Formula for the nnth kk-Generalized Fibonacci-like Number

In this paper we provided a formula for the $n$th term of the $k$-generalized Fibonacci-like sequence, a generalization of the well-known Fibonacci sequence, having $k$ arbitrary initial terms, where the succeeding terms are obtained by adding its previous $k$ terms. The formula for the $n$th term of the $k$-generalized Fibonacci-like sequence was obtained by observing patterns in the derived formula for the nth term of the Fibonacci-like, Tribonacci-like, and Tetrabonacci-like sequence. The formula for the $k$-generalized Fibonacci sequence was also derived and was used in the process of proving the main result of this paper

Measuring track vertical stiffness through dynamic monitoring

[EN] This paper proposes a methodology for the evaluation of the track condition by means of the measurement of the track stiffness. This magnitude is calculated from vertical acceleration data measured at the axle box of trains during their normal operation. From the corresponding vertical acceleration spectra, the dominant vibration frequencies for each track stretch are identified and the combined stiffness is then determined. Then the stiffness without the contribution of the rail is calculated. The results obtained for a High Speed ballasted track in several track stretches are within the range 120-130 kN/mm, a result consistent with direct stiffness measurements taken during previous studies. Therefore, the proposed methodology may be used to obtain a first insight to the track condition by means of a continuous measurement of the track combined stiffness. This offers an alternative to traditional stationary stiffness measuring devices and might be a useful complement to dedicated continuous monitoring vehicles.Cano, MJ.; Martínez Fernández, P.; Insa Franco, R. (2016). Measuring track vertical stiffness through dynamic monitoring. Proceedings of the Institution of Civil Engineers - Transport. 169(1). doi:10.1680/jtran.14.00081S169

Evaluation of dose-dependent treatment effects after mid-trial dose escalation in biomarker, clinical, and cognitive outcomes for gantenerumab or solanezumab in dominantly inherited Alzheimer\u27s disease

INTRODUCTION: While the Dominantly Inherited Alzheimer Network Trials Unit (DIAN-TU) was ongoing, external data suggested higher doses were needed to achieve targeted effects; therefore, doses of gantenerumab were increased 5-fold, and solanezumab was increased 4-fold. We evaluated to what extent mid-trial dose increases produced a dose-dependent treatment effect. METHODS: Using generalized linear mixed effects (LME) models, we estimated the annual low- and high-dose treatment effects in clinical, cognitive, and biomarker outcomes. RESULTS: Both gantenerumab and solanezumab demonstrated dose-dependent treatment effects (significant for gantenerumab, non-significant for solanezumab) in their respective target amyloid biomarkers (Pittsburgh compound B positron emission tomography standardized uptake value ratio and cerebrospinal fluid amyloid beta 42), with gantenerumab demonstrating additional treatment effects in some downstream biomarkers. No dose-dependent treatment effects were observed in clinical or cognitive outcomes. CONCLUSIONS: Mid-trial dose escalation can be implemented as a remedy for an insufficient initial dose and can be more cost effective and less burdensome to participants than starting a new trial with higher doses, especially in rare diseases. HIGHLIGHTS: We evaluated the dose-dependent treatment effect of two different amyloid-specific immunotherapies.Dose-dependent treatment effects were observed in some biomarkers.No dose-dependent treatment effects were observed in clinical/cognitive outcomes, potentially due to the fact that the modified study may not have been powered to detect such treatment effects in symptomatic subjects at a mild stage of disease exposed to high (or maximal) doses of medication for prolonged durations

The Human Endogenous Circadian System Causes Greatest Platelet Activation during the Biological Morning Independent of Behaviors

Platelets are involved in the thromboses that are central to myocardial infarctions and ischemic strokes. Such adverse cardiovascular events have day/night patterns with peaks in the morning (~9 AM), potentially related to endogenous circadian clock control of platelet activation. The objective was to test if the human endogenous circadian system influences (1) platelet function and (2) platelet response to standardized behavioral stressors. We also aimed to compare the magnitude of any effects on platelet function caused by the circadian system with that caused by varied standardized behavioral stressors, including mental arithmetic, passive postural tilt and mild cycling exercise.We studied 12 healthy adults (6 female) who lived in individual laboratory suites in dim light for 240 h, with all behaviors scheduled on a 20-h recurring cycle to permit assessment of endogenous circadian function independent from environmental and behavioral effects including the sleep/wake cycle. Circadian phase was assessed from core body temperature. There were highly significant endogenous circadian rhythms in platelet surface activated glycoprotein (GP) IIb-IIIa, GPIb and P-selectin (6-17% peak-trough amplitudes; p ≤ 0.01). These circadian peaks occurred at a circadian phase corresponding to 8-9 AM. Platelet count, ATP release, aggregability, and plasma epinephrine also had significant circadian rhythms but with later peaks (corresponding to 3-8 PM). The circadian effects on the platelet activation markers were always larger than that of any of the three behavioral stressors.These data demonstrate robust effects of the endogenous circadian system on platelet activation in humans--independent of the sleep/wake cycle, other behavioral influences and the environment. The 9 AM timing of the circadian peaks of the three platelet surface markers, including platelet surface activated GPIIb-IIIa, the final common pathway of platelet aggregation, suggests that endogenous circadian influences on platelet function could contribute to the morning peak in adverse cardiovascular events as seen in many epidemiological studies

Evaluation of dose-dependent treatment effects after mid-trial dose escalation in biomarker, clinical, and cognitive outcomes for gantenerumab or solanezumab in dominantly inherited Alzheimer's disease

Introduction: While the Dominantly Inherited Alzheimer Network Trials Unit (DIAN-TU) was ongoing, external data suggested higher doses were needed to achieve targeted effects; therefore, doses of gantenerumab were increased 5-fold, and solanezumab was increased 4-fold. We evaluated to what extent mid-trial dose increases produced a dose-dependent treatment effect. Methods: Using generalized linear mixed effects (LME) models, we estimated the annual low- and high-dose treatment effects in clinical, cognitive, and biomarker outcomes. Results: Both gantenerumab and solanezumab demonstrated dose-dependent treatment effects (significant for gantenerumab, non-significant for solanezumab) in their respective target amyloid biomarkers (Pittsburgh compound B positron emission tomography standardized uptake value ratio and cerebrospinal fluid amyloid beta 42), with gantenerumab demonstrating additional treatment effects in some downstream biomarkers. No dose-dependent treatment effects were observed in clinical or cognitive outcomes. Conclusions: Mid-trial dose escalation can be implemented as a remedy for an insufficient initial dose and can be more cost effective and less burdensome to participants than starting a new trial with higher doses, especially in rare diseases. Highlights: We evaluated the dose-dependent treatment effect of two different amyloid-specific immunotherapies. Dose-dependent treatment effects were observed in some biomarkers. No dose-dependent treatment effects were observed in clinical/cognitive outcomes, potentially due to the fact that the modified study may not have been powered to detect such treatment effects in symptomatic subjects at a mild stage of disease exposed to high (or maximal) doses of medication for prolonged durations

T1 and FLAIR signal intensities are related to tau pathology in dominantly inherited Alzheimer disease

Carriers of mutations responsible for dominantly inherited Alzheimer disease provide a unique opportunity to study potential imaging biomarkers. Biomarkers based on routinely acquired clinical MR images, could supplement the extant invasive or logistically challenging) biomarker studies. We used 1104 longitudinal MR, 324 amyloid beta, and 87 tau positron emission tomography imaging sessions from 525 participants enrolled in the Dominantly Inherited Alzheimer Network Observational Study to extract novel imaging metrics representing the mean (μ) and standard deviation (σ) of standardized image intensities of T1-weighted and Fluid attenuated inversion recovery (FLAIR) MR scans. There was an exponential decrease in FLAIR-μ in mutation carriers and an increase in FLAIR and T1 signal heterogeneity (T1-σ and FLAIR-σ) as participants approached the symptom onset in both supramarginal, the right postcentral and right superior temporal gyri as well as both caudate nuclei, putamina, thalami, and amygdalae. After controlling for the effect of regional atrophy, FLAIR-μ decreased and T1-σ and FLAIR-σ increased with increasing amyloid beta and tau deposition in numerous cortical regions. In symptomatic mutation carriers and independent of the effect of regional atrophy, tau pathology demonstrated a stronger relationship with image intensity metrics, compared with amyloid pathology. We propose novel MR imaging intensity-based metrics using standard clinical T1 and FLAIR images which strongly associates with the progression of pathology in dominantly inherited Alzheimer disease. We suggest that tau pathology may be a key driver of the observed changes in this cohort of patients