Geiringer theorems: from population genetics to computational intelligence, memory evolutive systems and Hebbian learning

The classical Geiringer theorem addresses the limiting frequency of occurrence of various alleles after repeated application of crossover. It has been adopted to the setting of evolutionary algorithms and, a lot more recently, reinforcement learning and Monte-Carlo tree search methodology to cope with a rather challenging question of action evaluation at the chance nodes. The theorem motivates novel dynamic parallel algorithms that are explicitly described in the current paper for the first time. The algorithms involve independent agents traversing a dynamically constructed directed graph that possibly has loops and multiple edges. A rather elegant and profound category-theoretic model of cognition in biological neural networks developed by a well-known French mathematician, professor Andree Ehresmann jointly with a neurosurgeon, Jan Paul Vanbremeersch over the last thirty years provides a hint at the connection between such algorithms and Hebbian learning.     

On quadratic two-parameter families of spheres and their envelopes

In the present paper we investigate rational two-parameter families of spheres and their envelope surfaces in Euclidean . The four dimensional cyclographic model of the set of spheres in is an appropriate framework to show that a quadratic triangular Bézier patch in corresponds to a two-parameter family of spheres with rational envelope surface. The construction shows also that the envelope has rational offsets. Further we outline how to generalize the construction to obtain a much larger class of surfaces with similar properties.     

Influence of grain boundary weak links on the nonequilibrium response of YBaCuO thin films to short laser pulses

The transient voltage response in both epitaxial and granular YBaCuO thin films to 80 ps pulses of YAGNd laser radiation of wavelength 0.63 and 1.54 m was studied. In the normal and resistive states both types of films demonstrate two components: a nonequilibrium picosecond component and a bolometric nanosecond one. The normalized amplitudes are almost the same for all films. In the superconducting state we observed a kinetic inductive response and two-component shape after integration. The normalized amplitude of the response in granular films is up to five orders of magnitude larger than in epitaxial films. We interpret the nonequilibrium response in terms of a suppression of the order parameter by the excess of quasiparticles followed by the change of resistance in the normal and resistive states or kinetic inductance in the superconducting state. The sharp rise of inductive response in granular films is explained both by a diminishing of the cross section for current percolation through the disordered network of Josephson weak links and by a decrease of condensate density in neighboring regions.     

Overcoming Anode Instability in Solid-State Batteries through Control of the Lithium Metal Microstructure

Enabling the lithium metal anode (LMA) in solid-state batteries (SSBs) is the key to developing high energy density battery technologies. However, maintaining a stable electrode–electrolyte interface presents a critical challenge to high cycling rate and prolonged cycle life. One such issue is the interfacial pore formation in LMA during stripping. To overcome this, either higher stack pressure or binary lithium alloy anodes are used. Herein, it is shown that fine-grained (d = 20 µm) polycrystalline LMA can avoid pore formation by exploiting the microstructural dependence of the creep rates. In a symmetric cell set-up, i.e., LiǀLi_6.25Al_0.25La₃Zr₂O₁₂(LLZO)ǀLi, fine-grained LMA achieves > 11.0 mAh cm⁻² compared to ≈ 3.6 mAh cm⁻² for coarse-grained LMA (d = 295 µm) at 0.1 mA cm⁻² and at moderate stress of 2.0 MPa. Smaller diffusion lengths (≈ 20 µm) and higher diffusivity pathway along dislocations (D_d ≈ 10⁻⁷ cm² s⁻¹), generated during cell fabrication, result in enhanced viscoplastic deformation in fine-grained polycrystalline LMA. The electrochemical performances corroborate well with estimated creep rates. Thus, microstructural control of LMA can significantly reduce the required stack pressure during stripping. These results are particularly relevant for “anode-free” SSBs wherein both the microstructure and the mechanical state of the lithium are critical parameters.     

Highly Exposed ?NH2 Edge on Fragmented g-C3N4 Framework with Integrated Molybdenum Atoms for Catalytic CO2 Cycloaddition: DFT and Techno-Economic Assessment

This study focuses on the applicability of single-atom Mo-doped graphitic carbon nitride (GCN) nanosheets which are specifically engineered with high surface area (exfoliated GCN),  NH₂ rich edges, and maximum utilization of isolated atomic Mo for propylene carbonate (PC) production through CO₂ cycloaddition of propylene oxide (PO). Various operational parameters are optimized, for example, temperature (130 °C), pressure (20 bar), catalyst (Mo₂GCN), and catalyst mass (0.1 g). Under optimal conditions, 2% Mo-doped GCN (Mo₂GCN) has the highest catalytic performance, especially the turnover frequency (TOF) obtained, 36.4 h⁻¹ is higher than most reported studies. DFT simulations prove the catalytic performance of Mo₂GCN significantly decreases the activation energy barrier for PO ring-opening from 50–60 to 4.903 kcal mol⁻¹. Coexistence of Lewis acid/base group improves the CO₂ cycloaddition performance by the formation of coordination bond between electron-deficient Mo atom with O atom of PO, while  NH₂ surface group disrupts the stability of CO₂ bond by donating electrons into its low-level empty orbital. Steady-state process simulation of the industrial-scale consumes 4.4 ton h⁻¹ of CO₂ with PC production of 10.2 ton h⁻¹. Techno-economic assessment profit from Mo₂GCN is estimated to be 60.39 million USD year⁻¹ at a catalyst loss rate of 0.01 wt% h⁻¹.     

Agents’ model of uncertainty

Multi-agent systems play an increasing role in sensor networks, software engineering, web design, e-commerce, robotics, and many others areas. Uncertainty is a fundamental property of these areas. Agent-based systems use probabilistic and other uncertainty models developed earlier without explicit consideration of agents. This paper explores the impact of agents on uncertainty models and theories. We compare two methods of introducing agents to uncertainty theories and propose a new theory called the agent-based uncertainty theory (AUT). We show advantages of AUT for advancing multi-agent systems and for solving an internal fundamental question of uncertainty theories, that is identifying coherent approaches to uncertainty. The advantages of AUT are that it provides a uniform agent-based representation and an operational empirical interpretation for several uncertainty theories such as rough set theory, fuzzy sets theory, evidence theory, and probability theory. We show also that the introduction of agents to intuitionist uncertainty formalisms can reduce their conceptual complexity. To build such uniformity the AUT exploits the fact that agents as independent entities can give conflicting evaluations of the same attribute. The AUT is based on complex aggregations of crisp (non-fuzzy) conflicting judgments of agents. The generality of AUT is derived from the logical classification of types (orders) of conflicts in the agent populations. At the first order of conflict, the two agent populations are disjoint and there is no interference of logic values assigned to any statement p and its negation by agents. The second order of conflict models superposition (interference) of logic values for overlapping agent populations where an agent assigns conflicting logic values (true, false) to the same attribute simultaneously.

Properties of Gauss Digitized Shapes and Digital Surface Integration

This paper presents new topological and geometric properties of Gauss digitizations of Euclidean shapes, most of them holding in arbitrary dimension d. We focus on r-regular shapes sampled by Gauss digitization at gridstep h. The digitized boundary is shown to be close to the Euclidean boundary in the Hausdorff sense, the minimum distance \(\frac{\sqrt{d}}{2}h\) being achieved by the projection map \(\xi \) induced by the Euclidean distance. Although it is known that Gauss digitized boundaries may not be manifold when \(d \ge 3\), we show that non-manifoldness may only occur in places where the normal vector is almost aligned with some digitization axis, and the limit angle decreases with h. We then have a closer look at the projection of the digitized boundary onto the continuous boundary by \(\xi \). We show that the size of its non-injective part tends to zero with h. This leads us to study the classical digital surface integration scheme, which allocates a measure to each surface element that is proportional to the cosine of the angle between an estimated normal vector and the trivial surface element normal vector. We show that digital integration is convergent whenever the normal estimator is multigrid convergent, and we explicit the convergence speed. Since convergent estimators are now available in the literature, digital integration provides a convergent measure for digitized objects.     

Generating heavy particles with energy and momentum conservation

We propose a novel algorithm, called REGGAE, for the generation of momenta of a given sample of particle masses, evenly distributed in Lorentz-invariant phase space and obeying energy and momentum conservation. In comparison to other existing algorithms, REGGAE is designed for the use in multiparticle production in hadronic and nuclear collisions where many hadrons are produced and a large part of the available energy is stored in the form of their masses. The algorithm uses a loop simulating multiple collisions which lead to production of configurations with reasonably large weights.

Program summary

Program title: REGGAE (REscattering-after-Genbod GenerAtor of Events)Catalogue identifier: AEJR_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJR_v1_0.htmlProgram obtainable from: CPC Program Library, Queen?s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 1523No. of bytes in distributed program, including test data, etc.: 9608Distribution format: tar.gzProgramming language: C++Computer: PC Pentium 4, though no particular tuning for this machine was performed.Operating system: Originally designed on Linux PC with g++, but it has been compiled and ran successfully on OS X with g++ and MS Windows with Microsoft Visual C++ 2008 Express Edition, as well.RAM: This depends on the number of particles which are generated. For 10 particles like in the attached example it requires about 120 kB.Classification: 11.2Nature of problem: The task is to generate momenta of a sample of particles with given masses which obey energy and momentum conservation. Generated samples should be evenly distributed in the available Lorentz-invariant phase space.Solution method: In general, the algorithm works in two steps. First, all momenta are generated with the GENBOD algorithm. There, particle production is modeled as a sequence of two-body decays of heavy resonances. After all momenta are generated this way, they are reshuffled. Each particle undergoes a collision with some other partner such that in the pair center of mass system the new directions of momenta are distributed isotropically. After each particle collides only a few times, the momenta are distributed evenly across the whole available phase space. Starting with GENBOD is not essential for the procedure but it improves the performance.Running time: This depends on the number of particles and number of events one wants to generate. On a LINUX PC with 2 GHz processor, generation of 1000 events with 10 particles each takes about 3 s.