The Optimal Uncertainty Algorithm in the Mystic Framework

We have recently proposed a rigorous framework for Uncertainty Quantification (UQ) in which UQ objectives and assumption/information set are brought into the forefront, providing a framework for the communication and comparison of UQ results. In particular, this framework does not implicitly impose inappropriate assumptions nor does it repudiate relevant information. This framework, which we call Optimal Uncertainty Quantification (OUQ), is based on the observation that given a set of assumptions and information, there exist bounds on uncertainties obtained as values of optimization problems and that these bounds are optimal. It provides a uniform environment for the optimal solution of the problems of validation, certification, experimental design, reduced order modeling, prediction, extrapolation, all under aleatoric and epistemic uncertainties. OUQ optimization problems are extremely large, and even though under general conditions they have finite-dimensional reductions, they must often be solved numerically. This general algorithmic framework for OUQ has been implemented in the mystic optimization framework. We describe this implementation, and demonstrate its use in the context of the Caltech surrogate model for hypervelocity impact

Optimal Uncertainty Quantification

We propose a rigorous framework for Uncertainty Quantification (UQ) in which the UQ objectives and the assumptions/information set are brought to the forefront. This framework, which we call Optimal Uncertainty Quantification (OUQ), is based on the observation that, given a set of assumptions and information about the problem, there exist optimal bounds on uncertainties: these are obtained as extreme values of well-defined optimization problems corresponding to extremizing probabilities of failure, or of deviations, subject to the constraints imposed by the scenarios compatible with the assumptions and information. In particular, this framework does not implicitly impose inappropriate assumptions, nor does it repudiate relevant information. Although OUQ optimization problems are extremely large, we show that under general conditions, they have finite-dimensional reductions. As an application, we develop Optimal Concentration Inequalities (OCI) of Hoeffding and McDiarmid type. Surprisingly, contrary to the classical sensitivity analysis paradigm, these results show that uncertainties in input parameters do not necessarily propagate to output uncertainties. In addition, a general algorithmic framework is developed for OUQ and is tested on the Caltech surrogate model for hypervelocity impact, suggesting the feasibility of the framework for important complex systems

Recolonization of Raoul Island by Kermadec red-crowned parakeets Cyanoramphus novaezelandiae cyanurus after eradication of invasive predators, Kermadec Islands archipelago, New Zealand

The Kermadec red-crowned parakeet Cyanoramphus novaezelandiae was driven to extinction on Raoul Island over 150 years ago by introduced cats Felis catus and rats (Rattus norvegicus and R. exulans). These predators were eradicated from the island (2,938 ha) between 2002-04 during the world’s largest multispecies eradication project. In 2008 we documented a unique recolonisation event when parakeets were observed to have returned to Raoul, presumably from a nearby island group, The Herald Islets (51 ha). We captured and aged 100 parakeets, of which 44% were born in 2008, and breeding was observed on Raoul Island. This represents the first evidence of nesting of this species on Raoul Island since 1836. Our findings highlight the global conservation potential for island avifaunas by prioritising eradication areas through consideration of proximity of remnant populations to target management locations, instead of the classical translocation approach alone. The natural recolonization of parakeets on Raoul Island from a satellite source population is to our knowledge, a first for parrot conservation and the first documented population expansion and island recolonization of a parrot species after removal of invasive predators

Integrable two-channel p_x+ip_y-wave superfluid model

We present a new two-channel integrable model describing a system of spinless fermions interacting through a p-wave Feshbach resonance. Unlike the BCS-BEC crossover of the s-wave case, the p-wave model has a third order quantum phase transition. The critical point coincides with the deconfinement of a single molecule within a BEC of bound dipolar molecules. The exact many-body wavefunction provides a unique perspective of the quantum critical region suggesting that the size of the condensate wavefunction, that diverges logarithmically with the chemical potential, could be used as an experimental indicator of the phase transition.Comment: 4 pages, 4 figure

Optimal uncertainty quantification for legacy data observations of Lipschitz functions

We consider the problem of providing optimal uncertainty quantification (UQ) --- and hence rigorous certification --- for partially-observed functions. We present a UQ framework within which the observations may be small or large in number, and need not carry information about the probability distribution of the system in operation. The UQ objectives are posed as optimization problems, the solutions of which are optimal bounds on the quantities of interest; we consider two typical settings, namely parameter sensitivities (McDiarmid diameters) and output deviation (or failure) probabilities. The solutions of these optimization problems depend non-trivially (even non-monotonically and discontinuously) upon the specified legacy data. Furthermore, the extreme values are often determined by only a few members of the data set; in our principal physically-motivated example, the bounds are determined by just 2 out of 32 data points, and the remainder carry no information and could be neglected without changing the final answer. We propose an analogue of the simplex algorithm from linear programming that uses these observations to offer efficient and rigorous UQ for high-dimensional systems with high-cardinality legacy data. These findings suggest natural methods for selecting optimal (maximally informative) next experiments.Comment: 38 page

Comparative aspects of phytase and xylanase effects on performance, mineral digestibility, and ileal phytate degradation in broilers and turkeys

Two experiments were performed, using broilers or turkeys, each utilizing a 3 × 2 factorial arrangement, to compare their response to phytase and xylanase supplementation with growth performance, nutrient digestibility, and ileal phytate degradation as response criteria. For both experiments, 960 Ross 308 or 960 BUT 10 (0-day-old) birds were allocated to 6 treatments: (1) control diet, containing phytase at 500 FTU/kg; (2) the control diet with xylanase (16,000 BXU/kg); (3) the control diet supplemented on top with phytase (1,500 FTU/kg); (4) diet supplemented with 1,500 FTU/kg phytase and xylanase (16,000 BXU/kg); (5) the control diet supplemented with phytase (3,000 FTU/kg); and (6) diet supplemented with 3,000 FTU/kg phytase and xylanase (16,000 BXU/kg). Each treatment had 8 replicates of 20 birds each. Water and diets based on wheat, soybean meal, oilseed rape meal, and barley were available ad libitum. Body weight gain and feed intake were measured from 0 to 28 D, and feed conversion ratio (FCR) corrected for mortality was calculated. Ileal digestibility for dry matter and minerals on day 7 and 28 were analyzed in addition to levels of inositol phosphate esters (InsP6-3) and myo-inositol. Statistical comparisons were performed using ANOVA. Xylanase supplementation improved 28D FCR in broilers and turkeys. Increasing doses of phytase reduced FI and improved FCR only in broilers. In broilers, the age × phytase interaction for phosphorous digestibility showed that increasing phytase dose was more visible on day 7, than on day 28. Mineral digestibility was lower in 28-day-old turkey compared with 7-day-old turkey. InsP6 disappearance increased with increasing phytase levels in both species, with lower levels analyzed in turkeys. InsP6 disappearance was greater in younger turkeys (day 7 compared with day 28). In conclusion, although broilers and turkeys shared several similarities in their growth and nutrient utilization responses, the outcomes of the 2 trials also differed in many aspects. Whether this is because of difference in diets (InsP or Ca level) or differences between species needs further investigation

A combinatorial approach of Proteomics and Systems Biology in unravelling the mechanisms of acute kidney injury (AKI): involvement of NMDA receptor GRIN1 in murine AKI

BACKGROUND: Acute kidney injury (AKI) is a frequent condition in hospitalised patients undergoing major surgery or the critically ill and is associated with increased mortality. Based on the volume of the published literature addressing this condition, reporting both supporting as well as conflicting molecular evidence, it is apparent that a comprehensive analysis strategy is required to understand and fully delineate molecular events and pathways which can be used to describe disease induction and progression as well as lead to a more targeted approach in intervention therapies.<p></p> RESULTS: We used a Systems Biology approach coupled with a de-novo high-resolution proteomic analysis of kidney cortex samples from a mouse model of folic acid-induced AKI (12 animals in total) and show comprehensive mapping of signalling cascades, gene activation events and metabolite interference by mapping high-resolution proteomic datasets onto a de-novo hypothesis-free dataspace. The findings support the involvement of the glutamatergic signalling system in AKI, induced by over-activation of the N-methyl-D-aspartate (NMDA)-receptor leading to apoptosis and necrosis by Ca2+-influx, calpain and caspase activation, and co-occurring reactive oxygen species (ROS) production to DNA fragmentation and NAD-rundown. The specific over-activation of the NMDA receptor may be triggered by the p53-induced protein kinase Dapk1, which is a known non-reversible cell death inducer in a neurological context. The pathway mapping is consistent with the involvement of the Renin-Angiotensin Aldosterone System (RAAS), corticoid and TNFalpha signalling, leading to ROS production and gene activation through NFkappaB, PPARgamma, SMAD and HIF1alpha trans-activation, as well as p53 signalling cascade activation. Key elements of the RAAS-glutamatergic axis were assembled as a novel hypothetical pathway and validated by immunohistochemistry.<p></p> CONCLUSIONS: This study shows to our knowledge for the first time in a molecular signal transduction pathway map how AKI is induced, progresses through specific signalling cascades that may lead to end-effects such as apoptosis and necrosis by uncoupling of the NMDA receptor. Our results can potentially pave the way for a targeted pharmacological intervention in disease progression or induction.<p></p&gt