splits in a natural way in a piece that does not contain surface terms and a piece consisting of solely the so-called edge states. For open strings, we illustrate that surface contributions to the higher spin fields correspond to open strings piercing the Rindler origin, unifying the higher spin surface contributions in string language. For closed strings, we demonstrate that the string partition function is not quite the same as the sum over the partition functions of the fields in the spectrum: an infinite overcounting is present for the latter. Next we study the partition functions obtained by excluding the surface terms. Using recent results of JHEP 1505 (2015) 106, this construction, first done by Emparan, can be put on much firmer ground. We generalize to type II and heterotic superstrings and demonstrate modular invariance. All of these exhibit an IR divergence that can be interpreted as a maximal acceleration close to the black hole horizon. Ultimately, since these partition functions are only part of the full story, divergences here should not be viewed as a failure of string theory: maximal acceleration is a feature of a faulty treatment of the higher spin fields in the string spectrum. We comment on the relevance of this to Solodukhin's recent proposal. A possible link with the firewall paradox is apparent.Comment: 33 pages, v2: added several clarifications including a section on the difference between closed strings and the sum-of-fields approach, matches published versio

Integrating Multiple Sketch Recognition Methods to Improve Accuracy and Speed

Sketch recognition is the computer understanding of hand drawn diagrams. Recognizing sketches instantaneously is necessary to build beautiful interfaces with real time feedback. There are various techniques to quickly recognize sketches into ten or twenty classes. However for much larger datasets of sketches from a large number of classes, these existing techniques can take an extended period of time to accurately classify an incoming sketch and require significant computational overhead. Thus, to make classification of large datasets feasible, we propose using multiple stages of recognition. In the initial stage, gesture-based feature values are calculated and the trained model is used to classify the incoming sketch. Sketches with an accuracy less than a threshold value, go through a second stage of geometric recognition techniques. In the second geometric stage, the sketch is segmented, and sent to shape-specific recognizers. The sketches are matched against predefined shape descriptions, and confidence values are calculated. The system outputs a list of classes that the sketch could be classified as, along with the accuracy, and precision for each sketch. This process both significantly reduces the time taken to classify such huge datasets of sketches, and increases both the accuracy and precision of the recognition

Integrating Multiple Sketch Recognition Methods to Improve Accuracy and Speed

Sketch recognition is the computer understanding of hand drawn diagrams. Recognizing sketches instantaneously is necessary to build beautiful interfaces with real time feedback. There are various techniques to quickly recognize sketches into ten or twenty classes. However for much larger datasets of sketches from a large number of classes, these existing techniques can take an extended period of time to accurately classify an incoming sketch and require significant computational overhead. Thus, to make classification of large datasets feasible, we propose using multiple stages of recognition. In the initial stage, gesture-based feature values are calculated and the trained model is used to classify the incoming sketch. Sketches with an accuracy less than a threshold value, go through a second stage of geometric recognition techniques. In the second geometric stage, the sketch is segmented, and sent to shape-specific recognizers. The sketches are matched against predefined shape descriptions, and confidence values are calculated. The system outputs a list of classes that the sketch could be classified as, along with the accuracy, and precision for each sketch. This process both significantly reduces the time taken to classify such huge datasets of sketches, and increases both the accuracy and precision of the recognition

Interactive interpretation of structured documents: Application to the recognition of handwritten architectural plans

International audienceThis paper addresses a whole architecture, including the IMISketch method. IMISketch method incorporates two aspects: document analysis and interactivity. This paper describes a global vision of all the parts of the project. IMISketch is a generic method for an interactive interpretation of handwritten sketches. The analysis of complex documents requires the management of uncertainty. While, in practice the similar methods often induce a large combinatorics, IMISketch method presents several optimization strategies to reduce the combinatorics. The goal of these optimizations is to have a time analysis compatible with user expectations. The decision process is able to solicit the user in the case of strong ambiguity: when it is not sure to make the right decision, the user explicitly validates the right decision to avoid a fastidious a posteriori verification phase due to propagation of errors.This interaction requires solving two major problems: how interpretation results will be presented to the user, and how the user will interact with analysis process. We propose to study the effects of those two aspects. The experiments demonstrate that (i) a progressive presentation of the analysis results, (ii) user interventions during it and (iii) the user solicitation by the analysis process are an efficient strategy for the recognition of complex off-line documents.To validate this interactive analysis method, several experiments are reported on off-line handwritten 2D architectural floor plans

Interacting Dipoles from Matrix Formulation of Noncommutative Gauge Theories

We study the IR behavior of noncommutative gauge theory in the matrix formulation. We find that in this approach, the nature of the UV/IR mixing is easily understood, which allows us to perform a reliable calculation of the quantum effective action for the long wavelength modes of the noncommutative gauge field. At one loop, we find that our description is weakly coupled only in the supersymmetric theory. At two loops, we find non-trivial interaction terms suggestive of dipole degrees of freedom. These dipoles exhibit a channel duality reminiscent of string theory.Comment: LaTeX 11 pages, 4 figures; v.2 minor changes and some references added; v.3 many more technical details added and significantly different presentation, use REVTeX 4, to appear in PR

ChemInk: A Natural Real-Time Recognition System for Chemical Drawings

We describe a new sketch recognition framework for chemical structure drawings that combines multiple levels of visual features using a jointly trained conditional random field. This joint model of appearance at different levels of detail makes our framework less sensitive to noise and drawing variations, improving accuracy and robustness. In addition, we present a novel learning-based approach to corner detection that achieves nearly perfect accuracy in our domain. The result is a recognizer that is better able to handle the wide range of drawing styles found in messy freehand sketches. Our system handles both graphics and text, producing a complete molecular structure as output. It works in real time, providing visual feedback about the recognition progress. On a dataset of chemical drawings our system achieved an accuracy rate of 97.4%, an improvement over the best reported results in literature. A preliminary user study also showed that participants were on average over twice as fast using our sketch-based system compared to ChemDraw, a popular CAD-based tool for authoring chemical diagrams. This was the case even though most of the users had years of experience using ChemDraw and little or no experience using Tablet PCs.National Science Foundation (U.S.) (Grant 0729422)United States. Dept. of Homeland Security (Graduate Research Fellowship)Pfizer Inc

On-line hand-drawn electric circuit diagram recognition using 2D dynamic programming

9 pagesInternational audienceIn order to facilitate sketch recognition, most online existing works assume that people will not start to draw a new symbol before the current one has been finished. We propose in this paper a method that relaxes this constraint. The proposed methodology relies on a two-dimensional dynamic programming (2D-DP) technique allowing symbol hypothesis generation, which can correctly segment and recognize interspersed symbols. In addition, as discriminative classifiers usually have limited capability to reject outliers, some domain specific knowledge is included to circumvent those errors due to untrained patterns corresponding to erroneous segmentation hypotheses. With a point-level measurement, the experiment shows that the proposed novel approach is able to achieve an accuracy of more than 90 percent