A new theory of stochastic integration

In this dissertation, we focus mainly on the further study of the new stochastic integral introduced by Ayed and Kuo in 2008. Several properties of this new stochastic integral are obtained. We first introduce the concept of near-martingale for non-adapted stochastic processes. This concept is a generalization of the martingale property for adapted stochastic processes in the It\^o theory. We prove a special case of It\^o isometry for the stochastic integral of certain instantly independent processes. We obtain some formulas for expressing a new stochastic integral in terms of It\^o integrals and Riemann integrals. Several generalized versions of It\^o\u27s formula for the new stochastic integral obtained by Ayed and Kuo are given. We also provide some examples to illustrate the ideas

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首都大学東京, 2014-09-30, 博士（工学）首都大学東

Interval Estimation of Diagnostic Odds Ratio in Meta-analysis by Means of Profile Likelihoods

AbstractThe objectives of this paper are to (1) derive the profile maximum likelihood estimator (PMLE) for a true diagnostic odds ratio over across k studies in meta-analysis, (2) build the confidence intervals by replacing PMLE into the variance of logarithm of each diagnostic odds ratio, leading to two profile likelihood intervals (WPLF, WPLR), (3) create bootstrapping confidence interval (BOOT) from PMLE distribution by using the percentile, (4) compare the interval performance between all profile intervals with the conventional intervals, such as Mantel-Haenszel method (MH) and Weighted least squares method (WLS) in terms of the coverage probability and the width of interval. The results under a simulation plan indicated that for moderated study size (k = 8, 16) and small sample size , there were only three proposed interval estimates (WPLF, WPLR, and BOOT) that could be calibrated the coverage probability at 95% and the interval widths of WPLF and WPLR are narrower than the BOOT. Hence, we recommend to use WPLF and WPLR rather than the conventional intervals in such situations

Klebsiella pneumoniae Orbital Cellulitis with Extensive Vascular Occlusions in a Patient with Type 2 Diabetes

A 39-year-old woman visited the emergency room complaining of right eye pain and swelling over the preceding three days. The ophthalmologist's examination revealed orbital cellulitis and diabetic retinopathy in the right eye, although the patient had no prior diagnosis of diabetes. It was therefore suspected that she had diabetes and orbital cellulitis, and she was started on multiple antibiotic therapies initially. She then underwent computed tomography scans of the orbit and neck and magnetic resonance imaging of the brain. These studies showed an aggravated orbital cellulitis with abscess formation, associated with venous thrombophlebitis, thrombosis of the internal carotid artery, and mucosal thickening of maxillary sinus with multiple paranasal abscesses. Three days later, initial blood culture grew Klebsiella pneumoniae. She recovered after incision and drainage and antibiotic therapy for 37 days

Hybrid Equation/Agent-Based Model of Ischemia-Induced Hyperemia and Pressure Ulcer Formation Predicts Greater Propensity to Ulcerate in Subjects with Spinal Cord Injury

Pressure ulcers are costly and life-threatening complications for people with spinal cord injury (SCI). People with SCI also exhibit differential blood flow properties in non-ulcerated skin. We hypothesized that a computer simulation of the pressure ulcer formation process, informed by data regarding skin blood flow and reactive hyperemia in response to pressure, could provide insights into the pathogenesis and effective treatment of post-SCI pressure ulcers. Agent-Based Models (ABM) are useful in settings such as pressure ulcers, in which spatial realism is important. Ordinary Differential Equation-based (ODE) models are useful when modeling physiological phenomena such as reactive hyperemia. Accordingly, we constructed a hybrid model that combines ODEs related to blood flow along with an ABM of skin injury, inflammation, and ulcer formation. The relationship between pressure and the course of ulcer formation, as well as several other important characteristic patterns of pressure ulcer formation, was demonstrated in this model. The ODE portion of this model was calibrated to data related to blood flow following experimental pressure responses in non-injured human subjects or to data from people with SCI. This model predicted a higher propensity to form ulcers in response to pressure in people with SCI vs. non-injured control subjects, and thus may serve as novel diagnostic platform for post-SCI ulcer formation. © 2013 Solovyev et al

Manticore: Efficient Framework for Scalable Secure Multiparty Computation Protocols

We propose a novel MPC framework, Manticore, in the multiparty setting, with full threshold and semi-honest security model, supporting a combination of real number arithmetic (arithmetic shares), Boolean arithmetic (Boolean shares) and garbled circuits (Yao shares). In contrast to prior work [MZ17, MR18], Manticore never overflows, an important feature for machine learning applications. It achieves this without compromising efficiency or security. Compared to other overflow-free recent techniques such as MP-SPDZ [EGKRS20] that convert arithmetic to Boolean shares, we introduce a novel highly efficient modular lifting/truncation method that stays in the arithmetic domain. We revisit some of the basic MPC operations such as real-valued polynomial evaluation, division, logarithm, exponential and comparison by employing our modular lift in combination with existing efficient conversions between arithmetic, Boolean and Yao shares. Furthermore, we provide a highly efficient and scalable implementation supporting logistic regression models with real-world training data sizes and high numerical precision through PCA and blockwise variants (for memory and runtime optimizations). On a dataset of 50 million rows and 50 columns distributed among two players, it completes in one day with at least 10 decimal digits of precision.Our logistic regression solution placed first at Track 3 of the annual iDASH’2020 Competition. Finally, we mention a novel oblivious sorting algorithm built using Manticore