An Exact Formula for the Average Run Length to False Alarm of the Generalized Shiryaev-Roberts Procedure for Change-Point Detection under Exponential Observations

We derive analytically an exact closed-form formula for the standard minimax Average Run Length (ARL) to false alarm delivered by the Generalized Shiryaev-Roberts (GSR) change-point detection procedure devised to detect a shift in the baseline mean of a sequence of independent exponentially distributed observations. Specifically, the formula is found through direct solution of the respective integral (renewal) equation, and is a general result in that the GSR procedure's headstart is not restricted to a bounded range, nor is there a "ceiling" value for the detection threshold. Apart from the theoretical significance (in change-point detection, exact closed-form performance formulae are typically either difficult or impossible to get, especially for the GSR procedure), the obtained formula is also useful to a practitioner: in cases of practical interest, the formula is a function linear in both the detection threshold and the headstart, and, therefore, the ARL to false alarm of the GSR procedure can be easily computed.Comment: 9 pages; Accepted for publication in Proceedings of the 12-th German-Polish Workshop on Stochastic Models, Statistics and Their Application

Replacing the Transfusion of 1-2 Units of Blood with Plasma Expanders that Increase Oxygen Delivery Capacity: Evidence from Experimental Studies.

At least a third of the blood supply in the world is used to transfuse 1-2 units of packed red blood cells for each intervention and most clinical trials of blood substitutes have been carried out at this level of oxygen carrying capacity (OCC) restoration. However, the increase of oxygenation achieved is marginal or none at all for molecular hemoglobin (Hb) products, due to their lingering vasoactivity. This has provided the impetus for the development of "oxygen therapeutics" using Hb-based molecules that have high oxygen affinity and target delivery of oxygen to anoxic areas. However it is still unclear how these oxygen carriers counteract or mitigate the functional effects of anemia due to obstruction, vasoconstriction and under-perfusion. Indeed, they are administered as a low dosage/low volume therapeutic Hb (subsequently further diluted in the circulatory pool) and hence induce extremely small OCC changes. Hyperviscous plasma expanders provide an alternative to oxygen therapeutics by increasing the oxygen delivery capacity (ODC); in anemia they induce supra-perfusion and increase tissue perfusion (flow) by as much as 50%. Polyethylene glycol conjugate albumin (PEG-Alb) accomplishes this by enhancing the shear thinning behavior of diluted blood, which increases microvascular endothelial shear stress, causes vasodilation and lowering peripheral vascular resistance thus facilitating cardiac function. Induction of supra-perfusion takes advantage of the fact that ODC is the product of OCC and blood flow and hence can be maintained by increasing either or both. Animal studies suggest that this approach may save a considerable fraction of the blood supply. It has an additional benefit of enhancing tissue clearance of toxic metabolites

Lagrangian Liouville models of multiphase flows with randomly forced inertial particles

Eulerian-Lagrangian models of particle-laden (multiphase) flows describe fluid flow and particle dynamics in the Eulerian and Lagrangian frameworks respectively. Regardless of whether the flow is turbulent or laminar, the particle dynamics is stochastic because the suspended particles are subjected to random forces. We use a polynomial chaos expansion (PCE), rather than a postulated constitutive law, to capture structural and parametric uncertainties in the particles' forcing. The stochastic particle dynamics is described by a joint probability density function (PDF) of a particle's position and velocity and random coefficients in the PCE. We deploy the method of distributions (MoD) to derive a deterministic (Liouville-type) partial-differential equation for this PDF. We reformulate this PDF equation in a Lagrangian form, obtaining PDF flow maps and tracing events and their probability in the phase space. That is accomplished via a new high-order spectral scheme, which traces, marginalizes and computes moments of the high-dimensional joint PDF and comports with high-order carrier-phase solvers. Our approach has lower computational cost than either high-order Eulerian solvers or Monte Carlo methods, is not subjected to a CFL condition, does not suffer from Gibbs oscillations and does not require (order-reducing) filtering and regularization techniques. These features are demonstrated on several test cases

Self-similar Approximants of the Permeability in Heterogeneous Porous Media from Moment Equation Expansions

We use a mathematical technique, the self-similar functional renormalization, to construct formulas for the average conductivity that apply for large heterogeneity, based on perturbative expansions in powers of a small parameter, usually the log-variance $\sigma_Y^2$ of the local conductivity. Using perturbation expansions up to third order and fourth order in $\sigma_Y^2$ obtained from the moment equation approach, we construct the general functional dependence of the transport variables in the regime where $\sigma_Y^2$ is of order 1 and larger than 1. Comparison with available numerical simulations give encouraging results and show that the proposed method provides significant improvements over available expansions.Comment: Latex, 14 pages + 5 ps figure

High rate membrane-less microbial electrolysis cell for continuous hydrogen production

This study demonstrates hydrogen production in a membrane-less continuous flow microbial electrolysis cell (MEC) with a gas-phase cathode. The MEC used a carbon felt anode and a gas diffusion cathode with a Pt loading of 0.5 mg cm 122. No proton exchange membrane (PEM) was used in the setup. Instead, the electrodes were separated by a J-cloth. The absence of a PEM as well as a short distance maintained between the electrodes (0.3 mm) resulted in a low internal resistance of 19 \u3a9. Due to an improved design, the volumetric hydrogen production rate reached 6.3 LSTP View the MathML source d 121. In spite of the PEM absence, methane concentration in the gas collection chamber was below 2.1% and the presence of hydrogen in the anodic chamber was never observed.NRC publication: Ye

A Multifaceted Mathematical Approach for Complex Systems

Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significant impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee

Using biomarkers to predict TB treatment duration (Predict TB): a prospective, randomized, noninferiority, treatment shortening clinical trial

Background : By the early 1980s, tuberculosis treatment was shortened from 24 to 6 months, maintaining relapse rates of 1-2%. Subsequent trials attempting shorter durations have failed, with 4-month arms consistently having relapse rates of 15-20%. One trial shortened treatment only among those without baseline cavity on chest x-ray and whose month 2 sputum culture converted to negative. The 4-month arm relapse rate decreased to 7% but was still significantly worse than the 6-month arm (1.6%, P<0.01).  We hypothesize that PET/CT characteristics at baseline, PET/CT changes at one month, and markers of residual bacterial load will identify patients with tuberculosis who can be cured with 4 months (16 weeks) of standard treatment.Methods: This is a prospective, multicenter, randomized, phase 2b, noninferiority clinical trial of pulmonary tuberculosis participants. Those eligible start standard of care treatment. PET/CT scans are done at weeks 0, 4, and 16 or 24. Participants who do not meet early treatment completion criteria (baseline radiologic severity, radiologic response at one month, and GeneXpert-detectable bacilli at four months) are placed in Arm A (24 weeks of standard therapy). Those who meet the early treatment completion criteria are randomized at week 16 to continue treatment to week 24 (Arm B) or complete treatment at week 16 (Arm C). The primary endpoint compares the treatment success rate at 18 months between Arms B and C.Discussion: Multiple biomarkers have been assessed to predict TB treatment outcomes. This study uses PET/CT scans and GeneXpert (Xpert) cycle threshold to risk stratify participants. PET/CT scans are not applicable to global public health but could be used in clinical trials to stratify participants and possibly become a surrogate endpoint. If the Predict TB trial is successful, other immunological biomarkers or transcriptional signatures that correlate with treatment outcome may be identified. TRIAL REGISTRATION: NCT02821832

Dynamics of Wetting Fronts in Porous Media

We propose a new phenomenological approach for describing the dynamics of wetting front propagation in porous media. Unlike traditional models, the proposed approach is based on dynamic nature of the relation between capillary pressure and medium saturation. We choose a modified phase-field model of solidification as a particular case of such dynamic relation. We show that in the traveling wave regime the results obtained from our approach reproduce those derived from the standard model of flow in porous media. In more general case, the proposed approach reveals the dependence of front dynamics upon the flow regime.Comment: 4 pages, 2 figures, revte