Zone methods and the fermion sign problem

We review a recently proposed approach to the problem of alternating signs for fermionic many body Monte Carlo simulations in finite temperature simulations. We derive an estimate for fermion wandering lengths and introduce the notion of permutation zones, special regions of the lattice where identical fermions may interchange and outside of which they may not. Using successively larger permutation zones, one can extrapolate to obtain thermodynamic observables in regimes where direct simulation is impossible.Comment: 3 pages, 1 figure, Lattice2002(algor

Computing π(N)\pi(N): An elementary approach in O~(N)\tilde{O}(\sqrt{N}) time

We present an efficient and elementary algorithm for computing the number of primes up to $N$ in $\tilde{O}(\sqrt N)$ time, improving upon the existing combinatorial methods that require $\tilde{O}(N ^ {2/3})$ time. Our method has a similar time complexity to the analytical approach to prime counting, while avoiding complex analysis and the use of arbitrary precision complex numbers. While the most time-efficient version of our algorithm requires $\tilde{O}(\sqrt N)$ space, we present a continuous space-time trade-off, showing, e.g., how to reduce the space complexity to $\tilde{O}(\sqrt[3]{N})$ while slightly increasing the time complexity to $\tilde{O}(N^{8/15})$. We apply our techniques to improve the state-of-the-art complexity of elementary algorithms for computing other number-theoretic functions, such as the the Mertens function (in $\tilde{O}(\sqrt N)$ time compared to the known $\tilde{O}(N^{0.6})$), summing Euler's totient function, counting square-free numbers and summing primes. Implementation code is provided

A Framework for Single-Item NFT Auction Mechanism Design

Lately, Non-Fungible Tokens (NFTs), i.e., uniquely discernible assets on a blockchain, have skyrocketed in popularity by addressing a broad audience. However, the typical NFT auctioning procedures are conducted in various, ad hoc ways, while mostly ignoring the context that the blockchain provides. One of the main targets of this work is to shed light on the vastly unexplored design space of NFT Auction Mechanisms, especially in those characteristics that fundamentally differ from traditional and more contemporaneous forms of auctions. We focus on the case that bidders have a valuation for the auctioned NFT, i.e., what we term the single-item NFT auction case. In this setting, we formally define an NFT Auction Mechanism, give the properties that we would ideally like a perfect mechanism to satisfy (broadly known as incentive compatibility and collusion resistance) and prove that it is impossible to have such a perfect mechanism. Even though we cannot have an all-powerful protocol like that, we move on to consider relaxed notions of those properties that we may desire the protocol to satisfy, as a trade-off between implementability and economic guarantees. Specifically, we define the notion of an equilibrium-truthful auction, where neither the seller nor the bidders can improve their utility by acting non-truthfully, so long as the counter-party acts truthfully. We also define asymptotically second-price auctions, in which the seller does not lose asymptotically any revenue in comparison to the theoretically-optimal (static) second-price sealed-bid auction, in the case that the bidders' valuations are drawn independently from some distribution. We showcase why these two are very desirable properties for an auction mechanism to enjoy, and construct the first known NFT Auction Mechanism which provably possesses such formal guarantees.Comment: To appear in ACM DeFi 2022. 17 page

The role of mentorship in protege performance

The role of mentorship on protege performance is a matter of importance to academic, business, and governmental organizations. While the benefits of mentorship for proteges, mentors and their organizations are apparent, the extent to which proteges mimic their mentors' career choices and acquire their mentorship skills is unclear. Here, we investigate one aspect of mentor emulation by studying mentorship fecundity---the number of proteges a mentor trains---with data from the Mathematics Genealogy Project, which tracks the mentorship record of thousands of mathematicians over several centuries. We demonstrate that fecundity among academic mathematicians is correlated with other measures of academic success. We also find that the average fecundity of mentors remains stable over 60 years of recorded mentorship. We further uncover three significant correlations in mentorship fecundity. First, mentors with small mentorship fecundity train proteges that go on to have a 37% larger than expected mentorship fecundity. Second, in the first third of their career, mentors with large fecundity train proteges that go on to have a 29% larger than expected fecundity. Finally, in the last third of their career, mentors with large fecundity train proteges that go on to have a 31% smaller than expected fecundity.Comment: 23 pages double-spaced, 4 figure

Lipopolysaccharide (LPS) Inner-Core Phosphates Are Required for Complete LPS Synthesis and Transport to the Outer Membrane in Pseudomonas aeruginosa PAO1

Gram-negative outer membrane (OM) integrity is maintained in part by Mg2+ cross-links between phosphates on lipid A and on core sugars of adjacent lipopolysaccharide (LPS) molecules. In contrast to other Gram-negative bacteria, waaP, encoding an inner-core kinase, could not be inactivated in Pseudomonas aeruginosa. To examine this further, expression of the kinases WaaP or WapP/WapQ/PA5006 was placed under the control of the arabinose-regulated pBAD promoter. Growth of these strains was arabinose dependent, confirming that core phosphorylation is essential in P. aeruginosa. Transmission electron micrographs of kinase-depleted cells revealed marked invaginations of the inner membrane. SDS-PAGE of total LPS from WaaP-depleted cells showed accumulation of a fast-migrating band. Mass spectrometry (MS) analysis revealed that LPS from these cells exhibits a unique truncated core consisting of two 3-deoxy-d-manno-octulosonic acids (Kdo), two l-glycero-d-manno-heptoses (Hep), and one hexose but completely devoid of phosphates, indicating that phosphorylation by WaaP is necessary for subsequent core phosphorylations. MS analysis of lipid A from WaaP-depleted cells revealed extensive 4-amino-4-deoxy-l-arabinose modification. OM prepared from these cells by Sarkosyl extraction of total membranes or by sucrose density gradient centrifugation lacked truncated LPS. Instead, truncated LPS was detected in the inner membrane fractions, consistent with impaired transport/assembly of this species into the OM

Assessing Vividness of Mental Imagery: The Plymouth Sensory Imagery Questionnaire

Publisher allows archiving of submitted msMental imagery may occur in any sensory modality, although visual imagery has been most studied. A sensitive measure of the vividness of imagery across a range of modalities is needed: the shorter version of Bett’s QMI (Sheehan, 1967) uses outdated items and has an unreliable factor structure. We report the development and initial validation of the Plymouth Sensory Imagery Questionnaire (Psi-Q) comprising items for each of the following modalities: Vision, Sound, Smell, Taste, Touch, Bodily Sensation and Emotional Feeling. An Exploratory Factor Analysis on a 35-item form indicated that these modalities formed separate factors, rather than a single imagery factor, and this was replicated by confirmatory factor analysis. The Psi-Q was validated against the Spontaneous Use of Imagery Scale (Reisberg, Pearson & Kosslyn, 2003) and Marks’ (1995) Vividness of Visual Imagery Questionnaire-2. A short 21-item form comprising the best three items from the seven factors correlated with the total score and subscales of the full form, and with the VVIQ-2. Inspection of the data shows that while visual and sound imagery is most often rated as vivid, individuals who rate one modality as strong and the other as weak are not uncommon. Findings are interpreted within a working memory framework and point to the need for further research to identify the specific cognitive processes underlying the vividness of imagery across sensory modalities

Defining minimum income (and living) standards in Europe : methodological issues and policy debates

Minimum income protection is gaining new significance in European social policy. In an effort to promote social inclusion, the European Parliament has called on the European Commission and EU Member States to guarantee the minimum right to social safety nets. The Commission has been considering, in the context of the Europe 2020 strategy, the possibility of setting minimum standards for social protection. It is timely then to survey the debates surrounding minimum income standards for Europe and some of the different technologies available for setting reference budgets. A European needs-based (minimum) social protection floor should help guard against poverty and exclusion, but there can be no ‘one size fits all’ in Europe. For it is equally clear that higher social standards of protection may be required by citizens in more affluent parts of Europe. How can such distinctions be made, and what are the challenges arising from doing so

General scientific guidance for stakeholders on health claim applications

The European Food Safety Authority (EFSA) asked the Panel on Dietetic Products Nutrition and Allergies (NDA) to update the General guidance for stakeholders on the evaluation of Article 13.1, 13.5 and 14 health claims published in March 2011. Since then, the NDA Panel has completed the evaluation of Article 13.1 claims except for claims put on hold by the European Commission, and has evaluated additional health claim applications submitted pursuant to Articles 13.5, 14 and also 19. In addition, comments received from stakeholders indicate that general issues that are common to all health claims need to be further clarified and addressed. This guidance document aims to explain the general scientific principles applied by the NDA Panel for the evaluation of all health claims and outlines a series of steps for the compilation of applications. The general guidance document represents the views of the NDA Panel based on the experience gained to date with the evaluation of health claims, and it may be further updated, as appropriate, when additional issues are addressed