Noncolliding Squared Bessel Processes

We consider a particle system of the squared Bessel processes with index $\nu > -1$ conditioned never to collide with each other, in which if $-1 < \nu < 0$ the origin is assumed to be reflecting. When the number of particles is finite, we prove for any fixed initial configuration that this noncolliding diffusion process is determinantal in the sense that any multitime correlation function is given by a determinant with a continuous kernel called the correlation kernel. When the number of particles is infinite, we give sufficient conditions for initial configurations so that the system is well defined. There the process with an infinite number of particles is determinantal and the correlation kernel is expressed using an entire function represented by the Weierstrass canonical product, whose zeros on the positive part of the real axis are given by the particle-positions in the initial configuration. From the class of infinite-particle initial configurations satisfying our conditions, we report one example in detail, which is a fixed configuration such that every point of the square of positive zero of the Bessel function $J_{\nu}$ is occupied by one particle. The process starting from this initial configuration shows a relaxation phenomenon converging to the stationary process, which is determinantal with the extended Bessel kernel, in the long-term limit.Comment: v3: LaTeX2e, 26 pages, no figure, corrections made for publication in J. Stat. Phy

Consensus recommendations for mrd testing in adult b-cell acute lymphoblastic leukemia in ontario

Measurable (minimal) residual disease (MRD) is an established, key prognostic factor in adult B-cell acute lymphoblastic leukemia (B-ALL), and testing for MRD is known to be an important tool to help guide treatment decisions. The clinical value of MRD testing depends on the accuracy and reliability of results. Currently, there are no Canadian provincial or national guidelines for MRD testing in adult B-ALL, and consistent with the absence of such guidelines, there is no uniform Ontario MRD testing consensus. Moreover, there is great variability in Ontario in MRD testing with respect to where, when, and by which technique, MRD testing is performed, as well as in how the results are interpreted. To address these deficiencies, an expert multidisciplinary working group was convened to define consensus recommendations for improving the provision of such testing. The expert panel recommends that MRD testing should be implemented in a centralized manner to ensure expertise and accuracy in testing for this low volume indication, thereby to provide accurate, reliable results to clinicians and patients. All adult patients with B-ALL should receive MRD testing after induction chemotherapy. Philadelphia chromosome (Ph)-positive patients should have ongoing monitoring of MRD during treatment and thereafter, while samples from Ph-negative B-ALL patients should be tested at least once later during treatment, ideally at 12 to 16 weeks after treatment initiation. In Ph-negative adult B-ALL patients, standardized, ideally centralized, protocols must be used for MRD testing, including both flow cytometry and immunoglobulin (Ig) heavy chain and T-cell receptor (TCR) gene rearrangement analysis. For Ph-positive B-ALL patients, MRD testing using a standardized protocol for reverse transcription real-time quantitative PCR (RT-qPCR) for the BCR-ABL1 gene fusion transcript is recommended, with Ig/TCR gene rearrangement analysis done in parallel likely providing additional clinical information

Fluctuation properties of the TASEP with periodic initial configuration

We consider the joint distributions of particle positions for the continuous time totally asymmetric simple exclusion process (TASEP). They are expressed as Fredholm determinants with a kernel defining a signed determinantal point process. We then consider certain periodic initial conditions and determine the kernel in the scaling limit. This result has been announced first in a letter by one of us and here we provide a self-contained derivation. Connections to last passage directed percolation and random matrices are also briefly discussed.Comment: 33 pages, 4 figure, LaTeX; We added several references to the general framework and techniques use

Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights

We study a model of $n$ non-intersecting squared Bessel processes in the confluent case: all paths start at time $t = 0$ at the same positive value $x = a$, remain positive, and are conditioned to end at time $t = T$ at $x = 0$. In the limit $n \to \infty$, after appropriate rescaling, the paths fill out a region in the $tx$-plane that we describe explicitly. In particular, the paths initially stay away from the hard edge at $x = 0$, but at a certain critical time $t^*$ the smallest paths hit the hard edge and from then on are stuck to it. For $t \neq t^*$ we obtain the usual scaling limits from random matrix theory, namely the sine, Airy, and Bessel kernels. A key fact is that the positions of the paths at any time $t$ constitute a multiple orthogonal polynomial ensemble, corresponding to a system of two modified Bessel-type weights. As a consequence, there is a $3 \times 3$ matrix valued Riemann-Hilbert problem characterizing this model, that we analyze in the large $n$ limit using the Deift-Zhou steepest descent method. There are some novel ingredients in the Riemann-Hilbert analysis that are of independent interest.Comment: 59 pages, 11 figure

Gaussian Fluctuations of Eigenvalues in Wigner Random Matrices

We study the fluctuations of eigenvalues from a class of Wigner random matrices that generalize the Gaussian orthogonal ensemble. We begin by considering an $n \times n$ matrix from the Gaussian orthogonal ensemble (GOE) or Gaussian symplectic ensemble (GSE) and let $x_k$ denote eigenvalue number $k$. Under the condition that both $k$ and $n-k$ tend to infinity with $n$, we show that $x_k$ is normally distributed in the limit. We also consider the joint limit distribution of $m$ eigenvalues from the GOE or GSE with similar conditions on the indices. The result is an $m$-dimensional normal distribution. Using a recent universality result by Tao and Vu, we extend our results to a class of Wigner real symmetric matrices with non-Gaussian entries that have an exponentially decaying distribution and whose first four moments match the Gaussian moments.Comment: 21 pages, to appear, J. Stat. Phys. References and other corrections suggested by the referees have been incorporate

Direct monitoring of pulmonary disease treatment biomarkers using plasmonic gold nanorods with diffusion-sensitive OCT

The solid concentration of pulmonary mucus (wt%) is critical to respiratory health. In patients with respiratory disease, such as Cystic Fibrosis (CF) and Chronic Obstructive Pulmonary Disorder (COPD), mucus hydration is impaired, resulting in high wt%. Mucus with high wt% is a hallmark of pulmonary disease that leads to obstructed airways, inflammation, and infection. Methods to measure mucus hydration in situ and in real-time are needed for drug development and personalized therapy. We employed plasmonic gold nanorod (GNR) biosensors that intermittently collide with macromolecules comprising the mucus mesh as they self-diffuse, such that GNR translational diffusion (DT) is sensitive to wt%. GNRs are attractive candidates for bioprobes due to their anisotropic optical scattering that makes them easily distinguishable from native tissue using polarization-sensitive OCT. Using principles of heterodyne dynamic light scattering, we developed diffusion-sensitive optical coherence tomography (DS-OCT) to spatially-resolve changing DT in real-time. DS-OCT enables, for the first time, direct monitoring of changes in nanoparticle diffusion rates that are sensitive to nanoporosity with spatial and temporal resolutions of 4.7 μm and 0.2 s. DS-OCT therefore enables us to measure spatially-resolved changes in mucus wt% over time. In this study, we demonstrate the applicability of DS-OCT on well-differentiated primary human bronchial epithelial cells during a clinical mucus-hydrating therapy, hypertonic saline treatment (HST), to reveal, for the first time, mucus mixing, cellular secretions, and mucus hydration on the micrometer scale that translate to long-term therapeutic effects

Plasmon-Coupled Gold Nanoparticles in Stretched Shape-Memory Polymers for Mechanical/Thermal Sensing

The organization of plasmonic nanoparticles (NPs) determines the strength and polarization dependence of coupling of their surface plasmons. In this study, plasmon coupling of spherical Au NPs with an average diameter of 15 nm was investigated in shape-memory polymer films before and after mechanical stretching and then after thermally driving shape recovery. Clusters of Au NPs form when preparing the films that exhibit strong plasmon coupling. During stretching, a significant polarization-dependent response develops, where the optical extinction maximum corresponding to the surface plasmon resonance is redshifted by 19 nm and blueshifted by 7 nm for polarization parallel and perpendicular to the stretching direction, respectively. This result can be explained by non-uniform stretching on the nanoscale, where plasmon coupling increases parallel to the shear direction as Au NPs are pulled into each other during stretching. The polarization dependence vanishes after shape recovery, and structural characterization confirms the return of isotropy consistent with complete nanoscale recovery of the initial arrangement of Au NPs. Simulations of the polarized optical responses of Au NP dimers at different interparticle spacings establish a plasmon ruler for estimating the average interparticle spacings within the experimental samples. An investigation of the temperature-dependent recovery behavior demonstrates an application of these materials as optical thermal history sensors

Distribution of resonances for open quantum maps

We analyze simple models of classical chaotic open systems and of their quantizations (open quantum maps on the torus). Our models are similar to models recently studied in atomic and mesoscopic physics. They provide a numerical confirmation of the fractal Weyl law for the density of quantum resonances of such systems. The exponent in that law is related to the dimension of the classical repeller (or trapped set) of the system. In a simplified model, a rigorous argument gives the full resonance spectrum, which satisfies the fractal Weyl law. For this model, we can also compute a quantity characterizing the fluctuations of conductance through the system, namely the shot noise power: the value we obtain is close to the prediction of random matrix theory.Comment: 60 pages, no figures (numerical results are shown in other references

Origins of the Ambient Solar Wind: Implications for Space Weather

The Sun's outer atmosphere is heated to temperatures of millions of degrees, and solar plasma flows out into interplanetary space at supersonic speeds. This paper reviews our current understanding of these interrelated problems: coronal heating and the acceleration of the ambient solar wind. We also discuss where the community stands in its ability to forecast how variations in the solar wind (i.e., fast and slow wind streams) impact the Earth. Although the last few decades have seen significant progress in observations and modeling, we still do not have a complete understanding of the relevant physical processes, nor do we have a quantitatively precise census of which coronal structures contribute to specific types of solar wind. Fast streams are known to be connected to the central regions of large coronal holes. Slow streams, however, appear to come from a wide range of sources, including streamers, pseudostreamers, coronal loops, active regions, and coronal hole boundaries. Complicating our understanding even more is the fact that processes such as turbulence, stream-stream interactions, and Coulomb collisions can make it difficult to unambiguously map a parcel measured at 1 AU back down to its coronal source. We also review recent progress -- in theoretical modeling, observational data analysis, and forecasting techniques that sit at the interface between data and theory -- that gives us hope that the above problems are indeed solvable.Comment: Accepted for publication in Space Science Reviews. Special issue connected with a 2016 ISSI workshop on "The Scientific Foundations of Space Weather." 44 pages, 9 figure

Incretin-based therapy: a powerful and promising weapon in the treatment of type 2 diabetes mellitus

Type 2 diabetes mellitus (T2DM) is a progressive multisystemic disease that increases significantly cardiovascular morbidity and mortality. It is associated with obesity, insulin resistance, beta-cell dysfunction, and hyperglucagonemia, the combination of which typically leads to hyperglycemia. Incretin-based treatment modalities, and in particular glucagon-like peptide 1 (GLP-1) receptor agonists, are able to successfully counteract several of the underlying pathophysiological abnormalities of T2DM. The pancreatic effects of GLP-1 receptor agonists include glucose-lowering effects by stimulating insulin secretion and inhibiting glucagon release in a strictly glucose-dependent manner, increased beta-cell proliferation, and decreased beta-cell apoptosis. GLP-1 receptors are widely expressed throughout human body; thus, GLP-1-based therapies exert pleiotropic and multisystemic effects that extend far beyond pancreatic islets. A large body of experimental and clinical data have suggested a considerable protective role of GLP-1 analogs in the cardiovascular system (decreased blood pressure, improved endothelial and myocardial function, functional recovery of failing and ischemic heart, arterial vasodilatation), kidneys (increased diuresis and natriuresis), gastrointestinal tract (delayed gastric emptying, reduced gastric acid secretion), and central nervous system (appetite suppression, neuroprotective properties). The pharmacologic use of GLP-1 receptor agonists has been shown to reduce bodyweight and systolic blood pressure, and significantly improve glycemic control and lipid profile. Interestingly, weight reduction induced by GLP-1 analogs reflects mainly loss of abdominal visceral fat. The critical issue of whether the emerging positive cardiometabolic effects of GLP-1 analogs can be translated into better clinical outcomes for diabetic patients in terms of long-term hard endpoints, such as cardiovascular morbidity and mortality, remains to be elucidated with prospective, large-scale clinical trials