The growth of cognition: Free energy minimization and the embryogenesis of cortical computation

The assumption that during cortical embryogenesis neurons and synaptic connections are selected to form an ensemble maximising synchronous oscillation explains mesoscopic cortical development, and a mechanism for cortical information processing is implied by consistency with the Free Energy Principle and Dynamic Logic. A heteroclinic network emerges, with stable and unstable fixed points of oscillation corresponding to activity in symmetrically connected, versus asymmetrically connected, sets of neurons. Simulations of growth explain a wide range of anatomical observations for columnar and non-columnar cortex, superficial patch connections, and the organization and dynamic interactions of neurone response properties. An antenatal scaffold is created, upon which postnatal learning can establish continuously ordered neuronal representations, permitting matching of co-synchronous fields in multiple cortical areas to solve optimization problems as in Dynamic Logic. Fast synaptic competition partitions equilibria, minimizing “the curse of dimensionality”, while perturbations between imperfectly partitioned synchronous fields, under internal reinforcement, enable the cortex to become adaptively self-directed. As learning progresses variational free energy is minimized and entropy bounded.     

Strategic delegation under cost asymmetry revised

We revisit the Cournot duopoly game with strategic delegation and asymmetric costs of Delbono et al. (2016). In particular, the authors claim that a Prisoner Dilemma always arises. However, we show that, by setting properly the admissible parameter set, if the firms are sufficiently different, the efficient firm is better off when both firms delegate production. Therefore, in contrast with the traditional view, we claim that a Prisoner Dilemma is not an inevitable outcome in a strategic delegation game.     

Dynamic modeling of copper flash smelting process at a Smelter in China

Due to the highly dynamic characteristic in copper smelting process at a Copper Smelter in China, it is difficult to maintain high performance level control. As a key process indicator to evaluate smelting performance, matte grade is in urgent need of being monitored online. Thus, a real-time dynamic model of predicting matte grade was developed and validated with data collected at an actual plant. Based on desulfurization ratio of copper concentrate, the model couples dynamic mass balances on each species with equilibrium relationships for major component (Cu, Fe, S, SiO₂, et al.) to form a system of differential and algebraic equations. The simulation results illustrate that the maximum relative error and average relative error of matte grade between measured values and predicted value of the model proposed is 3.3%, and the average relative error is 0.54%, which verify the effectiveness of the model developed in providing the guidance for controlling the copper flash smelting process.     

Semi-classical orbits in a caterpillar like Sinaï billiard

The transport properties of a caterpillar-like Sinai billiard are investigated in the ballistic regime. The experimental kinetic coefficients exhibit pronounced features, characteristic of this kind of billiard. A Monte-Carlo style simulation of the semi-classical electron motion is performed in order to model the transmission probabilities T_ij of an ideal caterpillar structure. By visualising the spatial charge density distributions, the main features in the transmission probabilities are related to special electron orbits which dominate the electron dynamics at a given B. Finally, Poincaré sections are calculated close to the commensurability condition. The appearance of stability islands surrounded by the stochastic sea characterises the presence of regular electron skipping orbits involved in the ballistic transport phenomena.     

The dynamic stiffness matrix (DSM) of axially loaded multi-cracked frames

The presence of axial load, due to mechanical loading or to temperature effects, represents a strong peculiarity of frame applications both in direct and inverse problems involving the presence of cracks. The lack of explicit formulations of the Dynamic Stiffness Matrix (DSM) for cracked beam elements accounting for the influence of axial loads inspired and motivated the present work and the calculations herein reported. In this paper, the transcendental, frequency dependent, exact explicit expression of the DSM of an Euler-Bernoulli beam-column in presence of an arbitrary number of open cracks is presented. The advantage of the derived expression consists in a fourth order DSM whose dimension stays consistent independently as the number of cracks along the beam increases. Assembling DSMs of single beam-column elements, according to any required frame layout, leads to a number of degrees of freedom of the overall damaged frame structure exactly the same as those of the equivalent undamaged structure. Among other recent achievements on the vibration of damaged frames, the presented formulation provides a further original contribution, in the context of the dynamic stiffness method, which, in conjunction with the Wittrick & Williams algorithm, allows the exact evaluation of the frequencies and vibration modes of damaged frame structures in presence of axially loaded elements.     

Finite-stage stochastic decision processes with recursive reward structure I: optimality equations and deterministic strategies

In this paper we examine an N-stage stochastic decision model with a recursive reward structure whose state and action spaces are standard Borel ones. The central results relate to the validity of the optimality equations and to the sufficiency of deterministic strategies. The results expand statements known for classical dynamic programming problems with additive total rewards to a wide class of recursive reward functions under certain monotonicity and continuity assumptions. The existence of an expected utility representation of the total rewards is generally not presupposed     

Propensity Rules in Rotational Inelastic Collisions of NH_2(■A_1) under Molecular Beam Condition

Rotationalenergytransfer(RET)isoneofthemostcommonandsimplestinelasticmolecularcollisionalprocesses,anditreflectstheanisotropyoftheinteractionpotentialofthecouplingbetweentheorbitalmotionofthemoleculewithrespecttotheothercollisionpartnerandtherotationalmotion.Also,knowledgeoftheseenergytransferratesarealsoimportantinotherareas,suchaslaserdesignofchemicallaser,etc.Dixon','andAlwahabi'hadstudiedinelasticcollisionsofNH,(A'A,)inaflowingsystem.Butsincetheresultswerenotobtainedundersinglecollision…     

Expansion of cylindrical shells subjected to internal explosive detonations

Two explosively loaded cylindrical shell experiments were conducted to provide experimental data for benchmarking numerical codes. Each shell was subjected to internal high-explosive detonations, which caused it to expand outwardly at strain rates on the order of 10⁴ s^–1. At approximately 150 percent strain, multiple plastic instabilities appeared on the surface of these shells in a quasi-periodic pattem. These instabilities continued to develop into bands of localized shear and eventually formed cracks before causing the shell to fragment. Diagnostic equipment on these experiments included a Fabry-Perot interferometer and a fast-framing camera. The experiments and the data obtained from the diagnostic equipment are discussed and illustrated.     

Multi-scale defect interactions in high-rate failure of brittle materials,Part II: Application to design of protection materials

Micromechanics based damage models, such as the model presented in Part I of this 2 part series (Tonge and Ramesh, 2015), have the potential to suggest promising directions for materials design. However, to reach their full potential these models must demonstrate that they capture the relevant physical processes. In this work, we apply the multiscale material model described in Tonge and Ramesh (2015) to ballistic impacts on the advanced ceramic boron carbide and suggest possible directions for improving the performance of boron carbide under impact conditions. We simulate both dynamic uniaxial compression and simplified ballistic loading geometries to demonstrate that the material model captures the relevant physics in these problems and to interrogate the sensitivity of the simulation results to some of the model input parameters. Under dynamic compression, we show that the simulated peak strength is sensitive to the maximum crack growth velocity and the flaw distribution, while the stress collapse portion of the test is partially influenced by the granular flow behavior of the fully damaged material. From simulations of simplified ballistic impact, we suggest that the total amount of granular flow (a possible performance metric) can be reduced by either a larger granular flow slope (more angular fragments) or a larger granular flow timescale (larger fragments). We then discuss the implications for materials design.     

Dynamic chromatography: A stochastic approach

During the chromatographic separation process, analyte reactions are often observed leading to band broadening and/or elution of peak clusters. For many different chemical compounds the reaction can be reduced to a simple isomerisation kinetic scheme where elution is the result of adsorption–desorption on the surface stationary phase coupled with a flipping two-level reaction system. In this paper, the chromatographic peak shape for a reacting analyte is calculated in frequency domain when the reaction follows a simple reversible first order scheme. Both reaction and dynamic chromatographic systems have been considered. The derived solutions are expressed in closed form in the Fourier domain. Several limit solutions obtained under conditions of very slow and moderately fast kinetics are exploited. The effects of both kinetics rate constants and retention time on the chromatographic peak shape are singled out.