Convex Quadratic Equations and Functions

Three interconnected main results (1)-(3) are presented in closed forms. (1) Regarding the convex quadratic equation (CQE), an analytical equivalent solvability condition and parameterization of all solutions are completely formulated, in a unified framework. The design concept is based on the matrix algebra, while facilitated by a novel equivalence/coordinate transformation. Notably, the parameter-solution bijection is also verified. Two applications are selected as the other two main results. (2) The focus is set on both the infinite and finite-time horizon nonlinear optimal control. By virtue of (1), the CQEs associated with the underlying Hamilton-Jacobi Equation, Hamilton-Jacobi Inequality, and Hamilton-Jacobi-Bellman Equation are algebraically solved, respectively. Each solution set captures the gradient of the associated value function. Moving forward, a preliminary to recover the optimality using the state-dependent (differential) Riccati equation is provided, which can also be used to more efficiently implement the last main result. (3) The nonlinear programming/convex optimization is analyzed via a novel method and perspective. The philosophy is based on the new analysis of CQE in (1), which helps explain the geometric structure of the convex quadratic function (CQF), and the CQE-CQF relation. An impact on the quadratic programming (QP), a basis in the literature, is demonstrated. Specifically, the QPs subject to equality, inequality, equality-and-inequality, and extended constraints are algebraically solved, resp., without knowing a feasible point.Comment: This manuscript is only preliminary and still growing. Therefore, with expectations, we deeply appreciate all kinds of input

CFD as a tool for modelling membrane systems

Computational fluid dynamics (CFD) is a computer-based numerical method used to analyse systems that involve fluid flow and/or heat and mass transfer (Versteeg & Malalasekera, 2007). CFD bridges the two different approaches for solving engineering problems before the computer era, theoretical and experimental; it relies on mathematical models while being easy to adapt to almost any realistic condition (Anderson & Wendt, 1995). Another feature of CFD is its versatility, as it allows the analysis of systems for a variety of applications such as chemical reactions (Salehi et al., 2016), aerodynamics (Snel, 2003), dispersion of pollutants (Chu et al., 2005), blood flows (Byun & Rhee, 2004), among many others

Vision-Based Finger Detection, Tracking, and Event Identification Techniques for Multi-Touch Sensing and Display Systems

This study presents efficient vision-based finger detection, tracking, and event identification techniques and a low-cost hardware framework for multi-touch sensing and display applications. The proposed approach uses a fast bright-blob segmentation process based on automatic multilevel histogram thresholding to extract the pixels of touch blobs obtained from scattered infrared lights captured by a video camera. The advantage of this automatic multilevel thresholding approach is its robustness and adaptability when dealing with various ambient lighting conditions and spurious infrared noises. To extract the connected components of these touch blobs, a connected-component analysis procedure is applied to the bright pixels acquired by the previous stage. After extracting the touch blobs from each of the captured image frames, a blob tracking and event recognition process analyzes the spatial and temporal information of these touch blobs from consecutive frames to determine the possible touch events and actions performed by users. This process also refines the detection results and corrects for errors and occlusions caused by noise and errors during the blob extraction process. The proposed blob tracking and touch event recognition process includes two phases. First, the phase of blob tracking associates the motion correspondence of blobs in succeeding frames by analyzing their spatial and temporal features. The touch event recognition process can identify meaningful touch events based on the motion information of touch blobs, such as finger moving, rotating, pressing, hovering, and clicking actions. Experimental results demonstrate that the proposed vision-based finger detection, tracking, and event identification system is feasible and effective for multi-touch sensing applications in various operational environments and conditions

Prevalence of DDC genotypes in patients with aromatic L-amino acid decarboxylase (AADC) deficiency and in silico prediction of structural protein changes

Aromatic L-amino acid decarboxylase (AADC) deficiency is a rare autosomal recessive genetic disorder affecting the biosynthesis of dopamine, a precursor of both norepinephrine and epinephrine, and serotonin. Diagnosis is based on the analysis of CSF or plasma metabolites, AADC activity in plasma and genetic testing for variants in the DDC gene. The exact prevalence of AADC deficiency, the number of patients, and the variant and genotype prevalence are not known. Here, we present the DDC variant (n = 143) and genotype (n = 151) prevalence of 348 patients with AADC deficiency, 121 of whom were previously not reported. In addition, we report 26 new DDC variants, classify them according to the ACMG/AMP/ACGS recommendations for pathogenicity and score them based on the predicted structural effect. The splice variant c.714+4A>T, with a founder effect in Taiwan and China, was the most common variant (allele frequency = 32.4%), and c.[714+4A>T];[714+4A>T] was the most common genotype (genotype frequency = 21.3%). Approximately 90% of genotypes had variants classified as pathogenic or likely pathogenic, while 7% had one VUS allele and 3% had two VUS alleles. Only one benign variant was reported. Homozygous and compound heterozygous genotypes were interpreted in terms of AADC protein and categorized as: i) devoid of full-length AADC, ii) bearing one type of AADC homodimeric variant or iii) producing an AADC protein population composed of two homodimeric and one heterodimeric variant. Based on structural features, a score was attributed for all homodimers, and a tentative prediction was advanced for the heterodimer. Almost all AADC protein variants were pathogenic or likely pathogenic

Prevalence of DDC genotypes in patients with aromatic L-amino acid decarboxylase (AADC) deficiency and in silico prediction of structural protein changes

Aromatic L-amino acid decarboxylase (AADC) deficiency is a rare autosomal recessive genetic disorder affecting the biosynthesis of dopamine, a precursor of both norepinephrine and epinephrine, and serotonin. Diagnosis is based on the analysis of CSF or plasma metabolites, AADC activity in plasma and genetic testing for variants in the DDC gene. The exact prevalence of AADC deficiency, the number of patients, and the variant and genotype prevalence are not known. Here, we present the DDC variant (n = 143) and genotype (n = 151) prevalence of 348 patients with AADC deficiency, 121 of whom were previously not reported. In addition, we report 26 new DDC variants, classify them according to the ACMG/AMP/ACGS recommendations for pathogenicity and score them based on the predicted structural effect. The splice variant c.714+4A>T, with a founder effect in Taiwan and China, was the most common variant (allele frequency = 32.4%), and c.[714+4A>T];[714+4A>T] was the most common genotype (genotype frequency = 21.3%). Approximately 90% of genotypes had variants classified as pathogenic or likely pathogenic, while 7% had one VUS allele and 3% had two VUS alleles. Only one benign variant was reported. Homozygous and compound heterozygous genotypes were interpreted in terms of AADC protein and categorized as: i) devoid of full-length AADC, ii) bearing one type of AADC homodimeric variant or iii) producing an AADC protein population composed of two homodimeric and one heterodimeric variant. Based on structural features, a score was attributed for all homodimers, and a tentative prediction was advanced for the heterodimer. Almost all AADC protein variants were pathogenic or likely pathogenic

Impact of opioid-free analgesia on pain severity and patient satisfaction after discharge from surgery: multispecialty, prospective cohort study in 25 countries

Background: Balancing opioid stewardship and the need for adequate analgesia following discharge after surgery is challenging. This study aimed to compare the outcomes for patients discharged with opioid versus opioid-free analgesia after common surgical procedures.Methods: This international, multicentre, prospective cohort study collected data from patients undergoing common acute and elective general surgical, urological, gynaecological, and orthopaedic procedures. The primary outcomes were patient-reported time in severe pain measured on a numerical analogue scale from 0 to 100% and patient-reported satisfaction with pain relief during the first week following discharge. Data were collected by in-hospital chart review and patient telephone interview 1 week after discharge.Results: The study recruited 4273 patients from 144 centres in 25 countries; 1311 patients (30.7%) were prescribed opioid analgesia at discharge. Patients reported being in severe pain for 10 (i.q.r. 1-30)% of the first week after discharge and rated satisfaction with analgesia as 90 (i.q.r. 80-100) of 100. After adjustment for confounders, opioid analgesia on discharge was independently associated with increased pain severity (risk ratio 1.52, 95% c.i. 1.31 to 1.76; P < 0.001) and re-presentation to healthcare providers owing to side-effects of medication (OR 2.38, 95% c.i. 1.36 to 4.17; P = 0.004), but not with satisfaction with analgesia (beta coefficient 0.92, 95% c.i. -1.52 to 3.36; P = 0.468) compared with opioid-free analgesia. Although opioid prescribing varied greatly between high-income and low- and middle-income countries, patient-reported outcomes did not.Conclusion: Opioid analgesia prescription on surgical discharge is associated with a higher risk of re-presentation owing to side-effects of medication and increased patient-reported pain, but not with changes in patient-reported satisfaction. Opioid-free discharge analgesia should be adopted routinely

ADSMITH: A Structure-Based Heterogeneous Distributed Shared Memory on PVM

Message passing is the most often used communication model in distributed-memory systems. With message passing, programmers are forced to manage the data flows explicitly. They have to know where a piece of data is located and when to set up the send/receive pair between two communicating entities. Such a task is tedious and error-prone. On the other hand, with a virtual or physical shared memory, programmers can use shared variables for communication among concurrently executing threads --- just as in traditional sequential programs. Programmers need not manage the shared data explicitly. Thus, programs can be developed more easily. To provide a shared-memory environment on top of distributed-memory systems, the concept of distributed shared memory (DSM) was proposed and soon attracted wide spread attention. Current implementations of DSMs mostly concentrate on the hardware and/or operating system layers. Problems with such implementations are that they are difficult to support hetero..