Implementing fisher Black's simple discounting rule

We propose a simple implementation of Black’s (1988) elegant rule for discounting uncertain future cash flows. Black’s rule avoids the thorny problem of estimating an appropriate risk-adjusted discount rate. Instead, the rule calls for discounting conditional mean cash flows at appropriate riskless interest rates. Our contribution in this article is to describe and illustrate a method of estimating the conditional mean cash flows called for in Black’s rule. The method is quite flexible with respect to the types of information available concerning the distributions of future cash flows. We argue that this approach to computing present values offers a theoretically sound and generally feasible addition to the toolbox of financial managers.

Weighted Majoritarian Rules for the Location of Multiple Public Facilities

We consider collective decision problems given by a profile of single-peaked preferences defined over the real line and a set of pure public facilities to be located on the line. In this context, Bochet and Gordon (2012) provide a large class of priority rules based on efficiency, object-population monotonicity and sovereignty. Each such rule is described by a fixed priority ordering among interest groups. We show that any priority rule which treats agents symmetrically — anonymity — respects some form of coherence across collective decision problems — reinforcement — and only depends on peak information — peakonly — is a weighted majoritarian rule. Each such rule defines priorities based on the relative size of the interest groups and specific weights attached to locations. We give an explicit account of the richness of this class of rules.

What is the incidence of intracranial bleeding in patients with mild traumatic brain injury? A retrospective study in 3088 Canadian CT head rule patients

OBJECTIVE Only limited data exists in terms of the incidence of intracranial bleeding (ICB) in patients with mild traumatic brain injury (MTBI). METHODS We retrospectively identified 3088 patients (mean age 41 range (7-99) years) presenting with isolated MTBI and GCS 14-15 at our Emergency Department who had undergone cranial CT (CCT) between 2002 and 2011. Indication for CCT was according to the "Canadian CT head rules." Patients with ICB were either submitted for neurosurgical treatment or kept under surveillance for at least 24 hours. Pearson's correlation coefficient was used to correlate the incidence of ICB with age, gender, or intake of coumarins, platelet aggregation inhibitors, or heparins. RESULTS 149 patients (4.8%) had ICB on CCT. No patient with ICB died or deteriorated neurologically. The incidence of ICB increased with age and intake of anticoagulants without clinically relevant correlation (R = 0.11; P < 0.001; R = -0.06; P < 0.001). CONCLUSION Our data show an incidence of 4.8% for ICB after MTBI. However, neurological deterioration after MTBI seems to be rare, and the need for neurosurgical intervention is only required in selected cases. The general need for CCT in patients after MTBI is therefore questionable, and clinical surveillance may be sufficient when CCT is not available.

Prognostic value of the Geneva prediction rule in patients with pulmonary embolism

BACKGROUND Assessment of pre-test probability of pulmonary embolism (PE) and prognostic stratification are two widely recommended steps in the management of patients with suspected PE. Some items of the Geneva prediction rule may have a prognostic value. We analyzed whether the initial probability assessed by the Geneva rule was associated with the outcome of patients with PE. METHODS In a post-hoc analysis of a multicenter trial including 1,693 patients with suspected PE, the all-cause death or readmission rates during the 3-month follow-up of patients with confirmed PE were analyzed. PE probability group was prospectively assessed by the revised Geneva score (RGS). Similar analyses were made with the a posteriori-calculated simplified Geneva score (SGS). RESULTS PE was confirmed in 357 patients and 21 (5.9%) died during the 3-month follow-up. The mortality rate differed significantly with the initial RGS group, as with the SGS group. For the RGS, the mortality increased from 0% (95% Confidence Interval: [0-5.4%]) in the low-probability group to 14.3% (95% CI: [6.3-28.2%]) in the high-probability group, and for the SGS, from 0% (95% CI: [0-5.4%] to 17.9% (95% CI: [7.4-36%]). Readmission occurred in 58 out of the 352 patients with complete information on readmission (16.5%). No significant change of readmission rate was found among the RGS or SGS groups. CONCLUSIONS Returning to the initial PE probability evaluation may help clinicians predict 3-month mortality in patients with confirmed PE. (ClinicalTrials.gov: NCT00117169).

D-dimer to Rule Out Pulmonary Embolism in Renal Insufficiency

BACKGROUND D-dimer levels are often elevated in renal insufficiency. The diagnostic accuracy of D-dimer to rule out pulmonary embolism in patients with renal insufficiency is unclear. METHODS We evaluated the data of patients presenting to our Emergency Department and receiving computed tomography angiography to rule out pulmonary embolism with measurement of D-dimer and creatinine. Glomerular filtration rate was calculated using the Chronic Kidney Disease Epidemiology Collaboration formula. RESULTS There were 1305 patients included; 1067 (82%) had an estimated glomerular filtration rate (eGFR) exceeding 60 mL/min, 209 (16%) 30-60 mL/min, and 29 (2%) <30 mL/min. One hundred fifty-two patients (12%) had D-dimer below 500 μg/L. eGFR (R = -0.1122) correlated significantly with D-dimer (P <.0001). One hundred sixty-nine patients (13%) were found to have pulmonary embolism. Sensitivity of D-dimer for patients with an eGFR >60 mL/min was 96% (confidence interval [CI], 0.93-0.99) and 100% (CI, 100-100) for those with 30-60 mL/min, while specificity decreased significantly with impaired renal function. Area under the curve of the receiver operating characteristic for D-dimer was 0.734 in patients with an eGFR of >60 mL/min, and 0.673 for 30-60 mL/min. CONCLUSIONS D-dimer levels were elevated in patients with an eGFR <60 mL/min, but proved to be highly sensitive for the exclusion of pulmonary embolism. However, because almost all patients with impaired renal function had elevated D-dimer irrespective of the presence of pulmonary embolism, studies should be performed to determine renal function-adjusted D-dimer cutoffs.

Genetic Control of Plant Development by Overriding a Geometric Division Rule

Formative cell divisions are critical for multicellular patterning. In the early plant embryo, such divisions follow from orienting the division plane. A major unanswered question is how division plane orientation is genetically controlled, and in particular whether this relates to cell geometry. We have generated a complete 4D map of early Arabidopsis embryogenesis and used computational analysis to demonstrate that several divisions follow a rule that uses the smallest wall area going through the center of the cell. In other cases, however, cell division clearly deviates from this rule, which invariably leads to asymmetric cell division. By analyzing mutant embryos and through targeted genetic perturbation, we show that response to the hormone auxin triggers a deviation from the ``shortest wall'' rule. Our work demonstrates that a simple default rule couples division orientation to cell geometry in the embryo and that genetic regulation can create patterns by overriding the default rule.

Shared Rule in Federal Political Systems: Conceptual Lessons from Subnational Switzerland

This article reconceptualizes shared rule and uses novel data to measure it, thus addressing two shortcomings of federal literature. First, while most studies focus on self-rule, one question that is largely neglected is how lower-level governments can influence politics at a higher level in the absence of “second” chambers. The answer is through shared rule. A second shortcoming is that even when addressing this question, scholars concentrate on constitutional-administrative aspects of vertical intergovernmentalism, neglecting more informal, “political” dynamics. Comparing the twenty-six Swiss cantons allows drawing two lessons for federal studies: That shared rule is multifaceted and complex, and that to study informal territorial actors as well as direct political processes is indispensable to understand how power is actually distributed in federal political systems.