Machine-Checked Proofs For Realizability Checking Algorithms

Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate architectural descriptions, assume/guarantee contracts, and compositional reasoning rules, these techniques can be used to prove important safety properties about the architecture prior to system construction. For these proofs to be meaningful, each leaf-level component contract must be realizable; i.e., it is possible to construct a component such that for any input allowed by the contract assumptions, there is some output value that the component can produce that satisfies the contract guarantees. We have recently proposed (in [1]) a contract-based realizability checking algorithm for assume/guarantee contracts over infinite theories supported by SMT solvers such as linear integer/real arithmetic and uninterpreted functions. In that work, we used an SMT solver and an algorithm similar to k-induction to establish the realizability of a contract, and justified our approach via a hand proof. Given the central importance of realizability to our virtual integration approach, we wanted additional confidence that our approach was sound. This paper describes a complete formalization of the approach in the Coq proof and specification language. During formalization, we found several small mistakes and missing assumptions in our reasoning. Although these did not compromise the correctness of the algorithm used in the checking tools, they point to the value of machine-checked formalization. In addition, we believe this is the first machine-checked formalization for a realizability algorithm.Comment: 14 pages, 1 figur

Solvable Lie algebras are not that hypo

We study a type of left-invariant structure on Lie groups, or equivalently on Lie algebras. We introduce obstructions to the existence of a hypo structure, namely the 5-dimensional geometry of hypersurfaces in manifolds with holonomy SU(3). The choice of a splitting g^*=V_1 + V_2, and the vanishing of certain associated cohomology groups, determine a first obstruction. We also construct necessary conditions for the existence of a hypo structure with a fixed almost-contact form. For non-unimodular Lie algebras, we derive an obstruction to the existence of a hypo structure, with no choice involved. We apply these methods to classify solvable Lie algebras that admit a hypo structure.Comment: 21 pages; v2: presentation improved, typos corrected, notational conflicts eliminated. To appear in Transformation Group

Stacked dielectric gratings for sub-wavelength surface field synthesis

A method is developed to enhance the amplitudes of the non-propagating evanescent orders of resonant dielectric gratings. The origin of these resonances is analyzed in detail. The method relies on interactions between stacked gratings with different periods, and so a formalism is developed to model such stacks mathematically. In addition, a theoretical approach is developed to design gratings that enhance or blaze desired orders. These orders, controlled independently by incident fields from different angles, interfere and are optimized to produce steerable sub-Rayleigh field concentrations on a surface. These spots may function as a virtual scanning probe for non-invasive sub-Rayleigh microscopy. Optimization is conducted using a Monte Carlo Markov chain, and spots are generated which are both 1 order of magnitude narrower than the free space Rayleigh limit and robust to noise in the incident fields. © 2010 Optical Society of America

Noncoding RNAs and Duchenne muscular dystrophy

Noncoding RNAs (ncRNAs) such as miRNAs and long noncoding RNAs modulate gene transcription in response to environmental stressors and other stimuli. A role for ncRNAs in muscle pathologies has been demonstrated and further evidence suggests that ncRNAs also play a role in Duchenne muscular dystrophy (DMD). Studies investigating the differential expression of miRNAs in biological fluids between DMD patients and models of dystrophin deficiency (the MDX mouse model, canine models of DMD) and controls have been published, as these have a role in fibrosis. Long noncoding RNAs are differentially expressed in DMD patients and may, in part, have a mechanism of action via targeting of miRNAs. Although many of these recent findings need to be confirmed, ncRNAs may prove to be useful as potential biomarkers of disease. However, their use as therapeutic targets in DMD remains unclear

Blazing evanescent grating orders: A spectral approach to beating the Rayleigh limit

We develop a way to enhance the amplitudes of the nonpropagating evanescent orders of resonant dielectric gratings. We use this blazing to design gratings with spectra tailored to generate steerable sub-Rayleigh field concentrations on a surface. We investigate the enhancement and customization of evanescent fields necessary to create a virtual and passive scanning probe with no moving parts. Spot size can be decreased 1 order of magnitude below the free-space Rayleigh limit. © 2010 Optical Society of America

Towards equity and justice in ocean sciences

The global scientific community is currently going through a self-reckoning in which it is questioning and re-examining its existing practices, many of which are based on colonial and neo-colonial perceptions. This is particularly acute for the ocean research community, where unequal and unbalanced international collaborations have been rife. Consequently, numerous discussions and calls have been made to change the current status quo by developing guidelines and frameworks addressing the key issues plaguing our community. Here, we provide an overview of the key topics and issues that the scientific community has debated over the last three to four years, with an emphasis on ocean research, coupled with actions per stakeholder groups (research community, institutions, funding agencies, and publishers). We also outline some key discussions that are currently missing and suggest a path forward to tackle these gaps. We hope this contribution will further accelerate efforts to bring more equity and justice into ocean sciences

A Formalization of the Theorem of Existence of First-Order Most General Unifiers

This work presents a formalization of the theorem of existence of most general unifiers in first-order signatures in the higher-order proof assistant PVS. The distinguishing feature of this formalization is that it remains close to the textbook proofs that are based on proving the correctness of the well-known Robinson's first-order unification algorithm. The formalization was applied inside a PVS development for term rewriting systems that provides a complete formalization of the Knuth-Bendix Critical Pair theorem, among other relevant theorems of the theory of rewriting. In addition, the formalization methodology has been proved of practical use in order to verify the correctness of unification algorithms in the style of the original Robinson's unification algorithm.Comment: In Proceedings LSFA 2011, arXiv:1203.542

Autonomic dysregulation and self‐injurious thoughts and behaviours in children and young people: A systematic review and meta‐analysis

Background: self-injurious thoughts and behaviours (SITBs) have been associated with dysfunction of the Autonomic Nervous System (ANS) in children and young people, suggesting that objective ANS measures may aid assessment of suicide risk, but a systematic synthesis of this literature is currently lacking.Methods: following a pre-registered protocol (PROSPERO CRD42022327605), we conducted a systematic search of PubMed, Medline, Embase, PsycINFO, and Web of Science, for empirical studies published until 10th May 2022 that compared indices of ANS functioning in individuals aged 0–25 years with versus without SITBs, or reported continuous associations between ANS measures and SITBs. Study quality was assessed with the Newcastle-Ottawa Scales. Pooled effect sizes (Hedge's g) were estimated with random-effects meta-analytic models.Results: twenty studies (1979 participants) were included in our systematic review, with 16 included in meta-analyses. Results suggested that SITBs were associated with altered cardiac indices of arousal (g = −0.328, p < 0.001), which was driven by lower heart rate variability in individuals with SITBs (g = −0.375, p = 0.025). Overall results for electrodermal activity were not significant (g = 0.026, p = 0.857), but subgroup analyses showed increased activity in studies of individuals who engaged specifically in non-suicidal self-harm (g = 0.249, p = 0.014) but decreased activity in the remaining studies (g = −0.567, p = 0.004).Conclusions: our systematic review and meta-analysis found evidence of reduced parasympathetic regulation as well as more tentative evidence of altered electrodermal activity in children and young people displaying SITBs. Future longitudinal studies should test the clinical utility of these markers for detecting and monitoring suicide risk

Prediction of lethal and synthetically lethal knock-outs in regulatory networks

The complex interactions involved in regulation of a cell's function are captured by its interaction graph. More often than not, detailed knowledge about enhancing or suppressive regulatory influences and cooperative effects is lacking and merely the presence or absence of directed interactions is known. Here we investigate to which extent such reduced information allows to forecast the effect of a knock-out or a combination of knock-outs. Specifically we ask in how far the lethality of eliminating nodes may be predicted by their network centrality, such as degree and betweenness, without knowing the function of the system. The function is taken as the ability to reproduce a fixed point under a discrete Boolean dynamics. We investigate two types of stochastically generated networks: fully random networks and structures grown with a mechanism of node duplication and subsequent divergence of interactions. On all networks we find that the out-degree is a good predictor of the lethality of a single node knock-out. For knock-outs of node pairs, the fraction of successors shared between the two knocked-out nodes (out-overlap) is a good predictor of synthetic lethality. Out-degree and out-overlap are locally defined and computationally simple centrality measures that provide a predictive power close to the optimal predictor.Comment: published version, 10 pages, 6 figures, 2 tables; supplement at http://www.bioinf.uni-leipzig.de/publications/supplements/11-01