# gst: biased random walks on networks with stochastic resetting.

<< This study explores biased random walk dynamics with stochastic resetting on general networks. (AA) show that the combination of biased random walks and stochastic resetting makes significant contributions by analyzing the search efficiency. (They) derive two analytical expressions for the stationary distribution and the mean first passage time, which are related to the spectral representation of the probability transition matrix of a biased random walk without resetting. These expressions can be used to determine the capacity of a random walker to reach the specific target and probe a finite network. >>

AA << apply the analytical results to two types of networks, pseudofractal scale-free webs and T-fractals, which are constructed through an iterative process. (They) also extend a strategy to explore other complex structure networks or larger networks by leveraging the spectral properties. >>

Anlin Li, Xiaohan Sun. Biased random walks on networks with stochastic resetting. Phys. Rev. E 111, 054309. May 16, 2025.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.111.054309

Also: walk, random, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, randomness, random walk, stochasticity, stochastic resetting.

# gst: apropos of interweavings, linking dispersion and stirring in randomly braiding flows.

     Fig. 5 (a)

<< Many random flows, including 2D unsteady and stagnation-free 3D steady flows, exhibit non-trivial braiding of pathlines as they evolve in time or space. (AA) show that these random flows belong to a pathline braiding 'universality class' that quantitatively links dispersion and chaotic stirring, meaning that the Lyapunov exponent can be estimated from the purely advective transverse dispersivity. (AA) verify this quantitative link for both unsteady 2D and steady 3D random flows. This result uncovers a deep connection between transport and mixing over a broad class of random flows. >>️

Daniel R. Lester, Michael G. Trefry, Guy Metcalfe. Linking Dispersion and Stirring in Randomly Braiding Flows. arXiv: 2412.05407v1 [physics.flu-dyn]. Dec 6, 2024.

https://arxiv.org/abs/2412.05407

Also: random, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, random, random flows, randomly braiding flows, chaos

# gst: apropos of random walks, intermittent random walks under stochastic resetting

AA << analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which it does not react to the target. >>

AA << demonstrate that Poissonian resetting leads to the existence of a non-equilibrium steady state. (They) calculate the distribution of the first arrival time to a target along with its mean and show the existence of an optimal reset rate. In particular, (..) the initial condition of the walker, i.e., either starting diffusely or relocating, can significantly affect the long-time properties of the search process. >>

<< the presence of distinct parameter regimes for the global optimization of the mean first arrival time when ballistic and diffusive movements are in direct competition. >>️

Rosa Flaquer-Galmes, Daniel Campos,  Vicenc Mendez. Intermittent random walks under stochastic resetting. Phys. Rev. E 109, 034103. March 4, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.034103  

Also: walk, walking, random, in https://www.inkgmr.net/kwrds.html

Keywords: gst, walk, intermittent random walk, stochasticity, stochastic resetting

# evol: the hypothesis of quasi-stochastic 'jazzy' metamechanics of biological evolution (in Arabidopsis thaliana)

<< Mutations occur when DNA is damaged and left unrepaired, creating a new variation. The scientists wanted to know if mutation was purely random or something deeper. What they found was unexpected. >>️

<< We always thought of mutation as basically random across the genome, (..) It turns out that mutation is very non-random and it's non-random in a way that benefits the plant. It's a totally new way of thinking about mutation. >> Grey Monroe. ️

Study challenges evolutionary theory that DNA mutations are random. UC Davis. Jan 12, 2022.

https://phys.org/news/2022-01-evolutionary-theory-dna-mutations-random.html

Monroe JG, Srikant T, et al. Mutation bias reflects natural selection in Arabidopsis thaliana. Nature. doi: 10.1038/ s41586-021-04269-6. Jan 12, 2022.

https://www.nature.com/articles/s41586-021-04269-6

FonT 

for a long time I have developed the suspicion that the small plant cared for by grandmother on the windowsill could be a not trivial image of (r)evolution ... 

The three ways of the plastoquinone inside the photosystem II complex. May 23, 2017.

https://flashontrack.blogspot.com/2017/05/s-phyto-three-ways-of-plastoquinone.html

Also

keyword 'evolution'  in FonT

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keyword 'evolution' | 'evoluzione'  in Notes (quasi-stochastic poetry)

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https://inkpi.blogspot.com/search?q=evoluzione

keyword 'jazz' in FonT

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keyword 'jazz' in Notes (quasi-stochastic poetry):

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keywords: evol, dna, mutations, randomness, quasi-stochasticity, jazz

# gst: random walk model for dual cascades in wave turbulence.

<< Dual cascades in turbulent systems with two conserved quadratic quantities famously arise in both two-dimensional hydrodynamic turbulence and also in wave turbulence based on four-wave interactions. >>

<< in wave turbulence the systematic spectral fluxes observed in a dual cascade do not require an irreversible dynamical mechanism, rather, they arise as the inevitable outcome of blind chance. >>️️

Oliver Bühler. Random walk model for dual cascades in wave turbulence. Phys. Rev. E 109, 055102. May 1, 2024. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.109.055102

Also: waves, turbulence, random, weak, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, turbulence, weak turbulence, random, random walks

# gst: apropos of absorbing targets, persistence exponents of self-interacting random walks

<< The persistence exponent, which characterizes the long-time decay of the survival probability of stochastic processes in the presence of an absorbing target, plays a key role in quantifying the dynamics of fluctuating systems. Determining this exponent for non-Markovian processes is known to be a difficult task, and exact results remain scarce despite sustained efforts. >> 

In their Letter, AA << consider the fundamental class of self-interacting random walks (SIRWs), which display long-range memory effects that result from the interaction of the random walker at time 𝑡 with the territory already visited at earlier times 𝑡′ <𝑡. (AA)  compute exactly the persistence exponent for all physically relevant SIRWs. As a byproduct, (They) also determine the splitting probability of these processes. >>

<< Besides their intrinsic theoretical interest, these results provide a quantitative characterization of the exploration process of SIRWs, which are involved in fields as diverse as foraging theory, cell biology, and nonreversible Monte Carlo methods. >>

J. Brémont, L. Régnier, et al. Persistence Exponents of Self-Interacting Random Walks. Phys. Rev. Lett. 134, 197103. May 16, 2025.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.197103

arXiv:2410.18699v1 [cond-mat.stat-mech]. 

https://arxiv.org/abs/2410.18699

Also: walk, walking, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, walk, walking, self-interacting random walk, walker self-repulsion, walker self-attraction, stochasticity, absorbing targets.

# gst: apropos of ambiguous scenarios, very persistent random walkers reveal transitions in landscape topology

AA << study the typical behavior of random walkers on the microcanonical configuration space of mean-field disordered systems. Passive walks have an ergodicity-breaking transition at precisely the energy density associated with the dynamical glass transition, but persistent walks remain ergodic at lower energies. >>

<< In models where the energy landscape is thoroughly understood, (They) show that, in the limit of infinite persistence time, the ergodicity-breaking transition coincides with a transition in the topology of microcanonical configuration space. (They) conjecture that this correspondence generalizes to other models, and use it to determine the topological transition energy in situations where the landscape properties are ambiguous. >>

Jaron Kent-Dobias. Very persistent random walkers reveal transitions in landscape topology. arXiv: 2505.16653v2 [cond-mat.dis-nn]. May 23, 2025. 

https://arxiv.org/abs/2505.16653

Also: random, walk, walking, disorder, transition, in https://www.inkgmr.net/kwrds.html

Also: ambiguity in FonT  https://flashontrack.blogspot.com/search?q=ambiguity     ambiguity in Notes (quasi-stochastic poetry)  https://inkpi.blogspot.com/search?q=ambiguita

Keywords: mean-field disordered systems, disorder, randomness, random walker, transitions, topological transition energy, ambiguity.

# gst: apropos of weakly coupled oscillators, a new approach to depict about their spontaneous stochastic activities

<<  Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example linear dynamics of a stable focus with fluctuations, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to a train of pulses. Despite their diverse origins, the phenomenology of random oscillations can be strikingly similar. >>

<< Here (AA) introduce a nonlinear transformation of stochastic oscillators to a new complex-valued function Q∗1(x) that greatly simplifies and unifies the mathematical description of the oscillator's spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different oscillators that are weakly coupled. >>

AA << approach makes qualitatively different stochastic oscillators comparable, provides simple characteristics for the coherence of the random oscillation, and gives a framework for the description of weakly coupled oscillators. >>️

Alberto Pérez-Cervera, Boris Gutkin, et al. A Universal Description of Stochastic Oscillators. arXiv: 2303.03198v1 [nlin.AO]. Feb 27, 2023. 

https://arxiv.org/abs/2303.03198

Also

'oscillations' in FonT

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Keywords: gst, oscillations, random oscillations, weakly coupled oscillators

# gst: discontinuous transition to chaos in a canonical random neural network

AA << study a paradigmatic random recurrent neural network introduced by Sompolinsky, Crisanti, and Sommers (SCS). In the infinite size limit, this system exhibits a direct transition from a homogeneous rest state to chaotic behavior, with the Lyapunov exponent gradually increasing from zero. (AA)  generalize the SCS model considering odd saturating nonlinear transfer functions, beyond the usual choice 𝜙⁡(𝑥)=tanh⁡𝑥. A discontinuous transition to chaos occurs whenever the slope of 𝜙 at 0 is a local minimum [i.e., for 𝜙′′′⁢(0)>0]. Chaos appears out of the blue, by an attractor-repeller fold. Accordingly, the Lyapunov exponent stays away from zero at the birth of chaos. >>

In the figure 7 << the pink square is located at the doubly degenerate point (𝑔,𝜀)=(1,1/3). >>️️

Diego Pazó. Discontinuous transition to chaos in a canonical random neural network. Phys. Rev. E 110, 014201. July 1, 2024.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.014201

Also: chaos, random, network, transition, neuro, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, chaos, random, network, transition, neuro

# gst: apropos of transitions, randomness can stabilize edge states in short- lifetime regions of disordered periodically-driven systems

<< lifetimes of the edge states exhibit universal behavior when random potentials exist since the edge- and bulk- dominant eigenstates are mixed, leading to that lifetimes are prolonged by random potentials in the region II (short- lifetime region) and shortened in the region I (long- lifetime region). >>

<<  it is an intriguing phenomenon that random potentials tend to stabilize edge states in the region II (short- lifetime regions). >>

Ken Mochizuki, Kaoru Mizuta, Norio Kawakami. Fate of Topological Edge States in Disordered Periodically-driven Nonlinear Systems. arXiv: 2108.00649 (nlin). Aug 2, 2021.

https://arxiv.org/abs/2108.00649

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# gst: random walk to describe a interplay between the inter-chain hopping and the intra-chain hopping in amorphous Polyimide nanofibers

AA << report the observation of a crossover of heat conduction behavior from three dimensions (3D) to quasi-one dimension (1D) in Polyimide(PI) nanofibers at a given temperature. A theoretical model based on the random walk theory has been proposed to quantitatively describe the interplay between the inter-chain hopping and the intra-chain hopping in nanofibers. This model explains well the diameter dependence of thermal conductivity and also speculates the upper limit of thermal conductivity of amorphous polymers in the quasi-1D limit. >>

Lan Dong, Qing Xi, et al. Dimensional crossover of heat conduction in amorphous Polyimide nanofibers. National Science Review. nwy004.  doi: 10.1093/nsr/nwy004. Jan 09,  2018.

https://academic.oup.com/nsr/advance-article/doi/10.1093/nsr/nwy004/4794956

<< The intrinsic structure of amorphous polymers is highly disordered with long, entangled molecular chains >>

Science China Press. "Random walk" of heat carriers in amorphous polymers. Mar 01, 2018.

https://m.phys.org/news/2018-03-random-carriers-amorphous-polymers.html

gst: actually and counterintuitively a coherent jump could generate disorder.

AA << consider a quantized version of a model for “random walk in random environment.” (..) For a ring geometry (a chain with periodic boundary condition) it features a delocalization-transition as the bias in increased beyond a critical value, indicating that the relaxation becomes underdamped. Counterintuitively, the effective disorder is enhanced due to coherent hopping. >>

Ben Avnit, Doron Cohen. Quantum walk in stochastic environment. Phys. Rev. E 108, 054111. Nov 7, 2023. 

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.108.054111

Also:  Voli a casaccio. Notes (quasi-stochastic poetry). Oct 01, 2006.

https://inkpi.blogspot.com/2006/10/2066-voli-casaccio.html

Also: 'random', 'transition', 'disorder', 'chaos', in https://www.inkgmr.net/kwrds.html

Keywords: gst, walk, random walk, quantum walk, qu-walk, jump, transition, disorder, chaos

# gst: apropos of transitions, scrambling trajectories in a radiative random unitary circuit.

AA << study quantum information scrambling in a random unitary circuit that exchanges qubits with an environment (..). As a result, initially localized quantum information  not only spreads within the system, but also spills into the environment. >>

<< The transition is also easily extended to higher dimensions, where higher-dimensional DP (directed percolation) universality classes will control the critical behavior. >>

<<  The transition in operator spreading  coincides with an information-theoretic 3 transition, which can be framed by  viewing (AA) circuit as a toy model for an evaporating black hole (..). >>️

<< Depending on the initial state of the swapped-in qubits, (AA) observe a corresponding entanglement transition in the coherent information into the environment. >>

️

Zack Weinstein, Shane P. Kelly, Jamir Marino, Ehud Altman. Scrambling Transition in a Radiative Random Unitary Circuit. arXiv:2210.14242v1 [quant-ph]. Oct 25, 2022.

https://arxiv.org/abs/2210.14242

Also: 'transition', 'random', in https://www.inkgmr.net/kwrds.html

Keywords: transition, quantum information, entanglement transition, scrambling, directed percolation

# gst: Parrondo paradox revisited, a chaotic switching approach

<< Parrondo's paradox is a phenomenon where the switching of two losing games results in a winning outcome. >>

<< Suppose I present to you the outcome of the quantum walker at the end of 100 coin tosses, knowing the initial position, can you tell me the sequence of tosses that lead to this final outcome?" (..) In the case of random switching, it is almost impossible to determine the sequence of tosses that lead to the end result. However, for periodic tossing, we could get the sequence of tosses rather easily, because a periodic sequence has structure and is deterministic. >> Joel Lai.

<< This led to the idea of incorporating chaotic sequences as a means to perform the switching. The authors discovered that using chaotic switching through a pre-generated chaotic sequence significantly enhances the work. For an observer who does not know parts of the information required to generate the chaotic sequence, deciphering the sequence of tosses is analogous to determining a random sequence. However, for an agent with information on how to generate the chaotic sequence, this is analogous to a periodic sequence. According to the authors, this information on generating the chaotic sequence is likened to the keys in encryption. >>

Using quantum Parrondo's random walks for encryption. Singapore University of Technology and Design. Oct15, 2021.

https://phys.org/news/2021-10-quantum-parrondo-random-encryption.html

Joel Weijia Lai, Kang Hao Cheong. Chaotic switching for quantum coin Parrondo's games with application to encryption. Phys. Rev. Research 3, L022019. June 2, 2021. 

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.L022019

Also

<< usando l'output di una logistica (per certi valori dei parms) un ipotetico Donald potrebbe avere il vezzo di ottenere stessi risultati con serialita' numerica generata meccanicamente anziche' in modalita' casuale; >>️

#POTUS race: Donald, what he can do (with less than four lines ...). FonT. May 23, 2016. 

https://flashontrack.blogspot.com/2016/05/p-usa-potus-race-donald-what-he-can-do.html

Also

keyword 'parrondo' in FonT

https://flashontrack.blogspot.com/search?q=parrondo

keyword 'parrondo' in Notes  (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=parrondo

Also

keyword 'chaos' | 'chaotic' in Font

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https://flashontrack.blogspot.com/search?q=chaotic

keyword 'caos' | 'caotico' in Notes (quasi-stochastic poetry)

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https://inkpi.blogspot.com/search?q=caotico

keywords: gst, games, life, chaos, Parrondo, Parrondo chaotic switching approach

# gst: accelerated first detection in discrete-time quantum walks using sharp restarts.

<< Restart is a common strategy observed in nature that accelerates first-passage processes, and has been extensively studied using classical random walks. In the quantum regime, restart in continuous-time quantum walks (CTQWs) has been shown to expedite the quantum hitting times [Phys. Rev. Lett. 130, 050802 (2023)]. >>

 Here, AA << study how restarting monitored discrete-time quantum walks (DTQWs) affects the quantum hitting times. (They) show that the restarted DTQWs outperform classical random walks in target searches, benefiting from quantum ballistic propagation, a feature shared with their continuous-time counterparts. >>

Kunal Shukla, Riddhi Chatterjee, C. M. Chandrashekar. Accelerated first detection in discrete-time quantum walks using sharp restarts. Phys. Rev. Research 7, 023069. Apr 21, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.023069

Also: walk, random, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, randomness, walk, random walk, quantum walk, stochasticity, sharp restart.

# gst: apropos of transitions: effects of random waves interacting with a coherent structure

<< Solitary waves interacting with random (..) waves (..) are studied. Two opposing types of dynamics are identified: First, the random thermal waves can erode the solitary wave; second, this structure can grow as a result of this interaction. These two types of behavior depend on a dynamical property of the solitary wave (its angular frequency), and on a statistical property of the thermal waves (the chemical potential). >>

<< Either process leads to an increase of the wave entropy. >>

Yuanting Chen, Benno Rumpf. Growth or decay of a coherent structure interacting with random waves. Phys. Rev. E 104, 034213. Sep 15, 2021.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.034213

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keyword 'waves' in FonT

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keyword 'onda' in Notes (quasi-stochastic poetry)

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# gst: synchronization and chaos in complex systems with delayed interactions.

<< Explaining the wide range of dynamics observed in ecological communities is challenging due to the large number of species involved, the complex network of interactions among them, and the influence of multiple environmental variables. >>

AA << consider a general framework to model the dynamics of species-rich communities under the effects of external environmental factors, showing that it naturally leads to delayed interactions between species, and analyze the impact of such memory effects on population dynamics. >>

<< Employing the generalized Lotka-Volterra equations with time delays and random interactions, (AA) characterize the resulting dynamical phases in terms of the statistical properties of community interactions. (Their) findings reveal that memory effects can generate persistent and synchronized oscillations in species abundances in sufficiently competitive communities. This provides an additional explanation for synchronization in large communities, complementing known mechanisms such as predator-prey cycles and environmental periodic variability. >>

<< Furthermore, (AA) show that when reciprocal interactions are negatively correlated, time delays alone can induce chaotic behavior. This suggests that ecological complexity is not a prerequisite for unpredictable population dynamics, as intrinsic memory effects are sufficient to generate long-term fluctuations in species abundances. >>

Francesco Ferraro, Christian Grilletta, et al. Synchronization and chaos in complex ecological communities with delayed interactions. arXiv: 2503.21551v1 [q-bio.PE]. Mar 27, 2025.

https://arxiv.org/abs/2503.21551

Also: pause, silence, random, chaos, network, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, pause, silence, random, chaos, chaotic behavior, network, delay, time delay, delayed interactions, random interactions, memory effect 

# gst: route from avalanches with random fields to stochastic branching events

<< Many complex systems with discrete symmetry breaking exhibit avalanche dynamics. Under quasistatically slow external driving, the temporal evolution v(t) of physical observables appears to be split between long periods of quiescence and well-delimited fast transformation events, the so-called avalanches. >>

<< Due to their fast nature, such avalanches can be regarded as instantaneous and labeled as point events k in time with a branching parameter. (..) Many physical systems exhibit criticality in the form of scale-free avalanches rendering power-law distributions of sizes and durations. >>️

<< Avalanches in mean-field models can be mapped to memoryless branching processes defining a universality class. (AA) present a reduced expression mapping a broad family of critical and subcriticial avalanches in mean-field models at the thermodynamic limit to rooted trees in a memoryless Poisson branching processes with random occurrence times. (They) derive the exact mapping for the athermal random field Ising model and the democratic fiber bundle model, where avalanche statistics progress towards criticality, and as an approximation for the self-organized criticality in slip mean-field theory. Avalanche dynamics and statistics in the three models differ only on the evolution of the field density, interaction strength, and the product of both terms determining the branching number. >>

️

Jordi Baró, Álvaro Corral. A universal route from avalanches in mean-field models with random fields to stochastic Poisson branching events. arXiv: 2502.08526v3 [cond-mat.dis-nn]. Feb 15, 2025. 

https://arxiv.org/abs/2502.08526

Also: waves, instability, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, instability, transition

# behav: the benefit of ignorance for traffic through a random congestible network.

<< When traffic is routed through a network that is susceptible to congestion, the self-interested decisions made by individual users do not, in general, produce the optimal flow. This discrepancy is quantified by the so-called "price of anarchy." >>

AA << consider whether the traffic produced by self-interested users is made better or worse when users have uncertain knowledge about the cost functions of the links in the network, and define a parallel concept that (They) call the "price of ignorance."  >>

AA << introduce a simple model in which fast, congestible links and slow, incongestible links are mixed randomly in a large network and users plan their routes with finite uncertainty about which of the two cost functions describes each link. >>

<< One of (Their) key findings is that a small level of user ignorance universally improves traffic, regardless of the network composition. Further, there is an optimal level of ignorance which, in (the) model, causes the self-interested user behavior to coincide with the optimum. Many features of (AA) model can be understood analytically, including the optimal level of user ignorance and the existence of critical scaling near the percolation threshold for fast links, where the potential benefit of user ignorance is greatest. >>️

Alican Saray, Calvin Pozderac, et al. The benefit of ignorance for traffic through a random congestible network. arXiv: 2503.09684v1 [cond-mat.dis-nn]. Mar 12, 2025.

https://arxiv.org/abs/2503.09684

Also:  network, behav, random, uncertainty, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, behavior,  randomness, uncertainty, price of anarchy, price of ignorance

# gst: irregular sampling design to address behaviours

<< Animal movement studies have become ubiquitous in animal ecology for the estimation of space use and the analysis of movement behavior. In these studies, animal movement data are primarily collected at regular time intervals. (AA) propose an irregular sampling design that could lead to greater efficiency and information gain in animal movement studies. (The) novel sampling design, called lattice and random intermediate point (LARI), combines samples at regular and random time intervals. >>

<<  in each of the data and simulation examples explored in this paper, LARI sampling results in more accurate and precise parameter estimation and, thus, better prediction of missing data as well.  >>

Elizabeth Eisenhauer,  Ephraim Hanks. A lattice and random intermediate point sampling design for animal movement. Environmetrics. doi: 10.1002/env.2618. Jan 3, 2020.

https://onlinelibrary.wiley.com/doi/abs/10.1002/env.2618

Gail McCormick. Including irregular time intervals improves animal movement studies. Pennsylvania State University. Jan 15, 2020.

https://m.phys.org/news/2020-01-irregular-intervals-animal-movement.html

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