Decentralized Non-Convex Learning with Linearly Coupled Constraints

Motivated by the need for decentralized learning, this paper aims at designing a distributed algorithm for solving nonconvex problems with general linear constraints over a multi-agent network. In the considered problem, each agent owns some local information and a local variable for jointly minimizing a cost function, but local variables are coupled by linear constraints. Most of the existing methods for such problems are only applicable for convex problems or problems with specific linear constraints. There still lacks a distributed algorithm for such problems with general linear constraints and under nonconvex setting. In this paper, to tackle this problem, we propose a new algorithm, called "proximal dual consensus" (PDC) algorithm, which combines a proximal technique and a dual consensus method. We build the theoretical convergence conditions and show that the proposed PDC algorithm can converge to an $\epsilon$-Karush-Kuhn-Tucker solution within $\mathcal{O}(1/\epsilon)$ iterations. For computation reduction, the PDC algorithm can choose to perform cheap gradient descent per iteration while preserving the same order of $\mathcal{O}(1/\epsilon)$ iteration complexity. Numerical results are presented to demonstrate the good performance of the proposed algorithms for solving a regression problem and a classification problem over a network where agents have only partial observations of data features

(Z)-4-(2-Hy­droxy­benzyl­idene)-1-methyl-2-phenyl-1H-imidazol-5(4H)-one

In the title compound, C17H14N2O2, the asymmetric unit comprises two mol­ecules that are comformationally similar [the dihedral angles between the phenyl rings in each are 46.35 (2) and 48.04 (3)°], with the conformation stabilized by intra­molecular O—H⋯N hydrogen bonds, which generate S(7) rings. In the crystal, inversion-related mol­ecules are linked by pairs of weak C—H⋯O hydrogen bonds, forming dimers with an R 2 2(16) graph-set motif. Weak inter-ring π–π stacking is observed in the structure, the shortest centroid-to-centroid distance being 3.7480 (13) Å

(E)-4-[(4-Diethyl­amino-2-hy­droxy­benzyl­idene)amino]­benzonitrile

The title compound, C18H19N3O, displays an E conformation with respect to the C=N double bond. The dihedral angle between the mean planes of the two benzene rings is 24.49 (3)°. An intra­molecular O—H⋯N hydrogen bond generates an S(6) ring. In the crystal, mol­ecules are linked by nonclassical inter­molecular C—H⋯O hydrogen bonds to form an infinite one-dimensional chain along [010], generating a C(8) motif

Potential of Equatorial Atlantic Variability to Enhance El Nino Prediction

Extraordinarily strong El Niño events, such as those of 1982/83 and 1997/98, have been poorly predicted by operational seasonal forecasts made before boreal spring, despite significant advances in understanding, improved models, and enhanced observational networks. The Equatorial Atlantic Zonal Mode – a phenomenon similar to El Niño but much weaker and peaking in boreal summer – impacts winds over the Pacific, and hence affects El Niño, and also potentially its predictability. Here we use a climate model to perform a suite of seasonal predictions with and without SST in the Atlantic restored to observations. We show for the first time that knowledge of Equatorial Atlantic sea surface temperature (SST) significantly improves the prediction across boreal spring of major El Niño events and also weaker variability. This is because Atlantic SST acts to modulate El Niño variability, rather than triggering events. Our results suggest that better prediction of major El Niño events might be achieved through model improvement in the Equatorial Atlantic

Epidemiology and management of gout in Taiwan: a nationwide population study

INTRODUCTION: Gout is the most common inflammatory arthritis worldwide and is the only type of chronic arthritis that potentially can be ‘cured’. However, data on gout incidence, prevalence and management, assessed at multiple time points in the same population, are sparse, particularly in Asian populations. The aim of this study was to describe trends in the epidemiology of gout in the general population of Taiwan. METHODS: The National Health Insurance Research Database was used to identify patients with gout and to estimate the prevalence and incidence of gout for each calendar year from 2005 to 2010. The pattern of gout management was also examined. RESULTS: Of 23,371,362 beneficiaries in 2010, there were 1,458,569 prevalent and 56,595 incident cases of gout, giving a prevalence of 6.24% (95% confidence interval (CI), 6.23% to 6.25%) and an incidence of 2.74 (95% CI, 2.72 to 2.76) per 1,000 person-years. The annual percentage change (APC) of the standardised prevalence was −0.7% (95% CI, −1.7% to 0.3%; P = 0.14), suggesting that the prevalence of gout was essentially the same throughout the study period. However, The APC of incidence was −13.4 (95% CI, −16.1 to −10.6) between 2005 and 2007 and −2.1 (95% CI, −10.4 to 7.1) between 2007 and 2010. Regions with the highest prevalence and incidence were eastern coastal counties and offshore islets, where indigenous people are clustered. Among prevalent gout cases in 2010, only 22.93% (95% CI, 22.87% to 23.00%) were prescribed urate-lowering treatment (ULT), which remained unchanged between 2005 and 2010 at an APC of 0.0 (95% CI, −3.8 to 4.0). Uricosuric agents were more commonly prescribed than xanthine oxidase inhibitors in Taiwan. CONCLUSIONS: In Taiwan, 1 in 16 people have gout. Whereas the incidence has decreased recently, the prevalence remains unchanged. Management of gout in Taiwan is poor, with only one in five affected people being treated with ULT

Evaluation of anti-fatigue property of Porphyridium cruentum in mice

Purpose: To evaluate the potential effects of Porphyridium cruentum (PC) on fatigue induced by forced swimming test in mice. Methods: Mice were randomly divided into normal control group (NC, i.e., untreated non-swimming); model control group (MC, untreated swimming); Spirulina treated group (SP, 800 mg/kg); PC-treated groups (50, 100, and 200 mg/kg), respectively. After intragastric administration for 14 consecutive days, a weight-bearing swimming experiment was conducted for the mice, and the biochemical indicators related to fatigue were examined, including exhaustive swimming time, glucose levels (Glu), hepatic glycogen contents (HG), muscle glycogen contents (MG), glutathione peroxidase activities (GSH-Px), creatine kinase (CK), malondialdehyde (MDA), urea nitrogen levels (SUN), lactate dehydrogenase activities (LDH), lactic acid (LA) as well as superoxide dismutase (SOD). Results: PC significantly prolonged the swimming endurance time compared to MC. After PC treatment, Glu, HG and MG were effectively increased dose-dependently, SUN, LA, LDH and CK levels in serum were significantly reduced. Moreover, PC treatment elevated the bioactivities of two antioxidant enzymes, namely, GSH-Px and SOD, while MDA content decreased when compared to MC group. Conclusion: These results indicate that PC exhibits strong anti-fatigue effect. Thus, PC may be suitable for incorporation in functional food to counter fatigue

Familial aggregation of systemic lupus erythematosus and coaggregation of autoimmune diseases in affected families

IMPORTANCE: Relatives of patients with systemic lupus erythematosus (SLE) appear to be at higher risk of SLE and other autoimmune diseases, but estimates of individual familial risks are largely unavailable or unreliable. Furthermore, relative contributions of genetic, shared, and unshared environmental factors to SLE susceptibility remain unclear. OBJECTIVE: To examine familial aggregation and heritability of SLE and the relative risks (RRs) of other autoimmune diseases in relatives of patients with SLE. DESIGN, SETTING, AND PARTICIPANTS: A population-based family study using the Taiwan National Health Insurance Research Database was conducted. Participants included all individuals (N = 23,658,577) registered with that database in 2010; of these, 18,283 had SLE. We identified 21,009,551 parent-child relationships, 17,168,340 full sibling pairs, and 342,066 twin pairs. Diagnoses of SLE were ascertained from March 1, 1995, to December 31, 2010, and analysis was conducted between March 1 and August 15, 2014. MAIN OUTCOMES AND MEASURES: The prevalence and RRs of SLE and other autoimmune diseases in relatives and spouses of patients with SLE as well as the relative contributions of heritability, shared, and nonshared environmental factors to SLE susceptibility. RESULTS: Among the more than 23 million participants, the RRs (95% CIs) for SLE were 315.94 (210.66-473.82) for twins of the patients, 23.68 (20.13-27.84) for siblings, 11.44 (9.74-13.43) for parents, 14.42 (12.45-16.70) for offspring, and 4.44 (2.38-8.30) for spouses without genetic similarity. The accountability for phenotypic variance of SLE was 43.9% for heritability, 25.8% for shared environmental factors, and 30.3% for nonshared environmental factors. The RRs (95% CIs) in individuals with a first-degree relative with SLE were 5.87 (4.89-7.05) for primary Sjogren syndrome, 5.40 (3.37-8.65) for systemic sclerosis, 2.95 (2.04-4.26) for myasthenia gravis, 2.77 (1.45-5.32) for idiopathic inflammatory myositis, 2.66 (2.28-3.11) for rheumatoid arthritis, 2.58 (1.16-5.72) for multiple sclerosis, 1.68 (1.22-2.32) for type 1 diabetes mellitus, 1.39 (0.66-2.91) for inflammatory bowel diseases, and 0.86 (0.43-1.71) for vasculitis. CONCLUSIONS AND RELEVANCE: The individual risks of SLE and other autoimmune diseases were increased in families that included patients with SLE. The heritability of SLE was estimated to be 43.9%. These data should be considered when counseling families with affected members