Nonlinear modeling of the dynamic effects of arterial pressure and CO2 variations on cerebral blood flow in healthy humans

The effect of spontaneous beat-to-beat mean arterial blood pressure fluctuations and breath-to-breath end-tidal CO2 fluctuations on beat-to-beat cerebral blood flow velocity variations is studied using the Laguerre-Volterra network methodology for multiple-input nonlinear systems. The observations made from experimental measurements from ten healthy human subjects reveal that, whereas pressure fluctuations explain most of the high-frequency blood flow velocity variations (above 0.04 Hz), end-tidal CO2 fluctuations as well as nonlinear interactions between pressure and CO2 have a considerable effect in the lower frequencies (below 0.04 Hz). They also indicate that cerebral autoregulation is strongly nonlinear and dynamic (frequency-dependent). Nonlinearities are mainly active in the low-frequency range (below 0.04 Hz) and are more prominent in the dynamics of the end-tidal CO2-blood flow velocity relationship. Significant nonstationarities are also revealed by the obtained models, with greater variability evident for the effects of CO2 on blood flow velocity dynamics.     

Menshov’s “adjustment theorem” with respect to general measures

We prove Menshov’s theorem in the setting of arbitrary Borel measures.     

A Characterization of Vanishing Mean Oscillation

We show that a function has vanishing mean oscillation with respect to a nonatomic measure if and only if it satisfies an asymptotic reverse Jensen inequality.     

Nonlinear Modeling of the Dynamic Effects of Infused Insulin on Glucose: Comparison of Compartmental With Volterra Models

This paper presents the results of a computational study that compares simulated compartmental (differential equation) and Volterra models of the dynamic effects of insulin on blood glucose concentration in humans. In the first approach, we employ the widely accepted ldquominimal modelrdquo and an augmented form of it, which incorporates the effect of insulin secretion by the pancreas, in order to represent the actual closed-loop operating conditions of the system, and in the second modeling approach, we employ the general class of Volterra-type models that are estimated from input-output data. We demonstrate both the equivalence between the two approaches analytically and the feasibility of obtaining accurate Volterra models from insulin-glucose data generated from the compartmental models. The results corroborate the proposition that it may be preferable to obtain data-driven (i.e., inductive) models in a more general and realistic operating context, without resorting to the restrictive prior assumptions and simplifications regarding model structure and/or experimental protocols (e.g., glucose tolerance tests) that are necessary for the compartmental models proposed previously. These prior assumptions may lead to results that are improperly constrained or biased by preconceived (and possibly erroneous) notions-a risk that is avoided when we let the data guide the inductive selection of the appropriate model within the general class of Volterra-type models, as our simulation results suggest.     

Analysis of focusing of pulsed baseband signals inside a layeredtissue medium

The derivation and application of a method designed to investigate the focusing properties of pulsed baseband signals of short pulsewidth (~1 ns) in biological tissue media are reported. To this end, sources fed from TEM waveguides, concentrically placed at the periphery of a three-layer cylindrical lossy model, are assumed. A Fourier-series-based methodology, appropriate for a useful class of pulse train incident signals, is presented and utilized to study the dynamics of pulse propagation inside the tissue medium. The propagation of each spectral component of the incident field within the tissue medium is analyzed by applying an integral-equation technique and a Fourier-series representation is used in order to obtain the time dependence of the electromagnetic fields produced at any point within tissue due to the pulsed excitation of the array elements. Numerical results are computed and presented at several points in a three-layer geometry, 20 cm in diameter, irradiated by an eight-element waveguide array. Focusing at a specific point of interest within tissue is achieved by properly adjusting the time delay of the signals injected to the individual applicators of the array     

On a Problem Related to Sphere and Circle Packing

The paper proves that a set which contains spheres centeredat all points of a set of Hausdorff dimension greater than 1must have positive Lebesgue measure. It also proves the correspondingresult for circles, provided that the set of centers has Hausdorffdimension greater than 3/2.     

A note on the distance set problem in the plane

We use a simple geometric-combinatorial argument to establish a quantitative relation between the generalized Hausdorff measure of a set and its distance set, extending a result originally due to Falconer.

     

Norm estimates for a Kakeya‐type maximal operator

We prove L^p → L^q estimates for the 2‐dimensional analog of the Kakeya maximal function. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Weighted Weak Type Inequality for the Strong Maximal Function

We prove the natural Fefferman-Stein weak type inequality for the strong maximal function in the plane, under the assumption that the weight satisfies a strong Muckenhoupt condition. This complements the corresponding strong type result due to Jawerth. It also extends the weighted weak type inequality for strong A₁ weights due to Bagby and Kurtz.     

Direct Quantitation of Phytocannabinoids by One-Dimensional 1H qNMR and Two-Dimensional 1H-1H COSY qNMR in Complex Natural Mixtures

The widespread use of phytocannabinoids or cannabis extracts as ingredients in numerous types of products, in combination with the legal restrictions on THC content, has created a need for the development of new, rapid, and universal analytical methods for their quantitation that ideally could be applied without separation and standards. Based on previously described qNMR studies, we developed an expanded ¹H qNMR method and a novel 2D-COSY qNMR method for the rapid quantitation of ten major phytocannabinoids in cannabis plant extracts and cannabis-based products. The ¹H qNMR method was successfully developed for the quantitation of cannabidiol (CBD), cannabidiolic acid (CBDA), cannabinol (CBN), cannabichromene (CBC), cannabichromenic acid (CBCA), cannabigerol (CBG), cannabigerolic acid (CBGA), Δ9-tetrahydrocannabinol (Δ9-THC), Δ9-tetrahydrocannabinolic acid (Δ9-THCA), Δ8-tetrahydrocannabinol (Δ8-THC), cannabielsoin (CBE), and cannabidivarin (CBDV). Moreover, cannabidivarinic acid (CBDVA) and Δ9-tetrahydrocannabivarinic acid (Δ9-THCVA) can be distinguished from CBDA and Δ9-THCA respectively, while cannabigerovarin (CBGV) and Δ8-tetrahydrocannabivarin (Δ8-THCV) present the same ¹H-spectra as CBG and Δ8-THC, respectively. The COSY qNMR method was applied for the quantitation of CBD, CBDA, CBN, CBG/CBGA, and THC/THCA. The two methods were applied for the analysis of hemp plants; cannabis extracts; edible cannabis medium-chain triglycerides (MCT); and hemp seed oils and cosmetic products with cannabinoids. The ¹H-NMR method does not require the use of reference compounds, and it requires only a short time for analysis. However, complex extracts in ¹H-NMR may have a lot of signals, and quantitation with this method is often hampered by peak overlap, with 2D NMR providing a solution to this obstacle. The most important advantage of the COSY NMR quantitation method was the determination of the legality of cannabis plants, extracts, and edible oils based on their THC/THCA content, particularly in the cases of some samples for which the determination of THC/THCA content by ¹H qNMR was not feasible.