Encoding inductive invariants as barrier certificates: synthesis via difference-of-convex programming

A barrier certificate often serves as an inductive invariant that isolates an unsafe region from the reachable set of states, and hence is widely used in proving safety of hybrid systems possibly over an infinite time horizon. We present a novel condition on barrier certificates, termed the invariant barrier-certificate condition, that witnesses unbounded-time safety of differential dynamical systems. The proposed condition is the weakest possible one to attain inductive invariance. We show that discharging the invariant barrier-certificate condition -- thereby synthesizing invariant barrier certificates -- can be encoded as solving an optimization problem subject to bilinear matrix inequalities (BMIs). We further propose a synthesis algorithm based on difference-of-convex programming, which approaches a local optimum of the BMI problem via solving a series of convex optimization problems. This algorithm is incorporated in a branch-and-bound framework that searches for the global optimum in a divide-and-conquer fashion. We present a weak completeness result of our method, namely, a barrier certificate is guaranteed to be found (under some mild assumptions) whenever there exists an inductive invariant (in the form of a given template) that suffices to certify safety of the system. Experimental results on benchmarks demonstrate the effectiveness and efficiency of our approach.Comment: To be published in Inf. Comput. arXiv admin note: substantial text overlap with arXiv:2105.1431

Impact of participation in the Adalimumab (Humira) patient support program on rheumatoid arthritis treatment course : results from the PASSION study

Introduction: Patients with rheumatoid arthritis (RA) who are treated with adalimumab (ADA) are offered a proprietary patient support program (PSP, AbbVie Care (R)). The main objective of this study was to examine the effectiveness of ADA on RA treatment course over time in the context of PSP utilization. Methods: PASSION was a 78-week post-marketing observational study of RA patients with an insufficient response to >= 1 DMARD newly initiating ADA in routine clinical care that was conducted in Europe, Israel, Mexico, Puerto Rico, and Australia. One prior biologic DMARD was allowed. The primary endpoint was percentage of patients achieving the minimal clinically important difference (MCID; improvement of >= 0.22 compared to baseline) in Health Assessment Questionnaire (HAQ) Disability Index (HAQ-DI) at week 78. Additionally, multiple clinical and patient-reported outcomes (PROs) were evaluated over time. Patients were categorized based on their participation in the PSP: ever (PSP users) vs. never (PSP non-users). Safety events were monitored throughout the study. Results: Overall, 42.8% of PSP users achieved the MCID in HAQ-DI at week 78 (improvement of at least 0.22 compared to baseline). From 1025 enrolled, 48.7% of patients were PSP users while treated with ADA. The percentage of patients achieving MCID in the HAQ-DI was higher in PSP users vs. PSP non-users (48.1 vs. 37.8%) at week 78 (p < 0.001, NRI). Most of the studied clinical outcomes and PROs showed significant improvements (p < 0.05) from baseline to week 78 favoring PSP users over PSP non-users. Conclusions: In patients with moderate-to-severe RA who initiated ADA, improvements in clinical, functional, and PROs were achieved in real-world settings with significantly greater improvements among PSP users in comparison with PSP non-users

Lower Bounds for Possibly Divergent Probabilistic Programs

We present a new proof rule for verifying lower bounds on quantities of probabilistic programs. Our proof rule is not confined to almost-surely terminating programs -- as is the case for existing rules -- and can be used to establish non-trivial lower bounds on, e.g., termination probabilities and expected values, for possibly divergent probabilistic loops, e.g., the well-known three-dimensional random walk on a lattice

Realization of two-dimensional crystal of ions in a monolithic Paul trap

We present a simple Paul trap that stably accommodates up to a couple of dozens of \ensuremath{^{171}\mathrm{Yb}^+~} ions in a stationary two-dimensional lattice. The trap is constructed on a single plate of gold-plated laser-machined alumina and can produce a pancake-like pseudo-potential that makes ions form a self-assembly two-dimensional crystal which locates on the plane composed of axial and one of the transverse axes with around 5 $\mu$m spacing. We use Raman laser beams to coherently manipulate these ion-qubits where the net propagation direction is perpendicular to the plane of the crystal and micromotion. We perform the coherent operations and study the spectrum of vibrational modes through globally addressed Raman laser-beams on a dozen of ions in the two-dimensional crystal. We measure the amplitude of micro-motion by comparing the strengths of carrier and micro-motion sideband transitions with three ions, where the micro-motion amplitude is similar to that of a single ion. The spacings of ions are small enough for large coupling strengths, which is a favorable condition for two-dimensional quantum simulation.Comment: 10 pages, 9 figure

Jianpi Bushen, a Traditional Chinese Medicine Therapy, Combined with Chemotherapy for Gastric Cancer Treatment: A Meta-Analysis of Randomized Controlled Trials

Objective. To investigate the effects of Jianpi Bushen (JPBS), a traditional Chinese medicine that is used to invigorate the spleen and tonify the kidney, combined with chemotherapy for the treatment of gastric cancer. Methods. Literature retrieval was performed in PubMed, EMBASE, Cochrane Library, MEDLINE, CNKI, Wanfang Data Information Site, and VIP from inception to October 2017. Randomized controlled trials to evaluate the effects of JPBS combined with chemotherapy were identified. The primary reported outcomes were KPS (Karnofsky Performance Status), clinical curative efficiency, immune function, blood system, and nonhematologic system. Review Manager 5.3 (RevMan 5.3) was used for data analysis, and the quality of the studies was also appraised. Results. A total of 26 studies were included with 3098 individuals. The results of the meta-analysis indicated that treatment of gastric cancer with the combination of JPBS and chemotherapy resulted in better outcomes compared to chemotherapy alone. Conclusion. Evidence from the meta-analysis suggested that JPBS combined with chemotherapy has a positive effect on gastric cancer treatment. However, additional rigorously designed and large sample randomized controlled trials are required to confirm the efficacy and safety of this treatment