Splitting Proofs for Interpolation

We study interpolant extraction from local first-order refutations. We present a new theoretical perspective on interpolation based on clearly separating the condition on logical strength of the formula from the requirement on the com- mon signature. This allows us to highlight the space of all interpolants that can be extracted from a refutation as a space of simple choices on how to split the refuta- tion into two parts. We use this new insight to develop an algorithm for extracting interpolants which are linear in the size of the input refutation and can be further optimized using metrics such as number of non-logical symbols or quantifiers. We implemented the new algorithm in first-order theorem prover VAMPIRE and evaluated it on a large number of examples coming from the first-order proving community. Our experiments give practical evidence that our work improves the state-of-the-art in first-order interpolation.Comment: 26th Conference on Automated Deduction, 201

A Reduction from Unbounded Linear Mixed Arithmetic Problems into Bounded Problems

We present a combination of the Mixed-Echelon-Hermite transformation and the Double-Bounded Reduction for systems of linear mixed arithmetic that preserve satisfiability and can be computed in polynomial time. Together, the two transformations turn any system of linear mixed constraints into a bounded system, i.e., a system for which termination can be achieved easily. Existing approaches for linear mixed arithmetic, e.g., branch-and-bound and cuts from proofs, only explore a finite search space after application of our two transformations. Instead of generating a priori bounds for the variables, e.g., as suggested by Papadimitriou, unbounded variables are eliminated through the two transformations. The transformations orient themselves on the structure of an input system instead of computing a priori (over-)approximations out of the available constants. Experiments provide further evidence to the efficiency of the transformations in practice. We also present a polynomial method for converting certificates of (un)satisfiability from the transformed to the original system

Periplasmic Expression of 4/7 α-Conotoxin TxIA Analogs in E. coli Favors Ribbon Isomer Formation – Suggestion of a Binding Mode at the α7 nAChR

Peptides derived from animal venoms provide important research tools for biochemical and pharmacological characterization of receptors, ion channels, and transporters. Some venom peptides have been developed into drugs (such as the synthetic omega-conotoxin MVIIA, ziconotide) and several are currently undergoing clinical trials for various clinical indications. Challenges in the development of peptides include their usually limited supply from natural sources, cost-intensive chemical synthesis, and potentially complicated stereoselective disulfide-bond formation in the case of disulfide-rich peptides. In particular, if extended structure-function analysis is performed or incorporation of stable isotopes for NMR studies is required, the comparatively low yields and high costs of synthesized peptides might constitute a limiting factor. Here we investigated the expression of the 4/7 alpha-conotoxin TxIA, a potent blocker at alpha 3 beta 2 and alpha 7 nicotinic acetylcholine receptors (nAChRs), and three analogs in the form of maltose binding protein fusion proteins in Escherichia coli. Upon purification via nickel affinity chromatography and release of the toxins by protease cleavage, HPLC analysis revealed one major peak with the correct mass for all peptides. The final yield was 1-2 mg of recombinant peptide per liter of bacterial culture. Two-electrode voltage clamp analysis on oocyte-expressed nAChR subtypes demonstrated the functionality of these peptides but also revealed a 30 to 100-fold potency decrease of expressed TxIA compared to chemically synthesized TxIA. NMR spectroscopy analysis of TxIA and two of its analogs confirmed that the decreased activity was due to an alternative disulfide linkage rather than the missing C-terminal amidation, a post-translational modification that is common in alpha-conotoxins. All peptides preferentially formed in the ribbon conformation rather than the native globular conformation. Interestingly, in the case of the alpha 7 nAChR, but not the alpha 3 beta 2 subtype, the loss of potency could be rescued by an R5D substitution. In conclusion, we demonstrate efficient expression of functional but alternatively folded ribbon TxIA variants in E. coli and provide the first structure-function analysis for a ribbon 4/7-alpha-conotoxin at alpha 7 and alpha 3 beta 2 nAChRs. Computational analysis based on these data provide evidence for a ribbon alpha-conotoxin binding mode that might be exploited to design ligands with optimized selectivity

Computation of the Transient in Max-Plus Linear Systems via SMT-Solving

This paper proposes a new approach, grounded in Satisfiability Modulo Theories (SMT), to study the transient of a Max-Plus Linear (MPL) system, that is the number of steps leading to its periodic regime. Differently from state-of-the-art techniques, our approach allows the analysis of periodic behaviors for subsets of initial states, as well as the characterization of sets of initial states exhibiting the same specific periodic behavior and transient. Our experiments show that the proposed technique dramatically outperforms state-of-the-art methods based on max-plus algebra computations for systems of large dimensions.Comment: The paper consists of 22 pages (including references and Appendix). It is accepted in FORMATS 2020 First revisio

Formalising the Continuous/Discrete Modeling Step

Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete domains. The difference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.Comment: In Proceedings Refine 2011, arXiv:1106.348

Systematic interrogation of the Conus marmoreus venom duct transcriptome with ConoSorter reveals 158 novel conotoxins and 13 new gene superfamilies

International audienceConopeptides, often generically referred to as conotoxins, are small neurotoxins found in the venom of predatory marine cone snails. These molecules are highly stable and are able to efficiently and selectively interact with a wide variety of heterologous receptors and channels, making them valuable pharmacological probes and potential drug leads. Recent advances in next-generation RNA sequencing and high-throughput proteomics have led to the generation of large data sets that require purpose-built and dedicated bioinformatics tools for efficient data mining

Case–control, kin-cohort and meta-analyses provide no support for STK15 F31I as a low penetrance colorectal cancer allele

Recently, homozygosity for T91A single-nucleotide polymorphism (SNP) in the serine/threonine kinase (STK15) gene, which generates the substitution F31I has been proposed to increase the risk of a number of tumours including colorectal cancer (CRC). To further evaluate the relationship between STK15 F31I and risk of CRC, we genotyped 2558 CRC cases and 2680 controls for this polymorphism. We found no evidence that homozygosity for the STK15 31I genotype confers an increased risk of CRC (odds ratio=0.95, 95% confidence interval (CI): 0.74–1.24). We also conducted a kin-cohort analysis to assess risk among first-degree relatives of the CRC cases. The hazard ratio for I/I homozygotes compared to F/F homozygotes was 1.65 (95% CI: 0.39–3.17). A meta-analysis of our case–control data and three previous studies also provided no evidence of an elevated risk of CRC associated with homozygosity. These data provide no support for the hypothesis that sequence variation in STK15 defined by SNP F31I per se confers an elevated risk of CRC

New results on rewrite-based satisfiability procedures

Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for first-order logic is guaranteed to terminate on T-satisfiability problems, any theorem-proving strategy with that system and a fair search plan is a T-satisfiability procedure. We prove termination of a rewrite-based first-order engine on the theories of records, integer offsets, integer offsets modulo and lists. We give a modularity theorem stating sufficient conditions for termination on a combinations of theories, given termination on each. The above theories, as well as others, satisfy these conditions. We introduce several sets of benchmarks on these theories and their combinations, including both parametric synthetic benchmarks to test scalability, and real-world problems to test performances on huge sets of literals. We compare the rewrite-based theorem prover E with the validity checkers CVC and CVC Lite. Contrary to the folklore that a general-purpose prover cannot compete with reasoners with built-in theories, the experiments are overall favorable to the theorem prover, showing that not only the rewriting approach is elegant and conceptually simple, but has important practical implications.Comment: To appear in the ACM Transactions on Computational Logic, 49 page

Effects of Hepatitis B Surface Antigen on Virus-specific and Global T Cells in Patients With Chronic HBV infection

10.1053/j.gastro.2020.04.019Gastroenterolog

AChBP-targeted α-conotoxin correlates distinct binding orientations with nAChR subtype selectivity

Neuronal nAChRs are a diverse family of pentameric ion channels with wide distribution throughout cells of the nervous and immune systems. However, the role of specific subtypes in normal and pathological states remains poorly understood due to the lack of selective probes. Here, we used a binding assay based on acetylcholine-binding protein (AChBP), a homolog of the nicotinic acetylcholine ligand-binding domain, to discover a novel α-conotoxin (α-TxIA) in the venom of Conus textile. α-TxIA bound with high affinity to AChBPs from different species and selectively targeted the α3β2 nAChR subtype. A co-crystal structure of Ac-AChBP with the enhanced potency analog TxIA(A10L), revealed a 20° backbone tilt compared to other AChBP–conotoxin complexes. This reorientation was coordinated by a key salt bridge formed between Arg5 (TxIA) and Asp195 (Ac-AChBP). Mutagenesis studies, biochemical assays and electrophysiological recordings directly correlated the interactions observed in the co-crystal structure to binding affinity at AChBP and different nAChR subtypes. Together, these results establish a new pharmacophore for the design of novel subtype-selective ligands with therapeutic potential in nAChR-related diseases