A Combinatorial Approach to the Variable Selection in Multiple Linear Regression: Analysis of Selwood et al Data set -A Case Study.

A combinatorial protocol (CP) is introduced here to interface it with the multiple linear regression (MLR) for variable selection. The efficiency of CP-MLR is primarily based on the restriction of entry of correlated variables to the model development stage. It has been used for the analysis of Selwood et al data set [16], and the obtained models are compared with those reported from GFA [8] and MUSEUM [9] approaches. For this data set CP-MLR could identify three highly independent models (27, 28 and 31) with Q2 value in the range of 0.632-0.518. Also, these models are divergent and unique. Even though, the present study does not share any models with GFA [8], and MUSEUM [9] results, there are several descriptors common to all these studies, including the present one. Also a simulation is carried out on the same data set to explain the model formation in CP-MLR. The results demonstrate that the proposed method should be able to offer solutions to data sets with 50 to 60 descriptors in reasonable time frame. By carefully selecting the inter-parameter correlation cutoff values in CP-MLR one can identify divergent models and handle data sets larger than the present one without involving excessive computer time.

Trigger activity more than three years after left atrial linear ablation without pulmonary vein isolation in patients with atrial fibrillation.

OBJECTIVES The aim of this study was to analyze trigger activity in the long-term follow-up after left atrial (LA) linear ablation. BACKGROUND Interventional strategies for curative treatment of atrial fibrillation (AF) are targeted at the triggers and/or the maintaining substrate. After substrate modification using nonisolating linear lesions, the activity of triggers is unknown. METHODS With the LA linear lesion concept, 129 patients were treated using intraoperative ablation with minimal invasive surgical techniques. Contiguous radiofrequency energy-induced lesion lines involving the mitral annulus and the orifices of the pulmonary veins without isolation were placed under direct vision. RESULTS After a mean follow-up of 3.6 +/- 0.4 years, atrial ectopy, atrial runs, and reoccurrence of AF episodes were analyzed by digital 7-day electrocardiograms in 30 patients. Atrial ectopy was present in all patients. Atrial runs were present in 25 of 30 patients (83%), with a median number of 9 runs per patient/week (range 1 to 321) and a median duration of 1.2 s/run (range 0.7 to 25), without a significant difference in atrial ectopy and atrial runs between patients with former paroxysmal (n = 17) or persistent AF (n = 13). Overall, 87% of all patients were completely free from AF without antiarrhythmic drugs. CONCLUSIONS A detailed rhythm analysis late after specific LA linear lesion ablation shows that trigger activity remains relatively frequent but short and does not induce AF episodes in most patients. The long-term success rate of this concept is high in patients with paroxysmal or persistent AF.

Correlation between Accurate Electron Density and Linear Optical Properties in Amino Acid Derivatives: L-Histidinium Hydrogen Oxalate

The accurate electron density and linear optical properties of L-histidinium hydrogen oxalate are discussed. Two high-resolution single crystal X-ray diffraction experiments were performed and compared with density functional calculations in the solid state as well as in the gas phase. The crystal packing and the hydrogen bond network are accurately investigated using topological analysis based on quantum theory of atoms in molecules, Hirshfeld surface analysis, and electrostatic potential mapping. The refractive indices are computed from couple perturbed Kohn-Sham calculations and measured experimentally. Moreover, distributed atomic polarizabilities are used to analyze the origin of the linear susceptibility in the crystal, in order to separate molecular and intermolecular causes. The optical properties are also correlated with the electron density distribution. This compound also offers the possibility to test the electron density building block approach for material science and different refinement schemes for accurate positions and displacement parameters of hydrogen atoms, in the absence of neutron diffraction data.

A meta-analysis of cambium phenology and growth: linear and non-linear patterns in conifers of the northern hemisphere

Background and Aims Ongoing global warming has been implicated in shifting phenological patterns such as the timing and duration of the growing season across a wide variety of ecosystems. Linear models are routinely used to extrapolate these observed shifts in phenology into the future and to estimate changes in associated ecosystem properties such as net primary productivity. Yet, in nature, linear relationships may be special cases. Biological processes frequently follow more complex, non-linear patterns according to limiting factors that generate shifts and discontinuities, or contain thresholds beyond which responses change abruptly. This study investigates to what extent cambium phenology is associated with xylem growth and differentiation across conifer species of the northern hemisphere. Methods Xylem cell production is compared with the periods of cambial activity and cell differentiation assessed on a weekly time scale on histological sections of cambium and wood tissue collected from the stems of nine species in Canada and Europe over 1–9 years per site from 1998 to 2011. Key Results The dynamics of xylogenesis were surprisingly homogeneous among conifer species, although dispersions from the average were obviously observed. Within the range analysed, the relationships between the phenological timings were linear, with several slopes showing values close to or not statistically different from 1. The relationships between the phenological timings and cell production were distinctly non-linear, and involved an exponential pattern. Conclusions The trees adjust their phenological timings according to linear patterns. Thus, shifts of one phenological phase are associated with synchronous and comparable shifts of the successive phases. However, small increases in the duration of xylogenesis could correspond to a substantial increase in cell production. The findings suggest that the length of the growing season and the resulting amount of growth could respond differently to changes in environmental conditions.

Relating Crevassing to Non-Linear Strain in the Floating Part of Jakobshavn Isbrae, West Greenland

Jakobshavn Isbrae is a major ice stream that drains the west-central Greenland ice sheet and becomes afloat in Jakobshavn Isfiord (69degreesN, 49degreesW), where it has maintained the world's fastest-known sustained velocity and calving rate (7 km a(-1)) for at least four decades. The floating portion is approximately 12 km long and 6 km wide. Surface elevations and motion vectors were determined photogrammetrically for about 500 crevasses on the floating ice, and adjacent grounded ice, using aerial photographs obtained 2 weeks apart in July 1985. Surface strain rates were computed from a mesh of 399 quadrilateral elements having velocity measurements at each corner. It is shown that heavy crevassing of floating ice invalidates the assumptions of linear strain theory that (i) surface strain in the floating ice is homogeneous in both space and time, (ii) the squares and products of strain components are nil, and (iii) first- and second-order rotation components are small compared to strain components. Therefore, strain rates and rotation rates were also computed using non-linear strain theory. The percentage difference between computed linear and non-linear second invariants of strain rate per element were greatest (mostly in the range 40-70%) where crevassing is greatest. Isopleths of strain rate parallel and transverse to flow and elevation isopleths relate crevassing to known and inferred pinning points.

A mixed-integer linear programming approach to the optimization of event-bus schedules: a scheduling application in the tourism sector

This paper deals with “The Enchanted Journey,” which is a daily event tour booked by Bollywood-film fans. During the tour, the participants visit original sites of famous Bollywood films at various locations in Switzerland; moreover, the tour includes stops for lunch and shopping. Each day, up to five buses operate the tour. For operational reasons, however, two or more buses cannot stay at the same location simultaneously. Further operative constraints include time windows for all activities and precedence constraints between some activities. The planning problem is how to compute a feasible schedule for each bus. We implement a two-step hierarchical approach. In the first step, we minimize the total waiting time; in the second step, we minimize the total travel time of all buses. We present a basic formulation of this problem as a mixed-integer linear program. We enhance this basic formulation by symmetry-breaking constraints, which reduces the search space without loss of generality. We report on computational results obtained with the Gurobi Solver. Our numerical results show that all relevant problem instances can be solved using the basic formulation within reasonable CPU time, and that the symmetry-breaking constraints reduce that CPU time considerably.

EGFR inhibitors erlotinib and lapatinib ameliorate epidermal blistering in pemphigus vulgaris in a non-linear, V-shaped relationship.

Novel insights into intra-cellular signalling involved in pemphigus vulgaris (PV), an autoimmune blistering disease of skin and mucous membranes, are now revealing new therapeutic approaches such as the chemical inhibition of PV-associated signals in conjunction with standard immunosuppressive therapy. However, extensive inhibition of signalling molecules that are required for normal tissue function and integrity may hamper this approach. Using a neonatal PV mouse model, we demonstrate that epidermal blistering can be prevented in a dose-dependent manner by clinically approved EGFR inhibitors erlotinib and lapatinib, but only up to approximately 50% of normal EGFR activity. At lower EGFR activity, blisters again aggravated and were highly exacerbated in mice with a conditional deletion of EGFR. Statistical analysis of the relation between EGFR activity and the extent of skin blistering revealed the best fit with a non-linear, V-shaped curve with a median break point at 52% EGFR activity (P = 0.0005). Moreover, lapatinib (a dual EGFR/ErbB2 inhibitor) but not erlotinib significantly reduced blistering in the oral cavity, suggesting that signalling mechanisms differ between PV predilection sites. Our results demonstrate that future clinical trials evaluating EGFR/ErbB2 inhibitors in PV patients must select treatment doses that retain a specific level of signal molecule activity. These findings may also be of relevance for cancer patients treated with EGFR inhibitors, for whom skin lesions due to extensive EGFR inhibition represent a major threat.

Algebra of Classical Theoretical Term Reductions in the Sciences

An elementary algebra identifies conceptual and corresponding applicational limitations in John Kemeny and Paul Oppenheim’s (K-O) 1956 model of theoretical reduction in the sciences. The K-O model was once widely accepted, at least in spirit, but seems afterward to have been discredited, or in any event superceeded. Today, the K-O reduction model is seldom mentioned, except to clarify when a reduction in the Kemeny-Oppenheim sense is not intended. The present essay takes a fresh look at the basic mathematics of K-O comparative vocabulary theoretical term reductions, from historical and philosophical standpoints, as a contribution to the history of the philosophy of science. The K-O theoretical reduction model qualifies a theory replacement as a successful reduction when preconditions of explanatory adequacy and comparable systematicization are met, and there occur fewer numbers of theoretical terms identified as replicable syntax types in the most economical statement of a theory’s putative propositional truths, as compared with the theoretical term count for the theory it replaces. The challenge to the historical model developed here, to help explain its scope and limitations, involves the potential for equivocal theoretical meanings of multiple theoretical term tokens of the same syntactical type.

Diagnostic Accuracy of Full-Body Linear X-Ray Scanning in Multiple Trauma Patients in Comparison to Computed Tomography

Purpose: The purpose of this study was to evaluate the diagnostic accuracy of full-body linear X-ray scanning (LS) in multiple trauma patients in comparison to 128-multislice computed tomography (MSCT). Materials and Methods: 106 multiple trauma patients (female: 33; male: 73) were retrospectively included in this study. All patients underwent LS of the whole body, including extremities, and MSCT covering the neck, thorax, abdomen, and pelvis. The diagnostic accuracy of LS for the detection of fractures of the truncal skeleton and pneumothoraces was evaluated in comparison to MSCT by two observers in consensus. Extremity fractures detected by LS were documented. Results: The overall sensitivity of LS was 49.2 %, the specificity was 93.3 %, the positive predictive value was 91 %, and the negative predictive value was 57.5 %. The overall sensitivity for vertebral fractures was 16.7 %, and the specificity was 100 %. The sensitivity was 48.7 % and the specificity 98.2 % for all other fractures. Pneumothoraces were detected in 12 patients by CT, but not by LS. 40 extremity fractures were detected by LS, of which 4 fractures were dislocated, and 2 were fully covered by MSCT. Conclusion: The diagnostic accuracy of LS is limited in the evaluation of acute trauma of the truncal skeleton. LS allows fast whole-body X-ray imaging, and may be valuable for detecting extremity fractures in trauma patients in addition to MSCT. Key Points: • The overall sensitivity of LS for truncal skeleton injuries in multiple-trauma patients was < 50 %.• The diagnostic reference standard MSCT is the preferred and reliable imaging modality.• LS may be valuable for quick detection of extremity fractures. Citation Format: • Jöres APW., Heverhagen JT, Bonél H et al. Diagnostic Accuracy of Full-Body Linear X-Ray Scanning in Multiple Trauma Patients in Comparison to Computed Tomography. Fortschr Röntgenstr 2016; 188: 163 - 171.

Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors

In applied work economists often seek to relate a given response variable y to some causal parameter mu* associated with it. This parameter usually represents a summarization based on some explanatory variables of the distribution of y, such as a regression function, and treating it as a conditional expectation is central to its identification and estimation. However, the interpretation of mu* as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when mu* is modelled as a parametric function of explanatory variables because it is well known how instrumental variables techniques can be used to identify and estimate mu*. In contrast, handling endogenous regressors in nonparametric models, where mu* is regarded as fully unknown, presents di±cult theoretical and practical challenges. In this paper we consider an endogenous nonparametric model based on a conditional moment restriction. We investigate identification related properties of this model when the unknown function mu* belongs to a linear space. We also investigate underidentification of mu* along with the identification of its linear functionals. Several examples are provided in order to develop intuition about identification and estimation for endogenous nonparametric regression and related models.

Grundlehren der Algebra : Zum Gebrauch in Schulen und zum Selbstunterricht

Von J. Ineichen, Professor der Physik am Lyceum zu Luzern