A Generic Library for Floating-Point Numbers and Its Application to Exact Computing

International audienceIn this paper we present a general library to reason about floating-point numbers within the Coq system. Most of the results of the library are proved for an arbitrary floating-point format and an arbitrary base. A special emphasis has been put on proving properties for exact computing, i.e. computing without rounding errors

A Modular Integration of SAT/SMT Solvers to Coq through Proof Witnesses

International audienceWe present a way to enjoy the power of SAT and SMT provers in Coq without compromising soundness. This requires these provers to return not only a yes/no answer, but also a proof witness that can be independently rechecked. We present such a checker, written and fully certified in Coq. It is conceived in a modular way, in order to tame the proofs' complexity and to be extendable. It can currently check witnesses from the SAT solver ZChaff and from the SMT solver veriT. Experiments highlight the efficiency of this checker. On top of it, new reflexive Coq tactics have been built that can decide a subset of Coq's logic by calling external provers and carefully checking their answers

A Generic Library for Floating-Point Numbers and Its Application to Exact Computing

International audienceIn this paper we present a general library to reason about floating-point numbers within the Coq system. Most of the results of the library are proved for an arbitrary floating-point format and an arbitrary base. A special emphasis has been put on proving properties for exact computing, i.e. computing without rounding errors

Computable analysis and notions of continuity in Coq

We give a number of formal proofs of theorems from the field of computable analysis. Many of our results specify executable algorithms that work on infinite inputs by means of operating on finite approximations and are proven correct in the sense of computable analysis. The development is done in the proof assistant Coq and heavily relies on the Incone library for information theoretic continuity. This library is developed by one of the authors and the paper can be used as an introduction to the library as it describes many of its most important features in detail. While the ability to have full executability in a formal development of mathematical statements about real numbers and the like is not a feature that is unique to the Incone library, its original contribution is to adhere to the conventions of computable analysis to provide a general purpose interface for algorithmic reasoning on continuous structures. The results that provide complete computational content include that the algebraic operations and the efficient limit operator on the reals are computable, that certain countably infinite products are isomorphic to spaces of functions, compatibility of the enumeration representation of subsets of natural numbers with the abstract definition of the space of open subsets of the natural numbers, and that continuous realizability implies sequential continuity. We also formalize proofs of non-computational results that support the correctness of our definitions. These include that the information theoretic notion of continuity used in the library is equivalent to the metric notion of continuity on Baire space, a complete comparison of the different concepts of continuity that arise from metric and represented-space structures and the discontinuity of the unrestricted limit operator on the real numbers and the task of selecting an element of a closed subset of the natural numbers

Local actin nucleation tunes centrosomal microtubule nucleation during passage through mitosis

Cells going through mitosis undergo precisely timed changes in cell shape and organisation, which serve to ensure the fair partitioning of cellular components into the two daughter cells. These structural changes are driven by changes in actin filament and microtubule dynamics and organisation. While most evidence suggests that the two cytoskeletal systems are remodelled in parallel during mitosis, recent work in interphase cells has implicated the centrosome in both microtubule and actin nucleation, suggesting the potential for regulatory crosstalk between the two systems. Here, by using both in vitro and in vivo assays to study centrosomal actin nucleation as cells pass through mitosis, we show that mitotic exit is accompanied by a burst in cytoplasmic actin filament formation that depends on WASH and the Arp2/3 complex. This leads to the accumulation of actin around centrosomes as cells enter anaphase and to a corresponding reduction in the density of centrosomal microtubules. Taken together, these data suggest that the mitotic regulation of centrosomal WASH and the Arp2/3 complex controls local actin nucleation, which may function to tune the levels of centrosomal microtubules during passage through mitosis

Design and selection of optimal ErbB-targeting bispecific antibodies in pancreatic cancer

The ErbB family of receptor tyrosine kinases is a primary target for small molecules and antibodies for pancreatic cancer treatment. Nonetheless, the current treatments for this tumor are not optimal due to lack of efficacy, resistance, or toxicity. Here, using the novel BiXAb™ tetravalent format platform, we generated bispecific antibodies against EGFR, HER2, or HER3 by considering rational epitope combinations. We then screened these bispecific antibodies and compared them with the parental single antibodies and antibody pair combinations. The screen readouts included measuring binding to the cognate receptors (mono and bispecificity), intracellular phosphorylation signaling, cell proliferation, apoptosis and receptor expression, and also immune system engagement assays (antibody-dependent cell-mediated cytotoxicity and complement-dependent cytotoxicity). Among the 30 BiXAbs™ tested, we selected 3Patri-1Cetu-Fc, 3Patri-1Matu-Fc and 3Patri-2Trastu-Fc as lead candidates. The in vivo testing of these three highly efficient bispecific antibodies against EGFR and HER2 or HER3 in pre-clinical mouse models of pancreatic cancer showed deep antibody penetration in these dense tumors and robust tumor growth reduction. Application of such semi-rational/semi-empirical approach, which includes various immunological assays to compare pre-selected antibodies and their combinations with bispecific antibodies, represents the first attempt to identify potent bispecific antibodies against ErbB family members in pancreatic cancer