Quantum projection filter for a highly nonlinear model in cavity QED

Both in classical and quantum stochastic control theory a major role is played by the filtering equation, which recursively updates the information state of the system under observation. Unfortunately, the theory is plagued by infinite-dimensionality of the information state which severely limits its practical applicability, except in a few select cases (e.g. the linear Gaussian case.) One solution proposed in classical filtering theory is that of the projection filter. In this scheme, the filter is constrained to evolve in a finite-dimensional family of densities through orthogonal projection on the tangent space with respect to the Fisher metric. Here we apply this approach to the simple but highly nonlinear quantum model of optical phase bistability of a stongly coupled two-level atom in an optical cavity. We observe near-optimal performance of the quantum projection filter, demonstrating the utility of such an approach.Comment: 19 pages, 6 figures. A version with high quality images can be found at http://minty.caltech.edu/papers.ph

Sulfide-, fluorite-, barite-bearing siliceous "crusts" related to unconformity surfaces of different ages in Pyrenees and Alps: a new model in carbonate-hosted deposits?

Wumerous stratabound sulfide-, barite-, fluonte-bearing siliceous crusts, from dm to some tens of in thick, occur over large areas of the Alpine belt, ;.e. the Alps and the Pyrenees. They are linked to unconformlty landscapes evolved on various carbonate units of Paieozoic and Triassic sedimentq sequences. Since the study mineralizations constitute the transition between the underlying carbonates and the overlying detrital units, they can be considered as an independent lithostratigraphic units that record a particular metalogenetic process not only in the alpine chains but worldwide. These mineralizations exhibit several morphologies: tabular concordant with the unconfonnities bodies, columnar bodies, karstic cavity-fillings, laminites and veins. In addition, the study deposits are clearly affected by remobilization process occuned during diagenesis or metamorphism. Such processes are responsible for masking the occunence of the breccia/conglomerate typically located at the base of the orebodies.Although the study mineralizations have usually been included in MVT deposit class, constrastirig differences between their diagnostic features and those of MVT mineralizations, suggest that the inclusion of the mineralized crust deposits in the MVT group seem incorrect.These peculiar ore-bearing quartz-crusts, persistent over large areas and showing an independent and distinct character and constituting an important marker for some sedimentary sequences of different ages in Alpine belts, allow the authors to define a new metallogenic model named as "crust-type" (CT) deposits. Comparable mineralization in other geotectonic environments outside Alpine belts point out to CT deposits being a worldwide significant metallogenic event

Derivative pricing for a multi-curve extension of the Gaussian, exponentially quadratic short rate model

The recent financial crisis has led to so-called multi-curve models for the term structure. Here we study a multi-curve extension of short rate models where, in addition to the short rate itself, we introduce short rate spreads. In particular, we consider a Gaussian factor model where the short rate and the spreads are second order polynomials of Gaussian factor processes. This leads to an exponentially quadratic model class that is less well known than the exponentially affine class. In the latter class the factors enter linearly and for positivity one considers square root factor processes. While the square root factors in the affine class have more involved distributions, in the quadratic class the factors remain Gaussian and this leads to various advantages, in particular for derivative pricing. After some preliminaries on martingale modeling in the multi-curve setup, we concentrate on pricing of linear and optional derivatives. For linear derivatives, we exhibit an adjustment factor that allows one to pass from pre-crisis single curve values to the corresponding post-crisis multi-curve values

Can a Loan Valuation Adjustment (LVA) Approach Immunize Collateralized Debt from Defaults?

This study focuses on structuring tangible asset backed loans to inhibit their endemic option to default. We adapt the pragmatic approach of a margin loan in the configuring of collateralized debt to yield a quasi‐default‐free facility. We link our practical method to the current Basel III (2017) regulatory framework. Our new concept of the Loan Valuation Adjustment (LVA) and novel method to minimize the LVA converts the risky loan into a quasi risk‐free loan and achieves value maximization for the lending financial institution. As a result, entrepreneurial activities are promoted and economic growth invigorated. Information asymmetry, costly bailouts and resulting financial fragility are reduced while depositors are endowed with a safety net equivalent to deposit insurance but without the associated moral hazard between risk‐averse lenders and borrowers

Affine term structure models : a time-changed approach with perfect fit to market curves

We address the so-called calibration problem which consists of fitting in a tractable way a given model to a specified term structure like, e.g., yield or default probability curves. Time-homogeneous jump-diffusions like Vasicek or Cox-Ingersoll-Ross (possibly coupled with compounded Poisson jumps, JCIR), are tractable processes but have limited flexibility; they fail to replicate actual market curves. The deterministic shift extension of the latter (Hull-White or JCIR++) is a simple but yet efficient solution that is widely used by both academics and practitioners. However, the shift approach is often not appropriate when positivity is required, which is a common constraint when dealing with credit spreads or default intensities. In this paper, we tackle this problem by adopting a time change approach. On the top of providing an elegant solution to the calibration problem under positivity constraint, our model features additional interesting properties in terms of implied volatilities. It is compared to the shift extension on various credit risk applications such as credit default swap, credit default swaption and credit valuation adjustment under wrong-way risk. The time change approach is able to generate much larger volatility and covariance effects under the positivity constraint. Our model offers an appealing alternative to the shift in such cases.Comment: 44 pages, figures and table

Transorbital Sonography in Acute Optic Neuritis: A Case-Control Study

BACKGROUND AND PURPOSE: Acute unilateral optic neuritis is associated with a thickening of the retrobulbar portion of the optic nerve as revealed by transorbital sonography, but no comparison has been made between nerve sheath diameter and optic nerve diameter in patients with acute optic neuritis versus healthy controls. We evaluated optic nerve sheath diameter and optic nerve diameter in patients with acute optic neuritis and healthy controls and compared optic nerve sheath diameter and optic nerve diameter with visual-evoked potentials in patients. MATERIALS AND METHODS: A case-control study was performed in 2 centers. Twenty-one consecutive patients with onset of visual loss during the prior 10 days and established acute noncompressive unilateral optic neuritis were compared with 21 healthy controls, matched for sex and age (±5 years). Two experienced vascular sonographers performed the study by using B-mode transorbital sonography. Visual-evoked potentials were performed on the same day as the transorbital sonography and were evaluated by an expert neurophysiologist. Sonographers and the neurophysiologist were blinded to the status of the patient or control and to clinical information, including the side of the affected eye. RESULTS: The median optic nerve sheath diameter was thicker on the affected side (6.3 mm; interquartile range, 5.9–7.2 mm) compared with the nonaffected side (5.5 mm; interquartile range, 5.1–6.2 mm; P P P = not significant.). Both sides were thicker than those in controls (2.7 mm; interquartile range, 2.5–2.8 mm; P = .001 and .009). No correlation was found between optic nerve sheath diameter and optic nerve diameter and amplitude and latency of visual-evoked potentials in patients with optic neuritis. CONCLUSIONS: Transorbital sonography is a promising tool to support the clinical diagnosis of acute optic neuritis. Further studies are needed to define its specific role in the diagnosis and follow-up of optic neuritis

Management of osteoporosis in men: A narrative review

Male osteoporosis is a still largely underdiagnosed pathological condition. As a conse-quence, bone fragility in men remains undertreated mainly due to the low screening frequency and to controversies in the bone mineral density (BMD) testing standards. Up to the 40% of overall osteo-porotic fractures affect men, in spite of the fact that women have a significant higher prevalence of osteoporosis. In addition, in males, hip fractures are associated with increased morbidity and mortality as compared to women. Importantly, male fractures occur about 10 years later in life than women, and, therefore, due to the advanced age, men may have more comorbidities and, consequently, their mortality is about twice the rate in women. Gender differences, which begin during puberty, lead to wider bones in males as compared with females. In men, follicle-stimulating hormones, testosterone, estrogens, and sex hormone-binding levels, together with genetic factors, interact in determining the peak of bone mass, BMD maintenance, and lifetime decrease. As compared with women, men are more frequently affected by secondary osteoporosis. Therefore, in all osteoporotic men, a complete clinical history should be collected and a careful physical examination should be done, in order to find clues of a possible underlying diseases and, ultimately, to guide laboratory testing. Currently, the pharmacological therapy of male osteoporosis includes aminobisphosphonates, denosumab, and teriparatide. Hypogonadal patients may be treated with testosterone replacement therapy. Given that the fractures related to mortality are higher in men than in women, treating male subjects with osteoporosis is of the utmost importance in clinical practice, as it may impact on mortality even more than in women

Intravital three-dimensional bioprinting

Fabrication of three-dimensional (3D) structures and functional tissues directly in live animals would enable minimally invasive surgical techniques for organ repair or reconstruction. Here, we show that 3D cell-laden photosensitive polymer hydrogels can be bioprinted across and within tissues of live mice, using bio-orthogonal two-photon cycloaddition and crosslinking of the polymers at wavelengths longer than 850 nm. Such intravital 3D bioprinting—which does not create by-products and takes advantage of commonly available multiphoton microscopes for the accurate positioning and orientation of the bioprinted structures into specific anatomical sites—enables the fabrication of complex structures inside tissues of live mice, including the dermis, skeletal muscle and brain. We also show that intravital 3D bioprinting of donor-muscle-derived stem cells under the epimysium of hindlimb muscle in mice leads to the de novo formation of myofibres in the mice. Intravital 3D bioprinting could serve as an in vivo alternative to conventional bioprinting