Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.

We investigate the ground and excited states of interacting electrons in a quantum point contact using exact diagonalization method. We find that strongly localized states in the point contact appear when a new conductance channel opens due to momentum mismatch. These localized states form magnetic impurity states which are stable in a finite regime of chemical potential and excitation energy. Interestingly, these magnetic impurities have ferromagnetic coupling, which shed light on the experimentally observed puzzling coexistence of Kondo correlation and spin filtering in a quantum point contact.PACS numbers: 75.30. Hx, 73.63.Rt, 72.15.Qm Since two decades ago, it has been known that the conductance of a quantum point contact(QPC), a narrow constriction between two-dimensional electron gas, has plateaus at integer multiples of 2e. This conductance quantization is due to the fact that the density of states of one-dimensional conductor is inversely proportional to the electron velocity, which is now well understood within Landauer formalism [2]. Additional structure of the extra plateaus around 0.7(2e 2 /h), has been observed, but the origin of the structure has been controversial ever since its observation [3][4][5][6]. It has been suggested that the anomalous feature might be due to Kondo correlation because, similar to Kondo effect, there exist a zero-bias peak in the differential conductance which splits in a magnetic field and a crossover to perfect transmission below a characteristic temperature [4].The Kondo interpretation as an origin of 0.7 structure, however, is questioned mainly by two reasons. First, the counter-intuitive existence of the impurity state on top of the potential barrier. Second, spin-filtering effect has been observed in a quantum point contact [3,6], which is hardly explainable within the Kondo model. The spin filtering effect is better explained by a phenomenological spin polarization model [7] which assumes also counterintuitive low-dimensional spontaneous spin polarization. In this Letter, we provide generalized view allowing both Kondo correlation and spin filtering by confirming the existence of the ferromagnetically coupled magnetic impurities in a quantum point contact. We will demonstrate the existence of the magnetic impurity in a QPC through exact diagonalization technique and show that the magnetic impurities are ferromagnetically coupled. Our numerical results imply that the transport through a QPC may have both the Kondo correlation and spin-polarised transport due to the interplay between ferromagnetically coupled magnetic impurities.Let us consider a quantum point contact modeled by a harmonic potential locally formed in a two dimensional electron system shown in Fig. 1 (a). The single particle

Insulin is secreted in a pulsatile manner from multiple micro-organs called the islets of Langerhans. The amplitude and phase (shape) of insulin secretion are modulated by numerous factors including glucose. The role of phase modulation in glucose homeostasis is not well understood compared to the obvious contribution of amplitude modulation. In the present study, we measured Ca2+ oscillations in islets as a proxy for insulin pulses, and we observed their frequency and shape changes under constant/alternating glucose stimuli. Here we asked how the phase modulation of insulin pulses contributes to glucose regulation. To directly answer this question, we developed a phenomenological oscillator model that drastically simplifies insulin secretion, but precisely incorporates the observed phase modulation of insulin pulses in response to glucose stimuli. Then, we mathematically modeled how insulin pulses regulate the glucose concentration in the body. The model of insulin oscillation and glucose regulation describes the glucose-insulin feedback loop. The data-based model demonstrates that the existence of phase modulation narrows the range within which the glucose concentration is maintained through the suppression/enhancement of insulin secretion in conjunction with the amplitude modulation of this secretion. The phase modulation is the response of islets to glucose perturbations. When multiple islets are exposed to the same glucose stimuli, they can be entrained to generate synchronous insulin pulses. Thus, we conclude that the phase modulation of insulin pulses is essential for glucose regulation and inter-islet synchronization.