Abstract: The invention is a method, or a computer implementation thereof, which computes the boundaries of sets that result when two or more sets are multiplied or divided, in the vector sense attributed to Minkowski. In a preferred form, the invention is a novel and useful enabler for devising compensators that effect robust control. Control system designers desire compensators that are robust to uncertainties in plant parameters. The invention solves this problem by identifying, for any frequency, those points in the complex plane which can be mapped into compensators. When applied to the design of control systems, the invention pertains either in the case of a single frequency, or to multiple frequencies. It also pertains to either single or multiple inputs or outputs. The invention generalizes to multi-dimensional applications, not necessarily control-theoretic, wherein problems can be modeled by combinations of Minkowski quotients, products, and sums.

Abstract: The invention is an algorithmic method, or a computer implementation thereof, which synthesizes connectivities. In its prototypical form, the invention computes pairwise channels for an arbitrary number of nodes, minimizing both latency and the cost of channels, such that all, or nearly all, healthy nodes remain connected, despite a prescribed number or proportion of failures in channels and/or nodes. The invention also solves a similar problem, where minimum latency is replaced or augmented by maximum throughput. In general, channels may bear a non-uniform cost, nodes are assigned a value, each channel or node has a corresponding latency and capacity, and fault patterns may be probabilistic or deterministic. In particular, the invention optimizes the connectivity of large numbers of computers, perhaps dynamically self-organizing.

Abstract: The invention creates and reads digital business cards, forms, and stationery. In its capacity as creator, the invention digitizes contact information into a representation suitable for printing, or otherwise transferring, to business cards. More generally, the invention converts files created by any computer application into a digital representation especially suitable for printing, or otherwise transferring, to paper, cardboard, or alternate media. In its capacity as reader, the invention transfers such digitized representations from business cards, forms, or stationery to computer applications. Beneficial applications include the automated scanning of digital business cards into electronic address books and Personal Information Managers, as well as the automated transfer of application-specific forms from paper to online systems for filing and data processing.