Fast data-driven model reduction for nonlinear dynamical systems

We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). While the recently proposed reduced-order modeling method SSMLearn uses implicit optimization to fit a spectral submanifold to data and reduce the dynamics to a normal form, here, we reformulate these tasks as explicit problems under certain simplifying assumptions. In addition, we provide a novel method for timelag selection when delay-embedding signals from multimodal systems. We show that our alternative approach to data-driven SSM construction yields accurate and sparse rigorous models for essentially nonlinear (or non-linearizable) dynamics on both numerical and experimental datasets. Aside from a major reduction in complexity, our new method allows an increase in the training data dimensionality by several orders of magnitude. This promises to extend data-driven, SSM-based modeling to problems with hundreds of thousands of degrees of freedom.

     

Ab Initio Study of Fine and Hyperfine Interactions in Triplet POH

Phosphorous-containing molecules have a great relevance in prebiotic chemistry in view of the fact that phosphorous is a fundamental constituent of biomolecules, such as RNA, DNA, and ATP. Its biogenic importance has led astrochemists to investigate the possibility that P-bearing species could have formed in the interstellar medium (ISM) and subsequently been delivered to early Earth by rocky bodies. However, only two P-bearing molecules have been detected so far in the ISM, with the chemistry of interstellar phosphorous remaining poorly understood. Here, in order to shed further light on P-carriers in space, we report a theoretical spectroscopic characterisation of the rotational spectrum of POH in its 3A″ ground electronic state. State-of-the-art coupled-cluster schemes have been employed to derive rotational constants, centrifugal distortion terms, and most of the fine and hyperfine interaction parameters, while the electron spin–spin dipolar coupling has been investigated using the multi-configuration self-consistent-field method. The computed spectroscopic parameters have been used to simulate the appearance of triplet POH rotational and ro-vibrational spectra in different conditions, from cold to warm environments, either in gas-phase experiments or in molecular clouds. Finally, we point out that the predicted hyperfine structures represent a key pattern for the recognition of POH in laboratory and interstellar spectra.     

Effects of Vaccination Efficacy on Wealth Distribution in Kinetic Epidemic Models

The spread of the COVID-19 pandemic has highlighted the close link between economics and health in the context of emergency management. A widespread vaccination campaign is considered the main tool to contain the economic consequences. This paper will focus, at the level of wealth distribution modeling, on the economic improvements induced by the vaccination campaign in terms of its effectiveness rate. The economic trend during the pandemic is evaluated, resorting to a mathematical model joining a classical compartmental model including vaccinated individuals with a kinetic model of wealth distribution based on binary wealth exchanges. The interplay between wealth exchanges and the progress of the infectious disease is realized by assuming, on the one hand, that individuals in different compartments act differently in the economic process and, on the other hand, that the epidemic affects risk in economic transactions. Using the mathematical tools of kinetic theory, it is possible to identify the equilibrium states of the system and the formation of inequalities due to the pandemic in the wealth distribution of the population. Numerical experiments highlight the importance of the vaccination campaign and its positive effects in reducing economic inequalities in the multi-agent society.     

Spectroscopic Characterization of 3-Aminoisoxazole,a Prebiotic Precursor of Ribonucleotides

The processes and reactions that led to the formation of the first biomolecules on Earth play a key role in the highly debated theme of the origin of life. Whether the first chemical building blocks were generated on Earth (endogenous synthesis) or brought from space (exogenous delivery) is still unanswered. The detection of complex organic molecules in the interstellar medium provides valuable support to the latter hypothesis. To gather more insight, here we provide the astronomers with accurate rotational frequencies to guide the interstellar search of 3-aminoisoxazole, which has been recently envisaged as a key reactive species in the scenario of the so-called RNA-world hypothesis. Relying on an accurate computational characterization, we were able to register and analyze the rotational spectrum of 3-aminoisoxazole in the 6–24 GHz and 80–320 GHz frequency ranges for the first time, exploiting a Fourier-transform microwave spectrometer and a frequency-modulated millimeter/sub-millimeter spectrometer, respectively. Due to the inversion motion of the −NH₂ group, two states arise, and both of them were characterized, with more than 1300 lines being assigned. Although the fit statistics were affected by an evident Coriolis interaction, we were able to produce accurate line catalogs for astronomical observations of 3-aminoisoxazole.     

Borodin–Okounkov formula,string equation and topological solutions of Drinfeld–Sokolov hierarchies

Letters in Mathematical Physics - We give a general method to compute the expansion of topological tau functions for Drinfeld–Sokolov hierarchies associated with an arbitrary untwisted affine...     

Visible-Light-Driven Strain-Increase Ring Contraction Allows the Synthesis of Cyclobutyl Boronic Esters

There are a limited number of ring-contraction methodologies which convert readily available five-membered rings into strained four-membered rings. Here we report a photo-induced radical-mediated ring contraction of five-membered-ring alkenyl boronate complexes into cyclobutanes. The process involves the addition of an electrophilic radical to the electron-rich alkenyl boronate complex, leading to an α-boryl radical. Upon one-electron oxidation, ring-contractive 1,2-metalate rearrangement occurs to give a cyclobutyl boronic ester. A range of radical precursors and vinyl boronates can be employed, and chiral cyclobutanes can be accessed with high levels of stereocontrol. The process was extended to the preparation of benzofused cyclobutenes and the versatility of the boronic ester was demonstrated by conversion to other functional groups.     

Implementation of chaotic circuits with a digital time-delay block

In this paper, the implementation of time-delay chaotic circuits is investigated. To implement the time-delay block, a solution based on a digital circuitry has been adopted. This solution leads to a programmable hardware which can be realized by using available field programmable gate arrays. In this paper, issues raised from this implementation such as the behavior of the system with respect to the precision and the sampling rate of the conversion process have been investigated. The synchronization error is proposed as an indicator of the accuracy of the whole implementation.     

Asymmetric organocatalytic α-amination of 2-oxindoles with bis(2,2,2-trichloroethyl)azo-dicarboxylate

An enantioselective electrophilic amination of 3-substituted-2-oxindoles is reported, using bis(2,2,2-trichloroethyl)azo-dicarboxylate and commercially available Cinchona alkaloid organocatalysts. The best results were obtained in the reaction of 3-aryl substrates, with high to excellent yields (75% to quantitative) and good stereoselectivity (64–77% ee). Facile reductive conversion of the protected 3-hydrazino fragment into the corresponding primary amine was also demonstrated, to expand the synthetic flexibility of asymmetric electrophilic amination with azo-dicarboxylic esters en route to enantioenriched 3-amino-2-oxindoles. The absolute configuration of 3-amino-3-phenyl-2-oxindole was independently established by electronic circular dichroism (ECD), combined with time-dependent density functional theory (TDDFT).     

Logarithmic Picard groups,chip firing,and the combinatorial rank

Mathematische Zeitschrift - Illusie has suggested that one should think of the classifying group of $$M_X^{gp}$$ -torsors on a logarithmically smooth curve X over a standard logarithmic point as a...