The frequency of elliptic curve groups over prime finite fields

Letting $p$ vary over all primes and $E$ vary over all elliptic curves over the finite field $\mathbb{F}_p$, we study the frequency to which a given group $G$ arises as a group of points $E(\mathbb{F}_p)$. It is well-known that the only permissible groups are of the form $G_{m,k}:=\mathbb{Z}/m\mathbb{Z}\times \mathbb{Z}/mk\mathbb{Z}$. Given such a candidate group, we let $M(G_{m,k})$ be the frequency to which the group $G_{m,k}$ arises in this way. Previously, the second and fourth named authors determined an asymptotic formula for $M(G_{m,k})$ assuming a conjecture about primes in short arithmetic progressions. In this paper, we prove several unconditional bounds for $M(G_{m,k})$, pointwise and on average. In particular, we show that $M(G_{m,k})$ is bounded above by a constant multiple of the expected quantity when $m\le k^A$ and that the conjectured asymptotic for $M(G_{m,k})$ holds for almost all groups $G_{m,k}$ when $m\le k^{1/4-\epsilon}$. We also apply our methods to study the frequency to which a given integer $N$ arises as the group order $\#E(\mathbb{F}_p)$.Comment: 40 pages, with an appendix by Chantal David, Greg Martin and Ethan Smith. Final version, to appear in the Canad. J. Math. Major reorganization of the paper, with the addition of a new section, where the main results are summarized and explaine

Elliptic curves with a given number of points over finite fields

Given an elliptic curve $E$ and a positive integer $N$, we consider the problem of counting the number of primes $p$ for which the reduction of $E$ modulo $p$ possesses exactly $N$ points over $\mathbb F_p$. On average (over a family of elliptic curves), we show bounds that are significantly better than what is trivially obtained by the Hasse bound. Under some additional hypotheses, including a conjecture concerning the short interval distribution of primes in arithmetic progressions, we obtain an asymptotic formula for the average.Comment: A mistake was discovered in the derivation of the product formula for K(N). The included corrigendum corrects this mistake. All page numbers in the corrigendum refer to the journal version of the manuscrip

Integrated Treatment of Per- and Polyfluoroalkyl Substances in Existing Wastewater Treatment Plants ─ Scoping the Potential of Foam Partitioning

Foam fractionation is becoming increasingly popular as a treatment technology for water contaminated with per- and polyfluoroalkyl substances (PFAS). At many existing wastewater treatment facilities, particularly in aerated treatment steps, foam formation is frequently observed. This study aimed to investigate if foam fractionation for the removal of PFAS could be integrated with such existing treatment processes. Influent, effluent, water under the foam, and foam were sampled from ten different wastewater treatment facilities where foam formation was observed. These samples were analyzed for the concentration of 29 PFAS, also after the total oxidizable precursor (TOP) assay. Enrichment factors were defined as the PFAS concentration in the foam divided by the PFAS concentration in the influent. Although foam partitioning did not lead to decreased ∑PFAS concentrations from influent to effluent in any of the plants, certain long-chain PFAS were removed with efficiencies up to 76%. Moreover, ∑PFAS enrichment factors in the foam ranged up to 105, and enrichment factors of individual PFAS ranged even up to 106. Moving bed biofilm reactors (MBBRs) were more effective at enriching PFAS in the foam than activated sludge processes. Altogether, these high enrichment factors demonstrate that foam partitioning in existing wastewater treatment plants is a promising option for integrated removal. Promoting foam formation and removing foam from the water surface with skimming devices may improve the removal efficiencies further. These findings have important implications for PFAS removal and sampling strategies at wastewater treatment plants

Full Sequence Design of an Alpha-Helical Protein and Investigation of the Importance of Helix Dipole and Capping Effects in Helical Protein Design

Our goal is an objective, quantitative design algorithm based on the physical chemical forces which determine protein structure and stability. To this end, we have developed a cyclical protein design strategy which utilizes theory, computation, and experimentation using a variety of protein systems. We address the inverse folding problem using a protein design algorithm which objectively predicts protein sequences which are compatible with a given fold. Our protein design methodology was developed using a variety of proteins, and therefore should be generalizable to many folds and motifs. To test the generalizability and expand the size of proteins we have designed, engrailed homeodomain (enh), a 51-residue helix-turn-helix motif, was used as a target motif. A series of design calculations and experiments on the thirty surface positions of enh were performed to probe the importance of the helix dipole and capping effects in protein design. Rules for which types of residues were allowed at the helix termini were introduced systematically, resulting in progressively more stable proteins. The first design in the series, which had no considerations for the helix dipole or capping effects, was shown to have the same thermal stability as wild-type enh and the protein with the most stringent rules has a Tm of 75 °C, 32° higher than wild-type and the first design. Therefore, helix dipole and capping effects have a large impact on our ability to design stable proteins. The ten core residues of enh were included in the design calculation. The resulting protein, a 29-fold mutant of wild-type, has a Tm of 81 °C. The full sequence design of enh was computed stepwise. The eleven boundary residues were designed in the context of the surface-core design. The resulting protein, a 39-fold mutant of wild-type enh, has a melting temperature of 114 °C and is 4.7 kcal/mol more stable than wild-type. The structure of the boundary-surface-core design was solved by NMR techniques and found to be in excellent agreement with the target structure. The top 10 structure have a backbone root-mean-square standard deviation of 0.45 Å and the root-mean-square standard deviation between the model structure and experimental backbones is 1.25 Å. The side chain selection algorithm was also extended to the design of peptides to bind tightly to MHC class I proteins. A circular dichroism spectrometry assay was developed to determine the peptide dissociation constants. Three designed peptides were bound more tightly to the MHC class I molecule H-2Kd than known peptides. In addition, an investigation of the removal of disulfide bonds from toxin folds is discussed.</p

Pelvic floor muscle training versus no treatment, or inactive control treatments, for urinary incontinence in women

Background Pelvic floor muscle training (PFMT) is the most commonly used physical therapy treatment for women with stress urinary incontinence (SUI). It is sometimes also recommended for mixed urinary incontinence (MUI) and, less commonly, urgency urinary incontinence (UUI). This is an update of a Cochrane Review first published in 2001 and last updated in 2014. Objectives To assess the effects of PFMT for women with urinary incontinence (UI) in comparison to no treatment, placebo or sham treatments, or other inactive control treatments; and summarise the findings of relevant economic evaluations. Search methods We searched the Cochrane Incontinence Specialised Register (searched 12 February 2018), which contains trials identified from CENTRAL, MEDLINE, MEDLINE In‐Process, MEDLINE Epub Ahead of Print, ClinicalTrials.gov, WHO ICTRP, handsearching of journals and conference proceedings, and the reference lists of relevant articles. Selection criteria Randomised or quasi‐randomised controlled trials in women with SUI, UUI or MUI (based on symptoms, signs or urodynamics). One arm of the trial included PFMT. Another arm was a no treatment, placebo, sham or other inactive control treatment arm. Data collection and analysis At least two review authors independently assessed trials for eligibility and risk of bias. We extracted and cross‐checked data. A third review author resolved disagreements. We processed data as described in the Cochrane Handbook for Systematic Reviews of Interventions. We subgrouped trials by diagnosis of UI. We undertook formal meta‐analysis when appropriate. Main results The review included 31 trials (10 of which were new for this update) involving 1817 women from 14 countries. Overall, trials were of small‐to‐moderate size, with follow‐ups generally less than 12 months and many were at moderate risk of bias. There was considerable variation in the intervention's content and duration, study populations and outcome measures. There was only one study of women with MUI and only one study with UUI alone, with no data on cure, cure or improvement, or number of episodes of UI for these subgroups. Symptomatic cure of UI at the end of treatment: compared with no treatment or inactive control treatments, women with SUI who were in the PFMT groups were eight times more likely to report cure (56% versus 6%; risk ratio (RR) 8.38, 95% confidence interval (CI) 3.68 to 19.07; 4 trials, 165 women; high‐quality evidence). For women with any type of UI, PFMT groups were five times more likely to report cure (35% versus 6%; RR 5.34, 95% CI 2.78 to 10.26; 3 trials, 290 women; moderate‐quality evidence). Symptomatic cure or improvement of UI at the end of treatment: compared with no treatment or inactive control treatments, women with SUI who were in the PFMT groups were six times more likely to report cure or improvement (74% versus 11%; RR 6.33, 95% CI 3.88 to 10.33; 3 trials, 242 women; moderate‐quality evidence). For women with any type of UI, PFMT groups were two times more likely to report cure or improvement than women in the control groups (67% versus 29%; RR 2.39, 95% CI 1.64 to 3.47; 2 trials, 166 women; moderate‐quality evidence). UI‐specific symptoms and quality of life (QoL) at the end of treatment: compared with no treatment or inactive control treatments, women with SUI who were in the PFMT group were more likely to report significant improvement in UI symptoms (7 trials, 376 women; moderate‐quality evidence), and to report significant improvement in UI QoL (6 trials, 348 women; low‐quality evidence). For any type of UI, women in the PFMT group were more likely to report significant improvement in UI symptoms (1 trial, 121 women; moderate‐quality evidence) and to report significant improvement in UI QoL (4 trials, 258 women; moderate‐quality evidence). Finally, for women with mixed UI treated with PFMT, there was one small trial (12 women) reporting better QoL. Leakage episodes in 24 hours at the end of treatment: PFMT reduced leakage episodes by one in women with SUI (mean difference (MD) 1.23 lower, 95% CI 1.78 lower to 0.68 lower; 7 trials, 432 women; moderate‐quality evidence) and in women with all types of UI (MD 1.00 lower, 95% CI 1.37 lower to 0.64 lower; 4 trials, 349 women; moderate‐quality evidence). Leakage on short clinic‐based pad tests at the end of treatment: women with SUI in the PFMT groups lost significantly less urine in short (up to one hour) pad tests. The comparison showed considerable heterogeneity but the findings still favoured PFMT when using a random‐effects model (MD 9.71 g lower, 95% CI 18.92 lower to 0.50 lower; 4 trials, 185 women; moderate‐quality evidence). For women with all types of UI, PFMT groups also reported less urine loss on short pad tests than controls (MD 3.72 g lower, 95% CI 5.46 lower to 1.98 lower; 2 trials, 146 women; moderate‐quality evidence). Women in the PFMT group were also more satisfied with treatment and their sexual outcomes were better. Adverse events were rare and, in the two trials that did report any, they were minor. The findings of the review were largely supported by the 'Summary of findings' tables, but most of the evidence was downgraded to moderate on methodological grounds. The exception was 'participant‐perceived cure' in women with SUI, which was rated as high quality. Authors' conclusions Based on the data available, we can be confident that PFMT can cure or improve symptoms of SUI and all other types of UI. It may reduce the number of leakage episodes, the quantity of leakage on the short pad tests in the clinic and symptoms on UI‐specific symptom questionnaires. The authors of the one economic evaluation identified for the Brief Economic Commentary reported that the cost‐effectiveness of PFMT looks promising. The findings of the review suggest that PFMT could be included in first‐line conservative management programmes for women with UI. The long‐term effectiveness and cost‐effectiveness of PFMT needs to be further researched

Impact of Powder Variability on the Microstructure and Mechanical Behavior of Selective Laser Melted (SLM) Alloy 718

Nickel Alloy 718 has found wide use in high-temperature aerospace applications (up to 700C), due to a combination of good mechanical properties, environmental resistance, and workability at moderate cost. These properties have led Alloy 718 to early adoption by selective laser melting (SLM) additive manufacturing. This presentation will share results from a comprehensive industry survey of 718 powder feedstock for SLM. The survey focuses on the impact of variability in powder characteristics on build quality, microstructure, tensile and high cycle fatigue in the as-fabricated and machined surface conditions. The investigation includes sixteen powder lots from eight suppliers that are produced by gas atomization or rotary atomization in argon or nitrogen. This research was previously presented and published at the 9th International Symposium on Superalloy 718 & Derivatives and was funded by NASA Space Launch System Liquid Engine Office with the Human Exploration Operations Mission Directorate

Recentered importance sampling with applications to Bayesian model validation

Since its introduction in the early 1990s, the idea of using importance sampling (IS) with Markov chain Monte Carlo (MCMC) has found many applications. This article examines problems associated with its application to repeated evaluation of related posterior distributions with a particular focus on Bayesian model validation. We demonstrate that, in certain applications, the curse of dimensionality can be reduced by a simple modification of IS. In addition to providing new theoretical insight into the behavior of the IS approximation in a wide class of models, our result facilitates the implementation of computationally intensive Bayesian model checks. We illustrate the simplicity, computational savings, and potential inferential advantages of the proposed approach through two substantive case studies, notably computation of Bayesian p-values for linear regression models and simulation-based model checking. Supplementary materials including the Appendix and the R code for Section 3.1.2 are available online