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Context. This is the second paper of a series aiming to determine the birth rates of supernovae (SNe) in the local Universe. Aims. We aimed to estimate the SN rates in the local Universe and fit the delay-time distribution of type Ia SNe (SNe Ia) to put constraints on their progenitor scenarios. Methods. We performed a Monte Carlo simulation to estimate volumetric rates using the nearby SN sample introduced in Paper I. The rate evolution of core-collapse (CC) SNe closely follows the evolution of the cosmic star formation history, while the rate evolution of SNe Ia involves the convolution of the cosmic star formation history and a two-component delay-time distribution including a power law and a Gaussian component. Results. The volumetric rates of type Ia, Ibc, and II SNe are derived as 0.325 ± 0.040_−0.010^+0.016, 0.160 ± 0.028_−0.014^+0.044, and 0.528 ± 0.051_−0.013^+0.162(in units of 10⁻⁴yr⁻¹Mpc⁻³h₇₀³), respectively. The rate of CCSNe (0.688 ± 0.078_−0.027^+0.0206) is consistent with previous estimates, which trace the star formation history. Conversely, the newly derived local SN Ia rate is larger than existing results given at redshifts 0.01 < z < 0.1, favoring an increased rate from the Universe at z ∼ 0.1 to the local Universe at z < 0.01. A two-component model effectively reproduces the rate variation, with the power law component accounting for the rate evolution at larger redshifts and the Gaussian component with a delay time of 12.63 ± 0.38 Gyr accounting for the local rate evolution. This delayed component, with its exceptionally long delay time, suggests that the progenitors of these SNe Ia were formed around 1 Gyr after the birth of the Universe, which could only be explained by a double-degenerate progenitor scenario. Comparison with the Palomar Transient Factory (PTF) sample of SNe Ia at z = 0.073 and the morphology of their host galaxies, reveals that the increased SN Ia rate at z < 0.01 is primarily due to the SNe Ia of massive E and S0 galaxies with old stellar populations. Based on the above results, we estimate the Galactic SN rate as 3.08 ± 1.29 per century. 

The insula plays a fundamental role in a wide range of adaptive human behaviors, but its electrophysiological dynamics are poorly understood. Here, we used human intracranial electroencephalographic recordings to investigate the electrophysiological properties and hierarchical organization of spontaneous neuronal oscillations within the insula. We analyzed the neuronal oscillations of the insula directly and found that rhythms in the theta and beta frequency oscillations are widespread and spontaneously present. These oscillations are largely organized along the anterior–posterior (AP) axis of the insula. Both the left and right insula showed anterior-­to-posterior decreasing gradients for the power of oscillations in the beta frequency band. The left insula also showed a posterior-to-anterior decreasing frequency gradient and an anterior-to-posterior decreasing power gradient in the theta frequency band. In addition to measuring the power of these oscillations, we also examined the phase of these signals across simultaneous recording channels and found that the insula oscillations in the theta and beta bands are traveling waves. The strength of the traveling waves in each frequency was positively correlated with the amplitude of each oscillation. However, the theta and beta traveling waves were uncoupled to each other in terms of phase and amplitude, which suggested that insular traveling waves in the theta and beta bands operate independently. Our findings provide new insights into the spatiotemporal dynamics and hierarchical organization of neuronal oscillations within the insula, which, given its rich connectivity with widespread cortical regions, indicates that oscillations and traveling waves have an important role in intrainsular and interinsular communications.