Parallel symbolic state-space exploration is difficult, but what is the alternative?

State-space exploration is an essential step in many modeling and analysis problems. Its goal is to find the states reachable from the initial state of a discrete-state model described. The state space can used to answer important questions, e.g., "Is there a dead state?" and "Can N become negative?", or as a starting point for sophisticated investigations expressed in temporal logic. Unfortunately, the state space is often so large that ordinary explicit data structures and sequential algorithms cannot cope, prompting the exploration of (1) parallel approaches using multiple processors, from simple workstation networks to shared-memory supercomputers, to satisfy large memory and runtime requirements and (2) symbolic approaches using decision diagrams to encode the large structured sets and relations manipulated during state-space generation. Both approaches have merits and limitations. Parallel explicit state-space generation is challenging, but almost linear speedup can be achieved; however, the analysis is ultimately limited by the memory and processors available. Symbolic methods are a heuristic that can efficiently encode many, but not all, functions over a structured and exponentially large domain; here the pitfalls are subtler: their performance varies widely depending on the class of decision diagram chosen, the state variable order, and obscure algorithmic parameters. As symbolic approaches are often much more efficient than explicit ones for many practical models, we argue for the need to parallelize symbolic state-space generation algorithms, so that we can realize the advantage of both approaches. This is a challenging endeavor, as the most efficient symbolic algorithm, Saturation, is inherently sequential. We conclude by discussing challenges, efforts, and promising directions toward this goal

Anti-mullerian hormone and antral follicle count as predictors of ovarian response in assisted reproduction

Objective: The objective of this study was to test the hypothesis that AMH and antral follicle count (AFC) are good predictors of ovarian response to controlled ovarian stimulation and to compare them. Materials and Methods: This observational cross-sectional study included 56 subjects aged between 25 and 42 years who were enrolled between 1 st January and 31 st December 2010 for their first intracytoplasmic sperm injection (ICSI) program. Baseline hormone profiles including serum levels of Estradiol (E2), Follicle-stimulating hormone (FSH), Luteinizing hormone (LH), and Anti-mullerian Hormone (AMH) were determined on day 3 of the previous cycle. The antral follicle count measurements were performed on days 3-5 of the same menstrual cycle. Antral follicles within the bilateral ovaries between 2-6 mm were recorded. The subjects were treated with long protocol for ovarian stimulation. Ovulation was induced with 10,000 IU of human chorionic gonadotropin (hCG) when at least 3 follicles attained the size of more than 17 mm. Transvaginal oocyte retrieval was performed under ultrasound guidance 36 hours after hCG administration. An oocyte count less than 4 and absence of follicular growth with controlled ovarian hyper stimulation was considered as poor ovarian response. Oocyte count of 4 or more was considered as normal ovarian response. Results: Statistical analysis was performed using SPSS software trail version 16.0. Subjects were divided into 2 groups, depending on the ovarian response. The mean oocyte counts were 12.27 ± 6.06 and 2.22 ± 1.24 in normal and poor responders, respectively, ( P = 001). Multiple regression analysis revealed AMH and antral follicle count as predictors of ovarian response (β coefficient ± SE for AMH was 1.618 ± 0.602 ( P = 0.01) and for AFC, it was, 0.528 ± 0.175 ( P = 0.004). AFC was found to be a better predictor of ovarian response compared to AMH in controlled ovarian hyper stimulation. Conclusion: The observations made in this study revealed that both AMH and AFC are good predictors of ovarian response; AFC being a better predictor compared to AMH

Distributed Binary Decision Diagrams for Symbolic Reachability

Decision diagrams are used in symbolic verification to concisely represent state spaces. A crucial symbolic verification algorithm is reachability: systematically exploring all reachable system states. Although both parallel and distributed reachability algorithms exist, a combined solution is relatively unexplored. This paper contributes BDD-based reachability algorithms targeting compute clusters: high-performance networks of multi-core machines. The proposed algorithms may use the entire memory of every machine, allowing larger models to be processed while increasing performance by using all available computational power. To do this effectively, a distributed hash table, cluster-based work stealing algorithms, and several caching structures have been designed that all utilise the newest networking technology. The approach is evaluated extensively on a large collection of models, thereby demonstrating speedups up to 51,1x with 32 machines. The proposed algorithms not only benefit from the large amounts of available memory on compute clusters, but also from all available computational resources

GlycA Is a Novel Biomarker of Inflammation and Subclinical Cardiovascular Disease in Psoriasis.

RATIONALE: GlycA, an emerging inflammatory biomarker, predicted cardiovascular events in population-based studies. Psoriasis, an inflammatory disease associated with increased cardiovascular risk, provides a model to study inflammatory biomarkers in cardiovascular disease (CVD). Whether GlycA associates with psoriasis and how it predicts subclinical CVD beyond hsCRP in psoriasis is unknown. OBJECTIVE: To investigate the relationships between GlycA and psoriasis, and between GlycA and subclinical CVD. METHODS AND RESULTS: Psoriasis patients and controls (n=412) participated in a two-stage study. We measured GlycA by NMR spectroscopy. NIH participants underwent 18-FDG PET/CT scans to assess vascular inflammation (VI) and coronary CT angiography to quantify coronary artery disease (CAD) burden. Psoriasis cohorts were young (mean age=47.9), with low cardiovascular risk and moderate skin disease. HsCRP and GlycA were increased in psoriasis compared to controls [GlycA: (PENN: 408.8±75.4 vs. 289.4±60.2, p<0.0001, NIH: 415.8±63.2 vs. 346.2±46, p<0.0001)] and demonstrated a dose-response with psoriasis severity. In stage 2, VI (β=0.36, p<0.001) and CAD (β=0.29, p=0.004) associated with GlycA beyond CV risk factors in psoriasis. In ROC analysis, GlycA added value in predicting VI (p=0.01) and CAD (p<0.01). Finally, initiating anti-TNF therapy (n=16) reduced psoriasis severity (p<0.001), GlycA (463.7±92.5 vs. 370.1±78.5; p<0.001) and VI (1.93±0.36 vs. 1.76±0.19; p<0.001), while GlycA remained associated with VI (β=0.56, p<0.001) post-treatment. CONCLUSIONS: GlycA associated with psoriasis severity and subclinical CVD beyond traditional CV risk and hsCRP. Moreover, psoriasis treatment reduced GlycA and VI. These findings support the potential utility of GlycA in subclinical CVD risk assessment in psoriasis and potentially other inflammatory diseases