Theory of Handwriting

Handwriting production is viewed as a constrained modulation of an underlying oscillatory process. Coupled oscillations in horizontal and vertical directions produce letter forms, and when superimposed on a rightward constant velocity horizontal sweep result in spatially separated letters. Modulation of the vertical oscillation is responsible for control of letter height, either through altering the frequency or altering the acceleration amplitude. Modulation of the horizontal oscillation is responsible for control of corner shape through altering phase or amplitude. The vertical velocity zero crossing in the velocity space diagram is important from the standpoint of control. Changing the horizontal velocity value at this zero crossing controls corner shape, and such changes can be effected through modifying the horizontal oscillation amplitude and phase. Changing the slope at this zero crossing controls writing slant; this slope depends on the horizontal and vertical velocity zero amplitudes and on the relative phase difference. Letter height modulation is also best applied at the vertical velocity zero crossing to preserve an even baseline. The corner shape and slant constraints completely determine the amplitude and phase relations between the two oscillations. Under these constraints interletter separation is not an independent parameter. This theory applies generally to a number of acceleration oscillation patterns such as sinusoidal, rectangular and trapezoidal oscillations. The oscillation theory also provides an explanation for how handwriting might degenerate with speed. An implementation of the theory in the context of the spring muscle model is developed. Here sinusoidal oscillations arise from a purely mechanical sources; orthogonal antagonistic spring pairs generate particular cycloids depending on the initial conditions. Modulating between cycloids can be achieved by changing the spring zero settings at the appropriate times. Frequency can be modulated either by shifting between coactivation and alternating activation of the antagonistic springs or by presuming variable spring constant springs. An acceleration and position measuring apparatus was developed for measurements of human handwriting. Measurements of human writing are consistent with the oscillation theory. It is shown that the minimum energy movement for the spring muscle is bang-coast-bang. For certain parameter values a singular arc solution can be shown to be minimizing. Experimental measurements however indicate that handwriting is not a minimum energy movement.

Sparsely Faceted Arrays: A Mechanism Supporting Parallel Allocation, Communication, and Garbage Collection

Conventional parallel computer architectures do not provide support for non-uniformly distributed objects. In this thesis, I introduce sparsely faceted arrays (SFAs), a new low-level mechanism for naming regions of memory, or facets, on different processors in a distributed, shared memory parallel processing system. Sparsely faceted arrays address the disconnect between the global distributed arrays provided by conventional architectures (e.g. the Cray T3 series), and the requirements of high-level parallel programming methods that wish to use objects that are distributed over only a subset of processing elements. A sparsely faceted array names a virtual globally-distributed array, but actual facets are lazily allocated. By providing simple semantics and making efficient use of memory, SFAs enable efficient implementation of a variety of non-uniformly distributed data structures and related algorithms. I present example applications which use SFAs, and describe and evaluate simple hardware mechanisms for implementing SFAs. Keeping track of which nodes have allocated facets for a particular SFA is an important task that suggests the need for automatic memory management, including garbage collection. To address this need, I first argue that conventional tracing techniques such as mark/sweep and copying GC are inherently unscalable in parallel systems. I then present a parallel memory-management strategy, based on reference-counting, that is capable of garbage collecting sparsely faceted arrays. I also discuss opportunities for hardware support of this garbage collection strategy. I have implemented a high-level hardware/OS simulator featuring hardware support for sparsely faceted arrays and automatic garbage collection. I describe the simulator and outline a few of the numerous details associated with a "real" implementation of SFAs and SFA-aware garbage collection. Simulation results are used throughout this thesis in the evaluation of hardware support mechanisms.