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Showing posts from January, 2026

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...

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...

Inside cycleTrendR: Methods, Architecture, and Design Choices

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  Irregular time series are everywhere: wearable sensors, physiological recordings, ecological  monitoring, behavioral experiments, and more. Yet most analytical tools still assume regular sampling,  clean signals, and stable measurement conditions. cycleTrendR was designed to bridge this gap, not by  reinventing time‑series analysis, but by integrating robust, domain‑agnostic methods into a single  coherent pipeline. This post provides a technical overview of how cycleTrendR works under the hood: the algorithms it uses, the architectural decisions behind the package, and the principles that guided its design. 1. A unified pipeline for irregular time‑series analysis cycleTrendR is built around a simple idea: cycles, trends, and structural changes should be extracted together, not in isolation. The internal workflow follows a modular but integrated structure: Raw signal    ↓ Preprocessing (dates, gaps, normalization)    ↓ Tr...

Why Analyzing Cycles and Trends in Irregular Time Series Is Harder Than It Looks

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  Modern data streams rarely behave the way classical time series textbooks expect. Wearables, physiological sensors, ecological monitors, experimental devices — they all produce signals that are irregular, noisy, and full of gaps. Yet we often analyze them using tools designed for perfectly regular sampling. The result is predictable: distorted trends, misleading cycles, and interpretations driven more by sampling artifacts than by the underlying system. This post introduces the motivation behind cycleTrendR , an R package designed to extract cycles, trends, and state transitions from real-world, irregular time series. Before diving into code, let’s outline the conceptual problem the package aims to solve. Figure 1. Conceptual pipeline for analyzing irregular time series with cycleTrendR Legend of Figure 1.  The diagram summarizes the core workflow: starting from irregular data, the package applies adaptive trend smoothing, spectral estimation via Lomb–Scargle, and extracts ...

Unit Root Testing in Practice: A Tutorial on ADF–KPSS, Specification, and Diagnostics

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  Stationary Signals   A stationary signal is defined by the stability of its statistical properties over time. Specifically, this implies that the signal’s mean, variance, and autocorrelation function remain consistent, regardless of the time in which the signal is evaluated. There are two main types of stationarity: ·        Strict-sense stationarity refers to the property of a signal in which all statistical characteristics remain unchanged over time. This encompasses all moments of the distribution, indicating that the entire probability distribution remains constant throughout the observed period. ·        Wide-sense stationarity requires that the first two moments, specifically the mean and variance, remain constant over time. The autocorrelation function is dependent only on the time difference between two points, not on the exact time points themselves.   Importance in Signal...

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