Linear Recursive Functions

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The Power of Closed Reduction Strategies.

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The Power of Linear Functions

The linear lambda calculus is very weak in terms of expressive power: in particular, all functions terminate in linear time. In this paper we consider a simple extension with Booleans, natural numbers and a linear iterator. We show properties of this linear version of Gödel’s System T and study the class of functions that can be represented. Surprisingly, this linear calculus is extremely expressive: it is as powerful as System T

Enantioselective Reduction of Noncovalent Complexes of Amino Acids with Cu^II via Resonant Collision-Induced Dissociation: Collision Energy, Activation Duration Effects, and RRKM Modeling

Formation of noncovalent complexes is one of the approaches to perform chiral analysis with mass spectrometry. Enantiomeric distinction of amino acids (AAs) based on the relative rate constants of competitive fragmentations of quaternary copper complexes is an efficient method for chiral differentiation. Here, we studied the complex [CuII,(Phe,PhG,Pro-H)]+ (m/z 493) under resonant collision-induced dissociation conditions while varying the activation time. The precursor ion can yield two main fragments through the loss of the non-natural AA phenylglycine (PhG): the expected product ion [CuII,(Phe,Pro-H)]+ (m/z 342) and the reduced product ion [CuI,(Phe,Pro)]+ (m/z 343). Enantioselective reduction describes the difference in relative abundance of these ions, which depends on the chirality of the precursor ion: the formation of the reduced ion m/z 343 is favored in homochiral complexes (DDD) compared to heterochiral complexes (such as LDD). Energy-resolved mass spectrometry data show that reduction, which arises from rearrangement, is favored at a low collision energy (CE) and long activation time (ActT), whereas direct cleavage preferentially occurs at a high CE and short ActT. These results were confirmed with kinetic modeling based on RRKM theory. For this modeling, it was necessary to set a pre-exponential factor as a reference, so that the E0 values obtained are relative values. Interestingly, these simulations showed that the critical energy E0 required to form the reduced ion is comparable in both homochiral and heterochiral complexes. However, the formation of product ion m/z 342 through direct cleavage is associated with a lower E0 in heterochiral complexes. Consequently, enantioselectivity would not be caused by enhanced reduction in homochiral complexes but rather by direct cleavage being favored in heterochiral complexes

Chemical Exposure Highlighted without Any <i>A Priori</i> Information in an Epidemiological Study by Metabolomic FT-ICR-MS Fingerprinting at High Throughput and High Resolution

Epidemiological studies aim to assess associations between diseases and risk factors. Such investigations involve a large sample size and require powerful analytical methods to measure the effects of risk factors, resulting in a long analysis time. In this study, chemical exposure markers were detected as the main variables strongly affecting two components coming from a principal component analysis (PCA) exploration of the metabolomic data generated from urinary samples collected on a cohort of about 500 individuals using direct introduction coupled with a Fourier-transform ion cyclotron resonance instrument. The assignment of their chemical identity was first achieved based on their isotopic fine structures detected at very high resolution (Rp > 900,000). Their identification as dimethylbiguanide and sotalol was obtained at level 1, thanks to the available authentic chemical standards, tandem mass spectrometry (MS/MS) experiments, and collision cross section measurements. Epidemiological data confirmed that the subjects discriminated by PCA had declared to be prescribed these drugs for either type II diabetes or cardiac arrhythmia. Concentrations of these drugs in urine samples of interest were also estimated by rapid quantification using an external standard calibration method, direct introduction, and MS/MS experiments. Regression analyses showed a good correlation between the estimated drug concentrations and the scores of individuals distributed on these specific PCs. The detection of these chemical exposure markers proved the potential of the proposed high-throughput approach without any prior drug exposure knowledge as a powerful emerging tool for rapid and large-scale phenotyping of subjects enrolled in epidemiological studies to rapidly characterize the chemical exposome and adherence to medical prescriptions

Supplemental material for Evaluation and validation of an analytical approach for high-throughput metabolomic fingerprinting using direct introduction–high-resolution mass spectrometry: Applicability to classification of urine of scrapie-infected ewes

Supplemental material for Evaluation and validation of an analytical approach for high-throughput metabolomic fingerprinting using direct introduction–high-resolution mass spectrometry: Applicability to classification of urine of scrapie-infected ewes by Estelle Rathahao-Paris, Sandra Alves, Nawel Boussaid, Nicole Picard-Hagen, Véronique Gayrard, Pierre-Louis Toutain, Jean-Claude Tabet, Douglas N Rutledge and Alain Paris in European Journal of Mass Spectrometry</p

Energy Resolved Mass Spectrometry for Interoperable Non-resonant Collisional Spectra in Metabolomics

In untargeted metabolomics, the unambiguous identification of metabolites remains a major challenge. This requires high-quality spectral libraries for reliable metabolite identification, which is essential for translating metabolomics data into meaningful biological information. Several attempts have been made to generate reproducible product ion spectra (PIS) under a low collision energy (ELab) regime and nonresonant collisional conditions but have not fully succeeded. We examined the ERMS (energy-resolved mass spectrometry) breakdown curves of two lipo-amino acids and showed the possibility to highlight “singular points”, called descriptors hereafter (linked to respective ELab depending on the instrument), for each of the monomodal product ion profiles. Using several instruments based on different technologies, the PIS recorded at these specific ELab sites shows remarkable similarities. The descriptors appeared as being independent of the fragmentation mechanisms and can be used to overcome the main instrumental effects that limit the interoperability of spectral libraries. This proof-of-concept study, performed on two particular lipo-amino acids, demonstrates the high potential of ERMS-derived information to determine the instrument-specific ELab at which PIS recorded in nonresonant conditions become highly similar and instrument-independent, thus comparable across platforms. This innovative but straightforward approach could help remove some of the obstacles to metabolite identification in nontargeted metabolomics, putting an end to a challenging chimera