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

'Speak up, Speak out

“Tackling child poverty is a national mission - it is not something the Scottish Government can do alone, and it takes all of us to deliver the change needed”  -  Nicola Sturgeon MSP, former first minister The current Poverty and Inequality Commission was created by the Child Poverty (Scotland) Act 2017.  MSPs of all parties voted unanimously for its creation, and the adoption of statutory targets to reduce child poverty. The Commission came fully into being in July 2019, when it replaced the previous, non-statutory, Commission in place between 2017 and 2019. The Commission are, in government parlance, an 'advisory non-departmental public body'

The Power of Unentanglement

The class QMA(k). introduced by Kobayashi et al., consists of all languages that can be verified using k unentangled quantum proofs. Many of the simplest questions about this class have remained embarrassingly open: for example, can we give any evidence that k quantum proofs are more powerful than one? Does QMA(k) = QMA(2) for k ≥ 2? Can QMA(k) protocols be amplified to exponentially small error? In this paper, we make progress on all of the above questions. * We give a protocol by which a verifier can be convinced that a 3SAT formula of size m is satisfiable, with constant soundness, given Õ (√m) unentangled quantum witnesses with O(log m) qubits each. Our protocol relies on the existence of very short PCPs. * We show that assuming a weak version of the Additivity Conjecture from quantum information theory, any QMA(2) protocol can be amplified to exponentially small error, and QMA(k) = QMA(2) for all k ≥ 2. * We prove the nonexistence of "perfect disentanglers" for simulating multiple Merlins with one

Memes: The Interaction Between Imagery and Subculture: An Analysis of Situation, Race, and Gender on the Pi Kappa Delta Social Media App

Collegiate speech and debate participants are committed to performance excellence and organizational unity. Pi Kappa Delta, a central organization for this subculture, annually hosts a national competition, during which competitors can create and post memes via the tournament phone app. While it is well-known that memes are a function of participatory culture, no analysis has yet examined memes exclusively consumed by the same subculture which created them. In this study, we examine the implicit messaging of this memetic imagery, and by doing so, gain insight into both the collegiate forensics subculture, and the function of memes in a small group

COMPARATIVE ECONOMICS OF ALTERNATIVE AGRICULTURAL PRODUCTION SYSTEMS: A REVIEW

Farm Management,

Assessing the Density of Vegetation for Wildlife Cover in Regenerating Clearcuts via Analysis of Digital Imagery

Increasing the availability of shrubland habitat is a major conservation priority in the Northeastern United States because many wildlife species require this habitat and its extent has been decreasing in recent decades. Conservation agencies often monitor the number of hectares of shrubland habitat created, but rarely monitor the density of the resulting vegetation because the process is tedious and time-consuming. The current study tested a new approach to assess vegetation density: Digital Imagery Vegetation Analysis (DIVA). We compared the density estimates of DIVA with four other methods (Cover Board, Robel Pole, Height of Obstruction, and Line Intercept), and assessed the advantages and disadvantages of using these five methods in shru- bland studies. We concluded that DIVA offers two main advantages over the other methods: (a) it directly measures the vertical structure of the vegetation and thus better captures the complex wildlife habitat characteristics required by many wildlife, and (b) it does not rely on ocular estimates and thus avoids much of the bias associated with the other methods that estimate vertical structure. Furthermore, DIVA provides a rich documentation that permits quality control and other analyses to be conducted after the fieldwork is completed. However, DIVA is more time consuming than the other methods, thus we recommend either Robel Pole or Cover Board for routine monitoring