Volumes of Restricted Minkowski Sums and the Free Analogue of the Entropy Power Inequality

In noncommutative probability theory independence can be based on free products instead of tensor products. This yields a highly noncommutative theory: free probability . Here we show that the classical Shannon's entropy power inequality has a counterpart for the free analogue of entropy . The free entropy (introduced recently by the second named author), consistently with Boltzmann's formula $S=k\log W$, was defined via volumes of matricial microstates. Proving the free entropy power inequality naturally becomes a geometric question. Restricting the Minkowski sum of two sets means to specify the set of pairs of points which will be added. The relevant inequality, which holds when the set of "addable" points is sufficiently large, differs from the Brunn-Minkowski inequality by having the exponent $1/n$ replaced by $2/n$. Its proof uses the rearrangement inequality of Brascamp-Lieb-L\"uttinger

Strong Connections on Quantum Principal Bundles

A gauge invariant notion of a strong connection is presented and characterized. It is then used to justify the way in which a global curvature form is defined. Strong connections are interpreted as those that are induced from the base space of a quantum bundle. Examples of both strong and non-strong connections are provided. In particular, such connections are constructed on a quantum deformation of the fibration $S^2 -> RP^2$. A certain class of strong $U_q(2)$-connections on a trivial quantum principal bundle is shown to be equivalent to the class of connections on a free module that are compatible with the q-dependent hermitian metric. A particular form of the Yang-Mills action on a trivial U\sb q(2)-bundle is investigated. It is proved to coincide with the Yang-Mills action constructed by A.Connes and M.Rieffel. Furthermore, it is shown that the moduli space of critical points of this action functional is independent of q.Comment: AMS-LaTeX, 40 pages, major revision including examples of connections over a quantum real projective spac

Quantitative analysis of bone reactions to relative motions at implant-bone interfaces

Connective soft tissues at the interface between implants and bone, such as in human joint replacements, can endanger the stability of the implant fixation. The potential of an implant to generate interface bone resorption and form soft tissue depends on many variables, including mechanical ones. These mechanical factors can be expressed in terms of relative motions between bone and implant at the interface or deformation of the interfacial material.\ud \ud The purpose of this investigation was to determine if interface debonding and subsequent relative interface motions can be responsible for interface degradation and soft tissue interposition as seen in experiments and clinical results. A finite element computer program was augmented with a mathematical description of interface debonding, dependent on interface stress criteria, and soft tissue interface interposition, dependent on relative interface motions. Three simplified models of orthopaedic implants were constructed: a cortical bone screw for fracture fixation plates, a femoral resurfacing prosthesis and a straight stem model, cemented in a bone. The predicted computer configurations were compared with clinical observations. The computer results showed how interface disruption and fibrous tissue interposition interrelate and possibly enhance each other, whereby a progressive development of the soft tissue layer can occur.\ud \ud Around the cortical bone screw, the predicted resorption patterns were relatively large directly under the screw head and showed a pivot point in the opposite cortex. The resurfacing cup model predicted some fibrous tissue formation under the medial and lateral cup rim, whereby the medial layer developed first because of higher initial interface stresses. The straight stem model predicted initial interface failure at the proximal parts. After proximal resorption and fibrous tissue interposition, the medial interface was completely disrupted and developed an interface layer. The distal and mid lateral side maintained within the strength criterion.\ud \ud Although the applied models were relatively simple, the results showed reasonable qualitative agreement with resorption patterns found in clinical studies concerning bone screws and the resurfacing cup. The hypothesis that interface debonding and subsequent relative (micro)motions could be responsible for bone resorption and fibrous tissue propagation is thereby sustained by the results

Efficient photoionization for barium ion trapping using a dipole-allowed resonant two-photon transition

Two efficient and isotope-selective resonant two-photon ionization techniques for loading barium ions into radio-frequency (RF)-traps are demonstrated. The scheme of using a strong dipole-allowed transition at \lambda=553 nm as a first step towards ionization is compared to the established technique of using a weak intercombination line (\lambda=413 nm). An increase of two orders of magnitude in the ionization efficiency is found favoring the transition at 553 nm. This technique can be implemented using commercial all-solid-state laser systems and is expected to be advantageous compared to other narrowband photoionization schemes of barium in cases where highest efficiency and isotope-selectivity are required.Comment: 8 pages, 5 figure

Carbon emission savings and short-­term health care impacts from telemedicine: An evaluation in epilepsy

Objective: Health systems make a sizeable contribution to national emissions of greenhouse gases that contribute to global climate change. The UK National Health Service is committed to being a net zero emitter by 2040, and a potential contribution to this target could come from reductions in patient travel. Achieving this will require actions at many levels. We sought to determine potential savings and risks over the short term from telemedicine through virtual clinics. Methods: During the severe acute respiratory syndrome coronavirus 2 (SARS-2-CoV) pandemic, scheduled face-to-face epilepsy clinics at a specialist site were replaced by remote teleclinics. We used a standard methodology applying conversion factors to calculate emissions based on the total saved travel distance. A further conversion factor was used to derive emissions associated with electricity consumption to deliver remote clinics from which net savings could be calculated. Patients’ records and clinicians were interrogated to identify any adverse clinical outcomes. Results: We found that enforced telemedicine delivery for over 1200 patients resulted in the saving of ~224 000 km of travel with likely avoided emissions in the range of 35 000–40 000 kg carbon dioxide equivalent (CO2e) over a six and half month period. Emissions arising directly from remote delivery were calculated to be <200 kg CO2e (~0.5% of those for travel), representing a significant net reduction of greenhouse gas emissions. Only one direct adverse outcome was identified, with some additional benefits identified anecdotally. Significance: The use of telemedicine can make a contribution toward reduced emissions in the health care sector and, in the delivery of specialized epilepsy services, had minimal adverse clinical outcomes over the short term. However, these outcomes will likely vary with clinic locations, medical specialties and conditions

A Low Latitude Halo Stream around the Milky Way

We present evidence for a ring of stars in the plane of the Milky Way, extending at least from l = 180 deg to l = 227 deg; the ring could encircle the Galaxy. The low Galactic latitude structure is at a fairly constant distance of $R = 18 \pm 2$ kpc from the Galactic Center above the Galactic plane, and has $R = 20 \pm 2$ kpc in the region sampled below the Galactic plane. The evidence includes five hundred SDSS spectroscopic radial velocities of stars within 30 deg of the plane. The velocity dispersion of the stars associated with this structure is found to be 27 km/s at (l,b) = (198,-27), 22 km/s at (l,b) = (225, 28), 30 km/s at (l,b) = (188, 24), and 30 km/s at (l,b) = (182, 27) degrees. The structure co-rotates with the Galactic disk stars at $110 \pm 25$ km/s. The narrow measured velocity dispersion is inconsistent with power law spheroid or thick disk populations. We compare the velocity dispersion in this structure with the velocity dispersion of stars in the Sagittarius dwarf galaxy tidal stream, for which we measure a velocity dispersion of 20 km/s at (l,b) = (165, -55) degrees. We interpret our measurements as evidence for a tidally disrupted satellite of $2 \times 10^7$ to $5 \times 10^8$ solar masses which rings the Galaxy

Atomic Force Microscopy of height fluctuations of fibroblast cells

We investigated the nanometer scale height fluctuations of 3T3 fibroblast cells with the atomic force microscope (AFM) under physiological conditions. Correlation between these fluctuations and lateral cellular motility can be observed. Fluctuations measured on leading edges appear to be predominantly related to actin polymerization-depolymerization processes. We found fast (5 Hz) pulsatory behavior with 1--2 nm amplitude on a cell with low motility showing emphasized structure of stress fibres. Myosin driven contractions of stress fibres are thought to induce this pulsation.Comment: 6 pages, 5 figures, 1 tabl

Phonon and plasmon excitation in inelastic electron tunneling spectroscopy of graphite

The inelastic electron tunneling spectrum (IETS)of highly oriented pyrolitic graphite (HOPG) has been measured with scanning tunneling spectroscopy (STS) at 6K. The observed spectral features are in very good agreement with the vibrational density of states (vDOS) of graphite calculated from first principles. We discuss the enhancement of certain phonon modes by phonon-assisted tunneling in STS based on the restrictions imposed by the electronic structure of graphite. We also demonstrate for the first time the local excitation of surface-plasmons in IETS which are detected at an energy of 40 meV.Comment: PRB rapid communication, submitte

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio