A Characteristic Polynomial for the Transition Probability Matrix of Correlated Random Walks on a Graph

We define a correlated random walk (CRW) induced from the time evolution matrix (the Grover matrix) of the Grover walk on a graph $G$, and present a formula for the characteristic polynomial of the transition probability matrix of this CRW by using a determinant expression for the generalized weighted zeta function of $G$. As an application, we give the spectrum of the transition probability matrices for the CRWs induced from the Grover matrices of regular graphs and semiregular bipartite graphs. Furthermore, we consider another type of the CRW on a graph.

Movement patterns of the grey field slug (Deroceras reticulatum) in an arable field

We report the results of an experiment on radio-tracking of individual grey field slugs in an arable field and associated data modelling designed to investigate the effect of slug population density in their movement. Slugs were collected in a commercial winter wheat field in which a 5x6 trapping grid had been established with 2m distance between traps. The slugs were taken to the laboratory, radio-tagged using a recently developed procedure, and following a recovery period released into the same field. Seventeen tagged slugs were released singly (sparse release) on the same grid node on which they had been caught. Eleven tagged slugs were released as a group (dense release). Each of the slugs was radio-tracked for approximately 10 h during which their position was recorded ten times. The tracking data were analysed using the Correlated Random Walk framework. The analysis revealed that all components of slug movement (mean speed, turning angles and movement/resting times) were significantly different between the two treatments. On average, the slugs released as a group disperse more slowly than slugs released individually and their turning angle has a clear anticlockwise bias. The results clearly suggest that population density is a factor regulating slug movement.

Perovskite-Enhanced Silicon-Nanocrystal Optoelectronic Synaptic Devices for the Simulation of Biased and Correlated Random-Walk Learning

Silicon- (Si-) based optoelectronic synaptic devices mimicking biological synaptic functionalities may be critical to the development of large-scale integrated optoelectronic artificial neural networks. As a type of important Si materials, Si nanocrystals (NCs) have been successfully employed to fabricate optoelectronic synaptic devices. In this work, organometal halide perovskite with excellent optical asborption is employed to improve the performance of optically stimulated Si-NC-based optoelectronic synaptic devices. The improvement is evidenced by the increased optical sensitivity and decreased electrical energy consumption of the devices. It is found that the current simulation of biological synaptic plasticity is essentially enabled by photogating, which is based on the heterojuction between Si NCs and organometal halide perovskite. By using the synaptic plasticity, we have simulated the well-known biased and correlated random-walk (BCRW) learning.

Modelling the dispersal of riverine fish larvae: from a raster-based analysis of movement patterns within a racetrack flume to a rheoreaction-based correlated random walk (RCRW) model approach

Recruitment of Chondrostoma nasus and similar fish species in rivers is related to spatiotemporal linkages between larval hatching and nursery habitats. Active swimming behaviour contradicts the assumption that passive particle tracing models can serve as a proxy for larval dispersal models. A racetrack flume with an inshore area of near-natural slope was created to observe individual larval trajectories. A new three-step, raster-based analysis was developed to distinguish four types of movement patterns: active upstream, active downstream, active–passive, and passive. Both larval developmental stage-specific and release site-specific occurrences of these movement patterns were experimentally found for nine flow velocity classes (≤0.225 m·s−1). These current-induced movement patterns, and evaluated durations within them, were used to develop a biased and correlated random walk model that includes rheoreaction — a key behavioural response of fish to flow within rivers. The study introduces the concept and application of a rheoreaction-based correlated random walk model, which coupled with a 3D hydrodynamic model, allows prediction of the spatiotemporal effects of various river discharges, morphologies, and restoration scenarios on larval fish dispersal.