Defining block character

In this paper I propose a clear, efficient, and accurate method for determining if a block of contiguous buildings has an overall character. The work is needed because most contemporary design reviews presuppose the existence of visual character, but existing design principles are often too vague to make the required determination. Clarity is achieved by shifting from vague notions to a definite concept for block character: a design feature will be perceived as part of the overall character of that block if the frequency of the feature is greater than a critical threshold. An experiment suggested that the critical frequency was quite high: over 80%. A case history illustrates how the new concept of visual character could greatly increase the efficiency and accuracy of actual planning decisions.

Betti diagrams from graphs

The emergence of Boij-S\"oderberg theory has given rise to new connections between combinatorics and commutative algebra. Herzog, Sharifan, and Varbaro recently showed that every Betti diagram of an ideal with a k-linear minimal resolution arises from that of the Stanley-Reisner ideal of a simplicial complex. In this paper, we extend their result for the special case of 2-linear resolutions using purely combinatorial methods. Specifically, we show bijective correspondences between Betti diagrams of ideals with 2-linear resolutions, threshold graphs, and anti-lecture hall compositions. Moreover, we prove that any Betti diagram of a module with a 2-linear resolution is realized by a direct sum of Stanley-Reisner rings associated to threshold graphs. Our key observation is that these objects are the lattice points in a normal reflexive lattice polytope.Comment: To appear in Algebra and Number Theory, 15 pages, 7 figure

Television noise-reduction device

System greatly improves signal-to-noise ratio with little or no loss in picture resolution. By storage of luminance component, which is summed with chrominance component, system performs mathematical integration of basically-repetitive television signals. Integration of signals over interval of their repetition causes little change in original signals and eliminates random noise

Television noise reduction device

A noise reduction system that divides the color video signal into its luminance and chrominance components is reported. The luminance component of a given frame is summed with the luminance component of at least one preceding frame which was stored on a disc recorder. The summation is carried out so as to achieve a signal amplitude equivalent to that of the original signal. The averaged luminance signal is then recombined with the chrominance signal to achieve a noise-reduced television signal