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We calculate the force on a periodic array of spheres in a viscous flow at small Reynolds number and for small volume fraction. This generalizes the known results for the force on a periodic array due to Stokes flow (zero Reynolds number) and the Oseen correction to the Stokes formula for the force on a single sphere (zero volume fraction). We use a generalization of Hasimoto's approach that is based on an analysis of periodic Green's functions. We compare our results to the phenomenological ones of Kaneda for viscous flow past a random array of spheres.

The main accomplishments in this research project were (i) the development of a theory for virtual source imaging with passive arrays that allows imaging in very complex media using correlation based methods, and (ii) motion estimation in synthetic aperture imaging using matrix splitting methods and fast algorithms for their implementation.

We consider imaging in a scattering medium where the illumination goes through this medium but there is also an auxiliary, passive receiver array that is near the object to be imaged. Instead of imaging with the source-receiver array on the far side of the object we image with the data of the passive array on the near side of the object. The imaging is done with travel time migration using the cross correlations of the passive array data. We showed in [J. Garnier and G. Papanicolaou, Inverse Problems {28} (2012), 075002] that if (i) the source array is infinite, (ii) the scattering medium is modeled by either an isotropic random medium in the paraxial regime or a randomly layered medium, and (iii) the medium between the auxiliary array and the object to be imaged is homogeneous, then imaging with cross correlations completely eliminates the effects of the random medium. It is as if we imaged with an active array, instead of a passive one, near the object. The purpose of this paper is to analyze the resolution of the image when both the source array and the passive receiver array are finite. We show with a detailed analysis that for isotropic random media in the paraxial regime, imaging not only is not affected by the inhomogeneities but the resolution can in fact be enhanced. This is because the random medium can increase the diversity of the illumination. We also show analytically that this will not happen in a randomly layered medium, and there may be some loss of resolution in this case., 22 pages, 4 figures

We study active array imaging of small but strong scatterers in homogeneous media when multiple scattering between them is important. We use the Foldy-Lax equations to model wave propagation with multiple scattering when the scatterers are small relative to the wavelength. In active array imaging we seek to locate the positions and reflectivities of the scatterers, that is, to determine the support of the reflectivity vector and the values of its nonzero elements from echoes recorded on the array. This is a nonlinear inverse problem because of the multiple scattering. We show in this paper how to avoid the nonlinearity and form images non-iteratively through a two-step process which involves 1 norm minimization. However, under certain illuminations imaging may be affected by screening, where some scatterers are obscured by multiple scattering. This problem can be mitigated by using multiple and diverse illuminations. In this case, we determine solution vectors that have a common support. The uniqueness and stability of the support of the reflectivity vector obtained with single or multiple illuminations are analyzed, showing that the errors are proportional to the amount of noise in the data with a proportionality factor dependent on the sparsity of the solution and the mutual coherence of the sensing matrix, which is determined by the geometry of the imaging array. Finally, to filter out noise and improve the resolution of the images, we propose an approach that combines optimal illuminations using the singular value decomposition of the response matrix together with sparsity promoting optimization jointly for all illuminations. This work is an extension of our previous paper [5] on imaging using optimization techniques where we now account for multiple scattering effects. M. Moscoso was supported by AFOSR grant FA9550-11-1-0266 and by AFOSR NSSEFF fellowship. G. Papanicolaou was supported by AFOSR grant FA9550-11-1-0266

High blood pressure (BP) is more prevalent and contributes to more severe manifestations of cardiovascular disease (CVD) in African Americans than in any other United States ethnic group. Several small African-ancestry (AA) BP genome-wide association studies (GWASs) have been published, but their findings have failed to replicate to date. We report on a large AA BP GWAS meta-analysis that includes 29,378 individuals from 19 discovery cohorts and subsequent replication in additional samples of AA (n = 10,386), European ancestry (EA) (n = 69,395), and East Asian ancestry (n = 19,601). Five loci (EVX1-HOXA, ULK4, RSPO3, PLEKHG1, and SOX6) reached genome-wide significance (p < 1.0 × 10(-8)) for either systolic or diastolic BP in a transethnic meta-analysis after correction for multiple testing. Three of these BP loci (EVX1-HOXA, RSPO3, and PLEKHG1) lack previous associations with BP. We also identified one independent signal in a known BP locus (SOX6) and provide evidence for fine mapping in four additional validated BP loci. We also demonstrate that validated EA BP GWAS loci, considered jointly, show significant effects in AA samples. Consequently, these findings suggest that BP loci might have universal effects across studied populations, demonstrating that multiethnic samples are an essential component in identifying, fine mapping, and understanding their trait variability.

We introduce an output least-squares method for impedance tomography problems that have regions of high conductivity surrounded by regions of lower conductivity. The high conductivity is modelled on network approximation results from an asymptotic analysis and its recovery is based on this model. The smoothly varying part of the conductivity is recovered by a linearization process as is usual. We present the results of several numerical experiments that illustrate the performance of the method.

We derive and analyze transport equations for the energy density of waves of any kind in a random medium. The equations take account of nonuniformities of the background medium, scattering by random inhomogeneities, polarization effects, coupling of different types of waves, etc. We also show that diffusive behavior occurs on long time and distance scales and we determine the diffusion coefficients. The results are specialized to acoustic, electromagnetic, and elastic waves. The analysis is based on the governing equations of motion and uses the Wigner distribution.

We show that the asymptotic theory developed for the analysis of reflected wave pulses from randomly layered media can be used to solve statistical inverse problems. In particular, we recover the large scale behavior of medium properties from a single realization of reflected wave pulses observed at different points on the surface.

We prove long time diffusive behavior (homogenization) for convection-diffusion in a turbulent flow that it incompressible and has a stationary and square integrable stream matrix. Simple shear flow examples show that this result is sharp for flows that have stationary stream matrices.

Successful management of the difficult peripheral vascular injury requires a multidisciplinary approach. Prompt recognition of the vascular injury and adherence to the recognized principles of vascular repair provide a successful short-term surgical result. The long-term consequences of an injury are determined by the associated orthopedic, soft tissue, and nerve injuries.

The benefit of preoperative cardiac evaluation in the diabetic patient undergoing peripheral vascular surgery is uncertain. To investigate this issue we performed a retrospective review of 192 procedures performed in diabetic patients for chronic lower extremity arterial occlusive disease. The incidence of adverse postoperative cardiac events was determined, as well as its association with several preoperative factors including symptoms of coronary artery disease (CAD), extent and results of preoperative noninvasive cardiac evaluation, and operative site (aorta vs. lower extremity). The overall death and cardiac complication rates were 10.2% for lower extremity and 25.7% for aortic procedures (p = 0.02). For myocardial infarction and cardiac death alone, the rates were 5.1% and 5.7%, respectively (p0.10). Although a history of symptomatic CAD predicted the occurrence of any cardiac complication (28.3% vs. 8.2% [p0.01] for the aortic and lower extremity revascularization groups combined), no factor was found to be associated with the occurrence of myocardial infarction and cardiac death alone. In patients with a history of symptomatic CAD, there was no significant difference in the incidence of complications whether or not preoperative noninvasive cardiac testing was performed (28.1% vs. 28.6%, p0.10) or, if testing was performed, if the results were abnormal or normal (35.3% vs. 20.0%, p0.10). Similar results were obtained in patients with no history of symptomatic CAD. In summary, this retrospective review of our experience with noninvasive evaluation to detect CAD in diabetic patients undergoing peripheral vascular surgery failed to show any benefit in terms of reducing the incidence of postoperative cardiac events.

We compared the findings of intraoperative color duplex scanning and completion arteriography in patients undergoing infrainguinal vein bypasses to identify hemodynamic abnormalities that could result in a predisposition to early or late graft failure. We reviewed the records of 72 patients who underwent 81 vein bypass graft procedures. Three intraoperative diagnostic methods were used. In 28 procedures (group I) both color duplex and completion arteriography were used, in 21 procedures (group II) only color duplex was used, and in 26 procedures (group III) only completion arteriography was used. Grafts were followed using a duplex surveillance protocol for a mean interval of 16.1 months. Nine grafts in group I showed an abnormality on the duplex scan but not on the completion arteriogram. Seven grafts had a peak systolic velocity (PSV) greater than 200 cm/sec and two had a PSV less than 45 cm/sec. These findings led to six immediate repairs, one early revision, and two late revisions. Arteriography demonstrated additional defects in two procedures but repairs were not performed. In group II duplex scans showed an abnormality in eight procedures (seven grafts with PSV 200 to 250 cm/sec and one graft with a retained valve) resulting in three immediate repairs and five late revisions. In the remaining 13 procedures in group II, duplex scans were normal and no revisions were required during follow-up. In group III defects were detected by arteriography in four procedures (50% stenosis in three grafts and one arterial spasm) leading to three immediate repairs. In the remaining 22 studies arteriograms were interpreted as normal; however, seven of these grafts required late revisions. Our data suggest that grafts that appear normal on intraoperative duplex scans are not likely to develop a stenosis requiring revision. Intraoperative duplex ultrasound may be superior to completion arteriography.

Purpose: Our purpose was to investigate the hemodynamic theory that the blood flow rate through a stenotic arterial graft is limited by the onset of turbulence, which acts as a barrier at peak systole against further increases in systolic flow. Methods: We used duplex ultrasonography to examine 25 stenotic infrainguinal vein grafts. Theory predicts that the flow limitation occurs at peak systole at a stenotic velocity greater than 250 cm/sec, which corresponds to a residual stenotic lumenal diameter of 0.36 cm (Reynolds No. 2000). These numbers are based on the assumption that the 68 ml/min blood flow is supplied by the femoropopliteal graft to the resting lower leg only during systole. When the lumen is smaller than 0.36 cm, peak systolic velocity (PSV) must exceed 250 cm/sec. The increased velocity results in poststenotic turbulence. This turbulent condition restricts the averaged graft systolic flow to less than the 68 ml/min required by the lower leg, so diastolic flow is needed to make up the deficit. Results: Twenty vein grafts with PSVs of 250 cm/sec or greater had end-diastolic velocities of 50 cm/sec or greater as predicted; three grafts with PSVs of 256 to 300 cm/sec and two grafts with PSVs of less than 250 cm/sec had no forward diastolic flow ( p = 0.03). None of 10 normal grafts had forward diastolic flow. Conclusion: The onset of turbulence in a stenotic vein graft supplying the lower leg occurs at a PSV of 250 cm/sec or greater. The appearance of diastolic flow maintains the average graft volume flow.

This paper is Part I of a two-part work in which we derive localization theory for elastic waves in plane-stratified media, a multimode problem complicated by the interconversion of shear and compressional waves, both in propagation and in backscatter. We consider the low frequency limit, i.e., when the randomness constitutes a microstructure. In this part, we set up the general suite of problems and derive the probability density and moments for the fraction of reflected energy which remains in the same mode (shear or compressional) as the incident field. Our main mathematical tool is a limit theorem for stochastic differential equations with a small parameter. In Part II we will use the limit theorem of Part I and the Oseledec Theorem, which establishes the existence of the localization length and other structural information, to compute: the localization length and another deterministic length, called the equilibration length, which gives the scale for equilibration of shear and compressional energy in propagation; and the probability density of the ratio of shear to compressional energy in transmission through a large slab. This last quantity is shown to be asymptotically independent of the incident field. We also extend the results to the small fluctuation, rather than the low frequency case.

Purpose: The purpose of this study was to compare the accuracy of a limited B-mode compression technique (BMCT) with a complete color-flow duplex venous examination (CDVE) for the detection of proximal deep vein thrombosis (DVT). Methods: We prospectively studied 72 patients (20 men and 52 women) for DVT. Two technologists blinded to each other performed either BMCT or CDVE independently. The BMCT is an abbreviated technique compressing two sites per limb. One site was the saphenofemoral junction including the superficial femoral and deep femoral vein confluence; the other was the saphenopopliteal junction including tibial vein confluence. Total limbs studied were 144. CDVE was considered the gold standard for purposes of sensitivity, specificity, and accuracy. Results: The technical failure rate of BMCT was three of 144. In all technically satisfactory examinations, the BMCT result was positive in 15 of 141 limbs, and the CDVE result was positive in 13. Sensitivity of BMCT was 100%, specificity was 98%, and overall accuracy was 99%. There were two false-positive results with BMCT; both were cases of popliteal veins deep to the artery leading to difficulty in compression. The BMCT was able to detect chronic thrombus, floating thrombus, and small thrombus behind femoral vein valve cusps. Conclusion: These data suggest that BMCT is a rapid, acceptable, alternative technique for detecting proximal DVT. In cases of equivocal or positive findings, the spectral and color-flow Doppler examination should be used to confirm the results. (J VASC SURG 1995;22:553-7.)

During a 62-month period, carbon dioxide was used to supplement or completely replace iodinated contrast agents in performing 27 transluminal angioplasties in 26 patients. The arterial segments addressed included the following: renal in two cases, iliac in five, femoral/popliteal in 15, infrapopliteal in two, and combined in three. Indications for intervention included lower extremity gangrene in 11 cases, ischemic ulceration in 10, rest pain in three, claudication in one, and ischemic nephropathy in two. Contraindications to iodinated contrast agents included renal insufficiency resulting from diabetes (n = 20) or ischemic nephropathy (n = 2) and congestive heart failure (n = 4). Eight procedures used carbon dioxide as the sole contrast agent, whereas 19 required supplementation of carbon dioxide with a mean of 39 ml of nonionic contrast medium. Technical success was achieved in 25 procedures with significant hemodynamic improvement in 20 patients. Complications included transient deterioration in renal function in two patients and myocardial infarctions in two. At 30 days 18 patients had demonstrated significant clinical improvement. Patients at high risk for iodinated contrast-related complications may undergo transluminal angioplasty using carbon dioxide/digital subtraction arteriography to reduce or eliminate the need for iodinated contrast agents.

International audience; We consider a system of diffusion processes that interact through their empirical mean and have a stabilizing force acting on each of them, corresponding to a bistable potential. There are three parameters that characterize the system: the strength of the intrinsic stabilization, the strength of the external random perturbations, and the degree of cooperation or interaction between them. The last one is the rate of mean reversion of each component to the empirical mean of the system. We interpret this model in the context of systemic risk and analyze in detail the effect of cooperation between the components, that is, the rate of mean reversion. We show that in a certain regime of parameters increasing cooperation tends to increase the stability of the individual agents, but it also increases the overall or systemic risk. We use the theory of large deviations of diffusions interacting through their mean field.

INTRODUCTION: C-reactive protein (CRP) is a heritable biomarker of systemic inflammation and a predictor of cardiovascular disease (CVD). Cigarette smoking is a major risk factor in the development of CVD and has been shown to affect circulating levels of CRP. Therefore, we sought to determine how this important environmental exposure may influence genetic associations with CRP in a multi-ethnic setting. METHODS: Using the ITMAT Broad-CARe (IBC) SNP array, a custom 50,000 SNP gene-centric array having dense coverage of over 2,000 candidate genes for CVD pathways, we performed a meta-analysis of up to 26,065 participants of European descent and 7,584 participants of African descent for association with log-CRP level within smoking status stratum. The 2 smoking strata were: never smokers and ever smokers (comprising of current and former smokers). We conducted IBC-wide association scans for CRP within cohort-, race- and smoking-stratum and meta-analyzed by race. Samples were from the Candidate gene Association Resource (CARe) cohorts (Atherosclerosis Risk in Communities Study, Framingham Heart Study, Cardiovascular Health Study, Cleveland Family Study , Coronary Artery Risk Development in Young Adults Study, Jackson Heart Study, and Multi-Ethnic Study of Atherosclerosis Study). Results were considered to be panel wide statistically significant if p RESULTS: The overall sample size for ever smokers (never smokers) was 11,698 (10,344) in European Americans and 3,448 (4,330) in African Americans. The per-allele beta coefficients for genes previously established to be associated with CRP and present on the IBC chip ( CRP, APOE, GCKR, IL6R, LEPR, HNF1A, NLRP3 ) were very similar in magnitude between smoking strata in European Americans. However, in the African Americans, the estimated per-allele CRP and IL6R betas were 2-times larger for the ever smokers as compared to the never smokers. In the European American analysis, one gene not previously reported for association with CRP reached IBC-wide significance for a CRP-lowering effect in the never smokers ( GSTT1 , p=4.8E-07 for SNP rs405597 ), but not in the ever smokers (p=0.078). CONCLUSION: This large scale candidate gene based meta-analysis identified one novel locus for CRP ( GSTT1 ) associated with serum CRP levels in those reporting having never regularly smoked. Polymorphisms in GSTT1 , which plays a role in detoxification, have previously been reported to interact with smoking for other phenotypes including birth weight and colorectal cancer. We also observed evidence that smoking modifies the effects for previously established loci CRP and IL6R in African Americans. These results may identify important context genetic specific effects that influence chronic inflammation.

Array imaging in a strongly scattering medium is limited because coherent signals recorded at the array and coming from a reflector to be imaged are weak and dominated by incoherent signals coming from multiple scattering by the medium. If, however, an auxiliary passive array can be placed between the reflector to be imaged and the scattering medium then the cross correlations of the incoherent signals on this array can also be used to image the reflector. In this paper, we show both in the weakly scattering paraxial regime and in strongly scattering layered media that this cross-correlation approach produces images as if the medium between the sources and the passive array was homogeneous and the auxiliary passive array was an active one made up of both sources and receivers.

We introduce a class of distribution-valued stochastic processes that arise in the study of pulse reflection from random media and we analyze their asymptotic properties when they are scaled in a natural way.

We consider reflection of a pulse in a random medium with a strong reflector. We show that the wavefront of the reflected wave observed in the frame moving with the random propagation speed stabilizes to the deterministic waveform. The problem is studied using invariant imbedding. The results of numerical experiments illustrating the theory are presented.

A strongly heterogeneous stratified elastic medium occupies a slab of finite thickness. The medium parameters vary randomly with correlation length of O(ϵ2). A pulse with O(ϵ) wavelength enters the slab at one end. It travels coherently through the slab with a slowness near to that predicted by effective medium theory. Relative to a certain realization- dependent co-moving frame of reference the pulse stabilizes to its mean as ϵ tends to zero. It broadens as it travels as in the O'Doherty-Anstey theory, but here the variations in medium properties are not assumed to be small as in that theory, and the pulse travels with a travel time differing significantly from the characteristic first arrival time.

Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.

Nicholas West George Papanicolaou Peter Glynn Gianluca Iaccarino Institute for Computational and Mathematical Engineering, Stanford University, Stanford, CA, 94305 Department of Mathematics, Stanford University, Stanford, CA, 94305 Department of Management Sciences and Engineering, Stanford University, Stanford, CA, 94305 Department of Mechanical Engieering, Stanford University, Stanford, CA, 94305

http://iopscience.iop.org/0266-5611/; International audience; Coherent interferometric imaging is based on the backpropagation of local spacetime cross-correlations of array data and was introduced in order to improve images when the medium between the array and the object to be imaged is inhomogeneous and unknown (Borcea et al 2005 Inverse Problems 21 1419). Although this method has been shown to be effective and is well founded theoretically, the coherent interferometric imaging function is computationally expensive and therefore difficult to use. In this paper, we show that this function is equivalent to a windowed beamformer energy function, that is, a quadratic function that involves only time gating and time delaying signals in emission and in reception. In this form the coherent interferometric imaging can be implemented efficiently both in hardware and software, that is, at a computational cost that is comparable to the usual beamforming and migration imaging methods. We also revisit the trade-off between enhanced image stability and loss of resolution in coherent interferometry from the point of view of its equivalence to a windowed beamformer energy imaging function.

http://iopscience.iop.org/0266-5611/; International audience; We analyze the resolution and statistical fluctuations of images when the ambient medium is random and scattering can be modeled primarily by wavefront distortion. We compare the coherent interferometric imaging method to the widely used Kirchhoff migration and show how the latter loses statistical stability at an exponential rate with the distance of propagation. In Kirchhoff migration we form images by superposing the array data back-propagated to the image domain. In coherent interferometry, we back-propagate local cross-correlations of the array data. This is a denoising process that enhances the signal-to-noise ratio of images but also reduces the resolution. We quantify analytically the trade-off between enhanced stability and reduced resolution in coherent interferometric imaging.

We investigate the feasibility of using correlation-based methods for estimating the spatial location of distributed receiving nodes in an indoor environment. Our algorithms do not assume any knowledge regarding the transmitter locations or the transmitted signal, but do assume that there are ambient signal sources whose location and properties are, however, not known. The motivation for this kind of node localization is to avoid interaction between nodes. It is most useful in non-line-of-sight propagation environments, where there is a lot of scattering. Correlation-based node localization is able to exploit an abundance of bandwidth of ambient signals, as well as the features of the scattering environment. The key idea is to compute pairwise cross correlations of the signals received at the nodes and use them to estimate the travel time between these nodes. By doing this for all pairs of receivers, we can construct an approximate map of their location using multidimensional scaling methods. We test this localization algorithm in a cubicle-style office environment based on both ray-tracing simulations, and measurement data from a radio measurement campaign using the Stanford broadband channel sounder. Contrary to what is seen in other applications of cross-correlation methods, the strongly scattering nature of the indoor environment complicates distance estimation. However, using statistical methods, the rich multipath environment can be turned partially into an advantage by enhancing ambient signal diversity and therefore making distance estimation more robust. The main result is that with our correlation-based statistical estimation procedure applied to the real data, assisted by multidimensional scaling, we were able to compute spatial antenna locations with an average error of about 2 m and pairwise distance estimates with an average error of 1.84 m. The theoretical resolution limit for the distance estimates is 1.25 m.

We consider the problem of selective imaging extended reflectors in cluttered media. We propose a random travel time model for simulating the array response matrix in clutter and we compare it with the full wave solution. Our simplified model captures very well the full wave random medium behavior as this is illustrated by our numerical results. The algorithm for selective array imaging uses coherent interferometry on a filtered version of the data. The filter, which is based on the singular value decomposition of the response matrix, enhances the signal reflected by the edges of the reflector. We illustrate the performance of the imaging algorithm with numerical simulations in the regime of ultrasonic non-destructive testing in concrete.

We analyze in detail directivity enhancement in imaging with small arrays of closely spaced sensors, in homogeneous media. Imaging is done with Kirchhoff or travel time migration of the array data after applying an inverse filter that increases the resolution of the image. In general, the construction of such a filter requires invasive measurements on a control array in the vicinity of the object to be imaged, which we assume are not available. The form of the filter is, however, universal when the control array encloses the imaging sensor array. It is the inverse of the finite Fourier transform operator, which has the sinc function as its kernel. We analyze the dependence of resolution enhancement on the signal-to-noise ratio both with narrow and broadband signals.