相关论文: Long-range properties and data validity for hydrog…

Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…

Monitoring continental precipitation over Europe with high resolution (2 km, 15 minutes) has been possible since the operational production of the OPERA composites from the European weather radar networks. The OPERA data are the essential…

Ocean eddies play an important role in the transport and mixing processes of the ocean due to their ability to transport material, heat, salt, and other tracers across large distances. They exhibit at least two timescales; an Eulerian…

We consider open multi-class queueing networks with general arrival processes, general processing time sequences and Bernoulli routing. The network is assumed to be operating under an arbitrary work-conserving scheduling policy that makes…

Detrended Fluctuation Analysis (DFA) is the most popular fractal analytical technique used to evaluate the strength of long-range correlations in empirical time series in terms of the Hurst exponent, $H$. Specifically, DFA quantifies the…

We present a geometrical demonstration for persistence properties for a bi-Hamiltonian system modelling waves in a shallow water regime. Both periodic and non-periodic cases are considered and a key ingredient in our approach is one of the…

The flow past a bullet-shaped blunt body moving in a pipe is investigated through global linear stability analysis (LSA) and direct numerical simulation (DNS). A cartography of the bifurcation curves is provided thanks to LSA, covering the…

Persistence diagrams are efficient descriptors of the topology of a point cloud. As they do not naturally belong to a Hilbert space, standard statistical methods cannot be directly applied to them. Instead, feature maps (or representations)…

Many dynamic pipe flow simulator tools are capable of predicting the onset of hydrodynamic flow instability through detailed simulation. These instabilities provide a natural mechanism for flow regime transition. The quality and reliability…

Generic short-range interacting quantum systems with a conserved quantity exhibit universal diffusive transport at late times. We employ non-equilibrium quantum field theory and semi-classical phase-space simulations to show how this…

Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. {While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the…

Recent studies have actively employed persistent homology (PH), a topological data analysis technique, to analyze the topological information in time series data. Many successful studies have utilized graph representations of time series…

The 3D incompressible Euler equation is an important research topic in the mathematical study of fluid dynamics. Not only is the global regularity for smooth initial data an open issue, but the behaviour may also depend on the presence or…

Here we study the long time behavior of an advection-diffusion equation with a general time varying (including random) shear flow imposing no-flux boundary conditions on channel walls. We derive the asymptotic approximation of the scalar…

We investigate the probability of observing a given pattern of $n$ rises and falls in a random stationary data series. The data are modelled as a sequence of $n+1$ independent and identically distributed random numbers. This probabilistic…

In this work we investigate the statistical mechanics of a family of two dimensional (2D) fluid flows, described by the generalized Euler equations, or $\alpha$-models. These models describe both nonlocal and local dynamics, with one…

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such…

We present the application of topological data analysis (TDA) to study unweighted complex networks via their persistent homology. By endowing appropriate weights that capture the inherent topological characteristics of such a network, we…

Common modal decomposition techniques for flowfield analysis, data-driven modeling and flow control, such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are usually performed in an Eulerian (fixed) frame of…

Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework - zigzag persistence from topological data analysis -…