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Stochastic bursting in unidirectionally delay-coupled noisy excitable system
Chaos. 2019. Vol. 29. No. 041103. P. 1–9.
Пиковский А.
We show that “stochastic bursting” is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation, i.e., when the time delays in each connection are much larger than the characteristic duration of the spikes, the observed rather coherent spike pattern can be described by an idealized coupled point process with a leader–follower relationship.We derive analytically the statistics of the spikes in each unit, the pairwise correlations between any two units, and the spectrum of the total output from the network. Theory is in good agreement with the simulations with a network of theta-neurons.
Keywords: Noise
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
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Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
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Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
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Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
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Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
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Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
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Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.
An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...
Added: December 25, 2025
Popov V., / Series arXiv "math". 2025. No. 2502.01539.
We prove that the variety of flexes of algebraic curves
of degree 3 in the projective plane is an ideal theoretic complete
intersection in the product of a two-dimensional and a nine-dimensional projective spaces. ...
Added: December 16, 2025
Klinshov V., Некоркин В. И., Communications in Nonlinear Science and Numerical Simulation 2020 Vol. 83 P. 105067
Multistability is a common feature of various dynamical systems which manifests itself as the possibility to demonstrate various behaviors for the same parameter values. These behaviors or states of the system must be stable against weak perturbation in order to be observable in real life. However, a strong enough perturbation may destroy a certain state ...
Added: March 16, 2022
Zdorova N., Malyutina S., Laurinavichyute A. et al., /. 2021.
Noise, as part of real-life communication flow, degrades the quality of linguistic input and affects language processing. According to predictions of the noisy-channel model, noise makes comprehenders rely more on word-level semantics and good-enough processing instead of actual syntactic relations. However, empirical evidence of such qualitative effect of noise on sentence processing is still lacking. For the first time, ...
Added: October 28, 2021
Novikov N., Zakharov D., Moiseeva V. et al., Frontiers in Neural Circuits 2021 Vol. 15 Article 647944
According to mechanistic theories of working memory (WM), information is retained as stimulus-dependent persistent spiking activity of cortical neural networks. Yet, how this activity is related to changes in the oscillatory profile observed during WM tasks remains a largely open issue. We explore joint effects of input gamma-band oscillations and noise on the dynamics of ...
Added: September 2, 2021
Munyaev V., Smirnov L., Kostin V. et al., New Journal of Physics 2020 Vol. 22 Article 023036
We study populations of globally coupled noisy rotators(oscillators with inertia) allowing a nonequilibrium transition from a desynchronized state to a synchronous one (with the nonvanishing order parameter). The newly developed analytical approaches resulted in solutions describing the synchronous state with constant order parameter for weakly inertial rotators, including the case of zero inertia, when the ...
Added: October 31, 2020
Kechiev L., М.: Грифон, 2016.
For the first time in the domestic technical literature questions of designing of system of power delivery network (PDN) of electronic modules of electronic equipment are considered. Noise in the power supply system of high-speed digital modules are one of the basic problems without which decision working capacity of modules cannot be guaranteed. These decisions should be ...
Added: December 21, 2016
Kechiev L., Николаев П. А., М.: Грифон, 2015.
At the heart of the book all-round consideration of a problem EMC of vehicles lays. From system positions questions of a noise stability and noise emission are stated. The review of the basic test methods of motor transport is given. Parametres EMC an onboard electric equipment are resulted. Methods and means of multilevel maintenance EMC are in ...
Added: January 23, 2016
Kulikova S., Tolmacheva E. A., Anderson P. et al., European Journal of Neuroscience 2012 Vol. 36 No. 10 P. 3407–3419
Sensory and cognitive deficits are common in schizophrenia. They are associated with abnormal brain rhythms, including disturbances in γ frequency (30–80 Hz) oscillations (GFO) in cortex-related networks. However, the underlying anatomofunctional mechanisms remain elusive. Clinical and experimental evidence suggests that these deficits result from a hyporegulation of glutamate N-methyl-D-aspartate receptors. Here we modeled these deficits in ...
Added: October 22, 2015
McDonnell M. D., Iannella N., To M. -. et al., Network: Computation in Neural Systems 2015 Vol. 26 No. 2 P. 35–71
Stochastic resonance (SR) is said to be observed when the presence of noise in a nonlinear system enables an output signal from the system to better represent some feature of an input signal than it does in the absence of noise. The effect has been observed in models of individual neurons, and in experiments performed ...
Added: September 7, 2015