A Note on the Use of Sum in the Logic of Proofs

The Logic of Proofs~LP, introduced by Artemov, encodes the same reasoning as the modal logic~S4 using proofs explicitly present in the language. In particular, Artemov showed that three operations on proofs (application~$\cdot$, positive introspection~!, and sum~+) are sufficient to mimic provability concealed in S4~modality. While the first two operations go back to G{\"o}del, the exact role of~+ remained somewhat unclear. In particular, it was not known whether the other two operations are sufficient by themselves. We provide a positive answer to this question under a very weak restriction on the axiomatization of LP.

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.

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.

Approximate decoding approaches for network coded correlated data

This paper considers a framework where data from correlated sources are transmitted with the help of network coding in ad hoc network topologies. The correlated data are encoded independently at sensors and network coding is employed in the intermediate nodes in order to improve the data delivery performance. In such settings, we focus on the problem of reconstructing the sources at decoder when perfect decoding is not possible due to losses or bandwidth variations. We show that the source data similarity can be used at decoder to permit decoding based on a novel and simple approximate decoding scheme. We analyze the influence of the network coding parameters and in particular the size of finite coding fields on the decoding performance. We further determine the optimal field size that maximizes the expected decoding performance as a trade-off between information loss incurred by limiting the resolution of the source data and the error probability in the reconstructed data. Moreover, we show that the performance of the approximate decoding improves when the accuracy of the source model increases even with simple approximate decoding techniques. We provide illustrative examples showing how the proposed algorithm can be deployed in sensor networks and distributed imaging applications.

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).