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In wall-bounded parallel flows, sustained turbulence can occur even while laminar flow is still stable. Channel flow is one of such flows and displays spatio-temporal fluctuating patterns of localized turbulence along its way from/to…
Aims. We develop an extended percolation method to allow the comparison of geometrical properties of the real cosmic web with the simulated dark matter web for an ensemble of over- and under-density systems. Methods. We scan density fields…
The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only…
In this dissertation we study basic local differential geometry, projective differential geometry, and prolongations of overdetermined geometric partial differential equations. It is simple to prolong an n-th order linear ordinary…
Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to…
We prove non-universality results for first-passage percolation on the configuration model with i.i.d. degrees having infinite variance. We focus on the weight of the optimal path between two uniform vertices. Depending on the properties of…
Recently increasing attention has been addressed to the fluctuations observed in percolation defined in single and multiplex networks. These fluctuations are extremely important to characterize the robustness of real finite networks but…
Studies of the phase diagram of the coupled sine circle map lattice have identified the presence of two distinct universality classes of spatiotemporal intermittency viz. spatiotemporal intermittency of the directed percolation class with a…
The finite-size scaling behaviour for percolation and conduction is studied in two-dimensional triangular-shaped random resistor networks at the percolation threshold. The numerical simulations are performed using an efficient star-triangle…
We study hypersurfaces with fractional mean curvature in N-dimensional Euclidean space. These hypersurfaces are critical points of the fractional perimeter under a volume constraint. We use local inversion arguments to prove existence of…
We consider a general discrete-time branching random walk on a countable set X. We relate local, strong local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that,…
The huge amount of available data nowadays is a challenge for kernel-based machine learning algorithms like SVMs with respect to runtime and storage capacities. Local approaches might help to relieve these issues and to improve statistical…
Universal behavior is a typical emergent feature of critical systems. A paramount model of the non-equilibrium critical behavior is the directed bond percolation process that exhibits an active- to-absorbing state phase transition in the…
Techniques of `dynamic renormalization', developed earlier for undirected percolation and the contact model, are adapted to the setting of directed percolation, thereby obtaining solutions of several problems for directed percolation on…
Following H. Tomita and C. Murakami we propose an analytical model to predict critical probability of percolation. It is based on the excursion set theory which allows us to consider N-dimensional bounded regions. Details are given for the…
Continual learning is the problem of learning and retaining knowledge through time over multiple tasks and environments. Research has primarily focused on the incremental classification setting, where new tasks/classes are added at discrete…
Modulus of local continuity is used to evaluate the robustness of neural networks and fairness of their repeated uses in closed-loop models. Here, we revisit a connection between generalized derivatives and moduli of local continuity, and…
This note was motivated by natural questions related to oriented percolation on a layered environment that introduces long range dependence. As a convenient tool, we are led to deal with questions on the strict decrease of the percolation…
Global physical properties of random media change qualitatively at a percolation threshold, where isolated clusters merge to form one infinite connected component. The precise knowledge of percolation thresholds is thus of paramount…
The site percolation on the triangular lattice stands out as one of the few exactly solved statistical systems. By initially configuring critical percolation clusters of this model and randomly reassigning the color of each percolation…