PAC-Bayes Unleashed: Generalisation Bounds with Unbounded Losses

We present new PAC-Bayesian generalisation bounds for learning problems with unbounded loss functions. This extends the relevance and applicability of the PAC-Bayes learning framework, where most of the existing literature focuses on supervised learning problems with a bounded loss function (typically assumed to take values in the interval [0;1]). In order to relax this classical assumption, we propose to allow the range of the loss to depend on each predictor. This relaxation is captured by our new notion of HYPothesis-dependent rangE (HYPE). Based on this, we derive a novel PAC-Bayesian generalisation bound for unbounded loss functions, and we instantiate it on a linear regression problem. To make our theory usable by the largest audience possible, we include discussions on actual computation, practicality and limitations of our assumptions.     

Stabilization of the Low‐Spin State in a Mononuclear Iron(II) Complex and High‐Temperature Cooperative Spin Crossover Mediated by Hydrogen Bonding

The tetrapyridyl ligand bbpya (bbpya=N,N‐bis(2,2′‐bipyrid‐6‐yl)amine) and its mononuclear coordination compound [Fe(bbpya)(NCS)₂] ( 1 ) were prepared. According to magnetic susceptibility, differential scanning calorimetry fitted to Sorai’s domain model, and powder X‐ray diffraction measurements, 1 is low‐spin at room temperature, and it exhibits spin crossover (SCO) at an exceptionally high transition temperature of T_1/2=418 K. Although the SCO of compound 1 spans a temperature range of more than 150 K, it is characterized by a wide (21 K) and dissymmetric hysteresis cycle, which suggests cooperativity. The crystal structure of the LS phase of compound 1 shows strong N?H???S intermolecular H‐bonding interactions that explain, at least in part, the cooperative SCO behavior observed for complex 1 . DFT and CASPT2 calculations under vacuum demonstrate that the bbpya ligand generates a stronger ligand field around the iron(II) core than its analogue bapbpy (N,N′‐di(pyrid‐2‐yl)‐2,2′‐bipyridine‐6,6′‐diamine); this stabilizes the LS state and destabilizes the HS state in 1 compared with [Fe(bapbpy)(NCS)₂] ( 2 ). Periodic DFT calculations suggest that crystal‐packing effects are significant for compound 2 , in which they destabilize the HS state by about 1500 cm^?1. The much lower transition temperature found for the SCO of 2 compared to 1 appears to be due to the combined effects of the different ligand field strengths and crystal packing.     

Palladium-catalyzed synthesis of N-aryloxazolidinones from aryl chlorides

An efficient method for intermolecular N-arylation of oxazolidinones using Pd(2)dba(3) and various phosphine ligands in the presence of a weak base is reported. The conditions allow the use of cheaper aryl chlorides containing functionalities such as enolizable ketones, amides, etc., which would be incompatible with other coupling methods. The coupling reaction can be used to prepare enantiopure N-aryl beta-amino alcohols. Depending on the stereoelectronic nature of the aryl chloride, careful choice of ligand was necessary for the success of these reactions. [reaction: see text]     

Application of direct solid analysis of plant samples by electrothermal vaporization-inductively coupled plasma atomic emission spectrometry: Determination of Cd and Si for environmental purposes

Elemental determinations are usually performed on plant samples for agronomic or environmental studies. Direct solid sampling is possible when electrothermal vaporization (ETV) is used as a method of sample introduction in inductively coupled plasma atomic emission spectrometry (ICP-AES). ETV-ICP-AES was applied for elemental determinations in plant samples. The first application aimed at Cd determinations in very small size plant material samples. Several reference plant materials were used to validate the accuracy of the method. Quality control included the systematic analysis of a reference sample in each batch of unknown samples. The performance of the method in time was illustrated by a control chart. The second application aimed at the content of Si in plant materials. Quantification of Si in plant samples was carried out using samples issued from an inter-laboratory test. Detection limit of 30 μg g^− 1 was achieved for Si. In all cases, quantification was accomplished easily by means of aqueous standard solutions deposited on cellulose support.     

Synthesis of highly functionalized bicyclo[m.n.1]alkanones via a cationic reaction cascade

[reaction: see text] The acid-mediated Prins/pinacol and the triple domino reactions Diels-Alder/Prins/pinacol were used to construct highly functionalized bicyclo[m.n.1]alkanones 19-29 and 33a-c possessing various ring sizes from ketals 8-18 and 31a-c in 44-96% yields. This approach proves to be highly efficient and reliable to generate high molecular complexity in a single step.     

Synthesis and Characterization of New Water‐Soluble Hydrides of RuII: A Step towards Dinitrogen Activation?

The basic aqueous coordination chemistry of Ru^II has been studied using the catalytically important TPPTS phosphine (TPPTS=trisodium salt of 3,3′,3″‐phosphinetriylbenzenesulfonic acid) and small gas molecules (H₂, CO, N₂) as ligands. As a result, new water‐soluble ruthenium mixed hydride complexes, presumably key species in many industrial catalytic processes, have been formed and identified. The Ru^II mixed hydrides were synthesized, and their formation was followed in situ by multinuclear NMR spectroscopy, pressurizing aqueous Ru^II? TPPTS systems with H₂ and CO gas in sapphire NMR tubes. The formation equilibrium of these complexes is highly dependant on the temperature and the gas pressures. Under 50 atm of N₂, the unique [RuH(CO)(N₂)(TPPTS)₂(H₂O)]⁺ complex has been identified, which could be the first step toward dinitrogen activation.     

Convergence of the solutions of the discounted equation: the discrete case

We derive a discrete version of the results of Davini et al. (Convergence of the solutions of the discounted Hamilton–Jacobi equation. Invent Math, 2016). If M is a compact metric space, \(c : M\times M \rightarrow \mathbb {R}\) a continuous cost function and \(\lambda \in (0,1)\), the unique solution to the discrete \(\lambda \)-discounted equation is the only function \(u_\lambda : M\rightarrow \mathbb {R}\) such that

$$\begin{aligned} \forall x\in M, \quad u_\lambda (x) = \min _{y\in M} \lambda u_\lambda (y) + c(y,x). \end{aligned}$$

We prove that there exists a unique constant \(\alpha \in \mathbb {R}\) such that the family of \(u_\lambda +\alpha /(1-\lambda )\) is bounded as \(\lambda \rightarrow 1\) and that for this \(\alpha \), the family uniformly converges to a function \(u_0 : M\rightarrow \mathbb {R}\) which then verifies

$$\begin{aligned} \forall x\in X, \quad u_0(x) = \min _{y\in X}u_0(y) + c(y,x)+\alpha . \end{aligned}$$

The proofs make use of Discrete Weak KAM theory. We also characterize \(u_0\) in terms of Peierls barrier and projected Mather measures.

     

Evidence of reciprocal reorientation of the catalytic and hemopexin-like domains of full-length MMP-12

The proteolytic activity of matrix metalloproteinases toward extracellular matrix components (ECM), cytokines, chemokines, and membrane receptors is crucial for several homeostatic and pathological processes. Active MMPs are a family of single-chain enzymes (23 family members in the human genome), most of which constituted by a catalytic domain and by a hemopexin-like domain connected by a linker. The X-ray structures of MMP-1 and MMP-2 suggest a conserved and well-defined spatial relationship between the two domains. Here we present structural data for MMP-12, suitably stabilized against self-hydrolysis, both in solution (NMR and SAXS) and in the solid state (X-ray), showing that the hemopexin-like and the catalytic domains experience conformational freedom with respect to each other on a time scale shorter than 10(-8) s. Hints on the probable conformations are also obtained. This experimental finding opens new perspectives for the often hypothesized active role of the hemopexin-like domain in the enzymatic activity of MMPs.     

Bicyclo[1.1.1]pentane Embedded in Porphyrinoids**

We report a two-step approach to obtain synthetically versatile bicyclo[1.1.1]pentane (BCP) derivatives using Grignard reagents. This method allows the incorporation of BCP units in tetrapyrrolic macrocycles and the synthesis of a new class of calix[4]pyrrole analogues by replacing two bridging methylene groups with two BCP units. In addition, a doubly N-confused system was also formed in the presence of electron-withdrawing substituents at the BCP bridgeheads. The pyrrole rings in BCP containing macrocycles exist in 1,3-alternate or αβαβ conformations, as observed from single-crystal X-ray diffraction analyses and 2D NMR spectroscopy.     

Bioinspired Oxidative Cyclization of the Geissoschizine Skeleton for the Total Synthesis of (−)‐17‐nor‐Excelsinidine

We report the first total synthesis of (?)‐17‐nor‐excelsinidine, a zwitterionic monoterpene indole alkaloid that displays an unusual N4?C16 connection. Inspired by the postulated biosynthesis, we explored an oxidative coupling approach from the geissoschizine framework to forge the key ammonium–acetate connection. Two strategies allowed us to achieve this goal, namely an intramolecular nucleophilic substitution on a 16‐chlorolactam with the N4 nitrogen atom or a direct I₂‐mediated N4?C16 oxidative coupling from the enolate of geissoschizine.