Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...
New fabrication technologies have significantly decreased the cost of fabrication of shapes with highly complex geometric structure. One important application of complex fine-scale geometric structures is to create variable effective elastic material prope ...
Let d be a fixed positive integer and let epsilon > 0. It is shown that for every sufficiently large n >= n(0)( d, e), the d-dimensional unit cube can be decomposed into exactly n smaller cubes such that the ratio of the side length of the largest cube to ...
A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any ...
In dynamical systems, the full stability of fixed point solutions is determined by their basins of attraction. Characterizing the structure of these basins is, in general, a complicated task, especially in high dimensionality. Recent works have advocated t ...
We consider elliptic random walks in i.i.d. random environments on . The main goal of this paper is to study under which ellipticity conditions local trapping occurs. Our main result is to exhibit an ellipticity criterion for ballistic behavior which exten ...
Let P be a set of n > d points in for d >= 2. It was conjectured by Zvi Schur that the maximum number of (d-1)-dimensional regular simplices of edge length diam(P), whose every vertex belongs to P, is n. We prove this statement under the condition that any ...
The well-known "necklace splitting theorem" of Alon (1987) asserts that every k-colored necklace can be fairly split into q parts using at most t cuts, provided k(q - 1)
We present a high-throughput microfluidic platform capable of quantitating up to 384 biomarkers in 4 distinct samples by immunoassay. The microfluidic device contains 384 unit cells, which can be individually programmed with pairs of capture and detection ...
This paper addresses the problem of determining the node locations in ad-hoc sensor networks when only connectivity information is available. In previous work, we showed that the localization algorithm MDS-MAP proposed by Y. Shang et al. is able to localiz ...
The skin wrinkling phenomenon was investigated in the case of ultra-light sandwich structures with a honeycomb core manufactured by one-shot vacuum bag processing. The interplay between process pressure and compressive strength of the skin was established. ...
Self-assembly techniques allow for the fabrication of highly organized architectures with atomic-level precision. Here, we report on molecular-level scanning tunneling microscopy observations demonstrating the supramolecular engineering of complex, regular ...
