A Delayed Black and Scholes Formula I

In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the proposed model is sufficiently flexible to fit real market data, and is yet simple enough to allow for a closed-form representation of the option price. Furthermore, the model maintains the no-arbitrage property and the completeness of the market. The derivation of the option-pricing formula is based on an equivalent martingale measure

Froth-like minimizers of a non local free energy functional with competing interactions

We investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the antiferromagnetic interaction is assumed to have a range much larger than the ferromagnetic one. The competition between these two effects is expected to lead to the spontaneous emergence of a regular alternation of long intervals on which the spin profile is magnetized either up or down, with an oscillation scale intermediate between the range of the ferromagnetic and that of the antiferromagnetic interaction. In this sense, the optimal or quasi-optimal profiles are "froth-like": if seen on the scale of the antiferromagnetic potential they look neutral, but if seen at the microscope they actually consist of big bubbles of two different phases alternating among each other. In this paper we prove the validity of this picture, we compute the oscillation scale of the quasi-optimal profiles and we quantify their distance in norm from a reference periodic profile. The proof consists of two main steps: we first coarse grain the system on a scale intermediate between the range of the ferromagnetic potential and the expected optimal oscillation scale; in this way we reduce the original functional to an effective "sharp interface" one. Next, we study the latter by reflection positivity methods, which require as a key ingredient the exact locality of the short range term. Our proof has the conceptual interest of combining coarse graining with reflection positivity methods, an idea that is presumably useful in much more general contexts than the one studied here.Comment: 38 pages, 2 figure

Inter-rater reliability of the EPUAP pressure ulcer classification system using photographs

Background. Many classification systems for grading pressure ulcers are discussed in the literature. Correct identification and classification of a pressure ulcer is important for accurate reporting of the magnitude of the problem, and for timely prevention. The reliability of pressure ulcer classification systems has rarely been tested. Aims and objectives. The purpose of this paper is to examine the inter-rater reliability of classifying pressure ulcers according to the European Pressure Ulcer Advisory Panel classification system when using pressure ulcer photographs.Design. Survey was among pressure ulcer experts.Methods. Fifty-six photographs were presented to 44 pressure ulcer experts. The experts classified the lesions as normal skin, blanchable erythema, pressure ulcer (four grades) or incontinence lesion. Inter-rater reliability was calculated.Results. The multirater-Kappa for the entire group of experts was 0.80 (P < 0.001).Various groups of experts obtained comparable results. Differences in classifications are mainly limited to 1 degree of difference. Incontinence lesions are most often confused with grade 2 (blisters) and grade 3 pressure ulcers (superficial pressure ulcers).Conclusions. The inter-rater reliability of the European Pressure Ulcer Advisory Panel classification appears to be good for the assessment of photographs by experts. The difference between an incontinence lesion and a blister or a superficial pressure ulcer does not always seem clear.Relevance to clinical practice. The ability to determine correctly whether a lesion is a pressure ulcer lesion is important to assess the effectiveness of preventive measures. In addition, the ability to make a correct distinction between pressure ulcers and incontinence lesions is important as they require different preventive measures. A faulty classification leads to mistaken measures and negative results. Photographs can be used as a practice instrument to learn to discern pressure ulcers from incontinence lesions and to get to know the different grades of pressure ulcers. The Pressure Ulcer Classification software package has been developed to facilitate learning

Stellar structure and compact objects before 1940: Towards relativistic astrophysics

Since the mid-1920s, different strands of research used stars as "physics laboratories" for investigating the nature of matter under extreme densities and pressures, impossible to realize on Earth. To trace this process this paper is following the evolution of the concept of a dense core in stars, which was important both for an understanding of stellar evolution and as a testing ground for the fast-evolving field of nuclear physics. In spite of the divide between physicists and astrophysicists, some key actors working in the cross-fertilized soil of overlapping but different scientific cultures formulated models and tentative theories that gradually evolved into more realistic and structured astrophysical objects. These investigations culminated in the first contact with general relativity in 1939, when J. Robert Oppenheimer and his students George Volkoff and Hartland Snyder systematically applied the theory to the dense core of a collapsing neutron star. This pioneering application of Einstein's theory to an astrophysical compact object can be regarded as a milestone in the path eventually leading to the emergence of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal

Bending bad—testing caramel wafer bars (#TestATunnocks)

During the coronavirus pandemic, there have been significant challenges in the remote teaching and demonstration of experiments, especially those that require laboratory testing equipment. With a desire to give students a feel for our materials laboratory on open days and allow them to gain a deeper understanding of what materials science and engineering is about, we have designed an experiment focused on composite materials that can be performed remotely and without specialist equipment. This enabled students to experience a bend test sensorily through seeing, hearing and feeling it, creating a strong link to then being able to relate it to the pre-prepared experimental data taken in the laboratory. This fun, easy-to-run and engaging experiment allowed a shared experience and encouraged a discussion about students' observations, differences in results and implications of the bend strength of sandwich composites. We have found it not only works well universally by all ages but can be used with younger children to think about words such as 'stronger', 'stiffer' and 'flexible' and how materials can be different in different directions

Validation of the NANA (Novel Assessment of Nutrition and Ageing) touch screen system for use at home by older adults

Prospective measurement of nutrition, cognition, and physical activity in later life would facilitate early detection of detrimental change and early intervention but is hard to achieve in community settings. Technology can simplify the task and facilitate daily data collection. The Novel Assessment of Nutrition and Ageing (NANA) toolkit was developed to provide a holistic picture of an individual's function including diet, cognition and activity levels. This study aimed to validate the NANA toolkit for data collection in the community. Forty participants aged 65 years and over trialled the NANA toolkit in their homes for three 7-day periods at four-week intervals. Data collected using the NANA toolkit were compared with standard measures of diet (four-day food diary), cognitive ability (processing speed) and physical activity (self-report). Bland–Altman analysis of dietary intake (energy, carbohydrates, protein fat) found a good relationship with the food diary and cognitive processing speed and physical activity (hours) were significantly correlated with their standard counterparts. The NANA toolkit enables daily reporting of data that would otherwise be collected sporadically while reducing demands on participants; older adults can complete the daily reporting at home without a researcher being present; and it enables prospective investigation of several domains at onc

Grain Surface Models and Data for Astrochemistry

AbstractThe cross-disciplinary field of astrochemistry exists to understand the formation, destruction, and survival of molecules in astrophysical environments. Molecules in space are synthesized via a large variety of gas-phase reactions, and reactions on dust-grain surfaces, where the surface acts as a catalyst. A broad consensus has been reached in the astrochemistry community on how to suitably treat gas-phase processes in models, and also on how to present the necessary reaction data in databases; however, no such consensus has yet been reached for grain-surface processes. A team of ∼25 experts covering observational, laboratory and theoretical (astro)chemistry met in summer of 2014 at the Lorentz Center in Leiden with the aim to provide solutions for this problem and to review the current state-of-the-art of grain surface models, both in terms of technical implementation into models as well as the most up-to-date information available from experiments and chemical computations. This review builds on the results of this workshop and gives an outlook for future directions

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

Jet size dependence of single jet suppression in lead-lead collisions at sqrt(s(NN)) = 2.76 TeV with the ATLAS detector at the LHC

Measurements of inclusive jet suppression in heavy ion collisions at the LHC provide direct sensitivity to the physics of jet quenching. In a sample of lead-lead collisions at sqrt(s) = 2.76 TeV corresponding to an integrated luminosity of approximately 7 inverse microbarns, ATLAS has measured jets with a calorimeter over the pseudorapidity interval |eta| < 2.1 and over the transverse momentum range 38 < pT < 210 GeV. Jets were reconstructed using the anti-kt algorithm with values for the distance parameter that determines the nominal jet radius of R = 0.2, 0.3, 0.4 and 0.5. The centrality dependence of the jet yield is characterized by the jet "central-to-peripheral ratio," Rcp. Jet production is found to be suppressed by approximately a factor of two in the 10% most central collisions relative to peripheral collisions. Rcp varies smoothly with centrality as characterized by the number of participating nucleons. The observed suppression is only weakly dependent on jet radius and transverse momentum. These results provide the first direct measurement of inclusive jet suppression in heavy ion collisions and complement previous measurements of dijet transverse energy imbalance at the LHC.Comment: 15 pages plus author list (30 pages total), 8 figures, 2 tables, submitted to Physics Letters B. All figures including auxiliary figures are available at http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/HION-2011-02