The Representation of Natural Numbers in Quantum Mechanics

This paper represents one approach to making explicit some of the assumptions and conditions implied in the widespread representation of numbers by composite quantum systems. Any nonempty set and associated operations is a set of natural numbers or a model of arithmetic if the set and operations satisfy the axioms of number theory or arithmetic. This work is limited to k-ary representations of length L and to the axioms for arithmetic modulo k^{L}. A model of the axioms is described based on states in and operators on an abstract L fold tensor product Hilbert space H^{arith}. Unitary maps of this space onto a physical parameter based product space H^{phy} are then described. Each of these maps makes states in H^{phy}, and the induced operators, a model of the axioms. Consequences of the existence of many of these maps are discussed along with the dependence of Grover's and Shor's Algorithms on these maps. The importance of the main physical requirement, that the basic arithmetic operations are efficiently implementable, is discussed. This conditions states that there exist physically realizable Hamiltonians that can implement the basic arithmetic operations and that the space-time and thermodynamic resources required are polynomial in L.Comment: Much rewrite, including response to comments. To Appear in Phys. Rev.

Vitamin D supplementation for the prevention of depression and poor physical function in older persons: the D-Vitaal study, a randomized clinical trial

Background: Depressive symptoms and impaired physical functioning are prevalent among older adults. Supplementation with vitamin D might improve both conditions, particularly in persons with low vitamin D status. Objective: The D-Vitaal study primarily aimed to investigate the effect of vitamin D supplementation on depressive symptoms, functional limitations and physical performance in a high-risk older population with low vitamin D status. Secondary aims included examining the effect of vitamin D supplementation on anxiety symptoms, cognitive functioning, mobility, hand grip strength and health-related quality of life. Design: This study was a randomized placebo-controlled trial with 155 participants aged 60-80 years who had clinically relevant depressive symptoms, ≥1 functional limitation and serum 25-hydroxyvitamin D (25(OH)D) concentrations of 15-50/70 nmol/L (depending on season). Participants received 1200 IU/day vitamin D3 (n=76) or placebo tablets (n=77) for 12 months. Serum 25(OH)D was measured at baseline and 6 months; outcomes were assessed at baseline, 6 and 12 months. Linear mixed models analyses were conducted according to the intention-to-treat principle to assess the effect of the intervention. Results: The supplementation increased serum 25(OH)D concentrations in the intervention group to a mean of 85 nmol/L (SD: 16) against 43 nmol/L (SD: 18) in the placebo group after 6 months (P<0.001). No relevant differences between the treatment groups were observed regarding depressive symptoms, functional limitations, physical performance, or any of the secondary outcomes. Conclusions: Supplementation with 1200 IU/day vitamin D for 12 months had no effect on depressive symptoms and physical functioning in older persons with relatively low vitamin D status, clinically relevant depressive symptoms and poor physical functioning. KEYWORDS Vitamin D, 25(OH)D, Depressive symptoms, Physical functioning, Functional limitations, Physical performance, Older adults, Randomized Clinical Trial, Prevention, Supplementation

Adapting Agriculture to Climate Change: A Synopsis of Coordinated National Crop Wild Relative Seed Collecting Programs across Five Continents

The Adapting Agriculture to Climate Change Project set out to improve the diversity, quantity, and accessibility of germplasm collections of crop wild relatives (CWR). Between 2013 and 2018, partners in 25 countries, heirs to the globetrotting legacy of Nikolai Vavilov, undertook seed collecting expeditions targeting CWR of 28 crops of global significance for agriculture. Here, we describe the implementation of the 25 national collecting programs and present the key results. A total of 4587 unique seed samples from at least 355 CWR taxa were collected, conserved ex situ, safety duplicated in national and international genebanks, and made available through the Multilateral System (MLS) of the International Treaty on Plant Genetic Resources for Food and Agriculture (Plant Treaty). Collections of CWR were made for all 28 targeted crops. Potato and eggplant were the most collected genepools, although the greatest number of primary genepool collections were made for rice. Overall, alfalfa, Bambara groundnut, grass pea and wheat were the genepools for which targets were best achieved. Several of the newly collected samples have already been used in pre-breeding programs to adapt crops to future challenges.info:eu-repo/semantics/publishedVersio

Demand Function Estimation and the Law of One Price.

This paper shows that the method of estimating of demand functions may contain an erroneous, implicit assumption when aggregated data are used. This assumption, revealed by the choice of regressors, yields estimates of own price elasticity and other coefficients that are inconsistent. It can also cause heteroscedasticity in the second stage of two-stage least squares estimation where none would otherwise exist.

Evidence on Grades and Grade Inflation at Ontario's Universities

Using information on first-year university grades from across Ontario, we examine whether or not there has been grade inflation by discipline. In a survey of seven universities for the periods 1973-74 and 1993-94, we find significant grade inflation in various Arts and Science programs. The rate of inflation is not uniform. Some subjects, such as Mathematics experienced little or no change in average grades at most universities, while English and Biology experienced significant grade inflation.