We prove criteria for $\mathcal{H}^k$-rectifiability of subsets $\mathbb{R}^n$ with $C^{1,\alpha}$ maps, $0<\alpha\leq 1$, in terms suitable approximate tangent paraboloids. also provide a version the case when there is not an priori plane, measuring on dyadic scales how close set to lying $k$-plane. then discuss relation similar involving Peter Jones' $\beta$ numbers, particular proving that s...

The paper presents a unified perspective on geometric and algebraic criteria for reachability and controllability of controlled switched linear discrete-time systems. Direct connections between geometric and algebraic criteria are established as well as that between the subspace based controllability/reachability algorithmandKalman-type algebraic rank criteria. Also the existing geometric crite...

This paper considers physical layer security and the design of secure coset codes for wiretap channels, where information is not to be leaked to an eavesdropper having a degraded channel. The eavesdropper’s bounds for correct decoding probability and information are first revisited, and a new variant of the information bound is derived. The new bound is valid for a general channel with any fadi...

The design of constrained, “plant-friendly” multisine input signals that optimize a geometric discrepancy criterion arising from Weyl’s Theorem is examined in this paper. Such signals are meaningful for data-centric estimation methods, where uniform coverage of the output state-space is critical. The usefulness of this problem formulation is demonstrated by applying it to a linear example and t...

this study seeks to examine how a company can select the best intermediary for its marketing channels with minimum of criteria and time. a theoretical framework is proposed based on the most important tasks of intermediary and the criteria to measure them. there are four basic tasks and thirty criteria in three independent levels. subsequently, an exploratory case study in iranian food industry...

The GeomLib project addresses the important objective of developing an easy to use, reliable , and open library of robust and eecient geometric algorithms. This paper is a preliminary report on the project. We present here the criteria that have inspired the preliminary design of GeomLib, and discuss the guidelines that we have followed in the initial implementation. We exemplify the innovative...

1 Currently with HKS 2 Corresponding author ([email protected]) ABSTRACT Feature technology has been evolving since the early 1980s, yet is still found in few commercial CAD systems. Traditional CAD systems provide support for geometric design and limited parametric design. Two basic approaches to feature modeling have been developed: design by features and feature recognition. Each of these me...

The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the standard parametric form, but it can also be in the implicit form which is commonly used in algebraic geometry. Not all algebraic developable surfaces have rational parametrizations. In this paper, we focus on the rational developable surfaces. For a ...

This paper presents research on the prototyping of multi-agent systems for architectural design. It proposes a design exploration methodology at the intersection of architecture, engineering, and computer science. The motivation of the work includes exploring bottom up generative methods coupled with optimizing performance criteria including for geometric complexity and objective functions for ...