The Evaluation of American Option Prices Under Stochastic Volatility and Jump-Diffusion Dynamics Using the Method of Lines

This paper considers the problem of numerically evaluating American option prices when the dynamics of the underlying are driven by both stochastic volatility following the square root process of Heston (1993), and by a Poisson jump process of the type originally introduced by Merton (1976). We develop a method of lines algorithm to evaluate the price as well as the delta and gamma of the option, thereby extending the method developed by Meyer (1998) for the case of jump-diffusion dynamics. The accuracy of the method is tested against two numerical methods that directly solve the integro-partial differential pricing equation. The first is an extension to the jump-diffusion situation of the componentwise splitting method of Ikonen & Toivanen (2007). The second method is a Crank-Nicolson scheme that is solved using projected successive over relaxation which is taken as the benchmark. The relative efficiency of these methods for computing the American call option price, delta, gamma and free boundary is analysed. If one seeks an algorithm that gives not only the price but also the delta and gamma to the same level of accuracy for a given computational effort then the method of lines seems to perform best amongst the methods considered.American options; stochastic volatility; jump-diffusion processes; Volterra integral equations; free boundary problem; method of lines

Characterisation of the immune response to type I collagen in scleroderma

This study was conducted to examine the frequency, phenotype, and functional profile of T lymphocytes that proliferate in response to type I collagen (CI) in patients with scleroderma (SSc). Peripheral blood mononuclear cells (PBMCs) from SSc patients, healthy controls, and rheumatoid arthritis disease controls were labeled with carboxy-fluorescein diacetate, succinimidyl ester (CFSE), cultured with or without antigen (bovine CI) for 14 days, and analysed by flow cytometry. Surface markers of proliferating cells were identified by multi-color flow cytometry. T-cell lines were derived after sorting for proliferating T cells (CFSE(low)). Cytokine expression in CI-responsive T cells was detected by intracellular staining/flow cytometry and by multiplex cytokine bead assay (Bio-Plex). A T-cell proliferative response to CI was detected in 8 of 25 (32%) SSc patients, but was infrequent in healthy or disease controls (3.6%; p = 0.009). The proliferating T cells expressed a CD4(+), activated (CD25(+)), memory (CD45RO(+)) phenotype. Proliferation to CI did not correlate with disease duration or extent of skin involvement. T-cell lines were generated using in vitro CI stimulation to study the functional profile of these cells. Following activation of CI-reactive T cells, we detected intracellular interferon (IFN)-γ but not interleukin (IL)-4 by flow cytometry. Supernatants from the T-cell lines generated in vitro contained IL-2, IFN-γ, GM-CSF (granulocyte macrophage-colony-stimulating factor), and tumour necrosis factor-α, but little or no IL-4 and IL-10, suggesting that CI-responsive T cells express a predominantly Th1 cytokine pattern. In conclusion, circulating memory CD4 T cells that proliferate to CI are present in a subset of patients with SSc, but are infrequent in healthy or disease controls

Noncanonical Wnt signaling promotes apoptosis in thymocyte development

The Wnt–β-catenin signaling pathway has been shown to govern T cell development by regulating the growth and survival of progenitor T cells and immature thymocytes. We explore the role of noncanonical, Wnt–Ca2+ signaling in fetal T cell development by analyzing mice deficient for Wnt5a. Our findings reveal that Wnt5a produced in the thymic stromal epithelium does not alter the development of progenitor thymocytes, but regulates the survival of αβ lineage thymocytes. Loss of Wnt5a down-regulates Bax expression, promotes Bcl-2 expression, and inhibits apoptosis of CD4+CD8+ thymocytes, whereas exogenous Wnt5a increases apoptosis of fetal thymocytes in culture. Furthermore, Wnt5a overexpression increases apoptosis in T cells in vitro and increases protein kinase C (PKC) and calmodulin-dependent kinase II (CamKII) activity while inhibiting β-catenin expression and activity. Conversely, Wnt5a deficiency results in the inhibition of PKC activation, decreased CamKII activity, and elevation of β-catenin amounts in thymocytes. These results indicate that Wnt5a induction of the noncanonical Wnt–Ca2+ pathway alters canonical Wnt signaling and is critical for normal T cell development

Analog peptides of type II collagen can suppress arthritis in HLA-DR4 (DRB1*0401) transgenic mice

Rheumatoid arthritis (RA) is an autoimmune disease associated with the recognition of self proteins secluded in diarthrodial joints. We have previously established that mice transgenic for the human DR genes associated with RA are susceptible to collagen-induced arthritis (CIA) and we have identified a determinant of type II collagen (CII(263–270)) that triggers T-cell immune responses in these mice. We have also determined that an analog of CII(263–270 )would suppress disease in DR1 transgenic mice. Because the immunodominant determinant is the same for both DR1 transgenic and DR4 transgenic mice, we attempted to determine whether the analog peptide that was suppressive in DR1 transgenic mice would also be effective in suppressing CIA in DR4 transgenic mice. We treated DR4 transgenic mice with two analog peptides of CII that contained substitutions in the core of the immunodominant determinant: CII(256–276 )(F263N, E266D) and CII(256–270 )(F263N, E266A). Mice were observed for CIA, and T-cell proliferative responses were determined. Either peptide administered at the time of immunization with CII significantly downregulated arthritis. Binding studies demonstrated that replacement of the phenylalanine residue in position 263 of the CII peptide with asparagine significantly decreased the affinity of the peptide for the DR4 molecule. In contrast, replacement of the glutamic acid residue in position 266 with aspartic acid or with alanine had differing results. Aspartic acid reduced the affinity (35-fold) whereas alanine did not. Both peptides were capable of suppressing CIA. With the use of either peptide, CII(256–276 )(F263N, E266D) or CII(256–270 )(F263N, E266A), the modulation of CIA was associated with an increase in T-cell secretion of IL-4 together with a decrease in IFN-γ. We have identified two analog peptides that are potent suppressors of CIA in DR4 transgenic mice. These experiments represent the first description of an analog peptide of CII recognized by T cells in the context of HLA-DR4 that can suppress autoimmune arthritis

Insights into patient preferences for elective surgery during the COVID-19 pandemic.

AIMS: To investigate factors that contribute to patient decisions regarding attendance for arthroplasty during the COVID-19 pandemic. METHODS: A postal questionnaire was distributed to patients on the waiting list for hip or knee arthroplasty in a single tertiary centre within the UK. Patient factors that may have influenced the decision to attend for arthroplasty, global quality of life (QoL) (EuroQol five-dimension three-level (EQ-5D-3L)), and joint-specific QoL (Oxford Hip or Knee Score) were assessed. Patients were asked at which 'COVID-alert' level they would be willing to attend an NHS and a "COVID-light" hospital for arthroplasty. Independent predictors were assessed using multivariate logistic regression. RESULTS: Of 540 distributed questionnaires, 400 (74.1%; 236 awaiting hip arthroplasty, 164 awaiting knee arthroplasty) complete responses were received and included. Less than half (48.2%) were willing to attend for hip or knee arthroplasty while a UK COVID-19 epidemic was in circulation (COVID-alert levels 3 to 5). Patients with worse joint-specific QoL had a preference to proceed with surgery at COVID-alert levels 3 to 5 compared to levels 1 and 2 (hip arthroplasty odds ratio (OR) 1.54 (95% confidence interval (CI) 1.45 to 1.63); knee arthroplasty OR 1.16 (1.07 to 1.26)). The odds of patients with worse joint-specific QoL being willing to attend for surgery at COVID-alert levels 3 to 5 increased further if surgery in a private, "COVID-light" hospital was available (hip arthroplasty OR 3.50 (95% CI 3.26 to 3.71); knee arthroplasty OR 1.41 (95% CI 1.29 to 1.53). CONCLUSION: Patient decisions surrounding elective surgery have been influenced by the global COVID-19 pandemic, highlighting the importance of patient involvement in ensuring optimized provision of elective surgery during these challenging times. Cite this article: Bone Jt Open 2021;2(4):261-270

High-resolution diffraction reveals magnetoelastic coupling and coherent phase separation in tetragonal CuMnAs

Tetragonal CuMnAs was the first antiferromagnet where reorientation of the N\'eel vector was reported to occur by an inverse spin galvanic effect. A complicating factor in the formation of phase-pure tetragonal CuMnAs is the formation of an orthorhombic phase with nearly the same stoichiometry. Pure-phase tetragonal CuMnAs has been reported to require an excess of Cu to maintain a single phase in traditional solid state synthesis reactions. Here we show that subtle differences in diffraction patterns signal pervasive inhomogeneity and phase separation, even in Cu-rich Cu$_{1.18}$Mn$_{0.82}$As. From calorimetry and magnetometry measurements, we identify two transitions corresponding to the N\'eel temperature (T$_N$) and an antiferromagnet to weak ferromagnet transition in Cu$_{1.18}$Mn$_{0.82}$As and CuMn$_{0.964}$As$_{1.036}$. These transitions have clear crystallographic signatures, directly observable in the lattice parameters upon in-situ heating and cooling. The immiscibility and phase separation could arise from a spinoidal decomposition that occurs at high temperatures, and the presence of a ferromagnetic transition near room temperature warrants further investigation of its effect on the electrical switching behavior.Comment: 10 pages, 9 figures, added author middle initia

Simulating Electron Transport and Synchrotron Emission in Radio Galaxies: Shock Acceleration and Synchrotron Aging in Axis-Symmetric Flows

We introduce a simple and economical but effective method for including relativistic electron transport in multi-dimensional simulations of radio galaxies. The method is designed to follow explicitly diffusive acceleration at shocks, and, in smooth flows 2nd order Fermi acceleration plus adiabatic and synchrotron cooling. We are able to follow both the spatial and energy distributions of the electrons, so that direct synchrotron emission properties can be modeled in time-dependent flows for the first time. Here we present first results in the form of some axis-symmetric MHD simulations of Mach 20 light jet flows. These show clearly the importance of nonsteady terminal shocks that develop in such flows even when the jet inflow is steady. As a result of this and other consequences of the fundamentally driven character of jets, we find complex patterns of emissivities and synchrotron spectra, including steep spectral gradients in hot spots, islands of distinct spectra electrons within the lobes and spectral gradients coming from the dynamical histories of a given flow element rather than from synchrotron aging of the embedded electrons. In addition, spectral aging in the lobes tends to proceed more slowly than one would estimate from regions of high emissivity.Comment: 30 pages of Latex generated text plus 7 figures in gif format. Accepted for publication in the Astrophysical Journal. High resolution postscript figures available through anonymous ftp at ftp://ftp.msi.umn.edu/pub/users/twj/RGje

Bioresorbable silicon electronics for transient spatiotemporal mapping of electrical activity from the cerebral cortex.

Bioresorbable silicon electronics technology offers unprecedented opportunities to deploy advanced implantable monitoring systems that eliminate risks, cost and discomfort associated with surgical extraction. Applications include postoperative monitoring and transient physiologic recording after percutaneous or minimally invasive placement of vascular, cardiac, orthopaedic, neural or other devices. We present an embodiment of these materials in both passive and actively addressed arrays of bioresorbable silicon electrodes with multiplexing capabilities, which record in vivo electrophysiological signals from the cortical surface and the subgaleal space. The devices detect normal physiologic and epileptiform activity, both in acute and chronic recordings. Comparative studies show sensor performance comparable to standard clinical systems and reduced tissue reactivity relative to conventional clinical electrocorticography (ECoG) electrodes. This technology offers general applicability in neural interfaces, with additional potential utility in treatment of disorders where transient monitoring and modulation of physiologic function, implant integrity and tissue recovery or regeneration are required

Rapamycin rejuvenates oral health in aging mice.

Periodontal disease is an age-associated disorder clinically defined by periodontal bone loss, inflammation of the specialized tissues that surround and support the tooth, and microbiome dysbiosis. Currently, there is no therapy for reversing periodontal disease, and treatment is generally restricted to preventive measures or tooth extraction. The FDA-approved drug rapamycin slows aging and extends lifespan in multiple organisms, including mice. Here, we demonstrate that short-term treatment with rapamycin rejuvenates the aged oral cavity of elderly mice, including regeneration of periodontal bone, attenuation of gingival and periodontal bone inflammation, and revertive shift of the oral microbiome toward a more youthful composition. This provides a geroscience strategy to potentially rejuvenate oral health and reverse periodontal disease in the elderly