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Introduction: Head and neck squamous cell carcinoma (HNSCC), a highly heterogeneous malignancy is often associated with unfavorable prognosis. Due to its unique anatomical position and the absence of effective early inspection methods, surgical intervention alone is frequently inadequate for achieving complete remission. Therefore, the identification of reliable biomarker is crucial to enhance the accuracy of screening and treatment strategies for HNSCC.

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This paper deals with the trapping of a particle diffusing in a cylindrical cavity by two circular absorbing spots of arbitrary radii located in the centers of the cavity bases. The focus is on the mean particle lifetime, which is its mean first-passage time to one of the spots. When the spots are small and their radii are well below the cavity radius, this time can be analyzed using the narrow escape (NE) theory, which describes it as a function of the spot radii and the only parameter of the cavity, its volume, independent of the cavity shape and the particle initial position.

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The Morris Water Maze (MWM) is the most commonly used assay for evaluating learning and memory in laboratory mice. Despite its widespread use, contemporary reviews have highlighted substantial methodological variation in experimental protocols and that the associated testing procedures are acutely (each trial) and chronically (testing across days) stressful; stress impairs attention, memory consolidation and the retrieval of learned information. Moreover, the interpretation of behavior within the MWM is often difficult because of wall hugging, non-spatial swim strategies, floating, and jumping off the escape platform.

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Narrow escape with imperfect reactions.

Phys Rev E

November 2024

Department of Mathematics, University of Utah, Salt Lake City, Utah 84112, USA.

The imperfect narrow escape problem considers the mean first passage time (MFPT) of a Brownian particle through one of several small, partially reactive traps on an otherwise reflecting boundary within a confining domain. Mathematically, this problem is equivalent to Poisson's equation with mixed Neumann-Robin boundary conditions. Here, we obtain this MFPT in general three-dimensional domains by using strong localized perturbation theory in the small trap limit.

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