Metastability and low lying spectra in reversible Markov chains

We study a large class of reversible Markov chains with discrete state space and transition matrix $P_N$. We define the notion of a set of {\it metastable points} as a subset of the state space \G_N such that (i) this set is reached from any point x\in \G_N without return to x with probability at least $b_N$, while (ii) for any two point x,y in the metastable set, the probability $T^{-1}_{x,y}$ to reach y from x without return to x is smaller than $a_N^{-1}\ll b_N$. Under some additional non-degeneracy assumption, we show that in such a situation: \item{(i)} To each metastable point corresponds a metastable state, whose mean exit time can be computed precisely. \item{(ii)} To each metastable point corresponds one simple eigenvalue of $1-P_N$ which is essentially equal to the inverse mean exit time from this state. The corresponding eigenfunctions are close to the indicator function of the support of the metastable state. Moreover, these results imply very sharp uniform control of the deviation of the probability distribution of metastable exit times from the exponential distribution.Comment: 44pp, AMSTe

Metastability in stochastic dynamics of disordered mean-field models

We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the problem to the properties of the rate functions of the corresponding Gibbs measures. We derive the analog of the Wentzell-Freidlin theory in this case, showing that any transition can be decomposed, with probability exponentially close to one, into a deterministic sequence of ``admissible transitions''. For these admissible transitions we give upper and lower bounds on the expected transition times that differ only by a constant. The distribution rescaled transition times are shown to converge to the exponential distribution. We exemplify our results in the context of the random field Curie-Weiss model.Comment: 73pp, AMSTE

Optimal population-level infection detection strategies for malaria control and elimination in a spatial model of malaria transmission

Mass campaigns with antimalarial drugs are potentially a powerful tool for local elimination of malaria, yet current diagnostic technologies are insufficiently sensitive to identify all individuals who harbor infections. At the same time, overtreatment of uninfected individuals increases the risk of accelerating emergence of drug resistance and losing community acceptance. Local heterogeneity in transmission intensity may allow campaign strategies that respond to index cases to successfully target subpatent infections while simultaneously limiting overtreatment. While selective targeting of hotspots of transmission has been proposed as a strategy for malaria control, such targeting has not been tested in the context of malaria elimination. Using household locations, demographics, and prevalence data from a survey of four health facility catchment areas in southern Zambia and an agent-based model of malaria transmission and immunity acquisition, a transmission intensity was fit to each household based on neighborhood age-dependent malaria prevalence. A set of individual infection trajectories was constructed for every household in each catchment area, accounting for heterogeneous exposure and immunity. Various campaign strategies (mass drug administration, mass screen and treat, focal mass drug administration, snowball reactive case detection, pooled sampling, and a hypothetical serological diagnostic) were simulated and evaluated for performance at finding infections, minimizing overtreatment, reducing clinical case counts, and interrupting transmission. For malaria control, presumptive treatment leads to substantial overtreatment without additional morbidity reduction under all but the highest transmission conditions. Selective targeting of hotspots with drug campaigns is an ineffective tool for elimination due to limited sensitivity of available field diagnostics

Metastability and small eigenvalues in Markov chains

In this letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerable greater precision as was so far available. This includes a sharp uncertainty principle relating all low-lying eigenvalues to mean times of metastable transitions, a relation between the support of eigenfunctions and the attractor of a metastable state, and sharp estimates on the convergence of probability distribution of the metastable transition times to the exponential distribution.Comment: 5pp, AMSTe

Multi sensor transducer and weight factor

A multi-sensor transducer and processing method allow insitu monitoring of the senor accuracy and transducer `health`. In one embodiment, the transducer has multiple sensors to provide corresponding output signals in response to a stimulus, such as pressure. A processor applies individual weight factors to reach of the output signals and provide a single transducer output that reduces the contribution from inaccurate sensors. The weight factors can be updated and stored. The processor can use the weight factors to provide a `health` of the transducer based upon the number of accurate versus in-accurate sensors in the transducer

Malaria elimination campaigns in the Lake Kariba region of Zambia: a spatial dynamical model

Background As more regions approach malaria elimination, understanding how different interventions interact to reduce transmission becomes critical. The Lake Kariba area of Southern Province, Zambia, is part of a multi-country elimination effort and presents a particular challenge as it is an interconnected region of variable transmission intensities. Methods In 2012-13, six rounds of mass-screen-and-treat drug campaigns were carried out in the Lake Kariba region. A spatial dynamical model of malaria transmission in the Lake Kariba area, with transmission and climate modeled at the village scale, was calibrated to the 2012-13 prevalence survey data, with case management rates, insecticide-treated net usage, and drug campaign coverage informed by surveillance. The model was used to simulate the effect of various interventions implemented in 2014-22 on reducing regional transmission, achieving elimination by 2022, and maintaining elimination through 2028. Findings The model captured the spatio-temporal trends of decline and rebound in malaria prevalence in 2012-13 at the village scale. Simulations predicted that elimination required repeated mass drug administrations coupled with simultaneous increase in net usage. Drug campaigns targeted only at high-burden areas were as successful as campaigns covering the entire region. Interpretation Elimination in the Lake Kariba region is possible through coordinating mass drug campaigns with high-coverage vector control. Targeting regional hotspots is a viable alternative to global campaigns when human migration within an interconnected area is responsible for maintaining transmission in low-burden areas

Thermal ageing phenomena and strategies towards reactivation of NO x - storage catalysts

The thermal ageing and reactivation of Ba/CeO2 and Ba/Al2O3 based NO x -storage/ reduction (NSR) catalysts was studied on model catalysts and catalyst systems at the engine. The mixed oxides BaAl2O4 and BaCeO3, which lower the storage activity, are formed during ageing above 850°C and 900°C, respectively. Interestingly, the decomposition of BaCeO3 in an atmosphere containing H2O/NO2 leads again to NO x -storage active species, as evidenced by comparison of fresh, aged and reactivated Pt-Ba/CeO2 based model catalysts. This can be technically exploited, particularly for the Ba/CeO2 catalysts, as reactivation studies on thermally aged Ba/CeO2 and Ba/Al2O3 based NSR catalysts on an engine bench showed. An on-board reactivation procedure is presented, that improved the performance of a thermally aged catalyst significantl

Three-Dimensional Venturi Sensor for Measuring Extreme Winds

A three-dimensional (3D) Venturi sensor is being developed as a compact, rugged means of measuring wind vectors having magnitudes of as much as 300 mph (134 m/s). This sensor also incorporates auxiliary sensors for measuring temperature from -40 to +120 F (-40 to +49 C), relative humidity from 0 to 100 percent, and atmospheric pressure from 846 to 1,084 millibar (85 to 108 kPa). Conventional cup-and-vane anemometers are highly susceptible to damage by both high wind forces and debris, due to their moving parts and large profiles. In addition, they exhibit slow recovery times contributing to an inaccurately high average-speed reading. Ultrasonic and hot-wire anemometers overcome some of the disadvantages of the cup and-vane anemometers, but they have other disadvantageous features, including limited dynamic range and susceptibility to errors caused by external acoustic noise and rain. In contrast, the novel 3D Venturi sensor is less vulnerable to wind damage because of its smaller profile and ruggedness. Since the sensor has no moving parts, it provides increased reliability and lower maintenance costs. It has faster response and recovery times to changing wind conditions than traditional systems. In addition, it offers wide dynamic range and is expected to be relatively insensitive to rain and acoustic energy. The Venturi effect in this sensor is achieved by the mirrored double-inflection curve, which is then rotated 360 to create the desired detection surfaces. The curve is optimized to provide a good balance of pressure difference between sensor ports and overall maximum fluid velocity while in the shape. Four posts are used to separate the two shapes, and their size and location were chosen to minimize effects on the pressure measurements. The 3D Venturi sensor has smart software algorithms to map the wind pressure exerted on the surfaces of the design. Using Bernoulli's equation, the speed of the wind is calculated from the differences among the pressure readings at the various ports. The direction of the wind is calculated from the spatial distribution and magnitude of the pressure readings. All of the pressure port sizes and locations have been optimized to minimize measurement errors and to reside in areas demonstrating a stable pressure reading proportional to the velocity range