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In the real world, data is often noisy, affecting not only the quality of features but also the accuracy of labels. Current research on mitigating label errors stems primarily from advances in deep learning, and a gap exists in exploring…
One regards spaces of trees as stratified spaces, to study distributions of phylogenetic trees. Stratified spaces with may have cycles, however spaces of trees with a fixed number of leafs are contractible. Spaces of trees with three leafs,…
We prove some technical results relating to the Brownian snake on a stable L\'evy tree. This includes some estimates on the range of the snake, estimates on its occupation measure around its minimum and also a proof of the fact that the…
The phase diagrams and transitions of nonequilibrium systems with multiplicative noise are studied theoretically. We show the existence of both strong and weak-coupling critical behavior, of two distinct active phases, and of a nonzero…
In this paper we study the stability of a tree-shaped network of elastic strings and beams with some feedbacks at the ends. The whole system is asymptotically stable. Moreover, the energy of the solution decay exponentially to zero if there…
A random walk on a group is noise sensitive if resampling every step independantly with a small probability results in an almost independant output. We precisely define two notions: $\ell^1$-noise sensitivity and entropy noise sensitivity.…
Recent breakthrough results in compressive sensing (CS) have established that many high dimensional signals can be accurately recovered from a relatively small number of non-adaptive linear observations, provided that the signals possess a…
We introduce noisy beeping networks, where nodes have limited communication capabilities, namely, they can only emit energy or sense the channel for energy. Furthermore, imperfections may cause devices to malfunction with some fixed…
Computations on the dendritic trees of neurons have important constraints. Voltage dependent conductances in dendrites are not similar to arbitrary direct-current generation, they are the basis for dendritic nonlinearities and they do not…
We present a numerical study of multi-commodity transport in a noisy, nonlinear network. The nonlinearity determines the dynamics of the edge capacities, which can be amplified or suppressed depending on the local current flowing across an…
We define a dynamical simple symmetric random walk in one dimension, and show that there almost surely exist exceptional times at which the walk tends to infinity. This is in contrast to the usual dynamical simple symmetric random walk in…
For a harmonic function on a tree with random walk whose transition probabilities are bounded between two constants in (0,1/2), it is known that the radial and stochastic properties of convergence, boundedness and finiteness of energy are…
In this note, we investigate the tree pressure for multi-modal interval maps with a certain class of hyperbolic and non-exceptional upper semi-continuous functions. In particular, we obtain a generalized version of Corollary 2.2 in the…
We develop a theory of spin noise in semiconductor nanowires considered as prospective elements for spintronics. In these structures spin-orbit coupling can be realized as a random function of coordinate correlated on the spatial scale of…
Under the excitation of strings, the wooden structure of string instruments is generally assumed to undergo linear vibrations. As an alternative to the direct measurement of the distortion rate at several vibration levels and frequencies,…
The purpose of this paper is to analyze certain statistics of a recently introduced non-uniform random tree model, biased recursive trees. This model is based on constructing a random tree by establishing a correspondence with non-uniform…
Using the framework of boosting, we prove that all impurity-based decision tree learning algorithms, including the classic ID3, C4.5, and CART, are highly noise tolerant. Our guarantees hold under the strongest noise model of nasty noise,…
A well-known open problem in graph theory asks whether Stanley's chromatic symmetric function, a generalization of the chromatic polynomial of a graph, distinguishes between any two non-isomorphic trees. Previous work has proven the…
A tentative scaling theory is presented of a tree swaying in a turbulent wind. It is argued that the turbulence of the air within the crown is in the inertial regime. An eddy causes a dynamic bending response of the branches according to a…
We study the dynamical behaviour of weighted shifts defined on sequence spaces of a directed tree. In particular, we characterize their boundedness as well as when they are hypercyclic, weakly mixing and mixing.