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Determinantal Point Process (DPPs) are statistical models for repulsive point patterns. Both sampling and inference are tractable for DPPs, a rare feature among models with negative dependence that explains their popularity in machine…

A characterisation of quantum stochastic positive definite (PD) exponent is given in terms of the conditional positive definiteness (CPD) of their form-generator. The pseudo-Hilbert dilation of the stochastic form-generator and the…

Dissipative estimator (observer) design for continuous time-delay systems poses a significant challenge when an unlimited number of pointwise and general distributed delays (DDs) are concerned. We propose an effective solution to this…

Dissipative solitons are stable localized coherent structures with linear frequency chirp generated in normal-dispersion mode-locked lasers. The soliton energy in fiber lasers is limited by the Raman effect, but implementation of…

Dissipative Kerr-microresonator soliton combs (hereafter called soliton combs) has been rapidly progressing as compact frequency combs. Comb mode scanning of the soliton combs with a large range and fast speed is of paramount importance for…

Topological phases have become an enabling role in exploiting new applications of nonlinear optics in recent years. Here we theoretically propose a valley photonic crystal resonator emulating topologically protected dissipative Kerr soliton…

We show that scattering-based interaction among nearly degenerate optical modes is the key factor in low threshold generation of Kerr frequency combs in nonlinear optical resonators possessing small group velocity dispersion (GVD). The mode…

We report on new types of two-component one-dimensional dark solitons (DSs) in a model of a dual-core waveguide with normal group-velocity dispersion and Kerr nonlinearity in both cores, the coupling between which is dispersive too. In the…

Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…

We present a simple solution to enhance the separation ability of deterministic lateral displacement (DLD) systems by expanding the two-dimensional nature of these devices and driving the particles into size-dependent, fully…

We introduce a class of Markovian quantum master equations, able to describe the dissipative dynamics of a quantum system weakly coupled to one or several heat baths. The dissipative structure is driven by an entropic operator, the so…

Passive Kerr cavities driven by coherent laser fields display a rich landscape of nonlinear physics, including bistability, pattern formation, and localised dissipative structures (solitons). Their conceptual simplicity has for several…

Diffusion models have emerged as a powerful class of generative models for molecular design, capable of capturing complex structural distributions and achieving high fidelity in 3D molecule generation. However, their widespread use remains…

A distributed Kerr-lens mode locking regime can be realized in a waveguide laser by spatial profiling of the pump beam, thus creating a spatio-temporal soliton. Additional slow temporal modulation of the pump source stabilizes the…

Diffusion-based generative models have emerged as highly effective methods for synthesizing high-quality samples. Recent works have focused on analyzing the convergence of their generation process with minimal assumptions, either through…

An electrokinetically-driven deterministic lateral displacement (e-DLD) device is proposed for the continuous, two-dimensional fractionation of suspensions in microfluidic platforms. The suspended species are driven through an array of…

Kerr-induced synchronization (KIS) provides a new key tool for the control and stabilization of the repetition rate of a cavity soliton frequency comb. It enables direct external control of a given comb tooth of a dissipative Kerr soliton…

Oblique interaction of small- but finite-amplitude KdV-type electron-acoustic solitary excitations is examined in an unmagnetized two-electron-populated degenerate quantum electron-ion plasma in the framework of quantum hydrodynamics model…

We report results of systematic numerical studies of 2D matter-wave soliton families supported by an external potential, in a vicinity of the junction between stable and unstable branches of the families, where the norm of the solution…

Using the Colour Glass Condensate description of electron-nucleus collisions at high energy, we study the diffractive production of a pair of jets with transverse momenta much larger than the nuclear saturation momentum $Q_s$. At leading…