Search

Many decision-making theories are encoded in a class of processes known as evidence accumulation models (EAM). These assume that noisy evidence stochastically accumulates until a set threshold is reached, triggering a decision. One of the most successful and widely used of this class is the Diffusion Decision Model (DDM). The DDM however is limited in scope and does not account for processes such as evidence leakage, changes of evidence, or time varying caution. More complex EAMs can encode a wider array of hypotheses, but are currently limited by computational challenges. In this work, we develop the Python package PyBEAM (Bayesian Evidence Accumulation Models) to fill this gap. Toward this end, we develop a general probabilistic framework for predicting the choice and response time distributions for a general class of binary decision models. In addition, we have heavily computationally optimized this modeling process and integrated it with PyMC, a widely used Python package for Bayesian parameter estimation. This 1) substantially expands the class of EAM models to which Bayesian methods can be applied, 2) reduces the computational time to do so, and 3) lowers the entry fee for working with these models. Here we demonstrate the concepts behind this methodology, its application to parameter recovery for a variety of models, and apply it to a recently published data set to demonstrate its practical use., (© 2023. The Psychonomic Society, Inc.)

We find stationary excited states of a one-dimensional system of N spinless point bosons with repulsive interaction and zero boundary conditions by numerically solving the time-independent Gross–Pitaevskii equation. The solutions are compared with the exact ones found in the Bethe-ansatz approach. We show that the j th stationary excited state of a nonuniform condensate of atoms corresponds to a Bethe-ansatz solution with the quantum numbers n 1 = n 2 = ... = n N = j + 1 . On the other hand, such values of n 1 , ... , n N correspond to a condensate of N elementary excitations (the Bogoliubov quasiparticles) with the quasimomentum ℏ π j / L , where L is the system size. Thus, each stationary excited state of the condensate is 'doubly coherent', since it corresponds simultaneously to a condensate of N atoms and a condensate of N elementary excitations. We find the energy E and the particle density profile ρ (x) for such states. The possibility of experimental production of these states is also discussed. [ABSTRACT FROM AUTHOR]

This paper investigates the power-saving mechanisms of Discontinuous Reception (DRX), a technique used in wireless communication networks to reduce energy consumption. By employing a discrete-time Geo/Geo/1 queueing model with differentiated vacations and system disasters, we aim to more accurately capture the intermittent nature of data arrivals, often overlooked in continuous-time models. Our research addresses the existing gap in the literature by providing a more realistic representation of DRX behaviour. Understanding the performance and characteristics of DRX is crucial for optimizing energy efficiency and improving the overall performance of wireless networks. This paper contributes to this understanding by deriving steady-state probabilities, calculating key performance metrics, and visualizing the system behaviour through graphical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method for computing the sojourn times in the MAP/M/1 queueing systems with three types of negative customers due to three basic removal rules: the RCH, RCE and RCA. To this end, we first give a necessary and sufficient condition under which the system is stable by means of the mean drift technique. Then we obtain the queue size distributions and the average stationary queue lengths by using the matrix-analytic method. Based on this, we provide a new effective method for computing the average sojourn time of any arriving customer through using the first passage times and the PH distributions. Finally, we use some numerical examples to illustrate how the performance measures are influenced by some key system parameters. [ABSTRACT FROM AUTHOR]

The distribution of the first-passage time (FPT) Ta for a Brownian particle with drift μ subject to hitting an absorber at a level a > 0 is well-known and given by its density γ (t) = a 2 π t 3 e − (a − μ t) 2 2 t , t > 0 , which is normalized only if μ≥0. This article demonstrates the existence of two additional diffusion process categories (one with one parameter and the other with two) that have the same first passage-time distributions when μ < 0. For both, we identify the transition densities and thoroughly investigate the processes. A substantial implication is that the first-passage time distribution does not indicate whether the process originates from a drifted Brownian motion or from one of the new processes presented. [ABSTRACT FROM AUTHOR]

This paper investigates a single-server queuing system with heterogeneous service, failure, and maintenance. The proposed model features a server acting as both the main and backup server. System failure can occur at any stage. When a failure happens, instead of stopping the service entirely, the main server functions as a backup, providing service at a reduced rate. Once all jobs in the system have been serviced, the backup server enters the maintenance state. Following the repair process during maintenance, the server transitions to an idle state, awaiting incoming jobs. Explicit expressions for both transient and steady-state behaviours of the system are derived. Additionally, key system performance metrics are discussed in this paper, accompanied by graphical illustrations to visualize system size probabilities and performance indices. [ABSTRACT FROM AUTHOR]

In this article, a non-Gaussian long memory process is constructed by the aggregation of independent copies of a fractional Lévy Ornstein-Uhlenbeck process with random coefficients. Several properties and a limit theorem are studied for this new process. Finally, some simulations of the limit process are shown. [ABSTRACT FROM AUTHOR]