Binomial Setting Research Articles

Mixed volumes of networks with binomial steady-states

The steady-state degree of a chemical reaction network is the number of complex steady-states for generic rate constants and initial conditions. One way to bound the steady-state degree is through the mixed volume of an associated steady-state system. In this work, we show that for partitionable binomial chemical reaction systems, whose resulting steady-state systems are given by a set of binomials and a set of linear (not necessarily binomial) conservation equations, computing the mixed volume is equivalent to finding the volume of a single mixed cell that is the translate of a parallelotope. Additionally, we give a coloring condition on cycle networks to identify reaction systems with binomial steady-state ideals. We highlight both of these theorems using a class of networks referred to as species-overlapping networks and give a formula for the mixed volume of these networks.

American options with acceleration clauses

AbstractAcceleration clauses shorten the residual life of an option when an acceleration condition is met. Acceleration clauses are frequent in warrants, American call options on traded stocks. In warrants with the acceleration clause, if an index (e.g. the average underlying stock) triggers an acceleration threshold, the American call option can be exercised on a much shorter maturity (e.g. 30 days). The actual time-to-maturity of an American option with an acceleration condition is therefore stochastic. In order to evaluate these contracts we first reduce the generic American option with stochastic time-to-maturity to a compound American option with constant maturity, and provide estimates for their prices. Finally we propose an efficient algorithm to price American call options with the acceleration clause in a binomial setting.

P-776 Impact of a poor-quality euploid blastocyst on the implantation of a good-quality one in double embryo transfers

Abstract Study question Does the transfer of a poor-quality blastocyst along with a good-quality blastocyst improve clinical outcomes compared to single good-quality blastocyst transfer in euploid-only transfer cycles? Summary answer Transferring a poor-quality with a good-quality blastocyst improved clinical pregnancy rates but live birth rates were not significantly increased compared to single good-quality blastocyst transfer. What is known already Single embryo transfers (SET) are often preferred when using euploid blastocysts with good morphological characteristics. However, co-transfer of a euploid blastocyst with poor morphological characteristics along with a good-quality euploid blastocyst is still practiced. Studies on embryos with unknown ploidy status suggested that poor-quality blastocysts may hinder the outcomes of good-quality blastocysts when transferred together. Controversial results imply that co-transfer of a poor-quality along with a good-quality blastocyst is associated with similar clinical pregnancy rates and significantly increases multiple pregnancy rates. Outcomes of such double embryo transfers (DET) compared to SETs are yet to be determined in euploid-only blastocyst transfers. Study design, size, duration Retrospective cohort of two centers including 500 SETs and 718 DETs using only euploid blastocysts in FET autologous cycles between March 2017 to January 2021. Transferred blastocysts were graded ≥BL3CC (Gardner criteria) and underwent trophectoderm biopsy on days 5-7 for aneuploidy testing with Next Generation Sequencing. Classification of blastocyst quality (good vs poor) was based on inner cell mass, trophectoderm grades, and the day of blastocyst biopsy. Participants/materials, setting, methods Patients underwent SET of good-quality or DET of good and poor-quality euploid-blastocysts. Endometrial preparation of frozen embryo transfer cycles was achieved with hormonal replacement or within a natural cycle. Reported outcomes included clinical pregnancy (CP), live birth (LB), and high-order pregnancy rates. For comparison of expected and observed LB rates, theoretical rates were estimated with Monte-Carlo simulations using binomial density function and SET data, under the assumption of independency for success rates of individual embryos. Main results and the role of chance After adjusting for Age, AMH, BMI, and cycle preparation method (artificial vs natural), DET of good-quality and poor-quality blastocysts was associated with higher CP rates compared to SET of a good-quality blastocyst (73.1% vs 63.8%, OR: 1.67, 95% CI: 1.12-2.55, P = 0.014). After adjusting for confounders, DET of good-quality and poor-quality blastocysts was not associated with significantly higher LB rates compared to SET of a good-quality blastocyst (56.8% vs 52.8%, OR: 1.25, 95% CI: 0.87-1.83, P = 0.234). Moreover, high-order pregnancy rates were significantly higher in the DET group compared to SET (40.4% vs 1.1%, P < 0.001). Using a model based on SET data, we estimated theoretical LB rates that should be achieved if the LB chance of co-transferred embryos were independent. The model showed that the observed LB rates of DET good and poor-quality blastocysts were significantly lower than the expected average (observed 56.8% vs expected 66.4% [95% CI: 59.0 to 73.8%], P = 0.0154). Limitations, reasons for caution This study has a retrospective design, and estimates are susceptible to residual confounding from unobserved or unaccounted variables. Theoretical rates were estimated under the assumption of independency of transferred embryos. Wider implications of the findings Despite higher CP, DET of poor and good-quality blastocysts did not increase LB compared to SET of good-quality blastocyst and was associated with higher multiple-pregnancy rates. Lower than expected LB rates imply DET to be detrimental to cumulative-LB, and sequential-SET may be preferable, regardless of morphological quality of euploid blastocysts. Trial registration number Not applicable

Predictable forward performance processes in complete markets

We establish existence of Predictable Forward Performance Processes (PFPPs) in conditionally complete markets, which has been previously shown only in the binomial setting. Our market model can be a discrete-time or a continuous-time model, and the investment horizon can be finite or infinite. We show that the main step in construction of PFPPs is solving a one-period problem involving an integral equation, which is the counterpart of the functional equation found in the binomial case. Although this integral equation has been partially studied in the existing literature, we provide a new solution method using the Fourier transform for tempered distributions. We also provide closed-form solutions for PFPPs with inverse marginal functions that are completely monotonic and establish uniqueness of PFPPs within this class. We apply our results to two special cases. The first one is the binomial market and is included to relate our work to the existing literature. The second example considers a generalized Black–Scholes model which, to the best of our knowledge, is a new result.

The Mental Health Evaluation System of College Students Based on Data Mining

In order to solve the problems of high misevaluation rate and low work efficiency in the current mental health evaluation process of college students, a mental health evaluation system based on data mining algorithms is proposed. First, analyze the research status of college students’ mental health evaluation and data mining algorithms and build a mental health evaluation system framework; then, collect college students’ mental health questionnaire data, use the Apriori algorithm based on a three-dimensional matrix to analyze and classify, traverse each attribute of each transaction in the two-dimensional matrix, and directly obtain the frequent item set, frequent binomial set, and frequent three-item set by reading the three-dimensional attribute matrix and the mental health evaluation data to obtain mental health intelligent evaluation results. Finally, specific simulation experiments are used to analyze the feasibility and superiority of the mental health intelligent evaluation system. The results show that the system in the article overcomes the shortcomings of the current mental health intelligent evaluation system, improves the accuracy of mental health intelligent evaluation, improves the efficiency of mental health intelligent evaluation, and the system is more stable, which can meet the actual requirements of current college students’ mental health evaluation.

Amelioration of related complications by the combined usage of Gymnadenia orchidis Lindl and pumpkin seed in type 2 diabetic mice

Inflammation, insulin resistance, hyperinsulinemia and cell damage are the major patho-physiological reasons behind type 2 diabetes (T2DM), which is one of the most prevalent non communicable metabolic disorders in the world. Oral hypoglycemic drugs and insulin shots are usually exercised to treat the diabetic patients but it produces many side effects. Thereby paving the way for natural hypoglycemic agents; a Himalayan herb and alternative nutritional therapy; low glycaemic indexed pumpkin seed, are used in combination for a better management of the disease. The aim of the study was to explore the combined efficacy of Gymnadenia orchidis Lindl root Salep and low-glycemic indexed-pumpkin seeds in better management of T2DM and associated complications. Balb/c mice were randomly allocated to six different groups (n=5). Streptozotocin along with high-fat-diet was used to induce T2DM. The experimental animals were supplemented with low-glycemic food or root Salep (200mg/kg body weight) or combination of both according to their groups for 21days, post which various biochemical tests were performed. T2DM augmented the IL-6, IFN-γ, TNF-α, BAX, Insulin levels, and HOMA-IR with concurrent reduction of IL-4, QUICKI, Bcl-2, estradiol and progesterone levels. FACS revealed augmented cellular damage in T2DM mice. Interestingly, root Salep and pumpkin seeds normalized those parameters in T2DM animals suggesting significant (p<0.001) improvement of immunity of the diseased animals and ameliorated associated complications. Root Salep and pumpkin seed display synergism among binomial set of herbal agents which may be safely used for T2DM management.

Corrections to “Value sets of sparse polynomials”

AbstractWe give a corrected version of our previous lower bound on the value set of binomials (Canad. Math. Bull., v.63, 2020, 187–196). The other results are not affected.

Minimal set of binomial generators for certain Veronese 3-fold projections

The goal of this paper is to explicitly describe a minimal binomial generating set of a class of lattice ideals, namely the ideal of certain Veronese 3-fold projections. More precisely, for any integer d≥4 and any d-th root e of 1 we denote by Xd the toric variety defined as the image of the morphism φTd:P3⟶Pμ(Td)−1 where Td are all monomials of degree d in k[x,y,z,t] invariant under the action of the diagonal matrix M(1,e,e2,e3). In this work, we describe a Z-basis of the lattice Lη associated to I(Xd) as well as a minimal binomial set of generators of the lattice ideal I(Xd)=I+(η).

Strongly Robust Toric Ideals in Codimension 2

A homogeneous ideal is robust if its universal Gröbner basis is also a minimal generating set. For toric ideals, one has the stronger definition: A toric ideal is strongly robust if its Graver basis equals the set of indispensable binomials. We characterize the codimension 2 strongly robust toric ideals by their Gale diagrams. This give a positive answer to a question of Petrovic, Thoma, and Vladoiu in the case of codimension 2 toric ideals.

Power priors based on multiple historical studies for binary outcomes.

Incorporating historical information into the design and analysis of a new clinical trial has been the subject of much recent discussion. For example, in the context of clinical trials of antibiotics for drug resistant infections, where patients with specific infections can be difficult to recruit, there is often only limited and heterogeneous information available from the historical trials. To make the best use of the combined information at hand, we consider an approach based on the multiple power prior that allows the prior weight of each historical study to be chosen adaptively by empirical Bayes. This choice of weight has advantages in that it varies commensurably with differences in the historical and current data and can choose weights near 1 if the data from the corresponding historical study are similar enough to the data from the current study. Fully Bayesian approaches are also considered. The methods are applied to data from antibiotics trials. An analysis of the operating characteristics in a binomial setting shows that the proposed empirical Bayes adaptive method works well, compared to several alternative approaches, including the meta-analytic prior.

Fixed-width confidence interval of log odds ratio for joint binomial and inverse binomial sampling

ABSTRACTThis article provides a two-stage procedure to develop a fixed-width confidence interval of log odds ratio in a joint binomial and inverse binomial setting where the stopping rule is obtained by adopting a two-stage procedure on the number of index subjects for the inverse sampling. A purely sequential version of this procedure is also studied. Different asymptotic results associated with the procedures are obtained. The findings are supported by detailed simulation study followed by one data example.

Adaptive power priors with empirical Bayes for clinical trials.

Incorporating historical information into the design and analysis of a new clinical trial has been the subject of much discussion as a way to increase the feasibility of trials in situations where patients are difficult to recruit. The best method to include this data is not yet clear, especially in the case when few historical studies are available. This paper looks at the power prior technique afresh in a binomial setting and examines some previously unexamined properties, such as Box P values, bias, and coverage. Additionally, it proposes an empirical Bayes-type approach to estimating the prior weight parameter by marginal likelihood. This estimate has advantages over previously criticised methods in that it varies commensurably with differences in the historical and current data and can choose weights near 1 when the data are similar enough. Fully Bayesian approaches are also considered. An analysis of the operating characteristics shows that the adaptive methods work well and that the various approaches have different strengths and weaknesses.

Metabolic and genetic patterns of soil microbial communities in response to different amendments under organic farming system

In the organic farming system plant production mostly depends on the decomposition of soil organic matter through the activity of the microbial biomass, which is able to provide significant quantities of essential nutrients for plant growth. The aim of this work was to compare the persistence of microbial heterotrophic metabolism along decimal dilutions of soil treated with different organic amendments, by using Biolog EcoPlate™. The amount of the different amendments was adjusted in order to meet the N requirement of tomato crop. The Biolog results were used to draw a binomial matrix of data by setting all the positive results to 1 and all the negative results to 0. The occurrence of the microbial oxidation of each Biolog Ecoplates™ C source was calculated as probability ‘p’ on the binomial set of data for each dilution. In terms of persistence of C sources utilization by soil microflora, along decimal soil dilutions, the treatments can be roughly divided in 3 different categories: the worst performing (control), the intermediate performing (biochar), and the best performing (biochar added to an organic fertilizer, the organic fertilizer alone and 3 composts). Biolog positive wells at the dilution 10−4 were used to carry out a molecular characterization of bacterial communities by 16S fingerprinting, through the H′ Shannon diversity index. Microbial communities utilizing cellulose and hemicelluloses as C source changed their species composition in response to the different amendments. In particular, amendments with biochar, regardless of the application of organic fertilizers, brought to the highest diversity of cellulose degrading bacteria.

Computing Gröbner bases associated with lattices

We specialize Moller's algorithm to the computation of Grobner bases related to lattices. We give the complexity analysis of our algorithm. Then we provide experiments showing that our algorithm is more efficient than Buchberger's algorithm for computing the associated Grobner bases. Furthermore we show that the binomial ideal associated to the lattice can be constructed from a set of binomials associated with a set of generators of the corresponding label code. This result is presented in a general way by means of three ideal constructions associated with group codes that constitute the same ideal. This generalizes earlier results for specific cases of group codes such as linear codes, codes over ${\mathbb Z}_m$ and label codes of lattices.

Binomial fibers and indispensable binomials

Let I be an arbitrary ideal generated by binomials. We show that certain equivalence classes of fibers are associated to any minimal binomial generating set of I. We provide a simple and efficient algorithm to compute the indispensable binomials of a binomial ideal from a given generating set of binomials and an algorithm to detect whether a binomial ideal is generated by indispensable binomials.

Household Wealth and Portfolio Choice When Tail Events Are Salient

Robust experimental evidence of systematic violations of expected utility (EU) establishes that individuals facing risk overweight utility from low probability gains and losses when making choices. These ndings motivated development of models of preferences with probability weighting functions, such as rank dependent utility (RDU). We solve for the optimal investing strategy of an RDU investor in a dynamic binomial setting from which we derive implications for investing behavior. We show that relative to EU investors with constant relative risk aversion, commonly measured probability weighting functions produce optimal RDU terminal wealth with signicant downside protection and upside exposure. We additionally nd that in contrast to EU investors, RDU investors optimally choose a portfolio that contains fair bets that provide payos that can be interpreted as lottery outcomes or exposure to idiosyncratic returns. In a calibrated version of the model, we calculate that RDU investors would be willing to pay 5% of their initial wealth for the freedom to trade away from an optimal EU wealth allocation. The dynamic trading strategy that supports the optimal wealth allocation implies portfolio weights that are independent of initial wealth but requires higher risky share after good stock return histories. Optimal trading also implies the possibility of non-participation when historical returns are poor. Our model lls a gap in the literature by providing new quantitative and qualitative predictions that can be tested experimentally or using data on household wealth and portfolio choice.

Goodness-of-fit statistics for log-link regression models

The use of log binomial regression, regression on binary outcomes using a log link, is becoming increasingly popular because it provides estimates of relative risk. However, little work has been done on model evaluation. We used simulations to compare the performance of five goodness-of-fit statistics applied to different models in a log binomial setting, namely the Hosmer–Lemeshow, the normalized Pearson chi-square, the normalized unweighted sum of squares, Le Cessie and van Howelingen's statistic based on smoothed residuals and the Hjort–Hosmer test. The normalized Pearson chi-square was unsuitable as the rejection rate depended also on the range of predicted probabilities. The Le Cessie and van Howelingen's test statistic had poor sampling properties when evaluating a correct model and was also considered to be unsuitable in this context. The performance of the remaining three statistics was comparable in most simulations. However, using real data the Hjort–Hosmer outperformed the other two statistics.

Weighted profile likelihood‐based confidence interval for the difference between two proportions with paired binomial data

Inference on the difference between two binomial proportions in the paired binomial setting is often an important problem in many biomedical investigations. Tang et al. (2010, Statistics in Medicine) discussed six methods to construct confidence intervals (henceforth, we abbreviate it as CI) for the difference between two proportions in paired binomial setting using method of variance estimates recovery. In this article, we propose weighted profile likelihood-based CIs for the difference between proportions of a paired binomial distribution. However, instead of the usual likelihood, we use weighted likelihood that is essentially making adjustments to the cell frequencies of a 2 × 2 table in the spirit of Agresti and Min (2005, Statistics in Medicine). We then conduct numerical studies to compare the performances of the proposed CIs with that of Tang et al. and Agresti and Min in terms of coverage probabilities and expected lengths. Our numerical study clearly indicates that the weighted profile likelihood-based intervals and Jeffreys interval (cf. Tang et al.) are superior in terms of achieving the nominal level, and in terms of expected lengths, they are competitive. Finally, we illustrate the use of the proposed CIs with real-life examples.

Vanishing ideals over complete multipartite graphs

We study the vanishing ideal of the parametrized algebraic toric set associated to the complete multipartite graph G=Kα1,…,αr over a finite field of order q. We give an explicit family of binomial generators for this lattice ideal, consisting of the generators of the ideal of the torus (referred to as type I generators), a set of quadratic binomials corresponding to the cycles of length 4 in G and which generate the toric algebra ofG (type II generators) and a set of binomials of degree q−1 obtained combinatorially from G (type III generators). Using this explicit family of generators of the ideal, we show that its Castelnuovo–Mumford regularity is equal to max{α1(q−2),…,αr(q−2),⌈(n−1)(q−2)/2⌉}, where n=α1+⋯+αr.

On the arithmetic operations over finite fields of characteristic three with low complexity

In this paper, the Hermite polynomial representation is adapted as a new way to represent certain finite fields of characteristic three. We give the multiplication method to multiply two elements of F3n in the Hermite polynomial representation with subquadratic computational complexity by using a divide-and-conquer idea. We show that in some cases there is a set of irreducible binomials in the Hermite polynomial representation to obtain modular reduction with a lower addition complexity than the standard polynomial representation. We also investigate the matrix vector product method for the multiplication of the field elements represented by Hermite polynomials.