Classifying blocks with abelian defect groups of rank 33 for the prime 22

In this paper we classify all blocks with defect group $C_{2^n}\times C_2\times C_2$ up to Morita equivalence. Together with a recent paper of Wu, Zhang and Zhou, this completes the classification of Morita equivalence classes of $2$-blocks with abelian defect groups of rank at most $3$. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field. The case considered in this paper is significant because it involves comparison of Morita equivalence classes between a group and a normal subgroup of index $2$, so requires novel reduction techniques which we hope will be of wider interest. We note that this also completes the classification of blocks with abelian defect groups of order dividing $16$ up to Morita equivalence. A consequence is that Broue's abelian defect group conjecture holds for all blocks mentioned above

Morita equivalence classes of 2-blocks of defect three

We give a complete description of the Morita equivalence classes of blocks with elementary abelian defect groups of order 8 and of the derived equivalences between them. A consequence is the verification of Brou\'e's abelian defect group conjecture for these blocks. It also completes the classification of Morita and derived equivalence classes of 2-blocks of defect at most three defined over a suitable field

Some examples of Picard groups of blocks

We calculate examples of Picard groups for 2-blocks with abelian defect groups with respect to a complete discrete valuation ring. These include all blocks with abelian 2-groups of 2-rank at most three with the exception of the principal block of J1. In particular this shows directly that all such Picard groups are finite and Picent, the group of Morita auto-equivalences fixing the centre, is trivial. These are amongst the first calculations of this kind. Further we prove some general results concerning Picard groups of blocks with normal defect groups as well as some other cases.Comment: 21 page

Towards Donovan's conjecture for abelian defect groups

We define a new invariant for a $p$-block, the strong Frobenius number, which we use to address the problem of reducing Donovan's conjecture to normal subgroups of index p. As an application we use the strong Frobenius number to complete the proof of Donovan's conjecture for 2-blocks with abelian defect groups of rank at most 4 and for 2-blocks with abelian defect groups of order at most 64

Underreporting Chargeable Time: A Continuing Problem for Public Accounting Firms

Prior research shows that underreporting chargeable time has been a concern for public accounting firms even though many of these firms have policies and procedures that prohibit eating time. The purpose of this study is to examine the current state of this problem and to provide recommendations to manage the problem more effectively. Practicing public accountants at all professional levels were surveyed to determine the extent, opportunity, ethical perception and perceived benefits of underreporting time. The results show that although the majority of the respondents believe underreporting time is unethical, the majority of them did not report all of their chargeable hours in the prior year. The main reasons for such behavior stem from the desire to: (1) receive better periodic performance evaluations, (2) be viewed as competent by superiors and (3) receive promotions

Residential proximity to major roadways and prevalent hypertension among postmenopausal women: results from the Women's Health Initiative San Diego Cohort.

BackgroundLiving near major roadways has been linked with increased risk of cardiovascular events and worse prognosis. Residential proximity to major roadways may also be associated with increased risk of hypertension, but few studies have evaluated this hypothesis.Methods and resultsWe examined the cross-sectional association between residential proximity to major roadways and prevalent hypertension among 5401 postmenopausal women enrolled into the San Diego cohort of the Women's Health Initiative. We used modified Poisson regression with robust error variance to estimate the association between prevalence of hypertension and residential distance to nearest major roadway, adjusting for participant demographics, medical history, indicators of individual and neighborhood socioeconomic status, and for local supermarket/grocery and fast food/convenience store density. The adjusted prevalence ratios for hypertension were 1.22 (95% CI: 1.07, 1.39), 1.13 (1.00, 1.27), and 1.05 (0.99, 1.12) for women living ≤100, >100 to 200, and >200 to 1000 versus >1000 m from a major roadway (P for trend=0.006). In a model treating the natural log of distance to major roadway as a continuous variable, a shift in distance from 1000 to 100 m from a major roadway was associated with a 9% (3%, 16%) higher prevalence of hypertension.ConclusionsIn this cohort of postmenopausal women, residential proximity to major roadways was positively associated with the prevalence of hypertension. If causal, these results suggest that living close to major roadways may be an important novel risk factor for hypertension

Racial differences in symptom management approaches among persons with radiographic knee osteoarthritis

Background The extent to which racial differences exist in use of treatments for osteoarthritis (OA) is debatable. The purpose of this study was to describe the differences between African Americans (AA) and Caucasian Americans (CA) in using treatment approaches to manage symptoms among individuals with radiographic-confirmed knee OA. Methods A cross-sectional study was conducted. Using data from the Osteoarthritis Initiative, we identified 508 AA and 2,075 CA with radiographic tibiofemoral OA in at least one knee. Trained interviewers asked questions relating to current OA treatments including seven CAM therapy categories—alternative medical systems, mind-body interventions, manipulation and body-based methods, energy therapies, and three types of biologically based therapies, as well as conventional medications. We categorized participants as: conventional medication only users, CAM only users, users of both and users of neither. Multinomial logistic regression models adjusting for sociodemographics and clinical/functional factors provided estimates of the association between race and treatment use. Results Overall, 16.5% of AA and 24.2% of CA exclusively used CAM to treat OA, 25.0% of AA and 23.8% of CA used CAM in conjunction with conventional medications, and 24.8% of AA and 14.6% of CA exclusively used conventional medications. After control for sociodemographic and clinical factors, AA were less likely than CA to use CAM therapies alone (adjusted odds ratio (OR) of using CAM alone relative to no CAM or conventional treatments: 0.68, 95% confidence interval (CI): 0.48–0.96) or with conventional medications (adjusted OR relative to no CAM or conventional treatments: 0.59, 95%CI: 0.42–0.83). However, no differences in use of conventional medications alone were observed after adjustment of covariates. Conclusion CAM use is common among people with knee OA, but is less likely to be used by AA relative to CA. For effective CAM therapies, targeted outreach to underserved populations including education about benefits of various CAM treatments and providing accessible care may attenuate observed disparities in effective CAM use by race

Building more accurate decision trees with the additive tree.

The expansion of machine learning to high-stakes application domains such as medicine, finance, and criminal justice, where making informed decisions requires clear understanding of the model, has increased the interest in interpretable machine learning. The widely used Classification and Regression Trees (CART) have played a major role in health sciences, due to their simple and intuitive explanation of predictions. Ensemble methods like gradient boosting can improve the accuracy of decision trees, but at the expense of the interpretability of the generated model. Additive models, such as those produced by gradient boosting, and full interaction models, such as CART, have been investigated largely in isolation. We show that these models exist along a spectrum, revealing previously unseen connections between these approaches. This paper introduces a rigorous formalization for the additive tree, an empirically validated learning technique for creating a single decision tree, and shows that this method can produce models equivalent to CART or gradient boosted stumps at the extremes by varying a single parameter. Although the additive tree is designed primarily to provide both the model interpretability and predictive performance needed for high-stakes applications like medicine, it also can produce decision trees represented by hybrid models between CART and boosted stumps that can outperform either of these approaches