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A credit default swap (CDS) is an exchange of premium payments for a compensation for the occurrence of a credit event. Counterparty risks refer to defaults of parties holding CDS contracts. In this paper we develop a valuation/pricing model for a CDS subject to counterparty risks. Using the Cox–Ingersoll–Ross (CIR) model for interest rate and first arrival times of Poisson processes with variable intensities for the occurrences of credit default and counterparty defaults, we derive a mathematical formulation and make a full theoretical investigation. In addition, we develop a full theory for the corresponding infinite horizon problem and establish its connection with the asymptotic long expiry behaviour of finite horizon problem. Furthermore, we establish a connection between two major frameworks for default times: the structure model approach and the intensity model approach. We show that a solution of the structure model can be obtained as the limit of a sequence of solutions of intensity models. Regarded as an important theoretical development, we remove a constraint typically imposed on the parameters of the CIR model; that is, the well-posedness (existence, uniqueness and continuous dependence of parameters) of the mathematical model holds for any empirically calibrated parameters for the CIR model.
The Weibel instability and the induced magnetic field are of great importance for both astrophysics and inertial confinement fusion. Because of the stochasticity of this magnetic field, its main wavelength and mean strength, which are key characteristics of the Weibel instability, are still unobtainable experimentally. In this paper, a theoretical model based on the autocorrelation tensor shows that in proton radiography of the Weibel-instability-induced magnetic field, the proton flux density on the detection plane can be related to the energy spectrum of the magnetic field. It allows us to extract the main wavelength and mean strength of the two-dimensionally isotropic and stochastic magnetic field directly from proton radiography for the first time. Numerical calculations are conducted to verify our theory and show good consistency between pre-set values and the results extracted from proton radiography.
SCN5A encodes sodium-channel α-subunit Nav1.5. The mutations of SCN5A can lead to hereditary cardiac arrhythmias such as the long-QT syndrome type 3 and Brugada syndrome. Here we sought to identify novel mutations in a family with arrhythmia.
Genomic DNA was isolated from blood of the proband, who was diagnosed with atrial flutter. Illumina Hiseq 2000 whole-exome sequencing was performed and an arrhythmia-related gene-filtering strategy was used to analyse the pathogenic genes. Sanger sequencing was applied to verify the mutation co-segregated in the family.
Results and conclusions
A novel missense mutation in SCN5A (C335R) was identified, and this mutation co-segregated within the affected family members. This missense mutation was predicted to result in amplitude reduction in peak Na+ current, further leading to channel protein dysfunction. Our study expands the spectrum of SCN5A mutations and contributes to genetic counselling of families with arrhythmia.
Very few recent studies are available that compare caregiver burden, sleep quality, and stress in caregivers of different types of dementia. We aimed to investigate caregiver burden, sleep quality, and stress in caregivers of patients with frontotemporal lobar degeneration and dementia with Lewy bodies, as compared with caregivers of patients with Alzheimer's disease.
This study was carried out from March 2011 to January 2014. In total, 492 dyads of patient and caregiver (frontotemporal lobar degeneration, n = 131; dementia with Lewy bodies, n = 36; Alzheimer's disease, n = 325) participated in this study. We compared patients with respect to the Neuropsychiatric Inventory and caregivers with respect to the Zarit Caregiver Burden Interview, Pittsburgh Sleep Quality Index, Patient Health Questionnaire-9, and Generalized Anxiety Disorder scale.
Frontotemporal lobar degeneration and dementia with Lewy bodies patients presented significantly more neuropsychiatric symptoms compared to Alzheimer's disease patients. Caregivers of frontotemporal lobar degeneration and dementia with Lewy bodies patients experienced significantly more burden compared to Alzheimer's disease caregivers. Furthermore, among caregivers of both frontotemporal lobar degeneration and dementia with Lewy bodies patients burden was predicted by the neuropsychiatric symptoms, PHQ-9 scores, and GAD-7 scores.
The frequency and severity of behavioral disturbances in patient and caregiver stress accounted for the increased caregiver burden, which suggests that frontotemporal lobar degeneration and dementia with Lewy bodies caregivers should receive more support than is currently available.
There is increasing demand for navigation capability for space vehicles. The idea to extend the application of Global Navigation Satellite Systems (GNSS) from terrestrial to space applications by the use of main beam and side lobe signals has been shown to be feasible. In order to understand the performance and the potential space applications GNSS can support, this paper characterises the Space Service Volume (SSV) in terms of the four parameters of minimum received power, satellite visibility, pseudorange accuracy and Geometric Dilution of Precision (GDOP). This new definition enables the position errors to be estimated. An analytical methodology is proposed to characterise minimum received power for the worst location. Satellite visibility and GDOP are assessed based on grid points at different height layers (to capture the relationship between height and visibility) for single and multiple GNSS constellations, the former represented by BeiDou III (BDS III) and the latter, BDS III in various combinations with GPS, GLONASS and GALILEO. Additional simulation shows that GNSS can potentially support lunar exploration spacecraft at the Earth phasing orbit. This initial assessment of SSV shows the potential of GNSS for space vehicle navigation.
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