Interaction Renormalization and Validity of Kinetic Equations for Turbulent States.

We consider turbulence of waves interacting weakly via four-wave scattering (sea waves, plasma waves, spin waves, etc.). In the first order in the interaction, a closed kinetic equation has stationary solutions describing turbulent cascades.

Multimode correlations and the entropy of turbulence in shell models.

We suggest a new focus for turbulence studies-multimode correlations-which reveal the hitherto hidden nature of turbulent state. We apply this approach to shell models describing basic properties of turbulence. The family of such models allows one to study turbulence close to thermal equilibrium, which happens when the interaction time weakly depends on the mode number.

Sum-of-squares bounds on correlation functions in a minimal model of turbulence.

We suggest a new computer-assisted approach to the development of turbulence theory. It allows one to impose lower and upper bounds on correlation functions using sum-of-squares polynomials. We demonstrate it on the minimal cascade model of two resonantly interacting modes when one is pumped and the other dissipates.

Information theory characteristics improve the prediction of lithium response in bipolar disorder patients using a support vector machine classifier.

Aim: Bipolar disorder (BD) is a mood disorder with a high morbidity and death rate. Lithium (Li), a prominent mood stabilizer, is often used as a first-line treatment. However, clinical studies have shown that Li is fully effective in roughly 30% of BD patients.

Direct observation of vortices in an electron fluid.

Vortices are the hallmarks of hydrodynamic flow. Strongly interacting electrons in ultrapure conductors can display signatures of hydrodynamic behaviour, including negative non-local resistance, higher-than-ballistic conduction, Poiseuille flow in narrow channels and violation of the Wiedemann-Franz law. Here we provide a visualization of whirlpools in an electron fluid.