An Axiomatic Approach to Liveness for Differential Equations

This paper presents an approach for deductive liveness verification for ordinary differential equations (ODEs) with differential dynamic logic. Numerous subtleties complicate the generalization of well-known discrete liveness verification techniques, such as loop variants, to the continuous setting. For example, ODE solutions may blow up in finite time or their progress towards the goal may converge to zero. Our approach handles these subtleties by successively refining ODE liveness properties using ODE invariance properties which have a well-understood deductive proof theory. This approach is widely applicable: we survey several liveness arguments in the literature and derive them all as special instances of our axiomatic refinement approach. We also correct several soundness errors in the surveyed arguments, which further highlights the subtlety of ODE liveness reasoning and the utility of our deductive approach. The library of common refinement steps identified through our approach enables both the sound development and justification of new ODE liveness proof rules from our axioms.Comment: FM 2019: 23rd International Symposium on Formal Methods, Porto, Portugal, October 9-11, 201

Saturation of a spin 1/2 particle by generalized Local control

We show how to apply a generalization of Local control design to the problem of saturation of a spin 1/2 particle by magnetic fields in Nuclear Magnetic Resonance. The generalization of local or Lyapunov control arises from the fact that the derivative of the Lyapunov function does not depend explicitly on the control field. The second derivative is used to determine the local control field. We compare the efficiency of this approach with respect to the time-optimal solution which has been recently derived using geometric methods.Comment: 12 pages, 4 figures, submitted to new journal of physics (2011

Ordering variable for parton showers

The parton splittings in a parton shower are ordered according to an ordering variable, for example the transverse momentum of the daughter partons relative to the direction of the mother, the virtuality of the splitting, or the angle between the daughter partons. We analyze the choice of the ordering variable and conclude that one particular choice has the advantage of factoring softer splittings from harder splittings graph by graph in a physical gauge.Comment: 28 pages, 5 figure

De Novo Missense Variants in SLC32A1 Cause a Developmental and Epileptic Encephalopathy Due to Impaired GABAergic Neurotransmission

Objective:Rare inherited missense variants inSLC32A1, the gene that encodes the vesicular gamma-aminobutyric acid(GABA) transporter, have recently been shown to cause genetic epilepsy with febrile seizures plus. We aimed to clarifyif de novo missense variants inSLC32A1can also cause epilepsy with impaired neurodevelopment.Methods:Using exome sequencing, we identified four individuals with a developmental and epileptic encephalopathyand de novo missense variants inSLC32A1. To assess causality, we performed functional evaluation of the identifiedvariants in a murine neuronal cell culture model.Results:The main phenotype comprises moderate-to-severe intellectual disability, infantile-onset epilepsy within thefirst 18 months of life, and a choreiform, dystonic, or dyskinetic movement disorder. In silico modeling and functionalanalyses reveal that three of these variants, which are located in helices that line the putative GABA transport pathway,result in reduced quantal size, consistent with impairedfilling of synaptic vesicles with GABA. The fourth variant,located in the vesicular gamma-aminobutyric acid N-terminus, does not affect quantal size, but increases presynapticrelease probability, leading to more severe synaptic depression during high-frequency stimulation. Thus, variants invesicular gamma-aminobutyric acid can impair GABAergic neurotransmission through at least two mechanisms, byaffecting synaptic vesiclefilling and by altering synaptic short-term plasticity.Interpretation:This work establishes de novo missense variants inSLC32A1as a novel cause of a developmental andepileptic encephalopathy

ExSample -- A Library for Sampling Sudakov-Type Distributions

Sudakov-type distributions are at the heart of generating radiation in parton showers as well as contemporary NLO matching algorithms along the lines of the POWHEG algorithm. In this paper, the C++ library ExSample is introduced, which implements adaptive sampling of Sudakov-type distributions for splitting kernels which are in general only known numerically. Besides the evolution variable, the splitting kernels can depend on an arbitrary number of other degrees of freedom to be sampled, and any number of further parameters which are fixed on an event-by-event basis.Comment: 6 pages, 6 figures, minor changes and figures added, corresponds to published versio

ModelPlex: Verified Runtime Validation of Verified Cyber-Physical System Models

Abstract. Formal verification and validation play a crucial role in making cyber-physical systems (CPS) safe. Formal methods make strong guarantees about the system behavior if accurate models of the system can be obtained, including mod-els of the controller and of the physical dynamics. In CPS, models are essential; but any model we could possibly build necessarily deviates from the real world. If the real system fits to the model, its behavior is guaranteed to satisfy the correct-ness properties verified w.r.t. the model. Otherwise, all bets are off. This paper introduces ModelPlex, a method ensuring that verification results about models apply to CPS implementations. ModelPlex provides correctness guarantees for CPS executions at runtime: it combines offline verification of CPS models with runtime validation of system executions for compliance with the model. Model-Plex ensures that the verification results obtained for the model apply to the ac-tual system runs by monitoring the behavior of the world for compliance with the model, assuming the system dynamics deviation is bounded. If, at some point, the observed behavior no longer complies with the model so that offline verifica-tion results no longer apply, ModelPlex initiates provably safe fallback actions. This paper, furthermore, develops a systematic technique to synthesize provably correct monitors automatically from CPS proofs in differential dynamic logic.

Interleaved Parton Showers and Tuning Prospects

General-purpose Monte Carlo event generators have become important tools in particle physics, allowing the simulation of exclusive hadronic final states. In this article we examine the Pythia 8 generator, in particular focusing on its parton-shower algorithms. Some relevant new additions to the code are introduced, that should allow for a better description of data. We also implement and compare with 2 to 3 real-emission QCD matrix elements, to check how well the shower algorithm fills the phase space away from the soft and collinear regions. A tuning of the generator to Tevatron data is performed for two PDF sets and the impact of first new LHC data is examined

On dynamic network entropy in cancer

The cellular phenotype is described by a complex network of molecular interactions. Elucidating network properties that distinguish disease from the healthy cellular state is therefore of critical importance for gaining systems-level insights into disease mechanisms and ultimately for developing improved therapies. By integrating gene expression data with a protein interaction network to induce a stochastic dynamics on the network, we here demonstrate that cancer cells are characterised by an increase in the dynamic network entropy, compared to cells of normal physiology. Using a fundamental relation between the macroscopic resilience of a dynamical system and the uncertainty (entropy) in the underlying microscopic processes, we argue that cancer cells will be more robust to random gene perturbations. In addition, we formally demonstrate that gene expression differences between normal and cancer tissue are anticorrelated with local dynamic entropy changes, thus providing a systemic link between gene expression changes at the nodes and their local network dynamics. In particular, we also find that genes which drive cell-proliferation in cancer cells and which often encode oncogenes are associated with reductions in the dynamic network entropy. In summary, our results support the view that the observed increased robustness of cancer cells to perturbation and therapy may be due to an increase in the dynamic network entropy that allows cells to adapt to the new cellular stresses. Conversely, genes that exhibit local flux entropy decreases in cancer may render cancer cells more susceptible to targeted intervention and may therefore represent promising drug targets.Comment: 10 pages, 3 figures, 4 tables. Submitte

A Soluble Form of the High Affinity IgE Receptor, Fc-Epsilon-RI, Circulates in Human Serum

Soluble IgE receptors are potential in vivo modulators of IgE-mediated immune responses and are thus important for our basic understanding of allergic responses. We here characterize a novel soluble version of the IgE-binding alpha-chain of Fc-epsilon-RI (sFcεRI), the high affinity receptor for IgE. sFcεRI immunoprecipitates as a protein of ∼40 kDa and contains an intact IgE-binding site. In human serum, sFcεRI is found as a soluble free IgE receptor as well as a complex with IgE. Using a newly established ELISA, we show that serum sFcεRI levels correlate with serum IgE in patients with elevated IgE. We also show that serum of individuals with normal IgE levels can be found to contain high levels of sFcεRI. After IgE-antigen-mediated crosslinking of surface FcεRI, we detect sFcεRI in the exosome-depleted, soluble fraction of cell culture supernatants. We further show that sFcεRI can block binding of IgE to FcεRI expressed at the cell surface. In summary, we here describe the alpha-chain of FcεRI as a circulating soluble IgE receptor isoform in human serum