A Math Research Project Inspired by Twin Motherhood

The phenomenon of twins, triplets, quadruplets, and other higher order multiples has fascinated humans for centuries and has even captured the attention of mathematicians who have sought to model the probabilities of multiple births. However, there has not been extensive research into the phenomenon of polyovulation, which is one of the biological mechanisms that produces multiple births. In this paper, I describe how my own experience becoming a mother to twins led me on a quest to better understand the scientific processes going on inside my own body and motivated me to conduct research on polyovulation frequencies. An overview of the previous mathematical research on multiple births, as well as my own contributions involving polyovulation, is presented. Furthermore, I discuss more generally how motherhood can influence and enrich the research agendas of mathematicians

Minimal Noise-Induced Stabilization of One-Dimensional Diffusions

The phenomenon of noise-induced stabilization occurs when an unstable deterministic system of ordinary differential equations is stabilized by the addition of randomness into the system. In this paper, we investigate under what conditions one-dimensional, autonomous stochastic differential equations are stable, where we take the notion of stability to be that of global stochastic boundedness. Specifically, we find the minimum amount of noise necessary for noise-induced stabilization to occur when the drift and noise coefficients are power, polynomial, exponential, or logarithmic functions

Probabilistic Analysis of Polyovulation Frequencies

Polyovulation is the production of more than one ovum, or egg, during a single menstrual cycle. This paper examines the probability of the human ovarian system ovulating $k$ eggs during a single cycle, for $k\geq0$. In order to obtain precise estimates for the probability of polyovulation, we use U.S. birth data from the 1950\u27s (before the introduction of artificial reproductive technologies). However, to utilize birth data, we model the various processes that eggs undergo in order to result in a live birth, including fertilization, possible division, implantation, and potential miscarriage. Our model produces novel estimates for the probability that a fertilized egg divides, as well as for the zygosity type frequencies of twins, triplets, and quadruplets

Minimal Noise-Induced Stabilization of One-Dimensional Diffusions

The phenomenon of noise-induced stabilization occurs when an unstable deterministic system of ordinary differential equations is stabilized by the addition of randomness into the system. In this paper, we investigate under what conditions one-dimensional, autonomous stochastic differential equations are stable, where we take the notion of stability to be that of global stochastic boundedness. Specifically, we find the minimum amount of noise necessary for noise-induced stabilization to occur when the drift and noise coefficients are power, polynomial, exponential, or logarithmic functions

The Burden of Sexual Problems: Perceived Effects on Men’s and Women’s Sexual Partners

Sexual dysfunction sometimes negatively affects the individual, his or her partner, and the relationship. We investigated the relationship between the distress experienced by men and women with orgasmic phase difficulties and the perceived distress of their partner(s). We also identified predictors of perceived partner distress, and related self and partner distress to severity of the problem and relationship quality. Data were drawn from 374 men with premature ejaculation (PE) and 377 women with anorgasmia who responded to a survey regarding their sexual functioning, including their distress about their condition and the perceived distress of their partners. Results yielded an overall distress score consisting of combined self and perceived partners distress, with women showing a higher overall score and higher perceived partner distress than men. For men, significant predictors of perceived partner distress included self-distress, relationship quality, interest in sex, and arousal difficulty; for women, only the level of self-distress significantly predicted perceived partner distress. These findings indicate the burden of experiencing sexual difficulty, identify factors related to perceived partner distress, and demonstrate differences in self versus partner distress across men and women. Overall, such findings reiterate the strong need for the inclusion of the partner in any attempted remediation of a sexual problem

Using the sample maximum to estimate the parameters of the underlying distribution

We propose novel estimators for the parameters of an exponential distribution and a normal distribution when the only known information is a sample of sample maxima; i.e., the known information consists of a sample of m values, each of which is the maximum of a sample of nindependent random variables drawn from the underlying exponential or normal distribution. We analyze the accuracy and precision of the estimators using extreme value theory, as well as through simulations of the sampling distributions. For the exponential distribution, the estimator of the mean is unbiased and its variance decreases as either m or n increases. Likewise, for the normal distribution, we show that the estimator of the mean has negligible bias and the estimator of the variance is unbiased. While the variance of the estimators for the normal distribution decreases as m, the number of sample maxima, increases, the variance increases as n, the sample size over which the maximum is computed, increases. We apply our method to estimate the mean length of pollen tubes in the flowering plant Arabidopsis thaliana, where the known biological information fits our context of a sample of sample maxima

The Burden of Sexual Problems: Perceived Effects on Men’s and Women’s Sexual Partners

Sexual dysfunction sometimes negatively affects the individual, his or her partner, and the relationship. We investigated the relationship between the distress experienced by men and women with orgasmic phase difficulties and the perceived distress of their partner(s). We also identified predictors of perceived partner distress, and related self and partner distress to severity of the problem and relationship quality. Data were drawn from 374 men with premature ejaculation (PE) and 377 women with anorgasmia who responded to a survey regarding their sexual functioning, including their distress about their condition and the perceived distress of their partners. Results yielded an overall distress score consisting of combined self and perceived partners distress, with women showing a higher overall score and higher perceived partner distress than men. For men, significant predictors of perceived partner distress included self-distress, relationship quality, interest in sex, and arousal difficulty; for women, only the level of self-distress significantly predicted perceived partner distress. These findings indicate the burden of experiencing sexual difficulty, identify factors related to perceived partner distress, and demonstrate differences in self versus partner distress across men and women. Overall, such findings reiterate the strong need for the inclusion of the partner in any attempted remediation of a sexual problem

Understanding the Effects of Establishing Various Cutoff Criteria in the Definition of Men with Premature Ejaculation

IntroductionOver the past decade, professional organizations and consensus groups have offered a variety of definitions for premature ejaculation (PE), all generally including a set of common concepts but all varying in specific language and operationalization. Clearly articulated definitions of such conditions are important because they not only affect prevalence rates but also diagnostic inclusionwho is deemed to have the condition and therefore who might be eligible for treatment. AimThe current study had two goals: (i) to examine the effects on prevalence rates of moving the cutoff points from more stringent to less stringent for each of three PE criteriaejaculatory latency, distress, and ejaculating before desired; and (ii) to explore in detail the relationships among the three criteria. MethodsUsing an Internet-based sample of 1,183 men, we examined the responses of 374 with PE-type symptoms based on consensus definitions, and determined the effect of decreasing restrictions on the cutoff criteria. In addition, we calculated both correlations and concordance rates among criteria. ResultsNumeric and graphic depiction of the effects of moving the cutoff point for each of the three criteria is provided in the URL PE Prevalence (c), a dynamic tool developed specifically for this study (). In addition, statistical relationships among the PE criteria suggest sufficient independence to warrant inclusion of all three in a diagnostic procedure as well as to consider a 2-minute ejaculatory latency as the threshold for a PE diagnosis. ConclusionsBased on our data, clinicians should approach the 1-minute ejaculatory latency time (ELT) criterion with flexibility, considering ELTs up to 2 minutes for a PE diagnosis. At the same time, frequency of occurrence of either ejaculating before desired or of distress about the condition, as long as they reach at least 50% of the time, had only minor impact on PE diagnostic inclusion. Rowland DL and Kolba TN. Understanding the effects of establishing various cutoff criteria in the definition of men with premature ejaculation. J Sex Med 2015;12:1175-1183

The Burden of Sexual Problems: Perceived Effects on Men’s and Women’s Sexual Partners

Sexual dysfunction sometimes negatively affects the individual, his or her partner, and the relationship. We investigated the relationship between the distress experienced by men and women with orgasmic phase difficulties and the perceived distress of their partner(s). We also identified predictors of perceived partner distress, and related self and partner distress to severity of the problem and relationship quality. Data were drawn from 374 men with premature ejaculation (PE) and 377 women with anorgasmia who responded to a survey regarding their sexual functioning, including their distress about their condition and the perceived distress of their partners. Results yielded an overall distress score consisting of combined self and perceived partners distress, with women showing a higher overall score and higher perceived partner distress than men. For men, significant predictors of perceived partner distress included self-distress, relationship quality, interest in sex, and arousal difficulty; for women, only the level of self-distress significantly predicted perceived partner distress. These findings indicate the burden of experiencing sexual difficulty, identify factors related to perceived partner distress, and demonstrate differences in self versus partner distress across men and women. Overall, such findings reiterate the strong need for the inclusion of the partner in any attempted remediation of a sexual problem