Learning normal form autoencoders for data-driven discovery of universal, parameter-dependent governing equations

Complex systems manifest a small number of instabilities and bifurcations that are canonical in nature, resulting in universal pattern forming characteristics as a function of some parametric dependence. Such parametric instabilities are mathematically characterized by their universal un-foldings, or normal form dynamics, whereby a parsimonious model can be used to represent the dynamics. Although center manifold theory guarantees the existence of such low-dimensional normal forms, finding them has remained a long standing challenge. In this work, we introduce deep learning autoencoders to discover coordinate transformations that capture the underlying parametric dependence of a dynamical system in terms of its canonical normal form, allowing for a simple representation of the parametric dependence and bifurcation structure. The autoencoder constrains the latent variable to adhere to a given normal form, thus allowing it to learn the appropriate coordinate transformation. We demonstrate the method on a number of example problems, showing that it can capture a diverse set of normal forms associated with Hopf, pitchfork, transcritical and/or saddle node bifurcations. This method shows how normal forms can be leveraged as canonical and universal building blocks in deep learning approaches for model discovery and reduced-order modeling.Comment: 18 pages, 7 figure

Mechanistic insight into proton-coupled mixed valency

Stabilisation of the mixed-valence state in [Mo2(TiPB)3(HDOP)]2+ (HTiPB = 2,4,6-triisopropylbenzoic acid, H2DOP = 3,6-dihydroxypyridazine) by electron transfer (ET) is related to the proton coordinate of the bridging ligands. Spectroelectrochemical studies suggest that ET is slower than 109 s−1. The mechanism has been probed using DFT calculations, which show that proton transfer induces a larger dipole in the molecule resulting in ET

Structural, spectroscopic and theoretical studies of a diruthenium(II,II) tetraformamidinate that reversibly binds dioxygen

The reaction of Ru2(O2CMe)4 with N,N'-bis(3,5-dimethoxyphenyl)formamidine (Hdmof) in refluxing toluene solutions yields Ru2(dmof)4 as a diamagnetic red solid that is extremely airsensitive. The crystal structure reveals the expected paddlewheel arrangement of ligands around the Ru2 4+ core, with a relatively long Ru-Ru bond (2.4999(8) Å) that is consistent with a σ2 π4 δ2 π*4 electronic configuration. This is supported DFT calculations that show this electronic structure results from destabilization of the δ* orbital due to antibonding interactions with the formamidinate ligands. The cyclic voltammogram of Ru2(dmof)4 in a 0.1 M n Bu4NPF6 / CH2Cl2 solution shows two redox processes, assigned as successive oxidations corresponding to the Ru2 4+/5+ and Ru2 5+/6 redox couples. Changes in the electronic absorption spectra associated with these oxidation processes were probed using a UV/vis spectroelectrochemical study. Ru2(dmof)4 reacts with dioxygen in solution to generate a purple compound that decomposes within an hour at room temperature. Bubbling N2 gas through the purple solution regenerates Ru2(dmof)4, as evidenced by UV/vis spectrometry and cyclic voltammetry, suggesting that the dioxygen reversibly binds to the diruthenium core

Liposomal Packaging Generates Wnt Protein with In Vivo Biological Activity

Wnt signals exercise strong cell-biological and regenerative effects of considerable therapeutic value. There are, however, no specific Wnt agonists and no method for in vivo delivery of purified Wnt proteins. Wnts contain lipid adducts that are required for activity and we exploited this lipophilicity by packaging purified Wnt3a protein into lipid vesicles. Rather than being encapsulated, Wnts are tethered to the liposomal surface, where they enhance and sustain Wnt signaling in vitro. Molecules that effectively antagonize soluble Wnt3a protein but are ineffective against the Wnt3a signal presented by a cell in a paracrine or autocrine manner are also unable to block liposomal Wnt3a activity, suggesting that liposomal packaging mimics the biological state of active Wnts. When delivered subcutaneously, Wnt3a liposomes induce hair follicle neogenesis, demonstrating their robust biological activity in a regenerative context

Курган с "коллективным погребением" у с. Кринички (по материалам работ 1957 г.)

Статья представляет собой публикацию материалов раскопок в 1957 г. кургана, расположенного в 2 км западнее с. Кринички Кировского района (Крым). Курган содержал скифский каменный склеп с коллективным погребением и более позднее впускное захоронение. Склеп был разрушен еще в древности. Судя по найденным в нем черепам, здесь было захоронено не менее 106 человек. Незамеченные древними грабителями вещи позволили датировать комплекс концом II - I вв. до н.э. Впускное погребение относится ко II в. н.э. и свидетельствует о полном запустении памятника в римское время.Стаття присвячена публикації матеріалів з розкопок у 1957 року кургана, який розташований у 2 км на захід від с. Кринички Кировського району (Крим). Курган містив скіфський кам'яний склеп з колективним похованням та пізнише впускне поховання. Склеп було зруйновано ще у давні часи. Судячи за знайденими у нему черепами, тут було поховано не менш ніж 106 людей. Непомічені стародавними грабіжниками речи дозволяють датувати комплекс кінцем II - I ст. до н.є. Впускне погребіння II століття свідчить про полний занепад пам'ятки у римський час.This article is publication of materials obtained during the 1957 excavation of the barrow located near v. Krinichki, by 2 km to the West in Kirov district (Crimea). This barrow contained the scythian monumental group burial vault with an later overlap grave. The vault was destroyed long ago in ancientry. To judge by skull finds, the burial might contain no less than 106 skeletons. The abandoned by ancient thieves artefacts of this burial permit the vault to be dated by end of II - I centuries B.C. The overlap grave of II century A.D. testifies to absolute neglect of the burial barrow at the Rome age

Mycobacteria counteract a TLR-mediated nitrosative defense mechanism in a zebrafish infection model.

Pulmonary tuberculosis (TB), caused by the intracellular bacterial pathogen Mycobacterium tuberculosis (Mtb), is a major world health problem. The production of reactive nitrogen species (RNS) is a potent cytostatic and cytotoxic defense mechanism against intracellular pathogens. Nevertheless, the protective role of RNS during Mtb infection remains controversial. Here we use an anti-nitrotyrosine antibody as a readout to study nitration output by the zebrafish host during early mycobacterial pathogenesis. We found that recognition of Mycobacterium marinum, a close relative of Mtb, was sufficient to induce a nitrosative defense mechanism in a manner dependent on MyD88, the central adaptor protein in Toll like receptor (TLR) mediated pathogen recognition. However, this host response was attenuated by mycobacteria via a virulence mechanism independent of the well-characterized RD1 virulence locus. Our results indicate a mechanism of pathogenic mycobacteria to circumvent host defense in vivo. Shifting the balance of host-pathogen interactions in favor of the host by targeting this virulence mechanism may help to alleviate the problem of infection with Mtb strains that are resistant to multiple drug treatments

Protection from ultraviolet damage and photocarcinogenesis by vitamin d compounds

© Springer Nature Switzerland AG 2020. Exposure of skin cells to UV radiation results in DNA damage, which if inadequately repaired, may cause mutations. UV-induced DNA damage and reactive oxygen and nitrogen species also cause local and systemic suppression of the adaptive immune system. Together, these changes underpin the development of skin tumours. The hormone derived from vitamin D, calcitriol (1,25-dihydroxyvitamin D3) and other related compounds, working via the vitamin D receptor and at least in part through endoplasmic reticulum protein 57 (ERp57), reduce cyclobutane pyrimidine dimers and oxidative DNA damage in keratinocytes and other skin cell types after UV. Calcitriol and related compounds enhance DNA repair in keratinocytes, in part through decreased reactive oxygen species, increased p53 expression and/or activation, increased repair proteins and increased energy availability in the cell when calcitriol is present after UV exposure. There is mitochondrial damage in keratinocytes after UV. In the presence of calcitriol, but not vehicle, glycolysis is increased after UV, along with increased energy-conserving autophagy and changes consistent with enhanced mitophagy. Reduced DNA damage and reduced ROS/RNS should help reduce UV-induced immune suppression. Reduced UV immune suppression is observed after topical treatment with calcitriol and related compounds in hairless mice. These protective effects of calcitriol and related compounds presumably contribute to the observed reduction in skin tumour formation in mice after chronic exposure to UV followed by topical post-irradiation treatment with calcitriol and some, though not all, related compounds