In this paper we present a user-friendly sketching-based suggestive interface for untangling mathematical knots with complicated structures. Rather than treating mathematical knots as if they were 3D ropes, our interface is designed to assist the user to interact with knots with the right sequence of mathematically legal moves. Our knot interface allows one to sketch and untangle knots by proposing the Reidemeister moves, and can guide the user to untangle mathematical knots to the fewest possible number of crossings by suggesting the moves needed. The system highlights parts of the knot where the Reidemeister moves are applicable, suggests the possible moves, and constrains the user's drawing to legal moves only. This ongoing suggestion is based on a Reidemeister move analyzer, that reads the evolving knot in its Gauss code and predicts the needed Reidemeister moves towards the fewest possible number of crossings. For our principal test case of mathematical knot diagrams, this for the first time permits us to visualize, analyze, and deform them in a mathematical visual interface. In addition, understanding of a fairly long mathematical deformation sequence in our interface can be aided by visual analysis and comparison over the identified "key moments" where only critical changes occur in the sequence. Our knot interface allows users to track and trace mathematical knot deformation with a significantly reduced number of visual frames containing only the Reidemeister moves being applied. All these combine to allow a much cleaner exploratory interface for us to analyze and study mathematical knots and their dynamics in topological space.

One challenge remains in teaching and learning data structure is to facilitate students’ understanding of the dynamic presentation from the collection of data elements in memory. Visualizing how each element points to the next, and how a collection of nodes together represent a sequence with graphs or linked-node diagram can help us understand not only the abstract data structure but also the dynamics of the data elements in the program execution. While printing (to a console) is a very common technique for understanding and debugging data structures, we in this paper presents an interactive visualization tool for data structure in Python. Our work focuses on visual and interactive methods to facilitate the communication of data structure and associated data operations by dynamic graphing corresponding to the programming process. By using the inner execution trace, our proposed method can monitor the run-time data structure change and render the corresponding presentation in real-time. The resulting serial of key frames featuring major data structure transformation are available for review and analysis. All these combine to fill the gap between the abstract data representation and a dynamic learning-by-coding process.

Over the past decade, cyberinfrastructure community like XSEDE has substantially fostered and enriched knowledge discovery of scholars, researchers, and engineers from a variety of domains through enabling access to advanced computing systems, where continuing support for classic packages and parallel computing frameworks (e.g., MPI and OpenMP) has been well established. However, with the rise of "Big Data" era, an ever increasing demand from user community is the desire to run sophisticated, state-of-the-art distributed frameworks that handle various data related tasks. Examples include Hadoop and Spark for data processing and analytics, Cassandra and Redis for scalable on-disk and in-memory data stores, Apache Airflow for distributed workflow engine, just to name a few. Though by design such frameworks provision high-level, user friendly programming APIs for business logic composition, their deployment process oftentimes is both complex and complicated, requiring expertise well beyond what the majority of cyberinfrastructure users may have. To bridge the gap, in this paper we propose the concept of provisioning such frameworks through "cyberinfrastructure managed", system wide services, especially through leveraging "high level, complexity hiding interfaces" principle when designing interfaces that are exposed to users for framework setup and shutdown. In particular, we use Spark-as-a-Service at Indiana University as a concrete case study to illustrate how we applied the design principles. Furthermore, to demonstrate the generality of the design, we showcase Cassandra-as-a-Service, a work-in-progress prototype.

Extracting good views from a large sequence of visual frames is quite difficult but a very important task across many fields. Fully automatic view selection suffers from high data redundancy and heavy computational cost, thus fails to provide a fast and intuitive visualization. In this paper we address the automatic viewpoint selection problem in the context of 3D knot deformation. After describing viewpoint selection criteria, we detail a brute-force algorithm with a minimal distance alignment method in a way to not only ensure the global best viewpoint but also present a sequence of visually continuous frames. Due to the intensive computation, we implement an efficient extraction method through parallelization. Moreover, we propose a fast and adaptive method to retrieve best viewpoints in real-time. Despite its local searching nature, it is able to generate a set of visually continuous key frames with an interactive rate. All these combine provide insights into 3D knot deformation where the critical changes of the deformation are fully represented.

Geometric problems of interest to mathematical visualization applications involve changing structures, such as the moves that transform one knot into an equivalent knot. In this paper, we describe mathematical entities (curves and surfaces) as link-node graphs, and make use of energy-driven relaxation algorithms to optimize their geometric shapes by moving knots and surfaces to their simplified equivalence. Furthermore, we design and conFigure parallel functional units in the relaxation algorithms to accelerate the computation these mathematical deformations require. Results show that we can achieve significant performance optimization via the proposed threading model and level of parallelization.

R is the preferred language for Data analytics due to its open source development and high extensibility. Exponential growth in data has caused longer processing times leading to the rise in parallel computing technologies for analysis. Using R together with high performance computing resources is a cumbersome task. This paper proposes a framework that provides users with access to high-performance computing resources and simplifies the configuration, programming, uploading data and job scheduling through a web user interface. In addition to that, it provides two modes of parallelization of data-intensive computing tasks, catering to a wide range of users. The case studies emphasize the utility and efficiency of the framework. The framework provides better performance, ease of use and high scalability.

Mathematical knots are different from everyday ropes in that they are infinitely stretchy and flexible when being deformed into their ambient isotopic. For this reason, a number of challenges arise when visualizing mathematical knot's static and changing structures during topological deformation. In this paper we focus on computational methods to visually communicate the mathematical knot's dynamics by computationally simulating the topological deformation and capturing the critical changes during the entire simulation. To further improve our visual experience, we propose a fast and adaptive method to extract key moments where only critical changes occur to represent and summarize the long deformation sequence. We conduct evaluation study to showcase the efficacy and efficiency of our methods.

The fundamental problem in knot theory is to determine whether a given knot is an unknot. Solving such problem with existing computational algorithms or heuristic methods still remains challenging. In this paper we describe a hybrid algorithm that employs simulated annealing (SA) algorithm and opposition-based learning strategy to simplify and accelerate the simulation of mathematical knot relaxation. In our work, mathematical knots are modeled as closed node-link diagrams with energies charged at each node. A mathematical force model with adaptive step sizes is incorporated into SA for new individual generation. One elementary move with a descending number of nodes is included to prune the conformation and reduce the redundant information following the isotopy consistency. However, the force-directed model may be trapped to a local energy minimum. To overcome such intrinsic limitation, we adopt an opposition force based learning strategy to tackle this problem. With a flexible neighborhood and the instructive disturbance information, the knot geometry is able to untangle quickly and can reach the global minimum state without extra intervention. Illustrative test cases are presented, including three unknots and two classical knots with complex isotopy.

As the volume of data and technical complexity of large-scale analysis increases, many domain experts desire powerful computational and familiar analysis interface to fully participate in the analysis workflow by just focusing on individual datasets, leaving the large-scale computation to the system. Towards this goal, we investigate and benchmark a family of Divide-and-Conquer strategies that can help domain experts perform large-scale simulations by scaling up their analysis code written in R, the most popular data science and interactive analysis language. We implement the Divide-and-Conquer strategies that use R as the analysis (and computing) language, allowing advanced users to provide custom R scripts and variables to be fully embedded into the large-scale analysis workflow in R. The whole process will divide large-scale simulations tasks and conquer tasks with Slurm array jobs and R. Simulations and final aggregations are scheduled as array jobs in parallel means to accelerate the knowledge discovery process. The objective is to provide a new analytics workflow for performing similar large-scale analysis loops where expert users only need to focus on the Divide-and-Conquer tasks with the domain knowledge.

As the volume of data and technical complexity of large-scale analysis increases, many domain experts can no longer be seated in the data exploration and analysis workflow. What is desired is a computational powerful but still familiar analysis interface for domain experts to fully participate in the analysis workflow by just focusing on individual datasets, leaving the large-scale computation to the system. Towards this goal, we present VisRden, a research prototype that combines user friendly visual programming and scalable computing backend for large-scale 3D reconstruction in carious lesion research. VisRden uses R as the analysis language, making a set of core functions available to the users by hiding the computational complexity behind a visual interface, and allowing advanced users to provide custom R scripts and variables to be fully embedded into the final analysis script. Using R as the analysis language allows cariologists to continue explore data and propose new analysis methods in the way they are already familiar with. VisRden conquers large-scale image processing and 3D reconstruction in a MapReduce-like framework using R and SGE (Sun Grid Engine) array jobs. Image-based operations and result aggregation are scheduled as array jobs in a parallel means to accelerate the knowledge discovery process. All these combine to provide a new analytics workflow for performing similar large-scale analysis loops that need expert users to closely supervise, provide feedback, and refine the subtasks.

As the volume of data and technical complexity of large-scale analysis increases, many domain experts desire a computational powerful but still familiar analysis interface to fully participate in the analysis workflow by just focusing on individual datasets, leaving the large-scale computation to the system. Towards this goal, we discuss Divide-and-Conquer strategies that can help domain experts perform large-scale simulations by scaling up their analysis code written in R, the most popuar data science and interactive analysis language. We then proceed to implementing the Divide-and-Conquer strategies as a dental imaging analysis framework, VisRden, that uses R as the analysis language, allowing advanced users to provide custom R scripts and variables to be fully embedded into the large-scale analysis workflow in R. VisRden can divide large-scale image processing tasks and conquer 3D reconstruction tasks with SGE (Sun Grid Engine) array jobs and R. Image-based operations and result aggregations are scheduled as array jobs in a parallel means to accelerate the knowledge discovery process. All these combine to provide a new analytics workflow for performing similar large-scale analysis loops where expert users only need to focus on the Divide-and-Conquer tasks with the domain knowledge.

In this paper we present a mathematical knot/braid diagram interface that exploits 3D computer graphics, interactive visualization, and multi-touch technology to enhance one's intuitive experience with mathematical theory of knots. Our interaction model is based on the clever but simple geometric construction named the Reide-meister moves, which allows 3D topological manipulations using rather simple 2D moves. Multi-touch interfaces can provide a natural way for us to interact with the extra degrees of freedom that characterize knots' mathematical, physical, and arithmetic properties. Relative to a specialized mouse-driven interface, the proposed multi-touch interface is easier and more intuitive to learn, and our pilot study shows that knot and braid manipulation with multi-touch is much faster and more efficient. All these combine to show that interactive computer graphics methods and computer interfaces can be used to construct virtual manipulatives and meet the challenge of exploring abstract mathematical worlds.

Many geometric problems of interest to mathematical visualization applications involve changing structures requiring mathematical simulations, such as the moves that transform one knot into an equivalent knot. In this paper, we propose to explore a unique paradigm that makes use of self-deformable object models embedded in mathematical space, supplemented by energy-driven relaxation and user-defined motion constraints to guide the simulation through the configuration space. Furthermore, we exploit web-based user interfaces and parallelization to accelerate mathematical simulations, and to extract key moments where successive terms in the sequence differ by one critical change to represent and analyze various mathematical evolutions. The presented work leverages the nature of the interrelationship between mathematics and computer science, especially computer graphics, graph algorithms, user interfaces, and accelerated computation.

We focus on a fundamental looking behavior in human-robot interactions - gazing at each other's face. Eye contact and mutual gaze between two social partners are critical in smooth human-human interactions. Therefore, investigating at what moments and in what ways a robot should look at a human user's face as a response to the human's gaze behavior is an important topic. Toward this goal, we developed a gaze-contingent human-robot interaction system, which relied on momentary gaze behaviors from a human user to control an interacting robot in real time. Using this system, we conducted an experiment in which human participants interacted with the robot in a joint attention task. In the experiment, we systematically manipulated the robot's gaze toward the human partner's face in real time and then analyzed the human's gaze behavior as a response to the robot's gaze behavior. We found that more face looks from the robot led to more look-backs (to the robot's face) from human participants and consequently created more mutual gaze and eye contact between the two. Moreover, participants demonstrated more coordinated and synchronized multimodal behaviors between speech and gaze when more eye contact was successfully established and maintained.

In this study we analyzed a series of LiDAR point clouds acquired over Taijiang district (part of Fujian province, China). The objective was to detect and extract water surface area from individual LiDAR point cloud, in a parallel means. To this end, interactive visualization of fine-grained data, global cluster algorithms, and statistical investigation were applied. We first rasterized point clouds into a series of matrices; then a density based algorithm (DBSCAN) allowed us to isolate the single cluster features which represented the water surfaces. Base on the clustered features, our framework created polygons for further quantitative assessments. The computations for the cluster analyses and their parallelized versions were carried out using R free software for statistical computing and graphics.

Dentistry is a particularly complex and sophisticated applied science; many problems have to be solved by analyzing intensive longitudinal data. For example, dynamic carious lesion assessment requires dental researchers to perform knowledge discovery in a situation with multiple specimens across different experimental phases. The technological development and availability of cyberinfrastructure today can enable dental researchers to perform existing procedures far faster and more accurately than ever. This paper uses dynamic carious lesion activity assessment as a case study, to illustrate how visual computing on advanced cyberinfrastructure can expand beyond statistical number crunching and information retrieval to make an imaginative and creative contribution to some aspects of dental science. Our work focuses on the generation of BIG pictures on cyberinfrastructure and the presentation of derived dental structures in an interactive means, which combine to allow researchers to navigate from observation to qualitative discovery and then to quantitative assessment with multiple variables and degrees of freedom. Our work has seen early use by our collaborators in oral health research, where our system has been used to pose and answer domain-specific questions for quantitative assessment of dynamic carious lesion activities.

Mining frequent subsequences of patterns, or sequential pattern mining, has wide application in customer shopping sequence analysis, web log stream analysis, multi-modal behavioral studies, to name a few. To detect unknown, anomalous, and unexpected patterns from large-scale interval-based temporal data without complete a priori knowledge is challenging. In this paper, we present a framework - PESMiner which allows parallel and quantitative mining of sequential patterns at scale. Whereas most existing sequential mining algorithms can only find sequential orders of temporal events, our work presents a novel interactive temporal data mining algorithm capable of extracting precise temporal properties of sequential patterns. Furthermore, our work provides a unified parallel solution that scales our algorithms to larger temporal data sets by exploiting iterative MapReduce tasks. Comprehensive performance evaluations demonstrate that PESMiner significantly outperforms existing interval-based mining algorithms in terms of both quality (i.e. accuracy, precision, and recall) and scalability.

Financial statistics covers a wide array of applications in the financial world, such as (high frequency) trading, risk management, pricing and valuation of securities and derivatives, and various business and economic analytics. Portfolio allocation is one of the most important problems in financial risk management. One most challenging part in portfolio allocation is the tremendous amount of data and the optimization procedures that require computing power beyond the currently available desktop systems. In this article, we focus on the portfolio allocation problem using high-frequency financial data, and propose a hybrid parallelization solution to carry out efficient asset allocations in a large portfolio via intra-day high-frequency data. We exploit a variety of HPC techniques, including parallel R, Intel Math Kernel Library, and automatic offloading to Intel Xeon Phi coprocessor in particular to speed up the simulation and optimization procedures in our statistical investigations. Our numerical studies are based on high-frequency price data on stocks traded in New York Stock Exchange in 2011. The analysis results show that portfolios constructed using high-frequency approach generally perform well by pooling together the strengths of regularization and estimation from a risk management perspective. We also investigate the computation aspects of large-scale multiple hypothesis testing for time series data. Using a combination of software and hardware parallelism, we demonstrate a high level of performance on high-frequency financial statistics.

Learning and interaction are viewed as two related but distinct topics in developmental robotics. Many studies focus solely on either building a robot that can acquire new knowledge and learn to perform new tasks, or designing smooth human-robot interactions with pre-acquired knowledge and skills. The present paper focuses on linking language learning with human-robot interaction, showing how better human-robot interaction can lead to better language learning by robot. Toward this goal, we developed a real-time human-robot interaction paradigm in which a robot learner acquired lexical knowledge from a human teacher through free-flowing interaction. With the same statistical learning mechanism in the robot's system, we systematically manipulated the degree of activity in human-robot interaction in three experimental conditions: the robot learner was either highly active with lots of speaking and looking acts, or moderately active with a few acts, or passive without actions. Our results show that more talking and looking acts from the robot, including those immature behaviors such as saying non-sense words or looking at random targets, motivated human teachers to be more engaged in the interaction. In addition, more activities from the robot revealed its robot's internal learning states in real time, which allowed human teachers to provide more useful and "on-demand" teaching signals to facilitate learning. Thus, compared with passive and batch-mode training, an active robot learner can create more and better training data through smooth and effective social interactions that consequentially lead to more successful language learning.

In this paper, we present a mathematical visualization paradigm for exploring curves embedded in 3D and surfaces in 4D mathematical world. The basic problem is that, 3D figures of 4D mathematical entities often twist, turn, and fold back on themselves, leaving important properties behind the surface sheets. We propose an interactive system to visualize the topological features of the original 4D surface by slicing its 3D figure into a series of feature diagram. A novel 4D visualization interface is designed to allow users to control 4D topological shapes via the collection of diagram handles using the established curve manipulation mechanism. Our system can support rich mathematical interaction of 4D mathematical objects which is very difficult with any existing approach. We further demonstrate the effectiveness of the proposed visualization tool using various experimental results and cases studies.

Over the years, R has been adopted as a major data analysis and mining tool in many domain fields. As Big Data overwhelms those fields, the computational needs and workload of existing R solutions increases significantly. With recent hardware and software developments, it is possible to enable massive parallelism with existing R solutions with little to no modification. In this paper, we evaluated approaches to speed up R computations with the utilization of the Intel Math Kernel Library and automatic offloading to Intel Xeon Phi SE10P Co-processor. The testing workload includes a popular R benchmark and a practical application in health informatics. There are up to five times speedup gains from using MKL with a 16 cores without modification to the existing code for certain computing tasks. Offloading to Phi co-processor further improves the performance. The performance gains through parallelization increases as the data size increases, a promising result for adopting R for big data problem in the future.

We present KnotPad, an interactive paper-like system for visualizing and exploring mathematical knots; we exploit topological drawing and math-aware deformation methods in particular to enable and enrich our interactions with knot diagrams. Whereas most previous efforts typically employ physically based modeling to simulate the 3D dynamics of knots and ropes, our tool offers a Reidemeister move based interactive environment that is much closer to the topological problems being solved in knot theory, yet without interfering with the traditional advantages of paper-based analysis and manipulation of knot diagrams. Drawing knot diagrams with many crossings and producing their equivalent is quite challenging and error-prone. KnotPad can restrict user manipulations to the three types of Reidemeister moves, resulting in a more fluid yet mathematically correct user experience with knots. For our principal test case of mathematical knots, KnotPad permits us to draw and edit their diagrams empowered by a family of interactive techniques. Furthermore, we exploit supplementary interface elements to enrich the user experiences. For example, KnotPad allows one to pull and drag on knot diagrams to produce mathematically valid moves. Navigation enhancements in KnotPad provide still further improvement: by remembering and displaying the sequence of valid moves applied during the entire interaction, KnotPad allows a much cleaner exploratory interface for the user to analyze and study knot equivalence. All these methods combine to reveal the complex spatial relationships of knot diagrams with a mathematically true and rich user experience.

Just as we can work with two-dimensional floor plans to communicate 3D architectural design, we can exploit reduced-dimension shadows to manipulate the higher-dimensional objects generating the shadows. In particular, by taking advantage of physically reactive 3D shadow-space controllers, we can transform the task of interacting with 4D objects to a new level of physical reality. We begin with a teaching tool that uses 2D knot diagrams to manipulate the geometry of 3D mathematical knots via their projections; our unique 2D haptic interface allows the user to become familiar with sketching, editing, exploration, and manipulation of 3D knots rendered as projected imageson a 2D shadow space. By combining graphics and collision-sensing haptics, we can enhance the 2D shadow-driven editing protocol to successfully leverage 2D pen-and-paper or blackboard skills. Building on the reduced-dimension 2D editing tool for manipulating 3D shapes, we develop the natural analogy to produce a reduced-dimension 3D tool for manipulating 4D shapes. By physically modeling the correct properties of 4D surfaces, their bending forces, and their collisions in the 3D haptic controller interface, we can support full-featured physical exploration of 4D mathematical objects in a manner that is otherwise far beyond the experience accessible to human beings. As far as we are aware, this paper reports the first interactive system with force-feedback that provides "4D haptic visualization" permitting the user to model and interact with 4D cloth-like objects.

We present a multimodal paradigm for exploring topological surfaces embedded in four dimensions; we exploit haptic methods in particular to overcome the intrinsic limitations of 3D graphics images and 3D physical models. The basic problem is that, just as 2D shadows of 3D curves lose structure where lines cross, 3D graphics projections of smooth 4D topological surfaces are interrupted where one surface intersects another. Furthermore, if one attempts to trace real knotted ropes or a plastic models of self-intersecting surfaces with a fingertip, one inevitably collides with parts of the physical artifact. In this work, we exploit the free motion of a computer-based haptic probe to support a continuous motion that follows the local continuity of the object being explored. For our principal test case of 4D-embedded surfaces projected to 3D, this permits us to follow the full local continuity of the surface as though in fact we were touching an actual 4D object. We exploit additional sensory cues to provide supplementary or redundant information. For example, we can use audio tags to note the relative 4D depth of illusory 3D surface intersections produced by projection from 4D, as well as providing automated refinement of the tactile exploration path to eliminate jitter and snagging, resulting in a much cleaner exploratory motion than a bare uncorrected motion. Visual enhancements provide still further improvement to the feedback: by opening a view-direction-defined cutaway into the interior of the 3D surface projection, we allow the viewer to keep the haptic probe continuously in view as it traverses any touchable part of the object. Finally, we extend the static tactile exploration framework using a dynamic mode that links each stylus motion to a change in orientation that creates at each instant a maximal-area screen projection of a neighborhood of the current point of interest. This minimizes 4D distortion and permits true metric sizes to be deduced locally at any point. All these methods combine to reveal the full richness of the complex spatial relationships of the target shapes, and to overcome many expected perceptual limitations in 4D visualization.