Some Results for Drawing Area Proportional Venn3 With Convex Curves

Many data sets are visualized effectively with area proportional Venn diagrams, where the area of the regions is in proportion to a defined specification. In particular, Venn diagrams with three intersecting curves are considered useful for visualizing data in many applications, including bioscience, ecology and medicine. To ease the understanding of such diagrams, using restricted nice shapes for the curves is considered beneficial. Many research questions on the use of such diagrams are still open. For instance, a general solution to the question of when given area specifications can be represented by Venn3 using convex curves is still unknown. In this paper we study symmetric Venn3 drawn with convex curves and show that there is a symmetric area specification that cannot be represented with such a diagram. In addition, by using symmetric diagrams drawn with polygons, we show that, if area specifications are restricted so that the double intersection areas are no greater than the triple intersection area then the specification can be drawn with convex curves. We also propose a construction that allows the representation of some area specifications when the double intersection areas are greater than the triple intersection area. Finally, we present some open questions on the topic

Generating Euler Diagrams from Existing Layouts

Euler diagrams have a wide variety of uses, from information visualization to logical reasoning. In all of their application areas, the ability to automatically layout Euler diagrams brings considerable benefits. In this paper, we present a novel approach to Euler diagram generation. We develop certain graphs associated with Euler diagrams in order to allow curves to be added by finding cycles in these graphs. This permits us to build Euler diagrams inductively, adding one curve at a time. Our technique is adaptable, allowing the easy specification, and enforcement, of sets of wellformednesss conditions; we present a series of results that identify properties of cycles that correspond to the wellformedness conditions. This improves upon other contributions towards the automated generation of Euler diagrams which implicitly assume some fixed set of wellformedness conditions must hold. In addition, unlike most of these other generation methods, our technique allows any abstract description to be drawn as an Euler diagram. To establish the utility of the approach, a prototype implementation has been developed

Drawing Area-Proportional Euler Diagrams Representing Up To Three Sets

Area-proportional Euler diagrams representing three sets are commonly used to visualize the results of medical experiments, business data, and information from other applications where statistical results are best shown using interlinking curves. Currently, there is no tool that will reliably visualize exact area-proportional diagrams for up to three sets. Limited success, in terms of diagram accuracy, has been achieved for a small number of cases, such as Venn-2 and Venn-3 where all intersections between the sets must be represented. Euler diagrams do not have to include all intersections and so permit the visualization of cases where some intersections have a zero value. This paper describes a general, implemented, method for visualizing all 40 Euler-3 diagrams in an area-proportional manner. We provide techniques for generating the curves with circles and convex polygons, analyze the drawability of data with these shapes, and give a mechanism for deciding whether such data can be drawn with circles. For the cases where non-convex curves are necessary, our method draws an appropriate diagram using non-convex polygons. Thus, we are now always able to automatically visualize data for up to three sets

Feast and Famine: Financial Services for Rural Kenya

The paper gives a brief description of the history and main institutional forms in the agricultural and rural financial services sector–commercial banks, the micro-finance industry, savings and credit cooperative societies, village banks, building societies and the Agricultural Finance Corporation. It ends by raising some of the issues that need to be addressed as we begin to deal with the institutional and regulatory framework for the subsector including the cost of funds and the array of existing policy and legislative proposals on the table. The main argument of the paper is that we need to step back and undertake a comprehensive assessment of the sector before government passes new laws, or spends public money in unproductive ways. The paper proposes that the agriculture sector ministries should play a leading role in pushing for that comprehensive assessment.Food Security, Food Policy, Financial Services, Kenya, Micro-finance, Agricultural Finance, Q18,

E-PUR: An Energy-Efficient Processing Unit for Recurrent Neural Networks

Recurrent Neural Networks (RNNs) are a key technology for emerging applications such as automatic speech recognition, machine translation or image description. Long Short Term Memory (LSTM) networks are the most successful RNN implementation, as they can learn long term dependencies to achieve high accuracy. Unfortunately, the recurrent nature of LSTM networks significantly constrains the amount of parallelism and, hence, multicore CPUs and many-core GPUs exhibit poor efficiency for RNN inference. In this paper, we present E-PUR, an energy-efficient processing unit tailored to the requirements of LSTM computation. The main goal of E-PUR is to support large recurrent neural networks for low-power mobile devices. E-PUR provides an efficient hardware implementation of LSTM networks that is flexible to support diverse applications. One of its main novelties is a technique that we call Maximizing Weight Locality (MWL), which improves the temporal locality of the memory accesses for fetching the synaptic weights, reducing the memory requirements by a large extent. Our experimental results show that E-PUR achieves real-time performance for different LSTM networks, while reducing energy consumption by orders of magnitude with respect to general-purpose processors and GPUs, and it requires a very small chip area. Compared to a modern mobile SoC, an NVIDIA Tegra X1, E-PUR provides an average energy reduction of 92x

On the Completeness of Spider Diagrams Augmented with Constants

Diagrammatic reasoning can be described formally by a number of diagrammatic logics; spider diagrams are one of these, and are used for expressing logical statements about set membership and containment. Here, existing work on spider diagrams is extended to include constant spiders that represent specific individuals. We give a formal syntax and semantics for the extended diagram language before introducing a collection of reasoning rules encapsulating logical equivalence and logical consequence. We prove that the resulting logic is sound, complete and decidable

Distortions to Agricultural Incentives in Kenya

Distorted incentives, agricultural and trade policy reforms, national agricultural development, Agricultural and Food Policy, International Relations/Trade, F13, F14, Q17, Q18,

How Should We Use Colour in Euler Diagrams?

This paper addresses the problem of how best to use colour in Euler diagrams. The choice of using coloured curves, rather than black curves, possibly with coloured fill is often made in tools that automatically draw Euler diagrams for information visualization as well as when they are drawn manually. We address the problem by empirically evaluating various different colour treatments: coloured or black curves combined with either no fill or coloured fill. By collecting performance data, we conclude that Euler diagrams with coloured curves and no fill significantly outperform all other colour treatments. Most automated layout algorithms adopt colour fill and are, thus, reducing the effectiveness of the Euler diagrams produced. As Euler diagrams can be used in a multitude of areas, ranging from crime control to social network analysis, our results stand to increase the ability of users to accurately and quickly extract information from their visualizations

Neuron-level fuzzy memoization in RNNs

The final publication is available at ACM via http://dx.doi.org/10.1145/3352460.3358309Recurrent Neural Networks (RNNs) are a key technology for applications such as automatic speech recognition or machine translation. Unlike conventional feed-forward DNNs, RNNs remember past information to improve the accuracy of future predictions and, therefore, they are very effective for sequence processing problems. For each application run, each recurrent layer is executed many times for processing a potentially large sequence of inputs (words, images, audio frames, etc.). In this paper, we make the observation that the output of a neuron exhibits small changes in consecutive invocations. We exploit this property to build a neuron-level fuzzy memoization scheme, which dynamically caches the output of each neuron and reuses it whenever it is predicted that the current output will be similar to a previously computed result, avoiding in this way the output computations. The main challenge in this scheme is determining whether the new neuron's output for the current input in the sequence will be similar to a recently computed result. To this end, we extend the recurrent layer with a much simpler Bitwise Neural Network (BNN), and show that the BNN and RNN outputs are highly correlated: if two BNN outputs are very similar, the corresponding outputs in the original RNN layer are likely to exhibit negligible changes. The BNN provides a low-cost and effective mechanism for deciding when fuzzy memoization can be applied with a small impact on accuracy. We evaluate our memoization scheme on top of a state-of-the-art accelerator for RNNs, for a variety of different neural networks from multiple application domains. We show that our technique avoids more than 24.2% of computations, resulting in 18.5% energy savings and 1.35x speedup on average.Peer ReviewedPostprint (author's final draft

A New Language for the Visualization of Logic and reasoning

Many visual languages based on Euler diagrams have emerged for expressing relationships between sets. The expressive power of these languages varies, but the majority can only express statements involving unary relations and, sometimes, equality. We present a new visual language called Visual First Order Logic (VFOL) that was developed from work on constraint diagrams which are designed for software specification. VFOL is likely to be useful for software specification, because it is similar to constraint diagrams, and may also fit into a Z-like framework. We show that for every First Order Predicate Logic (FOPL) formula there exists a semantically equivalent VFOL diagram. The translation we give from FOPL to VFOL is natural and, as such, VFOL could also be used to teach FOPL, for example