A Local Convergence Proof for the Minvar Algorithm for Computing Continuous Piecewise Linear Approximations

The class of continuous piecewise linear (PL) functions represents a useful family of approximants because invertibility can be readily imposed, and if a PL function is invertible, then it can be inverted in closed form. Many applications, arising, for example, in control systems and robotics, involve the simultaneous construction of a forward and inverse system model from data. Most approximation techniques require that separate forward and inverse models be trained, whereas an invertible continuous PL affords, simultaneously, the forward and inverse system model in a single representation. The minvar algorithm computes a continuous PL approximation to data. Local convergence of minvar is proven for the case when the data generating function is itself a PL function and available directly rather than through data

The Ursinus Weekly, November 22, 1937

Curtain Club places second in Philo competition • Cooper describes Eastern Pen to Y\u27s • Howard Gale and big-hearted Herbert take stage on alternate nights • English-U.S. relations next forum topic • Next speaker on Burma • Lewis and Padden are student members of college athletic council • Twenty new reporters added to Weekly staff • New ruling, internal disorder, cancels prison trip • 12-6 victory hands dorm crown to Brodbeck gang • Sophs prevail over yearlings, 6-0, in series revival • Bear booters deadlock Delaware 3-3 • Co-eds drop finale to Beaver, 2-0 • P.M.C. turkey day tilt last for 5 seniorshttps://digitalcommons.ursinus.edu/weekly/1883/thumbnail.jp

Invertible Piecewise Linear Approximations for Color Reproduction

We consider the use of linear splines with variable knots for the approximation of unknown functions from data, motivated by control and estimation problems arising in color systems management. Unlike most popular nonlinear-in-parameters representations, piecewise linear (PL) functions can be simply inverted in a closed form. For the one-dimensional case, we present a study comparing PL and neural network (NN) approximations for several function families. Preliminary results suggest that PL, in addition to their analytical benefits, are at least competitive with NN in terms of sum square error, computational effort and training time

A Framework for the Coordination of Legged Robot Gaits

This paper introduces a framework for representing, generating, and then tuning gaits of legged robots. We introduce a convenient parametrization of gait generators as dynamical systems possessing designer specified stable limit cycles over an appropriate torus. This parametrization affords a continuous selection of operation within a coordination design plane, inspired by biology, spanned by axes that determine the mix of feedforward/feedback and centralized/decentralized control. Tuning the gait generator parameters through repeated physical experiments with our robot hexapod, RHex, determines the appropriate operating point - the mix of feedback and degree of control decentralization - to achieve significantly increased performance relative to the centralized feedforward operating point that has governed its previous behavior. The present preliminary experiments with these new gaits suggest that they may permit for the first time locomotion over extremely rough terrain that is almost as reliable, rapid, and energy efficient as the very fastest or most efficient outcomes centralized feedforward gaits can achieve on level ground

Piecewise Linear Homeomorphisms: The Scalar Case

The class of piecewise linear homeomorphisms (PLH) provides a convenient functional representation for many applications wherein an approximation to data is required that is invertible in closed form. In this paper we introduce the graph intersection (GI) algorithm for learning piecewise linear scalar functions in two settings: approximation, where an oracle outputs accurate functional values in response to input queries; and estimation, where only a fixed discrete data base of input-output pairs is available. We provide a local convergence result for the approximation version of the GI algorithm as well as a study of its numerical performance in the estimation setting. We conclude that PLH offers accuracy closed to that of a neural net while requiring, via our GI algorithm, far shorter training time and preserving desired invariant properties unlike any other presently popular basis family

The Ursinus Weekly, June 7, 1937

Norman E. McClure is inaugurated as seventh president of Ursinus College • Brumbaugh urges seniors faith in democracy • Meminger offers seniors optimism • Edward Bell to head graduates next year • Board of Directors names new members • Guest heads forum committee under adopted constitution • Third volume of Dr. McClure\u27s Shakespeare edition completed • College physician active in medical circles, writing • Ursinus College yesterday and tomorrow • Editorial comment: The work of President McClure • Fats and Frankie need your support • Gettysburg tops league; 6 Grizzlies graduated • Gridmen start autumn training Labor Day • Brodbeck captures intramural trophy • 1936-37 summaries • Zoll, Bodley, Padden named as spring sports leaders • Netwomen win 7 out of 8; Ware captains new outfit • Tomlinson takes over reins at student council banquet • Degrees in course, Class of 1937 • Ruby out June 3; Trout wins titles • In Springtime pleases large audience Saturday • Thirteen seniors have jobs in education and business • Registrar\u27s office releases open scholarship awards • Alumni Athletic Club is headed by Malcolm Derk • Y leaders attend conclave • Professors in their childhood daze is feature of Class Day exercises • Mrs. Trinna Moser is new Ursinus Women\u27s Club head • Thirty-three hundred witness Class, Curtain Club, and Hedgerow Playershttps://digitalcommons.ursinus.edu/weekly/3101/thumbnail.jp

Representation of Color Space Transformations for Effective Calibration and Control

We propose the minvar algorithm for computing continuous, continuously invertible, piecewise linear (PL) approximations of color space transformations that can serve as functional replacements wherever look-up tables are presently used. After motivating the importance of invertible approximants in color space management applications, we review the parameterization and computational implementation of PL functions as representing one useful instance of this notion. Finally, we describe the present version of the minvar algorithm and compare the approximations it yields with standard industrial practice — interpolation of look-up table data

The Ursinus Weekly, October 25, 1937

College party again to mark Hallowe\u27en, sponsored by Y\u27s in gym • 8 seniors named as Who\u27s who nominees • Gottshall heads next dance • Knight says school must replace home in training child • Lantern offers $10 in prize money • 125 fathers meet with sons and daughters • Know German and Germany is club aim • Alumnus to write feature in education magazine • Seagrave and Sturges, stage newcomers, star in play • Apply Christianity to college, says speaker • Four leave school, two enter, bringing total to 521 • Philip conducts music hour for music lovers • Ohs and ahs resound with return of Ruby proofs • Clouse temporarily runs supply store • 26 candidates answer Weekly tryout call • Co-eds again to sell novelties at Xmas • Tornetta explains requirements of chemical society • Women debaters establish rules for forensic candidates • Sorority and society • Bears bog down after first quarter, drop first conference meet to Mules • Hockey team wins again, 6-0 • Frosh grid team goes out of existence • Old timers lose to varsity soccermen • Dietz and Wood fight for tennis trophy this week • Brodbeck takes first half of grid round robin • Alumnus wins Drexel comps • Tough Drexel Dragon is bear meat this week • Six new forensicists join mens debate team • Tomlinson takes on change in church in vespers • Singers, instrumentalists perform in Music Club • Business outlook good - Bone; Boswell recalls historyhttps://digitalcommons.ursinus.edu/weekly/1879/thumbnail.jp

Gait Generation and Optimization for Legged Robots

This paper presents a general framework for representing and generating gaitsfor legged robots. We introduce a convenient parametrization of gait generators as dynamical systems possessing specified stable limit cycles over an appropriate torus. Inspired by biology, this parametrization affords a continuous selection of operation within a coordination design plane spanned by axes that determine the mix of ”feedforward/feedback” and centralized/decentralized” control. Applying optimization to the parameterized gait generation system allowed RHex, our robotic hexapod, to learn new gaits demonstrating significant performance increases. For example, RHex can now run at 2.4m/s (up from 0.8m/s), run with a specific resistance of 0.6 (down from 2.0), climb 45◦ inclines (up from 25◦), and traverse 35◦ inclines (up from 15◦)

Strengthening Theoretical Testing in Criminology Using Agent-based Modeling

Objectives: The Journal of Research in Crime and Delinquency (JRCD) has published important contributions to both criminological theory and associated empirical tests. In this article, we consider some of the challenges associated with traditional approaches to social science research, and discuss a complementary approach that is gaining popularity—agent-based computational modeling—that may offer new opportunities to strengthen theories of crime and develop insights into phenomena of interest. Method: Two literature reviews are completed. The aim of the first is to identify those articles published in JRCD that have been the most influential and to classify the theoretical perspectives taken. The second is intended to identify those studies that have used an agent-based model (ABM) to examine criminological theories and to identify which theories have been explored. Results: Ecological theories of crime pattern formation have received the most attention from researchers using ABMs, but many other criminological theories are amenable to testing using such methods. Conclusion: Traditional methods of theory development and testing suffer from a number of potential issues that a more systematic use of ABMs—not without its own issues—may help to overcome. ABMs should become another method in the criminologists toolbox to aid theory testing and falsification