Chronic opioid therapy and opioid tolerance: a new hypothesis.

Opioids are efficacious and cost-effective analgesics, but tolerance limits their effectiveness. This paper does not present any new clinical or experimental data but demonstrates that there exist ascending sensory pathways that contain few opioid receptors. These pathways are located by brain PET scans and spinal cord autoradiography. These nonopioid ascending pathways include portions of the ventral spinal thalamic tract originating in Rexed layers VI-VIII, thalamocortical fibers that project to the primary somatosensory cortex (S1), and possibly a midline dorsal column visceral pathway. One hypothesis is that opioid tolerance and opioid-induced hyperalgesia may be caused by homeostatic upregulation during opioid exposure of nonopioid-dependent ascending pain pathways. Upregulation of sensory pathways is not a new concept and has been demonstrated in individuals impaired with deafness or blindness. A second hypothesis is that adjuvant nonopioid therapies may inhibit ascending nonopioid-dependent pathways and support the clinical observations that monotherapy with opioids usually fails. The uniqueness of opioid tolerance compared to tolerance associated with other central nervous system medications and lack of tolerance from excess hormone production is discussed. Experimental work that could prove or disprove the concepts as well as flaws in the concepts is discussed.

Fluid flow control with transformation media.

We introduce a new concept for the manipulation of fluid flow around three-dimensional bodies. Inspired by transformation optics, the concept is based on a mathematical idea of coordinate transformations and physically implemented with anisotropic porous media permeable to the flow of fluids. In two situations-for an impermeable object placed either in a free-flowing fluid or in a fluid-filled porous medium-we show that the object can be coated with an inhomogeneous, anisotropic permeable medium, such as to preserve the flow that would have existed in the absence of the object. The proposed fluid flow cloak eliminates downstream wake and compensates viscous drag, hinting at the possibility of novel propulsion techniques.

Slow light with a swept-frequency source.

ct: We introduce a new concept for stimulated-Brillouin-scattering-based slow light in optical fibers that is applicable for broadly-tunable frequency-swept sources. It allows slow light to be achieved, in principle, over the entire transparency window of the optical fiber. We demonstrate a slow light delay of 10 ns at 1.55 μm using a 10-m-long photonic crystal fiber with a source sweep rate of 400 MHz/μs and a pump power of 200 mW. We also show that there exists a maximal delay obtainable by this method, which is set by the SBS threshold, independent of sweep rate. For our fiber with optimum length, this maximum delay is ~38 ns, obtained for a pump power of 760 mW.

Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference.

Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufri\`{e}re Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.