Every mapping class group is generated by 6 involutions

Let Mod_{g,b} denote the mapping class group of a surface of genus g with b punctures. Feng Luo asked in a recent preprint if there is a universal upper bound, independent of genus, for the number of torsion elements needed to generate Mod_{g,b}. We answer Luo's question by proving that 3 torsion elements suffice to generate Mod_{g,0}. We also prove the more delicate result that there is an upper bound, independent of genus, not only for the number of torsion elements needed to generate Mod_{g,b} but also for the order of those elements. In particular, our main result is that 6 involutions (i.e. orientation-preserving diffeomorphisms of order two) suffice to generate Mod_{g,b} for every genus g >= 3, b = 0, and g >= 4, b = 1.Comment: 15 pages, 7 figures; slightly improved main result; minor revisions. to appear in J. Al

The Need for Market Segmentation in Buy-Till-You-Defect Models

Buy-till-you-defect [BTYD] models are built for companies operating in a non- contractual setting to predict customers’ transaction frequency, amount and timing as well as customer lifetime. These models tend to perform well, although they often predict unrealistically long lifetimes for a substantial fraction of the customer base. This obvious lack of face validity limits the adoption of these models by practitioners. Moreover, it highlights a flaw in these models. Based on a simulation study and an empirical analysis of different datasets, we argue that such long lifetime predictions can result from the existence of multiple segments in the customer base. In most cases there are at least two segments: one consisting of customers who purchase the service or product only a few times and the other of those who are frequent purchasers. Customer heterogeneity modeling in the current BTYD models is insufficient to account for such segments, thereby producing unrealistic lifetime predictions. We present an extension over the current BTYD models to address the extreme lifetime prediction issue where we allow for segments within the customer base. More specifically, we consider a mixture of log-normals distribution to capture the heterogeneity across customers. Our model can be seen as a variant of the hierarchical Bayes [HB] Pareto/NBD model. In addition, the proposed model allows us to relate segment membership as well as within segment customer heterogeneity to selected customer characteristics. Our model, therefore, also increases the explanatory power of BTYD models to a great extent. We are now able to evaluate the impact of customers’ characteristics on the membership probabilities of different segments. This allows, for example, one to a-priori predict which customers are likely to become frequent purchasers. The proposed model is compared against the benchmark Pareto/NBD model (Schmittlein, Morrison, and Colombo 1987) and its HB extension (Abe 2009) on simulated datasets as well as on a real dataset from a large grocery e-retailer in a Western European country. Our BTYD model indeed provides a useful customer segmentation that allows managers to draw conclusions on how customers’ purchase and defection behavior are associated with their shopping characteristics such as basket size and the delivery fee paid

"Counting Your Customers": When will they buy next? An empirical validation of probabilistic customer base analysis models based on purchase timing

This research provides a new way to validate and compare buy-till-you-defect [BTYD] models. These models specify a customer’s transaction and defection processes in a non-contractual setting. They are typically used to identify active customers in a com- pany’s customer base and to predict the number of purchases. Surprisingly, the literature shows that models with quite different assumptions tend to have a similar predictive performance. We show that BTYD models can also be used to predict the timing of the next purchase. Such predictions are managerially relevant as they enable managers to choose appropriate promotion strategies to improve revenues. Moreover, the predictive performance on the purchase timing can be more informative on the relative quality of BTYD models. For each of the established models, we discuss the prediction of the purchase timing. Next, we compare these models across three datasets on the predictive performance on the purchase timing as well as purchase frequency. We show that while the Pareto/NBD and its Hierarchical Bayes extension [HB] models perform the best in predicting transaction frequency, the PDO and HB models predict transaction timing more accurately. Furthermore, we find that differences in a model’s predictive performance across datasets can be explained by the correlation between behavioral parameters and the proportion of customers without repeat purchases

Comment on "Role of heavy meson exchange in near threshold N N --> d pi"

In a recent paper by C. J. Horowitz (Phys. Rev. C {\bf 48}, 2920 (1993)) a heavy meson exchange is incorporated into threshold NN --> d pi to enhance the grossly underestimated cross section. However, that calculation uses an unjustified assumption on the initial and final momenta, which causes an overestimate of this effect by a factor of 3--4. I point out that the inclusion of the Delta(1232) isobar increases the cross section significantly even at threshold.Comment: 7 pages, figures by fax or mail from [email protected]

Bridging Models and Business: Understanding heterogeneity in hidden drivers of customer purchase behavior

__Abstract__ Recent years have seen many advances in quantitative models in the marketing literature. Even though these advances enable model building for a better understanding of customer purchase behavior and customer heterogeneity such that firms develop optimal targeting and pricing strategies, it has been observed that not many of the advanced models have found their way into business practice. This thesis aims to bridge the gap between advanced models and their business applications by systematically extending the use of models. We first focus on probabilistic customer base analysis models that deal with understanding customer heterogeneity and predicting customer behavior. These models specify a customer's transaction and defection processes under a non-contractual setting. Through this study, we show that the timing of the next purchase for each customer can be predicted using these models. We also extend them by modeling customer heterogeneity in a more flexible and insightful way. As a result, managers can obtain a refined segmentation. Based on the customer heterogeneity insights, we then focus on pricing strategies for online retailers who derive their revenues from delivery fees and sales. In order to come up with optimal pricing strategies for delivery fees, we use ideas from the two-part tariff literature. Given the time and costs associated with implementing advanced models/theories in managerial practice, the marketing executives need to be convinced by clearly demonstrating the contributions of such models. Our study serves as a step toward bridging advanced models and business practice by empirically demonstrating their extended contributions

Quasi-free Compton Scattering from the Deuteron and Nucleon Polarizabilities

Cross sections for quasi-free Compton scattering from the deuteron were measured for incident energies of 236--260 MeV at the laboratory angle -135 degrees. The recoil nucleons were detected in a liquid-scintillator array situated at 20 degrees. The measured differential cross sections were used, with the calculations of Levchuk et al., to determine the polarizabilities of the bound nucleons. For the bound proton, the extracted values were consistent with the accepted value for the free proton. Combining our results for the bound neutron with those from Rose et al., we obtain one-sigma constraints of alpha_n = 7.6-14.0 and beta_n = 1.2-7.6.Comment: 4 pages, 3 figures, accepted in PR

Effects of Blade Discharge Angle, Blade Number and Splitter Blade Length on Deep Well Pump Performance

Impellers with splitter blades are used for pumps and compressors in the design of turbomachines. Design parameters such as the number of blades, blade discharge angle and impeller discharge diameter impact affect pump performance and energy consumption. In this study, the effect of the number of blades (z=5, 6, and 7), blade discharge angles (β2b=25, and β2b=35) and splitter blade lengths (40, 55, 70, and 85% of the main blade length) on Deep Well Pump (DWP) performance has been studied experimentally. In the experiments, pump casing, blade inlet angle, blade thickness, blade width and impeller inlet and discharge diameters have been kept fixed while other parameters such as the number of blades, blade discharge angles and splitter blade lengths have been allowed to vary. As a result of the experimental study, the highest efficiency of all the impellers for best efficiency point (b.e.p) has been obtained on the impeller with the number of blades z=6, blade discharge angle 2b=25 and 85% splitter blade addition compared to impellers without splitter blades

Effects of blade discharge angle, blade number and splitter blade length on deep well pump performance

Impellers with splitter blades are used for pumps and compressors in the design of turbomachines. Design parameters such as the number of blades, blade discharge angle and impeller discharge diameter impact affect pump performance and energy consumption. In this study, the effect of the number of blades (z = 5, 6, and 7), blade discharge angles (β2b = 25°, and β2b = 35°) and splitter blade lengths (40, 55, 70, and 85% of the main blade length) on Deep Well Pump (DWP) performance has been studied experimentally. In the experiments, pump casing, blade inlet angle, blade thickness, blade width and impeller inlet and discharge diameters have been kept fixed while other parameters such as the number of blades, blade discharge angles and splitter blade lengths have been allowed to vary. As a result of the experimental study, the highest efficiency of all the impellers for best efficiency point (b.e.p) has been obtained on the impeller with the number of blades z = 6, blade discharge angle β2b = 25° and 85% splitter blade addition compared to impellers without splitter blades

A Simplified Approach for Designing SRMs in Composite Continuous Twin-Tub Girder Bridges

High torsional rigidity and attractive aesthetics in construction of twin-tub girder bridges make them preferable for the design of curved bridges. However, according to the concepts associated with the term “Fracture Critical (FC)” that are in place today, all two-girder bridges are classified as having FC members (FCMs) due to their perceived lack of load path redundancy. For a steel bridge with FCMs, the fracture of any of the FCMs is assumed to result in complete catastrophic failure or significant loss of serviceability; hence, every two years twin-tub girder bridges undergo very expensive hands-on field inspections. This report presents a simplified approach to ensure newly designed twin-tub girder bridges will meet all the requirements defined in the 2018 AASHTO Guide Specifications without performing in-depth FEA. AASHTO-ready proposed specifications are included in Appendix A. It is anticipated that these provisions could be incorporated into the AASHTO LRFD BDS as a new article 6.6.3 Special Provisions for Twin Tub Girder Bridges

Addition of vardenafil into storage solution protects the endothelium in a hypoxia-reoxygenation model

OBJECTIVE: Based upon the well known protective effect of intracellular cyclic guanosine monophosphate (cGMP) accumulation, we tested the hypothesis that storage solution enriched with optimal concentration of the phosphodiestherase-5 inhibitor vardenafil could provide better protection of vascular grafts against reperfusion injury after long-term cold ischaemic storage. METHODS: Isolated thoracic aorta obtained from rats underwent 24-h cold ischaemic preservation in physiological saline or vardenafil (10(-11) M)-supplemented saline solution. Reperfusion injury was simulated by hypochlorite (200 muM) exposure for 30 minutes. Endothelium-dependent vasorelaxation was assessed, and histopathological and molecular-biological examination of the aortic tissue were performed. RESULTS: Compared with the control group, the saline group showed significantly attenuated endothelium-dependent maximal relaxation (Rmax) to acetylcholine after hypoxia-reoxygenation, which was significantly improved by vardenafil supplementation (Rmax control: 98 +/- 1%; saline: 48 +/- 6%; vardenafil: 75 +/- 4%; p < .05). Vardenafil treatment significantly reduced DNA strand breaks (control: 10.6 +/- 6.2%; saline: 72.5 +/- 4.0%; vardenafil: 14.2 +/- 5.2%; p < .05) and increased cGMP score in the aortic wall (control: 8.2 +/- 0.6; saline: 4.5 +/- 0.3; vardenafil: 6.7 +/- 0.6; p < .05). CONCLUSIONS: Our results support the view that impairment of intracellular cGMP signalling plays a role in the pathogenesis of the endothelial dysfunction induced by cold storage warm reperfusion, which can be effectively reversed by pharmacological phosphodiesterase-5 inhibition