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The evolution of a walker in standard "Discrete-time Quantum Walk (DTQW)" is determined by coin and shift unitary operators. The conditional shift operator shifts the position of the walker to right or left by unit step size while the…
Random walk sampling methods have been widely used in graph sampling in recent years, while it has bias towards higher degree nodes in the sample. To overcome this deficiency, classical methods such as MHRW design weighted walking by…
Random walk in random environment (RWRE) is a fundamental model of statistical mechanics, describing the movement of a particle in a highly disordered and inhomogeneous medium as a random walk with random jump probabilities. It has been…
Reinforced random walks are random walks on graphs whose transition probabilities along edges from a vertex are proportional to the weights of those edges, but where the weight of an edge evolves in a way that depends on the past traversals…
In this work, we present a new model of the Discrete-Time Open Quantum Walk (DTOQW) applicable to an arbitrary graph, thereby going beyond the case of quantum walks on regular graphs. We study the impact of noise in the dynamics of quantum…
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes…
We investigated the optical/ultraviolet (UV) color variations for a sample of 2169 quasars based on multi-epoch spectroscopy in the Sloan Digital Sky Survey (SDSS) data release seven (DR7) and data release nine (DR9). To correct the…
We investigate the dynamics of a particle executing a general Continuous Time Random Walk (CTRW) in three dimensions under the influence of arbitrary time-varying external fields. Contrary to the general approach in recent works, our method…
The damped harmonic oscillator is a workhorse for the study of dissipation in quantum mechanics. However, despite its simplicity, this system has given rise to some approximations whose validity and relation to more refined descriptions…
Levy walk (LW) process has been used as a simple model for describing anomalous diffusion in which the mean squared displacement of the walker grows non-linearly with time in contrast to the diffusive motion described by simple random walks…
We make use of the high photometric precision of Kepler to search for periodic modulations among 14 normal (DA- and DB-type, likely non-magnetic) hot white dwarfs (WDs). In five, and possibly up to seven of the WDs, we detect periodic, ~2…
We analyze a special class of 1-D quantum walks (QWs) realized using optical multi-ports. We assume non-perfect multi-ports showing errors in the connectivity, i.e. with a small probability the multi- ports can connect not to their nearest…
Graph sampling is a technique to pick a subset of vertices and/ or edges from original graph. Among various graph sampling approaches, Traversal Based Sampling (TBS) are widely used due to low cost and feasibility for many cases, in which…
Discrete-time quantum walks (DTQWs) in random artificial electric and gravitational fields are studied analytically and numerically. The analytical computations are carried by a new method which allows a direct exact analytical…
We conduct a systematic search for quasars with periodic variations from the archival photometric data of the Zwicky Transient Facility by cross-matching with the quasar catalogs of the Sloan Digital Sky Survey and V{\'e}ron-Cetty \&…
The discrete-time quantum walk (QW) is a quantum version of the random walk (RW) and has been widely investigated for the last two decades. Some remarkable properties of QW are well known. For example, QW has a ballistic spreading, i.e., QW…
Quasars have been proposed as a new class of standard candles analogous to Supernovae, as their large redshift range and high luminosities make them excellent candidates. Reverberation mapping (RM) method enables to estimate the distance to…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
Charge transport processes in disordered complex media are accompanied by anomalously slow relaxation for which usually a broad distribution of relaxation times is adopted. To account for those properties of the environment, a standard…
We introduce a class of multifractal processes, referred to as Multifractal Random Walks (MRWs). To our knowledge, it is the first multifractal processes with continuous dilation invariance properties and stationary increments. MRWs are…