S-Lemma with Equality and Its Applications

Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the system $f(x)<0, h(x)=0$ implies the existence of a real number $\mu$ such that $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$. The problem is much harder than the inequality version which asserts that, under Slater condition, $f(x)<0, h(x)\le0$ is unsolvable if and only if $f(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n$ for some $\mu\ge0$. In this paper, we show that the S-lemma with equality does not hold only when the matrix $A$ has exactly one negative eigenvalue and $h(x)$ is a non-constant linear function ($B=0, b\not=0$). As an application, we can globally solve $\inf\{f(x)\vert h(x)=0\}$ as well as the two-sided generalized trust region subproblem $\inf\{f(x)\vert l\le h(x)\le u\}$ without any condition. Moreover, the convexity of the joint numerical range $\{(f(x), h_1(x),\ldots, h_p(x)):~x\in\Bbb R^n\}$ where $f$ is a (possibly non-convex) quadratic function and $h_1(x),\ldots,h_p(x)$ are affine functions can be characterized using the newly developed S-lemma with equality.Comment: 34 page

MicroRNA-23a promotes myelination in the central nervous system.

Demyelinating disorders including leukodystrophies are devastating conditions that are still in need of better understanding, and both oligodendrocyte differentiation and myelin synthesis pathways are potential avenues for developing treatment. Overexpression of lamin B1 leads to leukodystrophy characterized by demyelination of the central nervous system, and microRNA-23 (miR-23) was found to suppress lamin B1 and enhance oligodendrocyte differentiation in vitro. Here, we demonstrated that miR-23a-overexpressing mice have increased myelin thickness, providing in vivo evidence that miR-23a enhances both oligodendrocyte differentiation and myelin synthesis. Using this mouse model, we explored possible miR-23a targets and revealed that the phosphatase and tensin homologue/phosphatidylinositol trisphosphate kinase/Akt/mammalian target of rapamycin pathway is modulated by miR-23a. Additionally, a long noncoding RNA, 2700046G09Rik, was identified as a miR-23a target and modulates phosphatase and tensin homologue itself in a miR-23a-dependent manner. The data presented here imply a unique role for miR-23a in the coordination of proteins and noncoding RNAs in generating and maintaining healthy myelin

Diarrhoea scores and weight changes in response to artificial milk supplementation or use of solulyte-neomycin solution in preweaning piglets

The objective of this study was to determine the effects of supplemental milk replacer and solulyte-neomix solution in preweaning piglets. A total of 199 five-day-old piglets from 22litters were available for this three-week study. 12 litters (110 piglets) were allocated into the milk replacer supplemented group (MILK), five litters (47 piglets) were allocated into the ELEC group which was given an antibiotic-fortified electrolyte solution for pigs, and five litters (45 piglets) remained as untreated control (CTRL). However, after matching for litter size and total litter weights among treatment groups, only 44 piglets (5litters) in the MILK group, 47 piglets (5 litters) in the ELEC group and 45 piglets from 5 litters in the CTRL group were considered in this report. All sows were fed the same diet (18 % protein, 3,952 kcal of ME/kg). Body weights of piglets were measured at days 5 and 25 of age. Fresh liquid commercial milk replacer and solulyte-neomix solution were prepared daily. The fluids were offered thrice daily at 100mL per litter for 5-day-old piglets. Supplementation was increased to 5 times daily at 200mL per litter when piglets were 9 days or older, till the end of the trial. Average litter weight gain was higher in the ELEC piglets given solulyte-neomix solution and creep feed (P<0.05). Milk replacer supplemented group (MILK) generally had lower average litter weight gains at 3.72 kg. However, the diarrhea scores were affected by the types of supplementation fluids given. The overall diarrhoea scores were higher in the MILK and CTRL piglets compared to the ELEC piglets. In conclusion, milk replacer supplementation offered no obvious benefit in terms of weight gain, final weight, and overall diarrhoea scores in piglets compared to solulyte-neomix supplemented piglets

SoC-based biomedical embedded system design of arrhythmia detector

Arrhythmia is an irregular heartbeat where the blood may not be delivered effectively throughout the body and cause sudden cardiac arrest (SCA). Immediate treatment is required to prevent SCA. However, most of the existing electrocardiogram (ECG) monitoring devices are bulky, cost expensive and lack arrhythmia detection and classification system. This paper proposes a front-end on-board graphical interface design of System-on-Chip (SoC) based arrhythmia detector which can be used as a first screening device for cardiac disease patient. The system consists of a knowledge-based arrhythmia classifier which is able to identify three types of arrhythmias which are ventricular fibrillation (VF), premature ventricular contractions (PVCs) and second-degree atrioventricular (AV) block. The system has been evaluated and benchmarked with ECG data from MIT-BIH arrhythmia database. The results show that its accuracy is up to 99.25% with a computation time of 6.385 seconds. It is highly portable and relatively inexpensive for installation in small clinics and home monitoring

Plasmoid ejection and secondary current sheet generation from magnetic reconnection in laser-plasma interaction

Reconnection of the self-generated magnetic fields in laser-plasma interaction was first investigated experimentally by Nilson {\it et al.} [Phys. Rev. Lett. 97, 255001 (2006)] by shining two laser pulses a distance apart on a solid target layer. An elongated current sheet (CS) was observed in the plasma between the two laser spots. In order to more closely model magnetotail reconnection, here two side-by-side thin target layers, instead of a single one, are used. It is found that at one end of the elongated CS a fan-like electron outflow region including three well-collimated electron jets appears. The ($>1$ MeV) tail of the jet energy distribution exhibits a power-law scaling. The enhanced electron acceleration is attributed to the intense inductive electric field in the narrow electron dominated reconnection region, as well as additional acceleration as they are trapped inside the rapidly moving plasmoid formed in and ejected from the CS. The ejection also induces a secondary CS

UpSizeR: Synthetically scaling an empirical relational database

Ministry of Education, Singapore under its Academic Research Funding Tier

Biobehavioral effects of Tai Chi Qigong in men with prostate cancer: Study design of a three-arm randomized clinical trial.

Fatigue is often one of the most commonly reported symptoms in prostate cancer survivors, but it is also one of the least understood cancer-related symptoms. Fatigue is associated with psychological distress, disruptions in sleep quality, and impairments in health-related quality of life. Moreover, inflammatory processes and changes related to the hypothalamic-pituitary-adrenal (HPA) axis and/or autonomic nervous system may also play a role in cancer-related fatigue. Thus, effective treatments for fatigue in prostate cancer survivors represent a current unmet need. Prior research has shown that Tai Chi Qigong, a mind-body exercise intervention, can improve physical and emotional health. Herein, we describe the protocol of the ongoing 3-arm randomized controlled Health Empowerment &amp; Recovery Outcomes (HERO) clincal trial. One hundred sixty-six prostate cancer survivors with fatigue are randomized to a modified Tai Chi Qigong intervention (TCQ), intensity-matched body training intervention (BT), or usual care (UC) condition. Guided by biopsychosocial and psychoneuroimmunology models, we propose that TCQ, as compared to BT or UC will: i) reduce fatigue (primary outcome) in prostate cancer survivors; ii) reduce inflammation; and iii) regulate the expression of genes from two major functional clusters: a) inflammation, vasodilation and metabolite sensing and b) energy and adrenergic activation. Assessments are conducted at baseline, the 6-week midpoint of the intervention, and 1 week, 3 months, and 12 months post-intervention. If our findings show that TCQ promotes recovery from prostate cancer and its treatment, this type of intervention can be integrated into survivorship care plans as the standard of care. The study's findings will also provide novel information about underlying biobehavioral mechanisms of cancer-related fatigue. Trial registration number:NCT03326713; clinicaltrials.gov

Fermion Pairing Dynamics in the Relativistic Scalar Plasma

Using many-body techniques we obtain the time-dependent Gaussian approximation for interacting fermion-scalar field models. This method is applied to an uniform system of relativistic spin-1/2 fermion field coupled, through a Yukawa term, to a scalar field in 3+1 dimensions, the so-called quantum scalar plasma model. The renormalization for the resulting Gaussian mean-field equations, both static and dynamical, are examined and initial conditions discussed. We also investigate solutions for the gap equation and show that the energy density has a single minimum.Comment: 21 pages, latex, 4 postscript figures, new sections, some literary changes, notation corrections, accepted for publication in Phys. Rev