Relaxation Methods for Mixed-Integer Optimal Control of Partial Differential Equations

We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators, where the task is to minimize costs associated with the dynamics of the system by choosing, for each instant in time, one of the actuators together with ordinary controls. We consider relaxation techniques that are already used successfully for mixed-integer optimal control of ordinary differential equations. Our analysis yields sufficient conditions such that the optimal value and the optimal state of the relaxed problem can be approximated with arbitrary precision by a control satisfying the integer restrictions. The results are obtained by semigroup theory methods. The approach is constructive and gives rise to a numerical method. We supplement the analysis with numerical experiments

Preparation of an Exciton Condensate of Photons on a 53-Qubit Quantum Computer

Quantum computation promises an exponential speedup of certain classes of classical calculations through the preparation and manipulation of entangled quantum states. So far most molecular simulations on quantum computers, however, have been limited to small numbers of particles. Here we prepare a highly entangled state on a 53-qubit IBM quantum computer, representing 53 particles, which reveals the formation of an exciton condensate of photon particles and holes. While elusive for more than 50 years, such condensates were recently achieved for electron-hole pairs in graphene bilayers and metal chalcogenides. Our result with a photon condensate has the potential to further the exploration of this new form of condensate that may play a significant role in realizing efficient room-temperature energy transport

No equity, no triple aim: strategic proposals to advance health equity in a volatile policy environment

Health professionals, including social workers, community health workers, public health workers, and licensed health care providers, share common interests and responsibilities in promoting health equity and improving social determinants of health—the conditions in which we live, work, play, and learn. This article summarizes underlying causes of health inequity and comparatively poor health outcomes in the U.S. It describes barriers to realizing the hope embedded in the 2010 Patient Protection and Affordable Care Act that moving away from fee-for-service payments will naturally drive care upstream as providers respond to greater financial risk for the health of their patients by undertaking greater prevention efforts. The article asserts that health equity should serve as the guiding framework for achieving the Triple Aim of health care reform. It outlines practical opportunities for improving care and for promoting stronger efforts to address social determinants of health. These proposals include developing a dashboard of measures to assist providers committed to health equity and community-based prevention and to promote institutional accountability for addressing socio-economic factors that influence health

Mutation of the co-chaperone Tsc1 in bladder cancer diminishes Hsp90 acetylation and reduces drug sensitivity and selectivity

The molecular chaperone Heat shock protein 90 (Hsp90) is essential for the folding, stability, and activity of several drivers of oncogenesis. Hsp90 inhibitors are currently under clinical evaluation for cancer treatment, however their efficacy is limited by lack of biomarkers to optimize patient selection. We have recently identified the tumor suppressor tuberous sclerosis complex 1 (Tsc1) as a new co-chaperone of Hsp90 that affects Hsp90 binding to its inhibitors. Highly variable mutations of TSC1 have been previously identified in bladder cancer and correlate with sensitivity to the Hsp90 inhibitors. Here we showed loss of TSC1 leads to hypoacetylation of Hsp90-K407/K419 and subsequent decreased binding to the Hsp90 inhibitor ganetespib. Pharmacologic inhibition of histone deacetylases (HDACs) restores acetylation of Hsp90 and sensitizes Tsc1-mutant bladder cancer cells to ganetespib, resulting in apoptosis. Our findings suggest that TSC1 status may predict response to Hsp90 inhibitors in patients with bladder cancer, and co-targeting HDACs can sensitize tumors with Tsc1 mutations to Hsp90 inhibitors

No equity, no triple aim: strategic proposals to advance health equity in a volatile policy environment

Health professionals, including social workers, community health workers, public health workers, and licensed health care providers, share common interests and responsibilities in promoting health equity and improving social determinants of health—the conditions in which we live, work, play, and learn. This article summarizes underlying causes of health inequity and comparatively poor health outcomes in the U.S. It describes barriers to realizing the hope embedded in the 2010 Patient Protection and Affordable Care Act that moving away from fee-for-service payments will naturally drive care upstream as providers respond to greater financial risk for the health of their patients by undertaking greater prevention efforts. The article asserts that health equity should serve as the guiding framework for achieving the Triple Aim of health care reform. It outlines practical opportunities for improving care and for promoting stronger efforts to address social determinants of health. These proposals include developing a dashboard of measures to assist providers committed to health equity and community-based prevention and to promote institutional accountability for addressing socio-economic factors that influence health

Unintentional high density p-type modulation doping of a GaAs/AlAs core-multi-shell nanowire

Achieving significant doping in GaAs/AlAs core/shell nanowires (NWs) is of considerable technological importance but remains a challenge due to the amphoteric behavior of the dopant atoms. Here we show that placing a narrow GaAs quantum well in the AlAs shell effectively getters residual carbon acceptors leading to an \emph{unintentional} p-type doping. Magneto-optical studies of such a GaAs/AlAs core multi-shell NW reveal quantum confined emission. Theoretical calculations of NW electronic structure confirm quantum confinement of carriers at the core/shell interface due to the presence of ionized carbon acceptors in the 1~nm GaAs layer in the shell. Micro-photoluminescence in high magnetic field shows a clear signature of avoided crossings of the $n=0$ Landau level emission line with the $n=2$ Landau level TO phonon replica. The coupling is caused by the resonant hole-phonon interaction, which points to a large 2D hole density in the structure.Comment: just published in Nano Letters (http://pubs.acs.org/doi/full/10.1021/nl500818k

Infinite ergodic theory and Non-extensive entropies

We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropie

Strong Coupling Corrections to the Ginzburg-Landau Theory of Superfluid ^{3}He

In the Ginzburg-Landau theory of superfluid $^{3}$He, the free energy is expressed as an expansion of invariants of a complex order parameter. Strong coupling effects, which increase with increasing pressure, are embodied in the set of coefficients of these order parameter invariants\cite{Leg75,Thu87}. Experiments can be used to determine four independent combinations of the coefficients of the five fourth order invariants. This leaves the phenomenological description of the thermodynamics near $T_{c}$ incomplete. Theoretical understanding of these coefficients is also quite limited. We analyze our measurements of the magnetic susceptibility and the NMR frequency shift in the $B$-phase which refine the four experimental inputs to the phenomenological theory. We propose a model based on existing experiments, combined with calculations by Sauls and Serene\cite{Sau81} of the pressure dependence of these coefficients, in order to determine all five fourth order terms. This model leads us to a better understanding of the thermodynamics of superfluid $^{3}$He in its various states. We discuss the surface tension of bulk superfluid $^{3}$He and predictions for novel states of the superfluid such as those that are stabilized by elastic scattering of quasiparticles from a highly porous silica aerogel.Comment: 9 pages, 7 figures, 2 table

Copper-nickel-rich, amalgamated ferromanganese crust-nodule deposits from Shatsky Rise, NW Pacific

A unique set of ferromanganese crusts and nodules collected from Shatsky Rise (SR), NW Pacific, were analyzed for mineralogical and chemical compositions, and dated using Be isotopes and cobalt chronometry. The composition of these midlatitude, deep-water deposits is markedly different from northwest-equatorial Pacific (PCZ) crusts, where most studies have been conducted. Crusts and nodules on SR formed in close proximity and some nodule deposits were cemented and overgrown by crusts, forming amalgamated deposits. The deep-water SR crusts are high in Cu, Li, and Th and low in Co, Te, and Tl concentrations compared to PCZ crusts. Thorium concentrations (ppm) are especially striking with a high of 152 (mean 56), compared to PCZ crusts (mean 11). The deep-water SR crusts show a diagenetic chemical signal, but not a diagenetic mineralogy, which together constrain the redox conditions to early oxic diagenesis. Diagenetic input to crusts is rare, but unequivocal in these deep-water crusts. Copper, Ni, and Li are strongly enriched in SR deep-water deposits, but only in layers older than about 3.4 Ma. Diagenetic reactions in the sediment and dissolution of biogenic calcite in the water column are the likely sources of these metals. The highest concentrations of Li are in crust layers that formed near the calcite compensation depth. The onset of Ni, Cu, and Li enrichment in the middle Miocene and cessation at about 3.4 Ma were accompanied by changes in the deep-water environment, especially composition and flow rates of water masses, and location of the carbonate compensation depth. Key Points - Fe-Mn crusts can have a diagenetic component - Mid-latitude N. Pacific deep-water Fe-Mn crusts are uniquely enriched in Cu, Th, Li - Temporal changes in deep-ocean geochemical processes are recorde