Interplay Between Transmission Delay, Average Data Rate, and Performance in Output Feedback Control over Digital Communication Channels

The performance of a noisy linear time-invariant (LTI) plant, controlled over a noiseless digital channel with transmission delay, is investigated in this paper. The rate-limited channel connects the single measurement output of the plant to its single control input through a causal, but otherwise arbitrary, coder-controller pair. An infomation-theoretic approach is utilized to analyze the minimal average data rate required to attain the quadratic performance when the channel imposes a known constant delay on the transmitted data. This infimum average data rate is shown to be lower bounded by minimizing the directed information rate across a set of LTI filters and an additive white Gaussian noise (AWGN) channel. It is demonstrated that the presence of time delay in the channel increases the data rate needed to achieve a certain level of performance. The applicability of the results is verified through a numerical example. In particular, we show by simulations that when the optimal filters are used but the AWGN channel (used in the lower bound) is replaced by a simple scalar uniform quantizer, the resulting operational data rates are at most around 0.3 bits above the lower bounds.Comment: A less-detailed version of this paper has been accepted for publication in the proceedings of ACC 201

Homomorphisms of Gray-categories as pseudo algebras

Given Gray-categories $P$ and $L$, there is a Gray-category $\mathrm{Tricat}_{\mathrm{ls}}(P,L)$ of locally strict trihomomorphisms with domain $P$ and codomain $L$, tritransformations, trimodifications, and perturbations. If the domain $P$ is small and the codomain $L$ is cocomplete, we show that this Gray-category is isomorphic as a Gray-category to the Gray-category $\mathrm{Ps}$-$T$-$\mathrm{Alg}$ of pseudo algebras, pseudo functors, transformations, and modifications for a Gray-monad $T$ derived from left Kan extension. Inspired by a similar situation in two-dimensional monad theory, we apply the coherence theory of three-dimensional monad theory and prove that the the inclusion of the functor category in the enriched sense into this Gray-category of locally strict trihomomorphisms has a left adjoint such that the components of the unit of the adjunction are internal biequivalences. This proves that any locally strict trihomomorphism between Gray-categories with small domain and cocomplete codomain is biequivalent to a Gray-functor. Moreover, the hom Gray-adjunction gives an isomorphism of the hom 2-categories of tritransformations between a locally strict trihomomorphism and a Gray-functor with the corresponding hom 2-categories in the functor Gray-category. A notable example is given by locally strict Gray-valued presheafs with small domain. Our results have applications in three-dimensional descent theory and point into the direction of a Yoneda lemma for tricategories.Comment: 62 page

A Quillen model structure for Gray-categories

A Quillen model structure on the category Gray-Cat of Gray-categories is described, for which the weak equivalences are the triequivalences. It is shown to restrict to the full subcategory Gray-Gpd of Gray-groupoids. This is used to provide a functorial and model-theoretic proof of the unpublished theorem of Joyal and Tierney that Gray-groupoids model homotopy 3-types. The model structure on Gray-Cat is conjectured to be Quillen equivalent to a model structure on the category Tricat of tricategories and strict homomorphisms of tricategories.Comment: v2: fuller discussion of relationship with work of Berger; localizations are done directly with simplicial set

Gray Market Goods: A Lighter Shade of Black Symposium: The Controversy over the Importation of Gray Market Goods: Is a Resolution Forthcoming

If a street vendor offers a famous brand-name product for a substantially lower price than one would expect, the average consumer\u27s initial reaction might be that the product had been stolen or was hot - a product of the black market. While such discounted goods might indeed be stolen, sophisticated consumers have come to expect similar discounts in stores and mail-order houses throughout the country on goods not from the black market but rather from the gray market. These products, naturally enough, are called gray market goods or simply gray goods. Gray goods are brand-name products manufactured abroad which bear an authentic trademark authorized by the owner of the trademark in the market for which the goods are intended. The owner of the trademark is usually foreign. These goods are normally intended for markets outside the United States at the time of manufacture. At some point, however, the gray goods are diverted or imported into the United States for the purpose of competing with the U.S. trademark owner\u27s authorized goods. Historically, the importation of gray goods was rare and sporadic. As a consequence, the U.S. Customs Service\u27s regulations which permit their importation were ignored. Gray goods, as a legal topic, were confined to the backwaters of antitrust and intellectual property law. In the last few years, however, the importation of gray goods has become a growth industry and has generated numerous lawsuits and commentaries. While the initial growth in the gray market was spurred by the very high value of the U.S. dollar in international currency markets, it appears that now a permanent gray market network has developed that will make the subject of gray-goods importation one of importance for years to come regardless of the value of the dollar

Induced mutations by gamma ray irradiation to Argomulyo soybean (Glycine max) variety

Hanafiah DS, Trikoesoemaningtyas, Yahya S, Wirnas D. 2010. Mutasi induksi irradiasi sinar gamma pada varietas kedelai Argomulyo (Glycine max). Nusantara Bioscience 2: 121-125. Induksi tanaman dengan irradiasi sinar gamma merupakan salah satu cara untuk meningkatkan keragaman genetik tanaman. Penelitian ini menggunakan irradiasi sinar gamma pada tingkat atau dosis rendah (mutasi mikro). Tujuan penelitian ini untuk mengetahui respon pemberian tingkat irradiasi mikro sinar gamma pada benih kedelai. Benih kedelai [Glycine max (L) Merr] yang diuji adalah kedelai varietas Argomulyo yang diirradiasi sinar gamma dengan dosis 0 Gray, 50 Gray, 100 Gray, 150 Gray dan 200 Gray. Keragaman yang diperoleh dari setiap peubah amatan yang diperoleh pada generasi M1 dan M2 menunjukkan bahwa perlakuan irradiasi dapat mempengaruhi pertumbuhan dan perkembangan tanaman secara kualitatif dan kuantitatif, yang akhirnya akan mempengaruhi produksi tanaman. Variasi fenotipe pada tanaman kedelai generasi M2 tertinggi rata-rata terjadi pada perlakuan 200 Gray. Hasil penelitian menunjukkan bahwa irradiasi sinar gamma pada dosis 200 Gray efektif menyebabkan terjadinya keragaman genetik tanaman. Kata kunci : mutasi induksi, mutasi mikro, irradiasi sinar gamma, kedelai varietas Argomulyo