Efficacy of Achieving Pregnancy with Fertility-Focused Intercourse

Purpose: To compare pregnancy rates when women have intercourse on self-estimated high and peak fertile days and when they only have intercourse on low fertile days during the fertile window (FW). Study Design and Methods: We used a prospective observational cohort study design. Our convenience sample included 124 women who utilized our online charting Web sites to achieve pregnancy from January 2010 to November 2012. Participants used an electronic hormonal fertility monitor (EHFM) or self-observed cervical mucus or both to determine fertility during the estimated FW. Pregnancy rates were determined with Kaplan–Meier survival analysis. Chi square analysis was used to evaluate the efficacy of achieving pregnancy between two different intercourse patterns. Results: The pregnancy rate was 87 per 100 women at 12 months when intercourse happened on high or peak days and 5 per 100 when intercourse occurred only on low days of the FW. Chi square analysis showed a greater proportion of pregnancies with intercourse on high and peak fertile days of the menstrual cycle (x2 = 40.2, p \u3c .001, df = 1). Nursing Implications: Focusing intercourse on high or peak fertile days during the estimated FW enhances the probability of achieving a desired pregnancy. Fertility awareness-based online charting system is effective in helping women to determine their FW and target intercourse accordingly to achieve pregnancy

Cohort Efficacy Study of Natural Family Planning among Perimenopause Age Women

Objective: To determine the efficacy of using natural family planning (NFP) methods to avoid unintended pregnancy among women of perimenopause age (i.e., age 40-55 years). Design: A secondary analysis of subset data from two prospective observational cohort studies. Setting: A university based in-person and online NFP service program. Participants: One hundred and sixty couples who used either a website or an in-person NFP service to learn how to avoid pregnancy from January 2001 to November 2012. Methods: A prospective 12-month effectiveness study among 160 women (between ages 40-55) who used NFP to avoid pregnancy. The women used either a hormonal fertility monitor, cervical mucus monitoring, or both to estimate the fertile phase of their menstrual cycles. Survival analysis was used to determine the pregnancy rate over 12 months of use. Results: There were a total of five unintended pregnancies among the participants. The typical use pregnancy rate was six per 100 women over 12 months. The monitor alone participants (n = 35) had a 12-month pregnancy rate of three, the participants (n = 73) who used mucus alone had a pregnancy rate of four, and the participants (n = 42) who used the fertility monitor plus mucus had a pregnancy rate of six. Conclusion: Natural family planning methods can be effective for older women to avoid an unintended pregnancy with correct use and adequate instructions. The pregnancy rate most likely was affected by diminished fertility and motivation to limit family size

Iterative Row Sampling

There has been significant interest and progress recently in algorithms that solve regression problems involving tall and thin matrices in input sparsity time. These algorithms find shorter equivalent of a n*d matrix where n >> d, which allows one to solve a poly(d) sized problem instead. In practice, the best performances are often obtained by invoking these routines in an iterative fashion. We show these iterative methods can be adapted to give theoretical guarantees comparable and better than the current state of the art. Our approaches are based on computing the importances of the rows, known as leverage scores, in an iterative manner. We show that alternating between computing a short matrix estimate and finding more accurate approximate leverage scores leads to a series of geometrically smaller instances. This gives an algorithm that runs in $O(nnz(A) + d^{\omega + \theta} \epsilon^{-2})$ time for any $\theta > 0$, where the $d^{\omega + \theta}$ term is comparable to the cost of solving a regression problem on the small approximation. Our results are built upon the close connection between randomized matrix algorithms, iterative methods, and graph sparsification.Comment: 26 pages, 2 figure

Supersolvability and Freeness for ψ-Graphical Arrangements

Let G be a simple graph on the vertex set {v[subscript 1],…,v[subscript n]} with edge set E. Let K be a field. The graphical arrangement A[subscript G] in K[superscript n] is the arrangement x[subscript i]−x[subscript j]=0,v[subscript i]v[subscript j] ∈ E. An arrangement A is supersolvable if the intersection lattice L(c(A)) of the cone c(A) contains a maximal chain of modular elements. The second author has shown that a graphical arrangement A[subscript G] is supersolvable if and only if G is a chordal graph. He later considered a generalization of graphical arrangements which are called ψ-graphical arrangements. He conjectured a characterization of the supersolvability and freeness (in the sense of Terao) of a ψ-graphical arrangement. We provide a proof of the first conjecture and state some conditions on free ψ-graphical arrangements.China Scholarship CouncilNational Science Foundation (U.S.) (Grant DMS-1068625

A Comparison of Two Hormonal Fertility Monitoring Systems for Ovulation Detection: A Pilot Study

Background and Objectives: Accuracy in detecting ovulation and estimating the fertile window in the menstrual cycle is essential for women to avoid or achieve pregnancy. There has been a rapid growth in fertility apps and home ovulation testing kits in recent years. Nevertheless, there lacks information on how well these apps perform in helping users understand their fertility in the menstrual cycle. This pilot study aimed to evaluate and compare the beginning, peak, and length of the fertile window as determined by a new luteinizing hormone (LH) fertility tracking app with the Clearblue Fertility Monitor (CBFM). Materials and Methods: A total of 30 women were randomized into either a quantitative Premom or a qualitative Easy@Home (EAH) LH testing system. The results of the two testing systems were compared with the results from the CBFM over three menstrual cycles of use. Potential LH levels for estimating the beginning of the fertile window were calculated along with user acceptability and satisfaction. Results: The estimates of peak fertility by the Premom and EAH LH testing were highly correlated with the CBFM peak results (R = 0.99, p \u3c 0.001). The participants had higher satisfaction and ease-of-use ratings with the CBFM compared to the Premom and EAH LH testing systems. LH 95% confidence levels for estimating the beginning of the fertile window were provided for both the Premom and EAH LH testing results. Conclusions: Our pilot study findings suggest that the Premom and EAH LH fertility testing app can accurately detect impending ovulation for women and are easy to use at home. However, successful utilization of these low-cost LH testing tools and apps for fertility self-monitoring and family planning needs further evaluation with a large and more diverse population

A greedy algorithm for dropping digits (Functional Pearl)

Consider the puzzle: given a number, remove $k$ digits such that the resulting number is as large as possible. Various techniques were employed to derive a linear-time solution to the puzzle: predicate logic was used to justify the structure of a greedy algorithm, a dependently-typed proof assistant was used to give a constructive proof of the greedy condition, and equational reasoning was used to calculate the greedy step as well as the final, linear-time optimisation

Multisite Effectiveness Study of the Marquette Method of Natural Family Planning Program

Women of reproductive age need reliable and effective family planning methods to manage their fertility. Natural family planning (NFP) methods or fertility awareness-based methods (FABMs) have been increasingly used by women due to their health benefits. Nevertheless, effectiveness of these natural methods remains inconsistent, and these methods are difficult for healthcare providers to implement in their clinical practice. The purpose of this study is to evaluate the effectiveness of the Marquette Model NFP system to avoid pregnancy for women at multiple teaching sites using twelve months of retrospectively collected teaching data. Survival analysis (Kaplan–Meier) was used to determine typical unintended pregnancy rates for a total of 1,221 women. There were forty-two unintended pregnancies which provided a typical use unintended pregnancy rate of 6.7 per 100 women over twelve months of use. Eleven of the forty-two unintended pregnancies were associated with correct use of the method. The total unintended pregnancy rate over twelve months of use was 2.8 per 100 for women with regular cycles, 8.0 per 100 women for the postpartum and breastfeeding women, and 4.3 per 100 for women with irregular menstrual cycles. The Marquette Model system of NFP was effective when provided by health professionals who completed the Marquette Model NFP teacher training program