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We present a visual navigation approach that uses context information to navigate an agent to find and reach a target object. To learn context from the objects present in the scene, we transform visual information into an intermediate representation called context grid which essentially represents how much the object at the location is semantically similar to the target object. As this representation can encode the target object and other objects together, it allows us to navigate an agent in a human-inspired way: the agent will go to the likely place by seeing surrounding context objects in the beginning when the target is not visible and, once the target object comes into sight, it will reach the target quickly. Since context grid does not directly contain visual or semantic feature values that change according to introductions of new objects, such as new instances of the same object with different appearance or an object from a slightly different class, our navigation model generalizes well to unseen scenes/objects. Experimental results show that our approach outperforms previous approaches in navigating in unseen scenes, especially for broad scenes. We also evaluated human performances in the target-driven navigation task and compared with machine learning based navigation approaches including this work.

This paper presents a novel approach to solving 2D motion planning problems using deep neural networks, which we refer to as PathNet. PathNet first takes a 2D environment map composed of obstacle zone and free zone and compresses it to a latent vector. The latent vector is afterward concatenated with the start and goal positions to generate a trajectory connecting those positions. Our learning-based neural planner can solve motion planning problems in unseen environments and is computationally efficient as it only needs one single pass in our network to generate trajectories.

This talk is about computing with mathematical quantities where the sizes or shapes are not known in advance. We consider polynomials where the exponents can be given by symbolic expressions, matrices with blocks or other internal structure of symbolic size, and piece-wise functions where the shapes of the domains are given by symbolic expressions.

The two-dimensional nature of mathematical formulas and the large set of mathematical characters with different variations in style and size form the main challenges in mathematical handwriting recognition. To address these difficulties, the way handwritten data is represented and the methods to compute certain features from the chosen representation are important questions. To this aim, we treat handwritten characters as approximated parametrized coordinate curves in Legendre-Sobolev bases. This representation empowers us to study the geometrical features of handwritten characters as a whole. These geometrical features are used to find to baselines, bounding boxes, loops, and cusps appearing in handwritten characters. Computing these features relies on mathematical operations such as derivatives, roots, and gcds of polynomials. This paper studies the problem of computing these operations without the conversion to the monomial basis, seeking improvement in speed and accuracy.

As with many other areas of study, mathematical knowledge has been produced for centuries and will continue to be produced for centuries to come. The records have taken many forms, from manuscripts, to printed journals, and now digital media. Unlike many other fields, however, much of mathematical knowledge has a high degree of precision and objectivity that both gives it permanent utility and makes it susceptible to mechanized treatment. We outline a path toward assembling the world’s mathematical knowledge. While initially in the form of a comprehensive digital library of page images, we expect evolution toward a knowledge base supporting sophisticated queries and automated reasoning. It is the aim of the nascent International Mathematical Knowledge Trust to provide a framework and to foster a community to make progress in this direction. We can foresee that such a knowledge base will enhance the capacity of individual mathematicians, accelerate discovery and allow new kinds of collaboration.

Hybrid sets are generalizations of sets and multisets, in which the multiplicities of elements can take any integers. This construction was proposed by Whitney in 1933 in terms of characteristic functions. Hybrid sets have been used by combinatorists to give combinatorial interpretationsfor several generalizations of binomial coefficients and Stirling numbers and by computer scientists to design fast algorithms for symbolic domain decompositions. We present in this paper some combinatorial results on subsets and partitions of hybrid sets.

In handwritten mathematics, it is common to have characters in various sizes and for writing not to follow simple baselines. For example, subscripts and superscripts appear relatively smaller than normal text and are written slightly below or above it. Rather than use the location, features and size to identify the character, it may be more effective to do the reverse --- to use knowledge about specific characters to determine baseline, size, etc. In this approach, it is necessary to find the location of certain expected features that are determined by particular points. In earlier work, we have presented a method to derive the determining points for a new instance of a symbol from those on an average model for each symbol type. For those characters that are significantly different from the average instance, one can use a numerical homotopy between the average instance and the target character, and apply the determining point algorithm at each step. The present article studies the factors to be taken into account in performing such homotopies. We examine two strategies for possible starting points for the homotopy, and we examine the relation between the distance and the number of steps required. The first starting point strategy performs a homotopy from the average of samples of the same type. The second strategy uses a homotopy from the nearest neighbour with known determining points. Our experimental results show a useful relation between the homotopy distance and the number of steps usually required and improved strategies to find determining points for poorly written characters.

The equation concept is one of the most fundamental in mathematics, yet the word "equation" means different things to different people. It is used not only with various precise technical meanings, but also as a metaphor for complex situations. We review some of the history of the equation and its present meaning and use in a variety of settings. Although some languages make distinctions among ideas such equations that are always satisfied versus those that may not be, or between equations with variables and relations without, we observe that it may not be possible to decide into which of these cases a particular equality falls.

Shape-based online handwriting recognition suffers on small characters, in which the distortions and variations are often commensurate in size with the characters themselves. This problem is emphasized in settings where characters may have widely different sizes and there is no absolute scale. We propose methods that use size information to adjust shape-based classification to take this phenomenon appropriately into account. These methods may be thought of as a pre-classification in a size-based feature space and are general in nature, avoiding hand-tuned heuristics based on particular characters.

We present an adaptive approach to the recognition of handwritten mathematical symbols, in which a recognition weight is associated with each training sample. The weight is computed from the distance to a test character in the space of coefficients of functional approximation of symbols. To determine the average size of the training set to achieve certain classification accuracy, we model the error drop as a function of the number of training samples in a class and compute the average parameters of the model with respect to all classes in the collection. The size is maintained by removing a training sample with the minimal average weight after each addition of a recognized symbol to the repository. Experiments show that the method allows rapid adaptation of a default training dataset to the handwriting of an author with efficient use of the storage space.

Digital ink curves are typically represented as series of points sampled at certain time intervals. We are interested in the problem of how to select a minimal subset of sample points to approximate a digital ink curve within a given error bound. We present an algorithm to find an approximation with a specified number of points and providing the minimum cumulative error. Alternatively, it may be used to select the minimum number of points required to satisfy an error bound. The method uses dynamic programming and has a cost linear in the number of points.

We present a method to compress digital ink based on piecewise-linear approximation within a given error threshold. The objective is to achieve good compression ratio with very fast execution. The method is especially effective on types of handwriting that have large portions with nearly linear parts, e.g. hand drawn geometric objects. We compare this method with an enhanced version of our earlier functional approximation method, finding the new technique to give slightly worse compression while performing significantly faster. This suggests the presented method can be used in applications where speed of processing is of higher priority than the compression ratio.

Research collaboration has always been important and has recently become even more so. I wish therefore to address a topic I believe to require attention now, and that is software support for mathematical collaboration.

Representing digital ink traces as points in a function space has proven useful for online recognition. Ink trace coordinates or their integral invariants are written as parametric functions and approximated by truncated orthogonal series. This representation captures the shape of the ink traces with a small number of coefficients in a form quite compact and independent of device resolution, and various geometric techniques may be employed for recognition. The simplicity and high performance of this method lead us to ask whether the same idea can be applied to another important aspect in online handwriting – the compression of digital ink strokes. We have investigated Chebyshev, Legendre and Legendre-Sobolev orthogonal polynomial bases as well as Fourier series and have found that Chebyshev representation is the most suitable apparatus for compressing digital curves. We obtain compression rates of 30* to 50* and have the added benefit that the Legendre- Sobolev form, used for recognition, may be obtained by a single linear transformation.

Accurate computer recognition of handwritten mathematics offers to provide a natural interface for mathematical computing, document creation and collaboration. Mathematical handwriting, however, provides a number of challenges beyond what is required for the recognition of handwritten natural languages. For example, it is usual to use symbols from a range of different alphabets and there are many similar-looking symbols. Many writers are unfamiliar with the symbols they must use and therefore write them incorrectly. Mathematical notation is two-dimensional and size and placement information is important. Additionally, there is no fixed vocabulary of mathematical “words” that can be used to disambiguate symbol sequences. On the other hand, there are some simplifications. For example, symbols do tend to be well-segmented. With these charactersitics, new methods of character recognition are important for accurate handwritten mathematics input.

We propose an efficient method to recognize multi-stroke handwritten symbols. The method is based on computing the truncated Legendre-Sobolev expansions of the coordinate functions of the stroke curves and classifying them using linear support vector machines. Earlier work has demonstrated the efficiency and robustness of this approach in the case of single-stroke characters. Here we show that the method can be successfully applied to multi-stroke characters by joining the strokes and including the number of strokes in the feature vector or in the class labels. Our experiments yield an error rate of 11-20%, and in 99% of cases the correct class is among the top 4. The recognition process causes virtually no delay, because computation of Legendre-Sobolev expansions and SVM classification proceed on-line, as the strokes are written.

With the increased availability of pen-based devices, it becomes interesting to conduct and to archive multi-party communication sessions that involve audio and digital ink on a shared canvas. Collaborative whiteboards do exist today but typically use complex or closed protocols for communication. As a rule, existing whiteboards are not interoperable across multiple platforms and do not support archival of collaborative sessions for later reference or analysis. We explore how various data formats may be used to represent, to transmit, to record and to synchronize ink and audio channels. We find InkML to be a suitable representation to support platform-independent digital ink in a form supporting both transmission and higher-level semantic analysis. To test our ideas we have developed a complete software implementation as a Skype add-on. This has revealed possible improvements to the page and streaming models of InkML.

Certain forms of mathematical expression are used more often than others in practice. A quantitative understanding of actual usage can provide additional information to improve the accuracy of software for the input of mathematical expressions from scanned documents or handwriting and more natural forms of presentation of mathematical expressions by computer algebra systems. Earlier work has examined this question for the diverse set of articles from the mathematics preprint archive arXiv.org. That analysis showed showed the variance between mathematical areas. The present work analyzes a particular mathematical domain more deeply. We have chosen to examine second year university engineering mathematics as taught in North America as the domain. We have analyzed the set of expressions occurring in the most popular textbooks, weighted by popularity. Assuming that early training influences later mathematical usage, we take this as a model of the set of mathematical expressions used by the population of North American engineers. We present an empirical analysis of the symbols and $n$-grams occurring in these expressions.

Earlier work has presented algorithms to factor and compute GCDs of symbolic Laurent polynomials, that is multivariate polynomials whose exponents are themselves integer-valued polynomials. This article extends the notion of univariate polynomial decomposition to symbolic polynomials and presents an algorithm to compute these decompositions. For example, the symbolic polynomial f(X) = 2Xn 2 +n - 4Xn 2 + 2Xn 2-n + 1 can be de-composed as f = g o h where g(X) = 2X2 + 1 and h(X) = Xn 2 /2+n/2 - Xn 2 /2-n/2.

We present an approach to basic arithmetic between abstract matrices, i.e., matrices of symbolic dimension with underspecified components. We define a simple basis function that enables the representation of abstract matrices composed of arbitrary regions in a single term that supports matrix addition and multiplication by regular arithmetic on terms. This can, in particular, be exploited to obtain general arithmetic closure properties for classes of structured matrices. We also describe an approach using alternative basis functions that allow more compact expressions and admit additional arithmetic simplifications.

We address the question of how to organize pen-based interfaces for mathematical software systems, both for computational mathematics packages and document processing software. Our architecture includes components for ink collection, mathematically-oriented recognizers, portability support and interfaces to applications. We summarize aspects of mathematical handwriting recognition and discuss the methods we have used for individual character recognition and overall expression analysis. We present our pen-based computing environment, Mathink, and give an overview of facilities for training, ink annotation, and testing.

We address the question of recognizing handwritten mathematics in Arabic and related languages. After presenting an overview of the major styles used to express mathematics in these settings we outline potential problems specific to the representations. Finally, we discuss how some existing strategies for on-line analysis of handwritten mathematics can be adapted for this context.

Recognition of mathematical symbols is a challenging task, with a large set with many similar symbols. We present a support vector machine based hybrid recognition system that uses both online and offline information for classification. Probabilistic outputs from the two support vector machine based multi-class classifiers running in parallel are combined by taking a weighted sum. Results from the experiments show that giving slightly higher weight to the on-line information produces better results. The overall error rate of the hybrid system is lower than that of both the online and offline recognition systems when used in isolation.

Ink markup language (InkML) provides a platform-neutral data format that can be used to represent, store and transmit digital ink data. Both streaming and archival applications are supported through different uses of InkML's primitives. While streaming ink and archival ink data can represent the same information, each supports certain operations more directly. Indeed, certain applications can benefit from access to both representations of the same digital ink data. In this paper we present an efficient method to convert archival style InkML to streaming style and vice-versa.

Summary form only given. Pen-based user interfaces offer tantalizing potential for mathematical software systems. In contrast to normal text, entering and editing mathematical formulae with a digital pen can be much more natural than using a keyboard. Machine recognition of mathematical handwriting, however, is more complex than recognizing natural language text. In this context it is necessary to deal with a vast array of similar symbols and the analysis of the two-dimensional syntactic structure of formulae. This talk outlines our work in this area. We describe our architecture for a mathematical handwriting component that can be embedded in various applications. These include computer algebra systems, such as Maple, and document processing applications, such as Microsoft Word. We describe the problem of mathematical character recognition and detail how recognition rates can be enhanced using data derived from the analysis of digital libraries

We present a pivot-free deterministic algorithm for the inversion of block matrices. The method is based on the Moore-Penrose inverse and is applicable over certain general classes of rings. This improves on previous methods that required at least one invertible on-diagonal block, and that otherwise required row- or column-based pivoting, disrupting the block structure. Our method is applicable to any invertible matrix and does not require any particular blocks to invertible. This is achieved at the cost of two additional specialized matrix multiplications and, in some cases, requires the inversion to be performed in an extended ring.

This paper studies the performance of generics, or templates as they are sometimes called, for scientific computing in various programming languages. In order to understand the cost of using generics, we develop a test suite for generics based on a standard numeric benchmark. We compare the results of this new benchmark for generics in C++, C# and Java, both between language implementations and against the specialized, non-generic benchmark. We also compare the efficiency of C++ with Aldor a language originally for computer algebra relying entirely on generics. We find that the implementation of generics in current compilers must be improved before they are used for efficiency-critical scientific applications, and we identify specific areas for potential optimization.

Ion beam induced charge (IBIC) microscopy is used mainly for analysis of various semiconductor parameters such as diffusion length and lifetime of the charge carriers. In this paper, we show that IBIC microscopy is also useful for the visualization of the electrical field distribution within depletion regions of electronic devices. The ions penetrating into the semiconductor generate electron-hole pairs that are separated and accelerated depending on the internal electric field distribution. The shape of the resulting current induced in this way is dependent on the electric field. This dependence and the large penetration depth of the light ions allow the analysis of electric field distributions within semiconductor devices up to a few tens of microns below the device surface. Therefore, IBIC microscopy is a very useful analytical tool for the characterization of the electrical field distribution within high-power devices, even when the semiconductor is covered with thick passivation or metallization layers

For a vast, sparsely populated continent like Australia, effective remote area telecommunications, power supplies, navigation aids and transport route signalling are critical and expensive. PV provides an attractive alternative to diesel and central grid supplies for maintaining these links. Over the last 10 years, another PV market has developed in water pumping and in remote electricity supply. Solar car races have also generated significant public interest in PV and created an important market for high efficiency cells. The PV market in Australia is now entering another phase, with growing interest in grid connection. The author describes how this market is set to expand rapidly due to technical advances, cost reductions, a strong push towards environmentally friendly energy supplies and active electricity utility interest.

International audience; We report on a symbolic-numeric algorithm for computing the Alexander polynomial of each singularity of a plane complex algebraic curve defined by a polynomial with coefficients of limited accuracy, i.e. the coefficients are both exact and inexact data. We base the algorithm on combinatorial methods from knot theory which we combine with computational geometry algorithms in order to compute efficient and accurate results. Nonetheless the problem we are dealing with is ill-posed, in the sense that tiny perturbations in the coefficients of the defining polynomial cause huge errors in the computed results.