Proving Tight Bounds on Univariate Expressions with Elementary Functions in Coq

International audienceThe verification of floating-point mathematical libraries requires computing numerical bounds on approximation errors. Due to the tightness of these bounds and the peculiar structure of approximation errors, such a verification is out of the reach of generic tools such as computer algebra systems. In fact, the inherent difficulty of computing such bounds often mandates a formal proof of them. In this paper, we present a tactic for the Coq proof assistant that is designed to automatically and formally prove bounds on univariate expressions. It is based on a formalization of floating-point and interval arithmetic, associated with an on-the-fly computation of Taylor expansions. All the computations are performed inside Coq's logic, in a reflexive setting. This paper also compares our tactic with various existing tools on a large set of examples

Нейросекреторная активность супраоптического ядра переднего гипоталамуса кроликов под действием транскутанной электростимуляции зрительного анализатора

На 8 кролях породи Метелик вивчали вплив непрямої черезшкірної електростимуляції зорового аналізатора на нейросекреторну активність магноцелюлярних клітин супраоптичного ядра переднього гіпоталамусу. На мікропрепаратах інтактних тварин переважали нейрони II морфофункціонального типу, що перебувають у стадії синтезу нейросекрету. Показано, що за дії электростимуляції спостерігається перерозподіл головних морфо-функціональних типів нейронів. Відзначено збільшення змісту клітин I й III типів, відповідно у стадіях спокою після виведення секрету й накопичення, що вказує на активацію процесів звільнення нейросекрету і його акумуляції. Виразність реакції нервової тканини однакова при силі стимулюючого струму 100 мкА й 300 мкА.The influence of indirect through-skin electrostimulation (different doses) of the optical analyser on neurosecretory activity of anterior hypothalamus magnocellular nucleus was stading during chronic experiment. The stady was carried out on rabbits. Five morphological types of neurons was exposed in the supraoptical nucleus of control animal groop: I type- phase of rest after neurosecrets leading, II- phase of synthesis, III- phase of accumulation, IV - leading phase, V - phase of degerneration, but neurons of II types was prevalenced (51%). The indirect electrostimulation of the optical analyser provokes quantitative changes of keeping same neurons types. The number of I and III types neurons increases (on 20% and 7%) . The kind of changes is indicative of electrostimulation activation influense on neurosecrets leading and accumulation. Expression of nervous tissue reaction was identical under different doses (100 mkA and 300 mkA) of afferent electrostimulation

Rigorous Polynomial Approximation using Taylor Models in Coq

International audienceOne of the most common and practical ways of representing a real function on machines is by using a polynomial approximation. It is then important to properly handle the error introduced by such an approximation. The purpose of this work is to offer guaranteed error bounds for a specific kind of rigorous polynomial approximation called Taylor model. We carry out this work in the Coq proof assistant, with a special focus on genericity and efficiency for our implementation. We give an abstract interface for rigorous polynomial approximations, parameter- ized by the type of coefficients and the implementation of polynomials, and we instantiate this interface to the case of Taylor models with inter- val coefficients, while providing all the machinery for computing them. We compare the performances of our implementation in Coq with those of the Sollya tool, which contains an implementation of Taylor models written in C. This is a milestone in our long-term goal of providing fully formally proved and efficient Taylor models

Formation and Growth of Oligomers: A Monte Carlo Study of an Amyloid Tau Fragment

Small oligomers formed early in the process of amyloid fibril formation may be the major toxic species in Alzheimer's disease. We investigate the early stages of amyloid aggregation for the tau fragment AcPHF6 (Ac-VQIVYK-NH2) using an implicit solvent all-atom model and extensive Monte Carlo simulations of 12, 24, and 36 chains. A variety of small metastable aggregates form and dissolve until an aggregate of a critical size and conformation arises. However, the stable oligomers, which are β-sheet-rich and feature many hydrophobic contacts, are not always growth-ready. The simulations indicate instead that these supercritical oligomers spend a lengthy period in equilibrium in which considerable reorganization takes place accompanied by exchange of chains with the solution. Growth competence of the stable oligomers correlates with the alignment of the strands in the β-sheets. The larger aggregates seen in our simulations are all composed of two twisted β-sheets, packed against each other with hydrophobic side chains at the sheet–sheet interface. These β-sandwiches show similarities with the proposed steric zipper structure for PHF6 fibrils but have a mixed parallel/antiparallel β-strand organization as opposed to the parallel organization found in experiments on fibrils. Interestingly, we find that the fraction of parallel β-sheet structure increases with aggregate size. We speculate that the reorganization of the β-sheets into parallel ones is an important rate-limiting step in the formation of PHF6 fibrils

Dimer Formation Enhances Structural Differences between Amyloid β-Protein (1–40) and (1–42): An Explicit-Solvent Molecular Dynamics Study

Amyloid -protein (A) is central to the pathology of Alzheimer's disease. A 5% difference in the primary structure of the two predominant alloforms, A and A, results in distinct assembly pathways and toxicity properties. Discrete molecular dynamics (DMD) studies of A and A assembly resulted in alloform-specific oligomer size distributions consistent with experimental findings. Here, a large ensemble of DMD–derived A and A monomers and dimers was subjected to fully atomistic molecular dynamics (MD) simulations using the OPLS-AA force field combined with two water models, SPCE and TIP3P. The resulting all-atom conformations were slightly larger, less compact, had similar turn and lower -strand propensities than those predicted by DMD. Fully atomistic A and A monomers populated qualitatively similar free energy landscapes. In contrast, the free energy landscape of A dimers indicated a larger conformational variability in comparison to that of A dimers. A dimers were characterized by an increased flexibility in the N-terminal region D1-R5 and a larger solvent exposure of charged amino acids relative to A dimers. Of the three positively charged amino acids, R5 was the most and K16 the least involved in salt bridge formation. This result was independent of the water model, alloform, and assembly state. Overall, salt bridge propensities increased upon dimer formation. An exception was the salt bridge propensity of K28, which decreased upon formation of A dimers and was significantly lower than in A dimers. The potential relevance of the three positively charged amino acids in mediating the A oligomer toxicity is discussed in the light of available experimental data

Robust detection of translocations in lymphoma FFPE samples using targeted locus capture-based sequencing

Preservation of cancer biopsies by FFPE introduces DNA fragmentation, hindering analysis of rearrangements. Here the authors introduce FFPE Targeted Locus Capture for identification of translocations in preserved samples.In routine diagnostic pathology, cancer biopsies are preserved by formalin-fixed, paraffin-embedding (FFPE) procedures for examination of (intra-) cellular morphology. Such procedures inadvertently induce DNA fragmentation, which compromises sequencing-based analyses of chromosomal rearrangements. Yet, rearrangements drive many types of hematolymphoid malignancies and solid tumors, and their manifestation is instructive for diagnosis, prognosis, and treatment. Here, we present FFPE-targeted locus capture (FFPE-TLC) for targeted sequencing of proximity-ligation products formed in FFPE tissue blocks, and PLIER, a computational framework that allows automated identification and characterization of rearrangements involving selected, clinically relevant, loci. FFPE-TLC, blindly applied to 149 lymphoma and control FFPE samples, identifies the known and previously uncharacterized rearrangement partners. It outperforms fluorescence in situ hybridization (FISH) in sensitivity and specificity, and shows clear advantages over standard capture-NGS methods, finding rearrangements involving repetitive sequences which they typically miss. FFPE-TLC is therefore a powerful clinical diagnostics tool for accurate targeted rearrangement detection in FFPE specimens.Immunobiology of allogeneic stem cell transplantation and immunotherapy of hematological disease

Floating-point arithmetic in the Coq system

The process of proving some mathematical theorems can be greatly reduced by relying on numerically-intensive computations with a certi ed arithmetic. This article presents a formalization of oating-point arithmetic that makes it possible to e ciently compute inside the proofs of the Coq system. This certi ed library is a multi-radix and multi-precision implementation free from under ow and over ow. It provides the basic arithmetic operators and a few elementary functions. Keywords: 1

Interval computations, known as either Interval Analysis or Interval Arithmetic

We present the design of the Boost interval arithmetic library, a C++ library designed to efficiently handle mathematical intervals in a generic way. Interval computations are an essential tool for reliable computing. Increasingly a number of mathematical proofs have relied on global optimization problems solved using branch-andbound algorithms with interval computations; it is therefore extremely important to have a mathematically correct implementation of interval arithmetic. Various implementations exist with diverse semantics. Our design is unique in that it uses policies to specify three independent variable behaviors: rounding, checking, comparisons. As a result, with the proper policies, our interval library is able to emulate almost any of the specialized libraries available for interval arithmetic, without any loss of performance nor sacrificing the ease of use. This library is openly available at www.boost.org. Key words: Interval arithmetic, software library, generic programming, policy-based design, robust computations, floating-point filter. ⋆ A preliminary version of this article appeared under the title “The Boost interval arithmetic library”at the 5th Conference on Real Numbers and Computers, 3-

BioExcel Deliverable 2.3 - User Feedback and Future Roadmap

This deliverable presents the first internal (partners) and external (collaborators, users) feedback for the transversal workflow Model Protein Mutants and for the project pilot use cases. The transversal workflow, used as a prototype to test the designed workflows development process in the project and also the computational infrastructure, has been the main source of feedback. An update of the technical work behind the five project pilot use cases is given, emphasizing the feedback received. Future roadmaps for the BioExcel Cloud Portal and for the workflows and computational infrastructures are presented, which showcase the work planned for the rest of the project. User experience will be the main focus for the cloud portal that is expected to offer a growing number of tools and deployable VMs in the coming months. Two kinds of benchmarks, a technical one (different computational infrastructures) and a scientific one (real scientific studies in an HPC exascale approach) are proposed using the transversal workflow