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This paper presents a novel framework for automatic learning of complex strategies in human decision making. The task that we are interested in is to better facilitate long term planning for complex, multi-step events. We observe temporal…
In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some…
We propose an experimental study of adaptive time-stepping methods for efficient modeling of the aggregation-fragmentation kinetics. Precise modeling of this phenomena usually requires utilization of the large systems of nonlinear ordinary…
In this paper, we propose a novel affordance model, which combines object, action, and effect information in the latent space of a predictive neural network architecture that is built on Conditional Neural Processes. Our model allows us to…
We present a comparative study of several algorithms for an in-plane random walk with a variable step. The goal is to check the efficiency of the algorithm in the case where the random walk terminates at some boundary. We recently found…
We examine the aggregate behavior of one-dimensional random walks in a model known as (one-dimensional) Internal Diffusion Limited Aggregation. In this model, a sequence of $n$ particles perform random walks on the integers, beginning at…
This paper studies the numerical computation of integrals, representing estimates or predictions, over the output $f(x)$ of a computational model with respect to a distribution $p(\mathrm{d}x)$ over uncertain inputs $x$ to the model. For…
Artificial neural networks that simulate human achieves great successes. From the perspective of simulating human memory method, we propose a stepped sampler based on the "repeated input". We repeatedly inputted data to the LSTM model…
Time-fractional parabolic equations with a Caputo time derivative are considered. For such equations, we explore and further develop the new methodology of the a-posteriori error estimation and adaptive time stepping proposed in [7]. We…
Stochastic search processes are ubiquitous in nature and are expected to become more efficient when equipped with a memory, where the searcher has been before. A natural realization of a search process with long-lasting memory is a…
We present a stochastic method for efficiently computing the solution of time-fractional partial differential equations (fPDEs) that model anomalous diffusion problems of the subdiffusive type. After discretizing the fPDE in space, the…
Let $T\$ be a stopping time associated with a sequence of independent random variables $Z_{1},Z_{2},...$ . By applying a suitable change in the probability measure we present relations between the moment or probability generating functions…
We formulate a fractional master equation in continuous time with random transition probabilities across the population of random walkers such that the effective underlying random walk exhibits ensemble self-reinforcement. The population…
We propose a two-phase systematical framework for approximation algorithm design and analysis via Lyapunov function. The first phase consists of using Lyapunov function as an input and outputs a continuous-time approximation algorithm with…
We consider reinforcement learning in parameterized Markov Decision Processes (MDPs), where the parameterization may induce correlation across transition probabilities or rewards. Consequently, observing a particular state transition might…
We obtain an exact formula for the first-passage time probability distribution for random walks on complex networks using inverse Laplace transform. We write the formula as the summation of finitely many terms with different frequencies…
We show that the same maximum entropy principle applied to recurrence microstates configures a new way to properly compute the time delay necessary to correctly sample a data set. The new method retrieves results obtained using traditional…
We show that the delay time distribution for wave reflection from a one-dimensional random potential is related directly to that of the reflection coefficient, derived with an arbitrarily small but uniform imaginary part added to the random…
The Poisson process of order $i$ is a weighted sum of independent Poisson processes and is used to model the flow of clients in different services. In the paper below we study some extensions of this process, for different forms of the…
The statistics of steps and dwell times in reversible molecular motors differ from those of cycle completion in enzyme kinetics. The reason is that a step is only one of several transitions in the mechanochemical cycle. As a result,…