Proving Expected Sensitivity of Probabilistic Programs with Randomized Variable-Dependent Termination Time

The notion of program sensitivity (aka Lipschitz continuity) specifies that changes in the program input result in proportional changes to the program output. For probabilistic programs the notion is naturally extended to expected sensitivity. A previous approach develops a relational program logic framework for proving expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded. In this work, we consider probabilistic while loops where the number of iterations is not fixed, but randomized and depends on the initial input values. We present a sound approach for proving expected sensitivity of such programs. Our sound approach is martingale-based and can be automated through existing martingale-synthesis algorithms. Furthermore, our approach is compositional for sequential composition of while loops under a mild side condition. We demonstrate the effectiveness of our approach on several classical examples from Gambler's Ruin, stochastic hybrid systems and stochastic gradient descent. We also present experimental results showing that our automated approach can handle various probabilistic programs in the literature

The spin alignment of vector mesons with light front quarks

The global spin alignment of the vector meson has been observed in relativistic heavy ion collisions, but is still on hot debates in the theoretical community. Here we propose to apply the light front framework to explain this phenomenon since the light front form explicitly describes the hadron spin including both the quark spin and the orbital angular momentum. After applying the light front spinor, we find that the spin alignment in the polarization of vector mesons with $\rho_{00}>1/3$ can be naturally manifested and in particular, the obtained spin alignment for $\phi$ meson is in good agreement with the experimental data. This implies that to explain the spin alignment it is important to properly include the contribution from the gluon interactions that are presented in terms of the orbital angular momentum of the hadron bound state.Comment: 7 pages, 2 figure

An Algebraic Method to Fidelity-based Model Checking over Quantum Markov Chains

Fidelity is one of the most widely used quantities in quantum information that measure the distance of quantum states through a noisy channel. In this paper, we introduce a quantum analogy of computation tree logic (CTL) called QCTL, which concerns fidelity instead of probability in probabilistic CTL, over quantum Markov chains (QMCs). Noisy channels are modelled by super-operators, which are specified by QCTL formulas; the initial quantum states are modelled by density operators, which are left parametric in the given QMC. The problem is to compute the minimumfidelity over all initial states for conservation. We achieve it by a reduction to quantifier elimination in the existential theory of the reals. The method is absolutely exact, so that QCTL formulas are proven to be decidable in exponential time. Finally, we implement the proposed method and demonstrate its effectiveness via a quantum IPv4 protocol

Antiviral activities and applications of ribosomally synthesized and post-translationally modified peptides (RiPPs)

The emergence and re-emergence of viral epidemics and the risks of antiviral drug resistance are a serious threat to global public health. New options to supplement or replace currently used drugs for antiviral therapy are urgently needed. The research in the field of ribosomally synthesized and post-translationally modified peptides (RiPPs) has been booming in the last few decades, in particular in view of their strong antimicrobial activities and high stability. The RiPPs with antiviral activity, especially those against enveloped viruses, are now also gaining more interest. RiPPs have a number of advantages over small molecule drugs in terms of specificity and affinity for targets, and over protein-based drugs in terms of cellular penetrability, stability and size. Moreover, the great engineering potential of RiPPs provides an efficient way to optimize them as potent antiviral drugs candidates. These intrinsic advantages underscore the good therapeutic prospects of RiPPs in viral treatment. With the aim to highlight the underrated antiviral potential of RiPPs and explore their development as antiviral drugs, we review the current literature describing the antiviral activities and mechanisms of action of RiPPs, discussing the ongoing efforts to improve their antiviral potential and demonstrate their suitability as antiviral therapeutics. We propose that antiviral RiPPs may overcome the limits of peptide-based antiviral therapy, providing an innovative option for the treatment of viral disease

Wrinkling of a film/substrate bilayer with periodic material properties: An assessment of the Winkler foundation model

The Winkler foundation model is often used to analyze the wrinkling of a film/substrate bilayer under compression, and it can be rigorously justified when both the film and substrate are homogeneous and the film is much stiffer than the substrate. We assess the validity of this model when the substrate is still homogeneous but the film has periodic material properties in the direction parallel to the interface. More precisely, we assume that each unit cell is piecewise homogeneous, and each piece can be described by the Euler-Bernoulli beam theory. We provide analytical results for the critical compression when the substrate is viewed as a Winkler foundation with stiffness modeled either approximately (as in some previous studies) or exactly (using the Floquet theory). The analytical results are then compared with those from Abaqus simulations based on the three-dimensional nonlinear elasticity theory in order to assess the validity of the Euler-Bernoulli beam theory and the Winkler foundation model in the current context

Proving expected sensitivity of probabilistic programs with randomized variable-dependent termination time

The notion of program sensitivity (aka Lipschitz continuity) specifies that changes in the program input result in proportional changes to the program output. For probabilistic programs the notion is naturally extended to expected sensitivity. A previous approach develops a relational program logic framework for proving expected sensitivity of probabilistic while loops, where the number of iterations is fixed and bounded. In this work, we consider probabilistic while loops where the number of iterations is not fixed, but randomized and depends on the initial input values. We present a sound approach for proving expected sensitivity of such programs. Our sound approach is martingale-based and can be automated through existing martingale-synthesis algorithms. Furthermore, our approach is compositional for sequential composition of while loops under a mild side condition. We demonstrate the effectiveness of our approach on several classical examples from Gambler's Ruin, stochastic hybrid systems and stochastic gradient descent. We also present experimental results showing that our automated approach can handle various probabilistic programs in the literature

A Sample-Driven Solving Procedure for the Repeated Reachability of Quantum CTMCs

Reachability analysis plays a central role in system design and verification. The reachability problem, denoted $\Diamond^J\,\Phi$, asks whether the system will meet the property $\Phi$ after some time in a given time interval $J$. Recently, it has been considered on a novel kind of real-time systems -- quantum continuous-time Markov chains (QCTMCs), and embedded into the model-checking algorithm. In this paper, we further study the repeated reachability problem in QCTMCs, denoted $\Box^I\,\Diamond^J\,\Phi$, which concerns whether the system starting from each \emph{absolute} time in $I$ will meet the property $\Phi$ after some coming \emph{relative} time in $J$. First of all, we reduce it to the real root isolation of a class of real-valued functions (exponential polynomials), whose solvability is conditional to Schanuel's conjecture being true. To speed up the procedure, we employ the strategy of sampling. The original problem is shown to be equivalent to the existence of a finite collection of satisfying samples. We then present a sample-driven procedure, which can effectively refine the sample space after each time of sampling, no matter whether the sample itself is successful or conflicting. The improvement on efficiency is validated by randomly generated instances. Hence the proposed method would be promising to attack the repeated reachability problems together with checking other $\omega$-regular properties in a wide scope of real-time systems

Enhanced heterologous protein productivity by genome reduction in Lactococcus lactis NZ9000

Background: The implementation of novel chassis organisms to be used as microbial cell factories in industrial applications is an intensive research field. Lactococcus lactis, which is one of the most extensively studied model organisms, exhibits superior ability to be used as engineered host for fermentation of desirable products. However, few studies have reported about genome reduction of L. lactis as a clean background for functional genomic studies and a model chassis for desirable product fermentation. Results: Four large nonessential DNA regions accounting for 2.83% in L. lactis NZ9000 (L. lactis 9 k) genome (2,530,294 bp) were deleted using the Cre-loxP deletion system as the first steps toward a minimized genome in this study. The mutants were compared with the parental strain in several physiological traits and evaluated as microbial cell factories for heterologous protein production (intracellular and secretory expression) with the red fluorescent protein (RFP) and the bacteriocin leucocin C (LecC) as reporters. The four mutants grew faster, yielded enhanced biomass, achieved increased adenosine triphosphate content, and diminished maintenance demands compared with the wild strain in the two media tested. In particular, L. lactis 9 k-4 with the largest deletion was identified as the optimum candidate host for recombinant protein production. With nisin induction, not only the transcriptional efficiency but also the production levels of the expressed reporters were approximately three-to fourfold improved compared with the wild strain. The expression of lecC gene controlled with strong constitutive promoters P5 and P8 in L. lactis 9 k-4 was also improved significantly. Conclusions: The genome-streamlined L. lactis 9 k-4 outcompeted the parental strain in several physiological traits assessed. Moreover, L. lactis 9 k-4 exhibited good properties as platform organism for protein production. In future works, the genome of L. lactis will be maximally reduced by using our specific design to provide an even more clean background for functional genomics studies than L. lactis 9 k-4 constructed in this study. Furthermore, an improved background will be potentially available for use in biotechology.Peer reviewe