A Real Nullstellensatz for Matrices of Non-Commutative Polynomials

This article extends the classical Real Nullstellensatz to matrices of polynomials in a free $\ast$-algebra \RR\axs with $x=(x_1, \ldots, x_n)$. This result is a generalization of a result of Cimpri\vc, Helton, McCullough, and the author. In the free left \RR\axs-module \RR^{1 \times \ell}\axs we introduce notions of the (noncommutative) zero set of a left \RR\axs-submodule and of a real left \RR\axs-submodule. We prove that every element from \RR^{1 \times \ell}\axs whose zero set contains the intersection of zero sets of elements from a finite subset S \subset \RR^{1 \times \ell}\axs belongs to the smallest real left \RR\axs-submodule containing $S$. Using this, we derive a nullstellensatz for matrices of polynomials in \RR\axs. The other main contribution of this article is an efficient, implementable algorithm which for every finite subset S \subset \RR^{1 \times \ell}\axs computes the smallest real left \RR\axs-submodule containing $S$. This algorithm terminates in a finite number of steps. By taking advantage of the rigid structure of \RR\axs, the algorithm presented here is an improvement upon the previously known algorithm for \RR\axs

Ornament and craft:Digital design and the profession

The separation of ornament from Modern architecture declared famously in Adolf Loos’ essay “Ornament and Crime” placed space as the primary concern of architecture, with evidence of craftsmanship and symbolism removed from the canonical and conventional public buildings of the past century. Yet, Harvard Graduate School of Design’s historian Professor Antoine Picon notes the widespread return of ornamental expression in architecture today is “inseparable from the massive diffusion of the computer” and furthered by a “weakening in the tectonic approach and the increased importance attached to surface.” In Cellular Tessellation (CT)—a project developed for Vivid Sydney 2014, an 18-day festival of light, music and ideas – this contemporary problem of the separation of surface from structure was addressed as a core area of interest, as were ornament and the expressive potential of architecture through digitally enabled craftsmanship

A Non-commutative Real Nullstellensatz Corresponds to a Non-commutative Real Ideal; Algorithms

This article takes up the challenge of extending the classical Real Nullstellensatz of Dubois and Risler to left ideals in a *-algebra A. After introducing the notions of non-commutative zero sets and real ideals, we develop three themes related to our basic question: does an element p of A having zero set containing the intersection of zero sets of elements from a finite set S of A belong to the smallest real ideal containing S? Firstly, we construct some general theory which shows that if a canonical topological closure of certain objects are permitted, then the answer is yes, while at the purely algebraic level it is no. Secondly for every finite subset S of the free *-algebra R of polynomials in g indeterminates and their formal adjoints, we give an implementable algorithm which computes the smallest real ideal containing S and prove that the algorithm succeeds in a finite number of steps. Lastly we provide examples of noncommutative real ideals for which a purely algebraic non-commutative real Nullstellensatz holds. For instance, this includes the real (left) ideals generated by a finite sets S in the *-algebra of n by n matrices whose entries are polynomials in one-variable. Further, explicit sufficient conditions on a left ideal in R are given which cover all the examples of such ideals of which we are aware and significantly more.Comment: Improved results compared to earlier version

U.K. inflation targeting and the exchange rate

The United Kingdom*s monetary policy strategy is one of floating exchange rates and inflation forecast targeting, with the targeted measure referring to consumer prices. We consider whether it is welfare-reducing to target inflation in the CPI rather than in a narrower index; and the role of the exchange rate in the transmission of monetary policy actions to CPI inflation. We argue that it is appropriate to model imports as intermediate goods rather than as goods consumed directly by households. This leads to a simpler transmission mechanism of monetary policy, while also offering a sustainable explanation fore the weakness of the exchange rate/inflation relationship and making consumer price inflation an appropriate monetary policy target.Inflation (Finance) - Great Britain ; Foreign exchange rates - Great Britain

Exploring the SDSS Dataset with Linked Scatter Plots: I. EMP, CEMP, and CV Stars

We present the results of a search for extremely metal-poor (EMP), carbon-enhanced metal-poor (CEMP), and cataclysmic variable (CV) stars using a new exploration tool based on linked scatter plots (LSPs). Our approach is especially designed to work with very large spectrum data sets such as the SDSS, LAMOST, RAVE, and Gaia data sets, and it can be applied to stellar, galaxy, and quasar spectra. As a demonstration, we conduct our search using the SDSS DR10 data set. We first created a 3326-dimensional phase space containing nearly 2 billion measures of the strengths of over 1600 spectral features in 569,738 SDSS stars. These measures capture essentially all the stellar atomic and molecular species visible at the resolution of SDSS spectra. We show how LSPs can be used to quickly isolate and examine interesting portions of this phase space. To illustrate, we use LSPs coupled with cuts in selected portions of phase space to extract EMP stars, CEMP stars, and CV stars. We present identifications for 59 previously unrecognized candidate EMP stars and 11 previously unrecognized candidate CEMP stars. We also call attention to 2 candidate He~II emission CV stars found by the LSP approach that have not yet been discussed in the literature.Comment: Accepted by the Astrophysical Journal Supplement (February 2017

Asymptotic safety, hypergeometric functions, and the Higgs mass in spectral action models

We study the renormalization group flow for the Higgs self coupling in the presence of gravitational correction terms. We show that the resulting equation is equivalent to a singular linear ODE, which has explicit solutions in terms of hypergeometric functions. We discuss the implications of this model with gravitational corrections on the Higgs mass estimates in particle physics models based on the spectral action functional.Comment: 25 pages, LaTeX, 8 PDF figure

Models of verbal working memory capacity: What does it take to make them work?

Theories of working memory (WM) capacity limits will be more useful when we know what aspects of performance are governed by the limits and what aspects are governed by other memory mechanisms. Whereas considerable progress has been made on models of WM capacity limits for visual arrays of separate objects, less progress has been made in understanding verbal materials, especially when words are mentally combined to form multiword units or chunks. Toward a more comprehensive theory of capacity limits, we examined models of forced-choice recognition of words within printed lists, using materials designed to produce multiword chunks in memory (e.g., leather brief case). Several simple models were tested against data from a variety of list lengths and potential chunk sizes, with test conditions that only imperfectly elicited the interword associations. According to the most successful model, participants retained about 3 chunks on average in a capacity-limited region of WM, with some chunks being only subsets of the presented associative information (e.g., leather brief case retained with leather as one chunk and brief case as another). The addition to the model of an activated long-term memory component unlimited in capacity was needed. A fixed-capacity limit appears critical to account for immediate verbal recognition and other forms of WM. We advance a model-based approach that allows capacity to be assessed despite other important processing contributions. Starting with a psychological-process model of WM capacity developed to understand visual arrays, we arrive at a more unified and complete model

Environmental attitudes towards wine tourism

Wine tourism marketers frequently seek new ways to promote destinations, often executing ecologically sustainable practices. As consumer environmental knowledge of a wine tourism destination increases, consumer attitudes change, influencing perceptions of the environmental policies of a wine region. In this consumer-driven economy, it is therefore important to search for effective ways to market destinations, and one approach is selective marketing. By focusing on consumers in this manner, it is possible to understand better their concerns and motivations, which should aid in marketing and advertising efforts. This study investigated wine consumers environmental concerns and attitudes about wine regions. Results suggest environmental attitudes differed by demographics regarding the impact of wine tourism, providing ideas on further marketing efforts for those involved in wine tourism