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Discourse coherence is strongly associated with text quality, making it important to natural language generation and understanding. Yet existing models of coherence focus on measuring individual aspects of coherence (lexical overlap,…
This paper establishes a nonlinear separation principle based on contraction theory and derives sharp stability conditions for recurrent neural networks (RNNs). First, we introduce a nonlinear separation principle that guarantees global…
Nonlinear responses in condensed matter are intensively studied because they provide rich information about materials and hold the possibility of being applied in diodes or high-frequency optical devices. While nonlinear responses in…
We present a diagrammatic theory for coherent backscattering from disordered dilute media in the nonlinear regime. The approach is non-perturbative in the strength of the nonlinearity. We show that the coherent backscattering enhancement…
An approximation to the solution of a stochastic parabolic equation is constructed using the Galerkin approximation followed by the Wiener Chaos decomposition. The result is applied to the nonlinear filtering problem for the time…
We consider the non-equilibrium physics induced by joining together two tight binding fermionic chains to form a single chain. Before being joined, each chain is in a many-fermion ground state. The fillings (densities) in the two chains…
We identify and discuss nonlinear phase noise arising in Kerr self-phase modulation of a coherent light pulse propagating through an attenuating medium with third-order nonlinearity in a dispersion-free setting. This phenomenon,…
Band theory for partially coherent light is introduced by using the formalism of second-order classical coherence theory under paraxial approximation. It is demonstrated that the cross-spectral density function, describing correlations…
The interplay of shaped signaling and fiber nonlinearities is reviewed in the asymptotic and finite-length regime. We present explanations and discuss implications of an optimum shaping length of just a few hundred symbols.
Weak phase noise present on an optical field can be amplified by a self-focusing nonlinearity and form intense "rogue wave" features. Here, we study the effect of the coherence length (or grain size) of this phase noise on the likelihood of…
The homogeneity of filter media is important for material selection and quality control, along with the specific weight (nominal grammage) and the distribution of the local weight. Cloudiness or formation is a concept used to describe…
We present an analysis of ensemble Kalman inversion, based on the continuous time limit of the algorithm. The analysis of the dynamical behaviour of the ensemble allows us to establish well-posedness and convergence results for a fixed…
This paper performs a detailed, multi-faceted analysis of key challenges and common design caveats related to the development of efficient neural networks (NN) nonlinear channel equalizers in coherent optical communication systems. Our…
This paper presents a combined numerical-theoretical study of the macroscopic behavior and local field distributions in a special class of two-dimensional periodic composites with viscoplastic phases. The emphasis is on strongly nonlinear…
We give a detailed and improved presentation of our recently proposed formalism for non-linear perturbations in cosmology, based on a covariant and fully non-perturbative approach. We work, in particular, with a covector combining the…
A discrete-time end-to-end fiber-optical channel model is derived based on the first-order perturbation approach. The model relates the discrete-time input symbol sequences of co-propagating wavelength channels to the received symbol…
It is shown that the inhomogeneous chiral condensate in the Gross-Neveu (GN) model takes the chiral spiral form, even though the thermodynamic functional depends only on the chiral scalar density. It is the inhomogeneity of the chiral…
The nonlinearity is an important feature in the field of optomechanics. Employing atomic coherence, we put forward a scheme to enhance the nonlinearity of the cavity optomechanical system. The effective Hamiltonian is derived, which shows…
Coherent optical transmission systems naturally lead to a four dimensional (4D) signal space, i.e., two polarizations each with two quadratures. In this paper we derive an analytical model to quantify the impact of Kerr nonlinearity on such…
In this paper, we aim to estimate the direction of an underlying signal from its nonlinear observations following the semi-parametric single index model (SIM). Unlike conventional compressed sensing where the signal is assumed to be sparse,…