The Structure of Differential Invariants and Differential Cut Elimination

The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more scalable verification. Search procedures for these proof certificates are still rather ad-hoc, though, because the problem structure is only understood poorly. We investigate differential invariants, which define an induction principle for differential equations and which can be checked for invariance along a differential equation just by using their differential structure, without having to solve them. We study the structural properties of differential invariants. To analyze trade-offs for proof search complexity, we identify more than a dozen relations between several classes of differential invariants and compare their deductive power. As our main results, we analyze the deductive power of differential cuts and the deductive power of differential invariants with auxiliary differential variables. We refute the differential cut elimination hypothesis and show that, unlike standard cuts, differential cuts are fundamental proof principles that strictly increase the deductive power. We also prove that the deductive power increases further when adding auxiliary differential variables to the dynamics

Collaborative Verification-Driven Engineering of Hybrid Systems

Hybrid systems with both discrete and continuous dynamics are an important model for real-world cyber-physical systems. The key challenge is to ensure their correct functioning w.r.t. safety requirements. Promising techniques to ensure safety seem to be model-driven engineering to develop hybrid systems in a well-defined and traceable manner, and formal verification to prove their correctness. Their combination forms the vision of verification-driven engineering. Often, hybrid systems are rather complex in that they require expertise from many domains (e.g., robotics, control systems, computer science, software engineering, and mechanical engineering). Moreover, despite the remarkable progress in automating formal verification of hybrid systems, the construction of proofs of complex systems often requires nontrivial human guidance, since hybrid systems verification tools solve undecidable problems. It is, thus, not uncommon for development and verification teams to consist of many players with diverse expertise. This paper introduces a verification-driven engineering toolset that extends our previous work on hybrid and arithmetic verification with tools for (i) graphical (UML) and textual modeling of hybrid systems, (ii) exchanging and comparing models and proofs, and (iii) managing verification tasks. This toolset makes it easier to tackle large-scale verification tasks

Forward Invariant Cuts to Simplify Proofs of Safety

The use of deductive techniques, such as theorem provers, has several advantages in safety verification of hybrid sys- tems; however, state-of-the-art theorem provers require ex- tensive manual intervention. Furthermore, there is often a gap between the type of assistance that a theorem prover requires to make progress on a proof task and the assis- tance that a system designer is able to provide. This paper presents an extension to KeYmaera, a deductive verification tool for differential dynamic logic; the new technique allows local reasoning using system designer intuition about per- formance within particular modes as part of a proof task. Our approach allows the theorem prover to leverage for- ward invariants, discovered using numerical techniques, as part of a proof of safety. We introduce a new inference rule into the proof calculus of KeYmaera, the forward invariant cut rule, and we present a methodology to discover useful forward invariants, which are then used with the new cut rule to complete verification tasks. We demonstrate how our new approach can be used to complete verification tasks that lie out of the reach of existing deductive approaches us- ing several examples, including one involving an automotive powertrain control system.Comment: Extended version of EMSOFT pape

Functional characterization of two novel 5' untranslated exons reveals a complex regulation of NOD2 protein expression

<p>Abstract</p> <p>Background</p> <p>NOD2 is an innate immune receptor for the bacterial cell wall component muramyl-dipeptide. Mutations in the leucine-rich repeat region of NOD2, which lead to an impaired recognition of muramyl-dipeptide, have been associated with Crohn disease, a human chronic inflammatory bowel disease. Tissue specific constitutive and inducible expression patterns of NOD2 have been described that result from complex regulatory events for which the molecular mechanisms are not yet fully understood.</p> <p>Results</p> <p>We have identified two novel exons of the <it>NOD2 </it>gene (designated exon 1a and 1b), which are spliced to the canonical exon 2 and constitute the 5' untranslated region of two alternative transcript isoforms (i.e. exon 1a/1b/2 and exon 1a/2). The two novel transcripts are abundantly expressed and seem to comprise the majority of NOD2 transcripts under physiological conditions. We confirm the expression of the previously known canonical first exon (designated exon 1c) of the gene in unstimulated mononuclear cells. The inclusion of the second alternative exon 1b, which harbours three short upstream open reading frames (uORFs), is downregulated upon stimulation with TNF-α or under pro-inflammatory conditions in the inflamed intestinal mucosa <it>in vivo</it>. Using the different 5' UTR splice forms fused to a firefly luciferase (LUC) reporter we demonstrate a rapamycin-sensitive inhibitory effect of the uORFs on translation efficacy.</p> <p>Conclusion</p> <p>The differential usage of two alternative promoters in the <it>NOD2 </it>gene leads to tissue-specific and context-dependent <it>NOD2 </it>transcript isoform patterns. We demonstrate for the first time that context-dependent alternative splicing is linked to uORF-mediated translational repression. The results suggest complex parallel control mechanisms that independently regulate NOD2 expression in the context of inflammatory signaling.</p

Systematic Association Mapping Identifies NELL1 as a Novel IBD Disease Gene

Crohn disease (CD), a sub-entity of inflammatory bowel disease (IBD), is a complex polygenic disorder. Although recent studies have successfully identified CD-associated genetic variants, these susceptibility loci explain only a fraction of the heritability of the disease. Here, we report on a multi-stage genome-wide scan of 393 German CD cases and 399 controls. Among the 116,161 single-nucleotide polymorphisms tested, an association with the known CD susceptibility gene NOD2, the 5q31 haplotype, and the recently reported CD locus at 5p13.1 was confirmed. In addition, SNP rs1793004 in the gene encoding nel-like 1 precursor (NELL1, chromosome 11p15.1) showed a consistent disease-association in independent German population- and family-based samples (942 cases, 1082 controls, 375 trios). Subsequent fine mapping and replication in an independent sample of 454 French/Canadian CD trios supported the authenticity of the NELL1 association. Further confirmation in a large German ulcerative colitis (UC) sample indicated that NELL1 is a ubiquitous IBD susceptibility locus (combined p<10−6; OR = 1.66, 95% CI: 1.30–2.11). The novel 5p13.1 locus was also replicated in the French/Canadian sample and in an independent UK CD patient panel (453 cases, 521 controls, combined p<10−6 for SNP rs1992660). Several associations were replicated in at least one independent sample, point to an involvement of ITGB6 (upstream), GRM8 (downstream), OR5V1 (downstream), PPP3R2 (downstream), NM_152575 (upstream) and HNF4G (intron)

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Differential Hybrid Games (CMU-CS-14-102)

This paper introduces differential hybrid games, which combine differential games with hybrid games. In both kinds of games, two players interact with continuous dynamics. The difference is that hybrid games also provide all the features of hybrid systems and discrete games, but only deterministic differential equations. Differential games, instead, provide differential equations with input by both players, but not the luxury of hybrid games, such as mode switches and discrete or alternating interaction. This paper augments differential game logic with modalities for the combined dynamics of differential hybrid games. It shows how hybrid games subsume differential games and introduces differential game invariants and differential game variants for proving properties of differential games inductively.</p

A Complete Axiomatization of Quantified Differential Dynamic Logic for Distributed Hybrid Systems

We address a fundamental mismatch between the combinations of dynamics that occur in cyber-physical systems and the limited kinds of dynamics supported in analysis. Modern applications combine communication, computation, and control. They may even form dynamic distributed networks, where neither structure nor dimension stay the same while the system follows hybrid dynamics, i.e., mixed discrete and continuous dynamics. We provide the logical foundations for closing this analytic gap. We develop a formal model for distributed hybrid systems. It combines quantified differential equations with quantified assignments and dynamic dimensionality-changes. We introduce a dynamic logic for verifying distributed hybrid systems and present a proof calculus for this logic. This is the first formal verification approach for distributed hybrid systems. We prove that our calculus is a sound and complete axiomatization of the behavior of distributed hybrid systems relative to quantified differential equations. In our calculus we have proven collision freedom in distributed car control even when an unbounded number of new cars may appear dynamically on the road.</p

Stochastic Differential Dynamic Logic for Stochastic Hybrid Programs (CMU-CS-11-111)

Logic is a powerful tool for analyzing and verifying systems, including programs, discrete systems, real-time systems, hybrid systems, and distributed systems. Some applications also have a stochastic behavior, however, either because of fundamental properties of nature, uncertain environments, or simplifications to overcome complexity. Discrete probabilistic systems have been studied using logic. But logic has been chronically underdeveloped in the context of stochastic hybrid systems, i.e., systems with interacting discrete, continuous, and stochastic dynamics. We aim at overcoming this deficiency and introduce a dynamic logic for stochastic hybrid systems. Our results indicate that logic is a promising tool for understanding stochastic hybrid systems and can help taming some of their complexity. We introduce a compositional model for stochastic hybrid systems. We prove adaptivity, cadl ` ag, and Markov time properties, and prove that the semantics ` of our logic is measurable. We present compositional proof rules, including rules for stochastic differential equations, and prove soundness.</p