Octupole response and stability of spherical shape in heavy nuclei

The isoscalar octupole response of a heavy spherical nucleus is analyzed in a semiclassical model based on the linearized Vlasov equation. The octupole strength function is evaluated with different degrees of approximation. The zero-order fixed-surface response displays a remarkable concentration of strength in the $1\hbar\omega$ and $3\hbar\omega$ regions, in excellent agreement with the quantum single-particle response. The collective fixed-surface response reproduces both the high- and low-energy octupole rsonances, but not the low-lying $3^{-}$ collective states, while the moving-surface response function gives a good qualitative description of all the main features of the octupole response in heavy nuclei. The role of triangular nucleon orbits, that have been related to a possible instability of the spherical shape with respect to octupole-type deformations, is discussed within this model. It is found that, rather than creating instability, the triangular trajectories are the only classical orbits contributing to the damping of low-energy octupole excitations.Comment: 10 pages, Latex file, 7 ps figure

List and Certificate Complexities in Replicable Learning

We investigate replicable learning algorithms. Ideally, we would like to design algorithms that output the same canonical model over multiple runs, even when different runs observe a different set of samples from the unknown data distribution. In general, such a strong notion of replicability is not achievable. Thus we consider two feasible notions of replicability called list replicability and certificate replicability. Intuitively, these notions capture the degree of (non) replicability. We design algorithms for certain learning problems that are optimal in list and certificate complexity. We establish matching impossibility results

Kinetic-theory approach to low-energy collective modes in nuclei

Two different solutions of the linearized Vlasov equation for finite systems, characterized by fixed and moving-surface boundary conditions, are discussed in a unified perspective. A condition determining the eigenfrequencies of collective nuclear oscillations, that can be obtained from the moving-surface solution, is studied for isoscalar vibrations of lowest multipolarity. Analytic expressions for the friction and mass parameters related to the low-enegy surface excitations are derived and their value is compared to values given by other models. Both similarities and differences are found with respect to the other approaches, however the close agreement obtained in many cases with one of the other models suggests that, in spite of some important differences, the two approaches are substantially equivalent. The formalism based on the Vlasov equation is more transparent since it leads to analytical expressions that can be a basis for further improvement of the model.Comment: 16 pages, 1 EPS figure, to be published in Nucl. Phys.

An International Study of the Ability and Cost-Effectiveness of Advertising Methods to Facilitate Study Participant Self-Enrolment Into a Pilot Pharmacovigilance Study During Early Pregnancy

Knowledge of the fetal effects of maternal medication use in pregnancy is often inadequate and current pregnancy pharmacovigilance (PV) surveillance methods have important limitations. Patient self-reporting may be able to mitigate some of these limitations, providing an adequately sized study sample can be recruited.To compare the ability and cost-effectiveness of several direct-to-participant advertising methods for the recruitment of pregnant participants into a study of self-reported gestational exposures and pregnancy outcomes.The Pharmacoepidemiological Research on Outcomes of Therapeutics by a European Consortium (PROTECT) pregnancy study is a non-interventional, prospective pilot study of self-reported medication use and obstetric outcomes provided by a cohort of pregnant women that was conducted in Denmark, the Netherlands, Poland, and the United Kingdom. Direct-to-participant advertisements were provided via websites, emails, leaflets, television, and social media platforms.Over a 70-week recruitment period direct-to-participant advertisements engaged 43,234 individuals with the study website or telephone system; 4.78% (2065/43,234) of which were successfully enrolled and provided study data. Of these 90.4% (1867/2065) were recruited via paid advertising methods, 23.0% (475/2065) of whom were in the first trimester of pregnancy. The overall costs per active recruited participant were lowest for email (€23.24) and website (€24.41) advertisements and highest for leaflet (€83.14) and television (€100.89). Website adverts were substantially superior in their ability to recruit participants during their first trimester of pregnancy (317/668, 47.5%) in comparison with other advertising methods (P<.001). However, we identified international variations in both the cost-effectiveness of the various advertisement methods used and in their ability to recruit participants in early pregnancy.Recruitment of a pregnant cohort using direct-to-participant advertisement methods is feasible, but the total costs incurred are not insubstantial. Future research is needed to identify advertising strategies capable of recruiting large numbers of demographically representative pregnant women, preferentially in early pregnancy

Geometry of Rounding: Near Optimal Bounds and a New Neighborhood Sperner's Lemma

A partition $\mathcal{P}$ of $\mathbb{R}^d$ is called a $(k,\varepsilon)$-secluded partition if, for every $\vec{p} \in \mathbb{R}^d$, the ball $\overline{B}_{\infty}(\varepsilon, \vec{p})$ intersects at most $k$ members of $\mathcal{P}$. A goal in designing such secluded partitions is to minimize $k$ while making $\varepsilon$ as large as possible. This partition problem has connections to a diverse range of topics, including deterministic rounding schemes, pseudodeterminism, replicability, as well as Sperner/KKM-type results. In this work, we establish near-optimal relationships between $k$ and $\varepsilon$. We show that, for any bounded measure partitions and for any $d\geq 1$, it must be that $k\geq(1+2\varepsilon)^d$. Thus, when $k=k(d)$ is restricted to ${\rm poly}(d)$, it follows that $\varepsilon=\varepsilon(d)\in O\left(\frac{\ln d}{d}\right)$. This bound is tight up to log factors, as it is known that there exist secluded partitions with $k(d)=d+1$ and $\varepsilon(d)=\frac{1}{2d}$. We also provide new constructions of secluded partitions that work for a broad spectrum of $k(d)$ and $\varepsilon(d)$ parameters. Specifically, we prove that, for any $f:\mathbb{N}\rightarrow\mathbb{N}$, there is a secluded partition with $k(d)=(f(d)+1)^{\lceil\frac{d}{f(d)}\rceil}$ and $\varepsilon(d)=\frac{1}{2f(d)}$. These new partitions are optimal up to $O(\log d)$ factors for various choices of $k(d)$ and $\varepsilon(d)$. Based on the lower bound result, we establish a new neighborhood version of Sperner's lemma over hypercubes, which is of independent interest. In addition, we prove a no-free-lunch theorem about the limitations of rounding schemes in the context of pseudodeterministic/replicable algorithms

Geometry of Rounding

Rounding has proven to be a fundamental tool in theoretical computer science. By observing that rounding and partitioning of $\mathbb{R}^d$ are equivalent, we introduce the following natural partition problem which we call the {\em secluded hypercube partition problem}: Given $k\in \mathbb{N}$ (ideally small) and $\epsilon>0$ (ideally large), is there a partition of $\mathbb{R}^d$ with unit hypercubes such that for every point $p \in \mathbb{R}^d$, its closed $\epsilon$-neighborhood (in the $\ell_{\infty}$ norm) intersects at most $k$ hypercubes? We undertake a comprehensive study of this partition problem. We prove that for every $d\in \mathbb{N}$, there is an explicit (and efficiently computable) hypercube partition of $\mathbb{R}^d$ with $k = d+1$ and $\epsilon = \frac{1}{2d}$. We complement this construction by proving that the value of $k=d+1$ is the best possible (for any $\epsilon$) for a broad class of ``reasonable'' partitions including hypercube partitions. We also investigate the optimality of the parameter $\epsilon$ and prove that any partition in this broad class that has $k=d+1$, must have $\epsilon\leq\frac{1}{2\sqrt{d}}$. These bounds imply limitations of certain deterministic rounding schemes existing in the literature. Furthermore, this general bound is based on the currently known lower bounds for the dissection number of the cube, and improvements to this bound will yield improvements to our bounds. While our work is motivated by the desire to understand rounding algorithms, one of our main conceptual contributions is the introduction of the {\em secluded hypercube partition problem}, which fits well with a long history of investigations by mathematicians on various hypercube partitions/tilings of Euclidean space

Neighborhood Variants of the KKM Lemma, Lebesgue Covering Theorem, and Sperner's Lemma on the Cube

We establish a "neighborhood" variant of the cubical KKM lemma and the Lebesgue covering theorem and deduce a discretized version which is a "neighborhood" variant of Sperner's lemma on the cube. The main result is the following: for any coloring of the unit $d$-cube $[0,1]^d$ in which points on opposite faces must be given different colors, and for any $\varepsilon>0$, there is an $\ell_\infty$ $\varepsilon$-ball which contains points of at least $(1+\frac{\varepsilon}{1+\varepsilon})^d$ different colors, (so in particular, at least $(1+\frac{2}{3}\varepsilon)^d$ different colors for all sensible $\varepsilon\in(0,\frac12]$).Comment: 18 pages plus appendices (30 pages total), 3 figure

Saving money on the PBS: Ranibizumab or Bevacizumab for Neovascular Macular Degeneration?

Federal Health Minister Nicola Roxon recently met with an alliance of consumer, industry and other stakeholders to justify the government’s plan to indefinitely delay the listing of seven new medicines on the Pharmaceutical Benefits Scheme (PBS). She argued that, after considering the advice of the Pharmaceutical Benefits Advisory Committee (PBAC), it was the government’s responsibility to decide whether or not to list a new drug, taking into account other priorities across the health portfolio and current fiscal circumstances. 1 Clearly, the cost of the PBS must be sustainable. However, there are other ways of reducing its cost apart from delaying the listing of drugs recommended by PBAC as cost-effective. The treatment of macular degeneration provides an illustrative example

Exploring metabolic engineering design principles for the photosynthetic production of lactic acid by Synechocystis sp. PCC6803

Background: Molecular engineering of the intermediary physiology of cyanobacteria has become important for the sustainable production of biofuels and commodity compounds from CO2 and sunlight by "designer microbes." The chemical commodity product L-lactic acid can be synthesized in one step from a key intermediary metabolite of these organisms, pyruvate, catalyzed by a lactate dehydrogenase. Synthetic biology engineering to make "designer microbes" includes the introduction and overexpression of the product-forming biochemical pathway. For further optimization of product formation, modifications in the surrounding biochemical network of intermediary metabolism have to be made. Results: To improve light-driven L-lactic acid production from CO2, we explored several metabolic engineering design principles, using a previously engineered L-lactic acid producing mutant strain of Synechocystis sp. PCC6803 as the benchmark. These strategies included: (i) increasing the expression level of the relevant product-forming enzyme, lactate dehydrogenase (LDH), for example, via expression from a replicative plasmid; (ii) co-expression of a heterologous pyruvate kinase to increase the flux towards pyruvate; and (iii) knockdown of phosphoenolpyruvate carboxylase to decrease the flux through a competing pathway (from phosphoenolpyruvate to oxaloacetate). In addition, we tested selected lactate dehydrogenases, some of which were further optimized through site-directed mutagenesis to improve the enzyme’s affinity for the co-factor nicotinamide adenine dinucleotide phosphate (NADPH). The carbon partitioning between biomass and lactic acid was increased from about 5% to over 50% by strain optimization. Conclusion: An efficient photosynthetic microbial cell factory will display a high rate and extent of conversion of substrate (CO2) into product (here: L-lactic acid). In the existing CO2-based cyanobacterial cell factories that have been described in the literature, by far most of the control over product formation resides in the genetically introduced fermentative pathway. Here we show that a strong promoter, in combination with increased gene expression, can take away a significant part of the control of this step in lactic acid production from CO2. Under these premises, modulation of the intracellular precursor, pyruvate, can significantly increase productivity. Additionally, production enhancement is achieved by protein engineering to increase co-factor specificity of the heterologously expressed LDH