Effects of intraspecific cooperative interactions in large ecosystems

We analyze the role of the Allee effect - a positive correlation between population density and mean individual fitness - for ecological communities formed by a large number of species. Our study is performed using the generalized Lotka-Volterra model with random interactions between species. We obtain the phase diagram and analyze the nature of the multiple equilibria phase. Remarkable differences emerge with respect to the logistic growth case, thus revealing the major role played by the functional response in determining aggregate behaviors of large ecosystems.

Thermalization of randomly coupled SYK models

We investigate the thermalization of Sachdev–Ye–Kitaev (SYK) models coupled via random interactions following quenches from the perspective of entanglement. Previous studies have shown that when a system of two SYK models coupled by random two-body terms is quenched from the thermofield double state with sufficiently low effective temperature, the Rényi entropies do not saturate to the expected thermal values in the large-N limit. Using numerical large-N methods, we first show that the Rényi entropies in a pair SYK models coupled by two-body terms can thermalize, if quenched from a state with sufficiently high effective temperature, and hence exhibit state-dependent thermalization. In contrast, SYK models coupled by single-body terms appear to always thermalize. We provide evidence that the subthermal behavior in the former system is likely a large-N artifact by repeating the quench for finite N and finding that the saturation value of the Rényi entropy extrapolates to the expected thermal value in the N → ∞ limit. Finally, as a finer grained measure of thermalization, we compute the late-time spectral form factor of the reduced density matrix after the quench. While a single SYK dot exhibits perfect agreement with random matrix theory, both the quadratically and quartically coupled SYK models exhibit slight deviations.

Counting equilibria of large complex systems by instability index

We consider a nonlinear autonomous system of N≫1 degrees of freedom randomly coupled by both relaxational (“gradient”) and nonrelaxational (“solenoidal”) random interactions. We show that with increased interaction strength, such systems generically undergo an abrupt transition from a trivial phase portrait with a single stable equilibrium into a topologically nontrivial regime of “absolute instability” where equilibria are on average exponentially abundant, but typically, all of them are unstable, unless the dynamics is purely gradient. When interactions increase even further, the stable equilibria eventually become on average exponentially abundant unless the interaction is purely solenoidal. We further calculate the mean proportion of equilibria that have a fixed fraction of unstable directions.

Stochastic analysis of average-based distributed algorithms

We analyze average-based distributed algorithms relying on simple and pairwise random interactions among a large and unknown number of anonymous agents. This allows the characterization of global properties emerging from these local interactions. Agents start with an initial integer value, and at each interaction keep the average integer part of both values as their new value. The convergence occurs when, with high probability, all the agents possess the same value, which means that they all know a property of the global system. Using a well-chosen stochastic coupling, we improve upon existing results by providing explicit and tight bounds on the convergence time. We apply these general results to both the proportion problem and the system size problem.

THE TECHNOLOGY OF PROCESSING AXISYMMETRIC PARTS WITH AUTOMATIC CONTROL OF THE MACHINING PROCESS, TAKING INTO ACCOUNT EXTERNAL RANDOM INFLUENCES

The article gives a brief description of the manufacturing process of non-rigid parts of two fundamental operations - dressing and machining. It is proved that during mechanical action on the workpiece random interactions due to texture inhomogeneities act. These effects lead to the excitation of oscillations of all parts, but energy is trans-ferred at a frequency close to the resonant. Stress inhomogeneities can be taken into account as random, delta - cor-related changes in the system frequency. The mechanism of energy absorption by crystallites (grains) is analyzed, due to which stress redistribution occurs.

Subsystem Rényi entropy of thermal ensembles for SYK-like models

The Sachdev-Ye-Kitaev model is an NN-modes fermionic model with infinite range random interactions. In this work, we study the thermal Rényi entropy for a subsystem of the SYK model using the path-integral formalism in the large-NN limit. The results are consistent with exact diagonalization and can be well approximated by thermal entropy with an effective temperature when subsystem size M\leq N/2M≤N/2. We also consider generalizations of the SYK model with quadratic random hopping term or U(1)U(1) charge conservation.