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Why Biological Systems Suddenly Change State: An Intuitive Guide to Freidlin–Wentzell Theory

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  Stochasticity is ubiquitous in biology and neuroscience, manifesting in various forms, including ion channel noise, synaptic variability, gene regulatory fluctuations, noisy population dynamics, and more. Many biological systems spend long periods in a stable “state” and only rarely transition to another state due to noise. For instance, a neuron typically remains inactive but may occasionally trigger a spontaneous spike. Similarly, a gene can switch from the OFF state to the ON state due to rare bursts of transcription factors. Cells can also transition out of metabolic or epigenetic states, populations might shift between different ecological equilibria, and a viral infection can fluctuate between phases of control and uncontrollability. Freidlin–Wentzell theory provides a mathematically rigorous framework to study these phenomena when noise is small but nonzero . It tells you, firstly, h ow likely rare transitions are,    secondly,   h ow fast they occ...
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Reference values of left atrial size and function according to age: should we redefine the normal upper limits?

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Different cut-offs have been proposed for left atrial (LA) size. Furthermore, conflicting results have been reported about the influence of age on LA size and data on the impact of age on LA myocardial function are scanty. The aim of this study was to derive references values for LA size and function in healthy subjects and to evaluate the impact of age. We conducted a systematic literature search of MEDLINE database. We included only studies evaluating healthy subjects, with age ranged between 18 and 80 years. Parameters were compared among four age groups, < 30, 30–45, > 45–60, > 60 years. Three hundred twenty-six studies met the inclusion criteria and the final population consisted of 62,821 subjects. LA volume index (LAVi) did not differ among different age groups (p = 0.21). The normal upper limit of LAVi was 24 mL/m 2 . LA reservoir function, measured by strain, did not differ among age groups (38 ± 3%, 32–43%; p = 0.74). Left ventricular (LV) size and fun...
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FixaTons: A collection of Human Fixations Datasets and Metrics for Scanpath Similarity

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In the last three decades, human visual attention has been a topic of great interest in various disciplines. In computer vision, many models have been proposed to predict the distribution of human fixations on a visual input. Recently, thanks to the creation of large collections of data, machine learning algorithms have obtained state-of-the-art performance on the task of saliency map estimation. On the other hand, computational models of scanpath are much less studied. Works are often only descriptive or task specific. Computational models of scanpath with general purpose are present in the literature, but are then evaluated in tasks of saliency prediction, losing therefore information about the dynamics and the behaviour. This is due to the fact that the scanpath is harder to model because it must include the description of a dynamic. In addition to the difficulty of the problem itself, two technical reasons have limited the research. The first reason is the lack of robust and uni...
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Understanding Anaerobic Threshold (VT2) and VO2 Max in Endurance Training

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  Introduction: The Science Behind Ventilatory Thresholds VT1 vs. VT2: Defining Energy Transitions p (Aerobic Threshold) : The transition from lipid metawwwpp (fat-burning) to a mixed metabolism, where both carbohydrates and fats fuel muscle activity. V0T2 (Anaerobic Threshold) : The point where the  shifts to a predominantly carbohydrate-based wmetabolism , leading to rapid lactate waccumpulation and increased reliance on anaerobic energy pathways. www w In p VT1 and VT2 Wwww ewAgep & Sex Younger athletes generally exhibit higher VT2 values , while aging naturally reduces aerobicw capacity. Men tend to have a higher VO2 Max due to greater lung capacity and muscle mass, but women can achieve similar endurance levels through optimized training. Body Composition & Health Status High body fat percentage may reduce VT2 efficiency, as excess weight increases ...
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Owen's Function: A Simple Solution to Complex Problems

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Definition   If you are interested in statistics or probability, you may have encountered the Owen's function , a special function that arises in various applications involving bivariate normal distributions. Let’s explain what Owen's function is, how it is defined and notated, and why it is useful.  The Owen's function is defined as follows: for any real numbers h and a, Owen's function T(h,a) is given by T ( h , a ) = 1 2 π · ∫ 0 a exp ( - h 2 2 · ( 1 ...
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Cell Count Analysis with cycleTrendR

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  1. Introduction Long‑term monitoring of adherent cell cultures (e.g., Vero, MDCK) is central to vaccine development, viral propagation, and QC workflows in CRO environments. Standard analyses typically focus on short‑term growth metrics such as doubling time, confluence progression, and endpoint viability. While informative, these metrics overlook slow drifts, cyclic environmental influences, and structural transitions that emerge over multi‑day or multi‑week monitoring. Operational routines (e.g., weekly medium changes), environmental oscillations (e.g., daily temperature cycles), and metabolic rhythms can introduce periodic components into cell‑density trajectories. These patterns are rarely analyzed explicitly, despite their potential impact on viral yield, infection kinetics, and batch‑to‑batch reproducibility. This post demonstrates how cycleTrendR can extract long‑term trends, dominant cycles, and structural transitions from a realistically simulated adherent cell‑co...
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