A Software Implementation of ECM for NFS

The Elliptic Curve Method (ECM) of factorization can be used in the relation collection phase of the Number Field Sieve (NFS) to help identify smooth integers. This requires rapidly finding small prime factors for a large number of composites, each of a few machine words in size. We present a software implementation of ECM that is optimized for high throughput operation and compare it with recently proposed hardware implementations of ECM

Improved Stage 2 to P±\pm1 Factoring Algorithms

International audienceSome implementations of stage 2 of the P-1 method of factorization use convolutions. We describe a space-efficient implementation, allowing convolution lengths around 2^23 and stage 2 limit around 10^16 while attempting to factor 230-digit numbers on modern PC's. We use the discrete cosine transform to multiply reciprocal polynomials. We present adjustments for the P+1 algorithm. We list some new findings

FFT extension for algebraic-group factorization algorithms

International audienceIt is well known that the second stage of factoring methods that exploit smoothness of group orders can be implemented efficiently using the fast Fourier transform (FFT). For Pollard's p−1 method [17] this originated with the Mont-gomery and Silverman paper [16], and for the elliptic curve factoring method [12] it was the subject of Peter Montgomery's PhD dissertation [14]. Along with Peter's most recent work on this subject [15], these developments are presented in this chapter

Factorisation of RSA-220 with CADO-NFS

We give details of the factorization of RSA-220 with CADO-NFS. This is a new record computation with this open-source software. We report on the factorization of RSA-220 (220 decimal digits), which is the 3rd largest integer factorization with the General Number Field Sieve (GNFS), after the factorization of RSA-768 (232 digits) in December 2009 [3], and that of 3 697 + 1 (221 digits) in February 2015 by NFS@home

Functional outcome of traumatic spinopelvic instabilities treated with lumbopelvic fixation.

The aim of this study was to assess the functional outcome after lumbopelvic fixation (LPF) using the SMFA (short musculoskeletal functional assessment) score and discuss the results in the context of the existing literature. The last consecutive 50 patients who underwent a LPF from January 1st 2011 to December 31st 2014 were identified and administered the SMFA-questionnaire. Inclusion criteria were: (1) patient underwent LPF at our institution, (2) complete medical records, (3) minimum follow-up of 12 months. Out of the 50 recipients, 22 questionnaires were returned. Five questionnaires were incomplete and therefore seventeen were included for analysis. The mean age was 60.3 years (32-86 years; 9m/8f) and the follow-up averaged 26.9 months (14-48 months). Six patients (35.3%) suffered from a low-energy trauma and 11 patients (64.7%) suffered a high-energy trauma. Patients in the low-energy group were significantly older compared to patients in the high-energy group (72.2 vs. 53.8 years; p = 0.030). Five patients (29.4%) suffered from multiple injuries. Compared to patients with low-energy trauma, patients suffering from high-energy trauma showed significantly lower scores in daily activities (89.6 vs. 57.1; p = 0.031), mobility (84.7 vs. 45.5; p = 0.015) and function (74.9 vs. 43.4; p = 0.020). Our results suggest that patients with older age and those with concomitant injuries show a greater impairment according to the SMFA score. Even though mostly favorable functional outcomes were reported throughout the literature, patients still show some level of impairment and do not reach normative data at final follow-up

Does adherence to a quality indicator regarding early weaning from invasive ventilation improve economic outcome? A single-centre retrospective study

ObjectivesTo measure and assess the economic impact of adherence to a single quality indicator (QI) regarding weaning from invasive ventilation.DesignRetrospective observational single-centre study, based on electronic medical and administrative records.SettingIntensive care unit (ICU) of a German university hospital, reference centre for acute respiratory distress syndrome.ParticipantsRecords of 3063 consecutive mechanically ventilated patients admitted to the ICU between 2012 and 2017 were extracted, of whom 583 were eligible adults for further analysis. Patients’ weaning protocols were evaluated for daily adherence to quality standards until ICU discharge. Patients with <65% compliance were assigned to the low adherence group (LAG), patients with ≥65% to the high adherence group (HAG).Primary and secondary outcome measuresEconomic healthcare costs, clinical outcomes and patients’ characteristics.ResultsThe LAG consisted of 378 patients with a median negative economic results of −€3969, HAG of 205 (−€1030), respectively (p<0.001). Median duration of ventilation was 476 (248; 769) hours in the LAG and 389 (247; 608) hours in the HAG (p<0.001). Length of stay (LOS) in the LAG on ICU was 21 (12; 35) days and 16 (11; 25) days in the HAG (p<0.001). LOS in the hospital was 36 (22; 61) days in the LAG, and within the HAG, respectively, 26 (18; 48) days (p=0.001).ConclusionsHigh adherence to this single QI is associated with better clinical outcome and improved economic returns. Therefore, the results support the adherence to QI. However, the examined QI does not influence economic outcome as the decisive factor