A Gradually Reinforced Sample-Average-Approximation Differentiable Homotopy Method for a System of Stochastic Equations

This paper intends to apply the sample-average-approximation (SAA) scheme to solve a system of stochastic equations (SSE), which has many applications in a variety of fields. The SAA is an effective paradigm to address risks and uncertainty in stochastic models from the perspective of Monte Carlo principle. Nonetheless, a numerical conflict arises from the sample size of SAA when one has to make a tradeoff between the accuracy of solutions and the computational cost. To alleviate this issue, we incorporate a gradually reinforced SAA scheme into a differentiable homotopy method and develop a gradually reinforced sample-average-approximation (GRSAA) differentiable homotopy method in this paper. By introducing a series of continuously differentiable functions of the homotopy parameter $t$ ranging between zero and one, we establish a differentiable homotopy system, which is able to gradually increase the sample size of SAA as $t$ descends from one to zero. The set of solutions to the homotopy system contains an everywhere smooth path, which starts from an arbitrary point and ends at a solution to the SAA with any desired accuracy. The GRSAA differentiable homotopy method serves as a bridge to link the gradually reinforced SAA scheme and a differentiable homotopy method and retains the nice property of global convergence the homotopy method possesses while greatly reducing the computational cost for attaining a desired solution to the original SSE. Several numerical experiments further confirm the effectiveness and efficiency of the proposed method

Synthetic aperture imagery for high-resolution imaging sonar

Synthetic aperture sonar (SAS) can provide high-resolution underwater images. Traditional fast imaging algorithms designed for multi-receiver synthetic aperture sonar (MSAS) are complex because the point target reference spectrum (PTRS) deduction and imaging algorithm development are complicated. This paper proposes an imaging algorithm for the MSAS system to solve this issue. The proposed method first approximates the two-round slant range based on the phase center approximation method. The PTRS, including the quasi-monostatic and bistatic deformation terms, can be easily deduced. After compensating for the bistatic deformation term based on the interpolation and complex multiplication with the preprocessing step, the MSAS imagery can be simplified to the focus of the traditional monostatic SAS. Therefore, the conventional imaging algorithms designed for traditional monostatic SAS can be used directly. The proposed method providing high-resolution imaging results is more efficient than the traditional methods

Directional mechanical stability of Bacteriophage φ29 motor’s 3WJ-pRNA: Extraordinary robustness along portal axis

The molecular motor exploited by bacteriophage φ29 to pack DNA into its capsid is regarded as one of the most powerful mechanical devices present in viral, bacterial, and eukaryotic systems alike. Acting as a linker element, a prohead RNA (pRNA) effectively joins the connector and ATPase (adenosine triphosphatase) components of the φ29 motor. During DNA packing, this pRNA needs to withstand enormous strain along the capsid’s portal axis—how this remarkable stability is achieved remains to be elucidated. We investigate the mechanical properties of the φ29 motor’s three-way junction (3WJ)–pRNA using a combined steered molecular dynamics and atomic force spectroscopy approach. The 3WJ exhibits strong resistance to stretching along its coaxial helices, demonstrating its super structural robustness. This resistance disappears, however, when external forces are applied to the transverse directions. From a molecular standpoint, we demonstrate that this direction-dependent stability can be attributed to two Mg clamps that cooperate and generate mechanical resistance in the pRNA’s coaxial direction. Our results suggest that the asymmetric nature of the 3WJ’s mechanical stability is entwined with its biological function: Enhanced rigidity along the portal axis is likely essential to withstand the strain caused by DNA condensation, and flexibility in other directions should aid in the assembly of the pRNA and its association with other motor components

Blood biomarkers for new-onset hypertension in midlife women:a nested case-control study

Objective Midlife in women is associated with an increase in prevalence of hypertension. Little is known on the risk factors of new-onset hypertension among middle-aged women. Methods In this nested case-control study, 1,430 women aged 40 to 60 years with repeated physical examinations between 2009 and 2019 were recruited. Data included age, body mass index, blood pressure (BP), and a series of blood biomarkers. Participants with hypertension were divided into two case-control samples: 388 cases with episodic new-onset hypertension (ie, one normal BP at the first visit and one abnormal BP during follow-up) each with two age-matched controls (n = 776) and 151 cases with regular new-onset hypertension (ie, normal BP at the first two visits and abnormal BP at two or more follow-up visits) each with three age-matched controls (n = 453). Multivariable-adjusted logistic regression was used to analyze the data. Results Our data showed very consistent results for episodic and regular new-onset hypertension, respectively, and verified known associations (odds ratio [95% confidence interval], per SD increase) with obesity (body mass index, 1.72 [1.49-1.98] and 1.81 [1.45-2.26]), inflammation (white blood cell count, 1.39 [1.23-1.58] and 1.38 [1.13-1.69]), and metabolic dysregulation (triglycerides, 1.25 [1.09-1.44] and 1.31 [1.08-1.58]; glucose, 1.46 [1.23-1.73] and 1.27 [1.05-1.54]) but, more surprisingly, also revealed positive associations with red blood cell count (1.27 [1.11-1.44] and 1.38 [1.14-1.68]), hemoglobin (1.18 [1.03-1.35] and 1.31 [1.05-1.64]), and platelet count (1.39 [1.20-1.61] and 1.33 [1.09-1.63]). Conclusions In addition to obesity and metabolic dysregulation, increased hemoglobin and counts of platelets, and red and white blood cells are associated with hypertension in this period. Future study may verify whether these associations are causal in nature and whether these variables are useful in risk stratification.</p

Blood biomarkers for new-onset hypertension in midlife women:a nested case-control study

Objective Midlife in women is associated with an increase in prevalence of hypertension. Little is known on the risk factors of new-onset hypertension among middle-aged women. Methods In this nested case-control study, 1,430 women aged 40 to 60 years with repeated physical examinations between 2009 and 2019 were recruited. Data included age, body mass index, blood pressure (BP), and a series of blood biomarkers. Participants with hypertension were divided into two case-control samples: 388 cases with episodic new-onset hypertension (ie, one normal BP at the first visit and one abnormal BP during follow-up) each with two age-matched controls (n = 776) and 151 cases with regular new-onset hypertension (ie, normal BP at the first two visits and abnormal BP at two or more follow-up visits) each with three age-matched controls (n = 453). Multivariable-adjusted logistic regression was used to analyze the data. Results Our data showed very consistent results for episodic and regular new-onset hypertension, respectively, and verified known associations (odds ratio [95% confidence interval], per SD increase) with obesity (body mass index, 1.72 [1.49-1.98] and 1.81 [1.45-2.26]), inflammation (white blood cell count, 1.39 [1.23-1.58] and 1.38 [1.13-1.69]), and metabolic dysregulation (triglycerides, 1.25 [1.09-1.44] and 1.31 [1.08-1.58]; glucose, 1.46 [1.23-1.73] and 1.27 [1.05-1.54]) but, more surprisingly, also revealed positive associations with red blood cell count (1.27 [1.11-1.44] and 1.38 [1.14-1.68]), hemoglobin (1.18 [1.03-1.35] and 1.31 [1.05-1.64]), and platelet count (1.39 [1.20-1.61] and 1.33 [1.09-1.63]). Conclusions In addition to obesity and metabolic dysregulation, increased hemoglobin and counts of platelets, and red and white blood cells are associated with hypertension in this period. Future study may verify whether these associations are causal in nature and whether these variables are useful in risk stratification.</p