Regularity of Edge Ideals and Their Powers

We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals of graphs and their powers. Our focus is on bounds and exact values of $\text{ reg } I(G)$ and the asymptotic linear function $\text{ reg } I(G)^q$, for $q \geq 1,$ in terms of combinatorial data of the given graph $G.$Comment: 31 pages, 15 figure

THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS ON THE LOJASIEWICZ EXPONENT AT INFINITY OF REAL POLYNOMIALS

Abstract Let f : R n → R be a nonconstant polynomial function. In this paper, using the information from "the curve of tangency" of f, we provide a method to determine the Lojasiewicz exponent at infinity of f. As a corollary, we give a computational criterion to decide if the Lojasiewicz exponent at infinity is finite or not. Then, we obtain a formula to calculate the set of points at which the polynomial f is not proper. Moreover, a relation between the Lojasiewicz exponent at infinity of f with the problem of computing the global optimum of f is also established

Simultaneous retrieval of selected optical water quality indicators from Landsat-8, Sentinel-2, and Sentinel-3

Constructing multi-source satellite-derived water quality (WQ) products in inland and nearshore coastal waters from the past, present, and future missions is a long-standing challenge. Despite inherent differences in sensors’ spectral capability, spatial sampling, and radiometric performance, research efforts focused on formulating, implementing, and validating universal WQ algorithms continue to evolve. This research extends a recently developed machine-learning (ML) model, i.e., Mixture Density Networks (MDNs) (Pahlevan et al., 2020; Smith et al., 2021), to the inverse problem of simultaneously retrieving WQ indicators, including chlorophyll-a (Chla), Total Suspended Solids (TSS), and the absorption by Colored Dissolved Organic Matter at 440 nm (acdom(440)), across a wide array of aquatic ecosystems. We use a database of in situ measurements to train and optimize MDN models developed for the relevant spectral measurements (400–800 nm) of the Operational Land Imager (OLI), MultiSpectral Instrument (MSI), and Ocean and Land Color Instrument (OLCI) aboard the Landsat-8, Sentinel-2, and Sentinel-3 missions, respectively. Our two performance assessment approaches, namely hold-out and leave-one-out, suggest significant, albeit varying degrees of improvements with respect to second-best algorithms, depending on the sensor and WQ indicator (e.g., 68%, 75%, 117% improvements based on the hold-out method for Chla, TSS, and acdom(440), respectively from MSI-like spectra). Using these two assessment methods, we provide theoretical upper and lower bounds on model performance when evaluating similar and/or out-of-sample datasets. To evaluate multi-mission product consistency across broad spatial scales, map products are demonstrated for three near-concurrent OLI, MSI, and OLCI acquisitions. Overall, estimated TSS and acdom(440) from these three missions are consistent within the uncertainty of the model, but Chla maps from MSI and OLCI achieve greater accuracy than those from OLI. By applying two different atmospheric correction processors to OLI and MSI images, we also conduct matchup analyses to quantify the sensitivity of the MDN model and best-practice algorithms to uncertainties in reflectance products. Our model is less or equally sensitive to these uncertainties compared to other algorithms. Recognizing their uncertainties, MDN models can be applied as a global algorithm to enable harmonized retrievals of Chla, TSS, and acdom(440) in various aquatic ecosystems from multi-source satellite imagery. Local and/or regional ML models tuned with an apt data distribution (e.g., a subset of our dataset) should nevertheless be expected to outperform our global model

Policy Recommendations From The Status Quo Of Elderly Population In The Population Ageing Process In Vietnam

Population ageing is a global issue, which involves all nations and countries worldwide. In the world as well as in Vietnam, ageing has become a typical sign in the 21st century with a rapidly increasing number and proportion of elderly people. The ageing population shares many common characteristics in the overall population, but also has many distinct ones. Analyzing the characteristics of this part of population is necessary to provide important arguments for proposing policy recommendations.The main aim of this paper is to analyze the status quo of the elderly population in the population ageing process in Vietnam through their of health, demographic and socio-economic characteristics, thereby proposing policy recommendations to improve their quality of life and make good preparations to obtain a “successful ageing population” in Vietnam

Industrial Solid Waste Control in Danang City

The risk of environmental pollution resulting from industrial solid waste is becoming a pressing issue in the environment protection in Vietnam in general and Danang in particular. This situation is due to the fact that the authorities concerned are not really interested in solid waste disposal and control as well as environmental protection in the industrial zones in the period of industrialization and modernization. Therefore, assessing the necessity of the control of solid waste in the industrial areas in Danang City, the author proposes recommendations to improve control efficiency and reduce environmental pollution, achieving the goal for Danang City – an environmental city in 2020

Modelling of Superheater System in A Thermal Power Plant Boiler

This paper proposes a new mathematical model for the two- stage super-heater system of thermal power plant boilers. The proposed model is then evaluated by comparing the simulation results on Matlab/Simulink with the experiment data obtained from two-stage super-heater system of the 196 t/h capacity thermal power plant boiler in Dung Quat refinery. The obtained results show good fitness of the simulation dynamic curve for the experimental data from the actual super-heater system with mean absolute deviation MAD = 5.1%, mean deviation MD = 2.3%, standard error SE = 0.7%. The error between the developed model and the real system in the steady state at some typical operating loads of the boiler also does not exceed 0.32%