Primal and dual conic representable sets: a fresh view on multiparametric analysis

This paper introduces the concepts of the primal and dual conic (linear inequality) representable sets and applies them to explore a novel kind of duality in multiparametric conic linear optimization. Such a kind of duality may be described by the set-valued mappings between the primal and dual conic representable sets, which allows us to generalize as well as treat previous results for mulitparametric analysis in a unified framework. In particular, it leads to the invariant region decomposition of a conic representable set that is more general than the known results in the literatures. We develop the classical duality theory in conic linear optimization and obtain the multiparametric KKT conditions. As their applications, we then discuss the behaviour of the optimal partition of a conic representable set and investigate the multiparametric analysis of conic linear optimization problems. All results are corroborated by examples having correlation.Comment: 38 pages, 3 figur

The existence of a strongly polynomial time simplex method

It is well known how to clarify whether there is a polynomial time simplex algorithm for linear programming (LP) is the most challenging open problem in optimization and discrete geometry. This paper gives a affirmative answer to this open question by the use of the parametric analysis technique that we recently proposed. We show that there is a simplex algorithm whose number of pivoting steps does not exceed the number of variables of a LP problem.Comment: 17 pages, 1 figur

Propagation of tidal waves up in Yangtze Estuary during the dry season

Tide is one of the most important hydrodynamic driving forces and has unique features in the Yangtze Estuary (YE) due to the complex geometry of third-order bifurcations and four outlets. This paper characterizes the tidal oscillations, tidal dampening, tidal asymmetry, and tidal wave propagation, which provides insights into the response of the estuary to tides during the dry season. The structural components of tidal oscillations are initially attained by tidal analysis. The increasingly richer spectrum inside the estuary shows an energy transfer corresponding to the generation and development of nonlinear overtides and compound tides. A 2-D numerical model is further set up to reproduce tidal dynamics in the estuary. The results show that the estuary is a strongly dissipative estuary with a strong nonlinear phenomenon. Three amplifications are presented in the evolution process of tidal ranges due to the channel convergence. Tidal asymmetry is spatiotemporally characterized by the M-4/M-2 amplitude ratio, the 2M(2)-M-4 phase difference, and the flood-ebb duration-asymmetry parameter, and the estuary tends to be flood-dominant. There exists mimic standing waves with the phase difference of the horizontal and vertical tide close to 90 degrees when tidal wave propagates into the estuary, especially during the neap tide. In addition, the differences in tidal distortion, tidal ranges, and tidal waves along the two routes in the South Branch (S-B) suggest the branched system behaves differently from a single system

Cluster analysis for the overall health status of elderly, multimorbid patients with diabetes

PurposeTo evaluate the overall health status and health-related abilities and problems of elderly patients with diabetes and multimorbidity compared with those with diabetes only. Additionally, we aimed to identify different subgroups of elderly, multimorbid patients with diabetes.MethodsThis cross-sectional study included 538 elderly patients with diabetes. The participants completed a series of questionnaires on self-rated health (SRH), diabetes self-management, self-efficacy, health literacy, depression, and diabetes distress. Differences in health-related abilities and problems were compared between elderly patients with diabetes and multimorbidity and those with diabetes only, with adjustments for covariates using propensity score matching. A cluster analysis was also performed to identify the overall health status subgroups of elderly, multimorbid patients with diabetes. Additionally, we conducted a multinomial logistic regression analysis to examine the predictors of health-related abilities and problem-cluster group membership.ResultsElderly patients with diabetes and multimorbidity experienced more health-related abilities and problems than those with diabetes only, particularly within the domains of depression (p < 0.001), and diabetes distress. The level of health literacy (p < 0.001) and self-management (p = 0.013) in elderly, multimorbid patients with diabetes was also significantly higher than that in elderly patients with diabetes only. Cluster analysis of elderly, multimorbid patients with diabetes revealed three distinct overall health status clusters. Multinomial logistic regression analysis indicated that age (OR = 1.090, p = 0.043), sex (OR = 0.503, p = 0.024), living situation (OR = 2.769, p = 0.011), BMI (OR = 0.838, p = 0.034), regular exercise (OR = 2.912, p = 0.041 in poor vs. good; OR = 3.510, p < 0.001 in intermediate vs. good), and cerebral infarction (OR = 26.280, p < 0.001) independently and significantly predicted cluster membership.ConclusionCompared with elderly patients with diabetes only, those with diabetes and multimorbidity experienced more health-related abilities and problems within the domains of depression, and diabetes distress. Additionally, the level of health literacy and self-management in elderly, multimorbid patients with diabetes was significantly higher than that in those with diabetes only. Among the multimorbid diabetes group, old age, male sex, living without a partner, slightly lower BMIs, not exercising regularly, and experiencing cerebral infarctions were all positively correlated with worse overall health status

Ampere-hour-scale soft-package potassium-ion hybrid capacitors enabling 6-minute fast-charging

Extreme fast charging of Ampere-hour (Ah)-scale electrochemical energy storage devices targeting charging times of less than 10 minutes are desired to increase widespread adoption. However, this metric is difficult to achieve in conventional Li-ion batteries due to their inherent reaction mechanism and safety hazards at high current densities. In this work, we report 1 Ah soft-package potassium-ion hybrid supercapacitors (PIHCs), which combine the merits of high-energy density of battery-type negative electrodes and high-power density of capacitor-type positive electrodes. The PIHC consists of a defect-rich, high specific surface area N-doped carbon nanotube-based positive electrode, MnO quantum dots inlaid spacing-expanded carbon nanotube-based negative electrode, carbonate-based non-aqueous electrolyte, and a binder- and current collector-free cell design. Through the optimization of the cell configuration, electrodes, and electrolyte, the full cells (1 Ah) exhibit a cell voltage up to 4.8 V, high full-cell level specific energy of 140 Wh kg-1 (based on the whole mass of device) with a full charge of 6 minutes. An 88% capacity retention after 200 cycles at 10 C (10 A) and a voltage retention of 99% at 25 ± 1 °C are also demonstrated

The impact of different rose bengal formulations on corneal thickness and the efficacy of rose bengal/green light corneal cross-linking in the rabbit eye

PURPOSE:To examine central corneal thickness (CCT) changes during in vivo rose bengal-green light corneal cross-linking (RG-CXL) and compare the CXL efficacy of different rose bengal formulations. METHODS:After epithelium removal, the right eyes of rabbits were immersed in rose bengal solution prepared by different solvents (water, phosphate buffered saline, dextran, and hydroxypropyl methylcellulos [HPMC]) for 2 or 20 minutes, then the rose bengal distribution in the corneal stroma was analyzed by confocal fluorescence detection. During the RG-CXL process, the CCT was measured at seven time points. The left eyes served as the untreated control group. Corneal enzymatic resistance and corneal biomechanics were tested to compare the RG-CXL efficacy. RESULTS:The rose bengal infiltration depths were 120 and 200 µm for the 2- and 20-minute groups, respectively. CCT increased significantly after infiltration, then decreased significantly in the first 200 seconds of irradiation and decreased slowly for the next 400 seconds. The CCT of the 20-minute groups was significantly thicker than that of the 2-minute groups (P < .0001). All RG-CXL treatments improved the corneal enzymatic resistance and corneal biomechanics, with the effects being greater in the 20-minute groups. The inclusion of 1.1% HPMC in the rose bengal formulation helped to maintain CCT during irradiation while not affecting either the infiltration of rose bengal or the efficacy of RG-CXL. CONCLUSIONS:Within the range studied, RG-CXL efficacy increased with infiltration time. The incorporation of a 20-minute infiltration of 0.1% rose bengal-1.1% HPMC into the RG-CXL procedure may further improve the safety of the treatment and its prospects for clinical use

Are climate warming and enhanced atmospheric deposition of sulfur and nitrogen threatening tufa landscapes in Jiuzhaigou National Nature Reserve, Sichuan, China?

Massive deposition of calcium carbonate in ambient temperature waters (tufa) can form magnificent tufa landscapes, many of which are designated as protected areas. However, tufa landscapes in many areas are threatened by both local anthropogenic activities and climate change. This study, for the first time, posed the question whether the tufa landscape degradation (characterized by tufa degradation and increased biomass of green algae) in Jiuzhaigou National Nature Reserve of China is partially caused by regional air pollution and climate warming. The results indicate that wet deposition (including rain and snow) polluted by anthropogenic SO2, NOx, and NH3 emissions dissolves exposed tufa and may considerably reduce tufa deposition rate and even cause tufa dissolution within shallow waters. These effects of wet deposition on tufa enhanced as pH of wet deposition decreased from 8.01 to 5.06. Annual Volume Weighted Mean concentration of reactive nitrogen (including NH4+ and NO3-) in wet deposition (26.1 μmol L-1) was 1.8 times of the corresponding value of runoff (14.8 μmol L-1) and exceeded China's national standard of total nitrogen in runoff for nature reserves (14.3 μmol L-1), indicating a direct nitrogen fertilization effect of wet deposition on green algae. As water temperature is the major limiting factor of algal growth in Jiuzhaigou and temperature in the top layer (0-5 cm) of runoff (depth < 1 m, no canopy coverage of trees and shrubs) was significantly higher at the sites with increased biomass of green algae (p < 0.05), climate warming in this region would favor algal growth. In sum, this study suggests that climate warming and enhanced sulfur and nitrogen deposition have contributed to the current degradation of tufa landscape in Jiuzhaigou, but in order to quantify the contributions, further studies are needed, as many other anthropogenic and natural processes also influence tufa landscape evolution

Engineering hibiscus-like riboflavin/ZIF-8 microsphere composites to enhance transepithelial corneal cross-linking

Riboflavin-5-phosphate (RF) is the most commonly used photosensitizer in corneal cross-linking (CXL), but its hydrophilicity and negative charge limit its penetration through the corneal epithelium into the stroma. To enhance the corneal permeability of RF and promote its efficacy in the treatment of keratoconus, novel hibiscus-like RF@ZIF-8 microsphere composites [6RF@ZIF-8 NF (nanoflake)] are prepared using ZIF-8 nanomaterials as carriers, which are characterized by their hydrophobicity, positive potential, biocompatibility, high loading capacities, and large surface areas. Both hematoxylin and eosin endothelial staining and TUNEL assays demonstrate excellent biocompatibility of 6RF@ZIF-8 NF. In in vivo studies, the 6RF@ZIF-8 NF displayed excellent corneal permeation, and outstanding transepithelial CXL (TE-CXL) efficacy, slightly better than the conventional CXL protocol. Furthermore, the special hibiscus-like structures of 6RF@ZIF-8 NF meant that it has better TE-CXL efficacy than that of 6RF@ZIF-8 NP (nanoparticles) due to the larger contact area with the epithelium and the shorter RF release passage. These results suggest that the 6RF@ZIF-8 NF are promising for transepithelial corneal cross-linking, avoiding the need for epithelial debridement

Wave spectra assimilation in typhoon wave modeling for the East China Sea

The East China Sea is a hot area for typhoon waves to occur. A wave spectra assimilation model has been developed to predict the typhoon wave more accurately and operationally. This is the first time where wave data from Taiwan have been used to predict typhoon wave along the mainland China coast. The two-dimensional spectra observed in Taiwan northeast coast modify the wave field output by SWAN model through the technology of optimal interpolation (OI) scheme. The wind field correction is not involved as it contributes less than a quarter of the correction achieved by assimilation of waves. The initialization issue for assimilation is discussed. A linear evolution law for noise in the wave field is derived from the SWAN governing equations. A two-dimensional digital low-pass filter is used to obtain the initialized wave fields. The data assimilation model is optimized during the typhoon Sinlaku. During typhoons Krosa and Morakot, data assimilation significantly improves the low frequency wave energy and wave propagation direction in Taiwan coast. For the far-field region, the assimilation model shows an expected ability of improving typhoon wave forecast as well, as data assimilation enhances the low frequency wave energy. The proportion of positive assimilation indexes is over 81% for all the periods of comparison. The paper also finds that the impact of data assimilation on the far-field region depends on the state of the typhoon developing and the swell propagation direction.<br/