Stochastic delay difference and differential equations: applications to financial markets

This thesis deals with the asymptotic behaviour of stochastic difference and functional differential equations of Itˆo type. Numerical methods which both minimise error and preserve asymptotic features of the underlying continuous equation are studied. The equations have a form which makes them suitable to model financial markets in which agents use past prices. The second chapter deals with the behaviour of moving average models of price formation. We show that the asset returns are positively and exponentially correlated, while the presence of feedback traders causes either excess volatility or a market bubble or crash. These results are robust to the presence of nonlinearities in the traders’ demand functions. In Chapters 3 and 4, we show that these phenomena persist if trading takes place continuously by modelling the returns using linear and nonlinear stochastic functional differential equations (SFDEs). In the fifth chapter, we assume that some traders base their demand on the difference between current returns and the maximum return over several trading periods, leading to an analysis of stochastic difference equations with maximum functionals. Once again it is shown that prices either fluctuate or undergo a bubble or crash. In common with the earlier chapters, the size of the largest fluctuations and the growth rate of the bubble or crash is determined. The last three chapters are devoted to the discretisation of the SFDE presented in Chapter 4. Chapter 6 highlights problems that standard numerical methods face in reproducing long–run features of the dynamics of the general continuous–time model, while showing these standard methods work in some cases. Chapter 7 develops an alternative method for discretising the solution of the continuous time equation, and shows that it preserves the desired long–run behaviour. Chapter 8 demonstrates that this alternative method converges to the solution of the continuous equation, given sufficient computational effort

Significant benefits of AIP testing and clinical screening in familial isolated and young-onset pituitary tumors

Context Germline mutations in the aryl hydrocarbon receptor-interacting protein (AIP) gene are responsible for a subset of familial isolated pituitary adenoma (FIPA) cases and sporadic pituitary neuroendocrine tumors (PitNETs). Objective To compare prospectively diagnosed AIP mutation-positive (AIPmut) PitNET patients with clinically presenting patients and to compare the clinical characteristics of AIPmut and AIPneg PitNET patients. Design 12-year prospective, observational study. Participants & Setting We studied probands and family members of FIPA kindreds and sporadic patients with disease onset ≤18 years or macroadenomas with onset ≤30 years (n = 1477). This was a collaborative study conducted at referral centers for pituitary diseases. Interventions & Outcome AIP testing and clinical screening for pituitary disease. Comparison of characteristics of prospectively diagnosed (n = 22) vs clinically presenting AIPmut PitNET patients (n = 145), and AIPmut (n = 167) vs AIPneg PitNET patients (n = 1310). Results Prospectively diagnosed AIPmut PitNET patients had smaller lesions with less suprasellar extension or cavernous sinus invasion and required fewer treatments with fewer operations and no radiotherapy compared with clinically presenting cases; there were fewer cases with active disease and hypopituitarism at last follow-up. When comparing AIPmut and AIPneg cases, AIPmut patients were more often males, younger, more often had GH excess, pituitary apoplexy, suprasellar extension, and more patients required multimodal therapy, including radiotherapy. AIPmut patients (n = 136) with GH excess were taller than AIPneg counterparts (n = 650). Conclusions Prospectively diagnosed AIPmut patients show better outcomes than clinically presenting cases, demonstrating the benefits of genetic and clinical screening. AIP-related pituitary disease has a wide spectrum ranging from aggressively growing lesions to stable or indolent disease course

A Multicenter Validity Study of Four Smartphone Hearing Test Apps in Optimized and Home Environments

Publication status: PublishedObjectivePure tone audiometry (PTA) is the gold standard for hearing assessment. However, it requires access to specialized equipment. Smartphone audiometry applications (apps) have been developed to perform automated threshold audiometry and could allow patients to perform self‐administered screening or monitoring. This study aimed to assess the validity and feasibility of patients using apps to self‐assess hearing thresholds at home, with comparison to PTA.MethodsA multi‐center, prospective randomized study was conducted amongst patients undergoing PTA in clinics. Participants were randomly allocated to one of four publicly‐available apps designed to measure pure tone thresholds. Participants used an app once in optimal sound‐treated conditions and a further three times at home. Ear‐specific frequency‐specific thresholds and pure tone average were compared using Pearson correlation coefficient. The percentage of app hearing tests with results within ±10 dB of PTA was calculated. Patient acceptability was assessed via an online survey.ResultsOne hundred thirty‐nine participants submitted data. The results of two at‐home automated smartphone apps correlated strongly/very strongly with PTA average and their frequency‐specific median was within ±10 dB accuracy. Smartphone audiometry performed in sound‐treated and home conditions were very strongly correlated. The apps were rated as easy/very easy to use by 90% of participants and 90% would be happy/very happy to use an app to monitor their hearing.ConclusionJudicious use of self‐performed smartphone audiometry was both valid and feasible for two of four apps. It could provide frequency‐specific threshold estimates at home, potentially allowing assessments of patients remotely or monitoring of fluctuating hearing loss.Level of Evidence2 Laryngoscope, 2024</jats:sec

Computer aided drug discovery of highly ligand efficient, low molecular weight imidazopyridine analogs as FLT3 inhibitors

The FLT3 kinase represents an attractive target to effectively treat AML. Unfortunately, no FLT3 targeted therapeutic is currently approved. In line with our continued interests in treating kinase related disease for anti-FLT3 mutant activity, we utilized pioneering synthetic methodology in combination with computer aided drug discovery and identified low molecular weight, highly ligand efficient, FLT3 kinase inhibitors. Compounds were analyzed for biochemical inhibition, their ability to selectively inhibit cell proliferation, for FLT3 mutant activity, and preliminary aqueous solubility. Validated hits were discovered that can serve as starting platforms for lead candidates

Landscape of Familial Isolated and Young-Onset Pituitary Adenomas: Prospective Diagnosis in AIP Mutation Carriers.

Familial isolated pituitary adenoma (FIPA) due to aryl hydrocarbon receptor interacting protein (AIP) gene mutations is an autosomal dominant disease with incomplete penetrance. Clinical screening of apparently unaffected AIP mutation (AIPmut) carriers could identify previously unrecognized disease.This article is freely available via PubMed Central. Click on the 'Additional Link' above to access the full text