Some upper and lower bounds on PSD-rank

Positive semidefinite rank (PSD-rank) is a relatively new quantity with applications to combinatorial optimization and communication complexity. We first study several basic properties of PSD-rank, and then develop new techniques for showing lower bounds on the PSD-rank. All of these bounds are based on viewing a positive semidefinite factorization of a matrix $M$ as a quantum communication protocol. These lower bounds depend on the entries of the matrix and not only on its support (the zero/nonzero pattern), overcoming a limitation of some previous techniques. We compare these new lower bounds with known bounds, and give examples where the new ones are better. As an application we determine the PSD-rank of (approximations of) some common matrices.Comment: 21 page

On the sum-of-squares degree of symmetric quadratic functions

We study how well functions over the boolean hypercube of the form $f_k(x)=(|x|-k)(|x|-k-1)$ can be approximated by sums of squares of low-degree polynomials, obtaining good bounds for the case of approximation in $\ell_{\infty}$-norm as well as in $\ell_1$-norm. We describe three complexity-theoretic applications: (1) a proof that the recent breakthrough lower bound of Lee, Raghavendra, and Steurer on the positive semidefinite extension complexity of the correlation and TSP polytopes cannot be improved further by showing better sum-of-squares degree lower bounds on $\ell_1$-approximation of $f_k$; (2) a proof that Grigoriev's lower bound on the degree of Positivstellensatz refutations for the knapsack problem is optimal, answering an open question from his work; (3) bounds on the query complexity of quantum algorithms whose expected output approximates such functions.Comment: 33 pages. Second version fixes some typos and adds reference

Two new results about quantum exact learning

We present two new results about exact learning by quantum computers. First, we show how to exactly learn a $k$-Fourier-sparse $n$-bit Boolean function from $O(k^{1.5}(\log k)^2)$ uniform quantum examples for that function. This improves over the bound of $\widetilde{\Theta}(kn)$ uniformly random classical examples (Haviv and Regev, CCC'15). Our main tool is an improvement of Chang's lemma for the special case of sparse functions. Second, we show that if a concept class $\mathcal{C}$ can be exactly learned using $Q$ quantum membership queries, then it can also be learned using $O\left(\frac{Q^2}{\log Q}\log|\mathcal{C}|\right)$ classical membership queries. This improves the previous-best simulation result (Servedio and Gortler, SICOMP'04) by a $\log Q$-factor.Comment: v3: 21 pages. Small corrections and clarification

Pastoral Khans: from Mongolian Steppe to African Savannah

The developing field of Mongolian International Studies offers a diverse range of research topics. A review of recent articles reflects an emphasis on geo-politics, particularly evolving relations with its superpower neighbours. Whilst state-to-state engagement with China and Russia predominates, regional countries (Japan, Korea) and the US and Europe are examined within the ‘Third Neighbour’ policy. Trade and economics are also studied, from Oyu Tolgoi and mining to the role of the IMF and international agencies. Currently lacking is a focus on human-driven engagement that reflects Mongolian livelihoods, spirituality and community environments. Such social and cultural dynamics are essential to both pastoral and rural livelihoods and to understanding the nation. In 2020-2022 international academic endeavours enabled Mongolian herder representatives to participate in a global drylands exchange network with dryland residents in thirteen countries. The process provided an exceptional opportunity to present Mongolian perspectives to pastoralists and academics from Africa, the Middle East and Central Asia. This grounded Mongolian livelihoods and situated rural dynamics in a global context. Here we report key engagements and findings as Mongolian herders shared lives and practices in the context of this international pastoral/drylands project. Moving beyond the political/economic rubric, as this project did, delivers a more representative and complete comprehension of Mongolia to the global international studies community

Many-electron expansion: A density functional hierarchy for strongly correlated systems

Density functional theory (DFT) is the de facto method for the electronic structure of weakly correlated systems. But for strongly correlated materials, common density functional approximations break down. Here, we derive a many-electron expansion (MEE) in DFT that accounts for successive one-, two-, three-, ... particle interactions within the system. To compute the correction terms, the density is first decomposed into a sum of localized, nodeless one-electron densities (ρ_{i}). These one-electron densities are used to construct relevant two- (ρ_{i}+ρ_{j}), three- (ρ_{i}+ρ_{j}+ρ_{k}), ... electron densities. Numerically exact results for these few-particle densities can then be used to correct an approximate density functional via any of several many-body expansions. We show that the resulting hierarchy gives accurate results for several important model systems: the Hubbard and Peierls-Hubbard models in 1D and the pure Hubbard model in 2D. We further show that the method is numerically convergent for strongly correlated systems: applying successively higher order corrections leads to systematic improvement of the results. MEE thus provides a hierarchy of density functional approximations that applies to both weakly and strongly correlated systems.National Science Foundation (U.S.) (NSF (CHE-1464804))David & Lucile Packard Foundation (grant

OUTCOMES FROM OUR VISITING TEACHING FELLOW PROGRAM IN THE SCHOOL OF PHYSICS

In 2017 a visiting teaching fellow program was introduced in the School of Physics, University of New South Wales. Each year a high school teacher is seconded to the university to teach first year classes and develop outreach materials. This has led to a very fruitful partnership between teachers and academics. Projects that the teaching fellows have worked on include the introduction of online depth study resources to support the introduction of new Higher School Certificate syllabi; the opening of the first year physics laboratory out of term for school excursions; and the introduction of a summer school program, SciX, to support the extension science syllabus. Many of these projects expanded from physics to encompass the entire science faculty. The teachers have found the experience rewarding and refreshing while academics have benefitted from having a high school teacher’s insights into the background of our incoming students

Becoming Solar:Towards More-Than-Human Understandings of Solar Energy

In this article we examine the experiences of the first and second author who have changed themselves to become newly attuned to the sun, or who have “become solar”. Motivated by calls to approach solar design in novel, less technocratic ways, we reflect on their one-year journey to gain a new relationship with solar energy as an explicitly more-than-human design (MTHD) approach. We argue that their perception of solar energy progressively worked to decentre them as human actors in this new solar-energy arrangement, revealing other nonhuman actors at play, instigating situations of care and attention to those nonhumans and ultimately guiding them towards what it means to be solar. For solar design, we see this approach as creating a new lens for solar designers to draw from. For MTHD, we see this acting as a practical example for designers seeking to begin transforming themselves in their own practice by taking initial steps towards a MTHD approach.</p

Pharmacokinetic and Pharmacodynamic Studies of Elacestrant, A Novel Oral Selective Estrogen Receptor Degrader, in Healthy Post-Menopausal Women

BACKGROUND AND OBJECTIVES: Advanced estrogen receptor-positive (ER+) breast cancer is currently treated with endocrine therapy. Elacestrant is a novel, nonsteroidal, selective estrogen receptor degrader with complex dose-related ER agonist/antagonist activity that is being developed as a treatment option for ER+ breast cancer. METHODS: Two first-in-human phase 1 studies of elacestrant in healthy postmenopausal women (Study 001/Study 004) were conducted to determine its pharmacokinetic and pharmacodynamic profile as well as its safety and maximum tolerated dose. RESULTS: In total, 140 postmenopausal subjects received at least one dose of study drug (114 received elacestrant and 26 received placebo). Single-ascending dose and multiple-ascending dose assessments showed that doses up to 1000 mg daily were safe and well tolerated, and the maximum tolerated dose was not reached. Oral administration of elacestrant had an absolute bioavailability of 10% and a mean half-life ranging from 27 to 47 h, reaching steady state after 5-6 days. Mean occupancy of the ER in the uterus after seven daily doses was 83% for 200 mg and 92% for 500 mg daily. The median ratio of elacestrant concentrations in the cerebral spinal fluid vs. plasma was 0.126% (500 mg dose) and 0.205% (200 mg dose). Most adverse events were related to the upper gastrointestinal tract. CONCLUSIONS: These data demonstrate that elacestrant has good bioavailability when administered orally with a half-life that supports once-daily administration. Engagement of the ER and some ability to cross the blood-brain barrier was demonstrated in addition to an acceptable safety profile

Correction to:Pharmacokinetic and Pharmacodynamic Studies of Elacestrant, A Novel Oral Selective Estrogen Receptor Degrader, in Healthy Post-Menopausal Women (European Journal of Drug Metabolism and Pharmacokinetics, (2020), 45, 5, (675-689), 10.1007/s13318-020-00635-3)

Authors would like to correct the errors in table 2