Type Of Decomposition Research Articles

Benders-type branch-and-cut algorithms for capacitated facility location with single-sourcing

We consider the capacitated facility location problem with (partial) single-sourcing (CFLP-SS). A natural mixed integer formulation for the problem involves 0–1 variables xj indicating whether faclility j is used or not and yij variables indicating the fraction of the demand of client i that is satisfied from facility j. When the x variables are fixed, the remaining problem is a transportation problem with single-sourcing. This structure suggest the use of a Benders’ type decomposition algorithm. Here we present three possible variants. Applied to CFLP-SS they are compared computationally with a commercial solver (CPLEX) on the original formulation, a CPLEX version of Benders and a recent cut-and-solve approach developed specifically for CFLP-SS. Our results show that for CFLP-SS, when the percentage of clients requiring single-sourcing is less equal than 25%, the Benders’ variants achieve speedups of between 1.2 and 3.7.

Atomic decompositions for noncommutative martingales

We prove an atomic type decomposition for the noncommutative martingale Hardy space hp for all 0<p<2 by an explicit constructive method using algebraic atoms as building blocks. Using this elementary construction, we obtain a weak form of the atomic decomposition of hp for all 0<p<1, and provide a constructive proof of the atomic decomposition for p=1 which resolves a main problem on the subject left open for the last twelve years. We also study (p,∞)c-atoms, and show that every (p,2)c-atom can be decomposed into a sum of (p,∞)c-atoms; consequently, for every 0<p≤1, the (p,q)c-atoms lead to the same atomic space for all 2≤q≤∞. As applications, we obtain a characterization of the dual space of the noncommutative martingale Hardy space hp (0<p<1) as a noncommutative Lipschitz space via the weak form of the atomic decomposition. Our constructive method can also be applied to prove some sharp martingale inequalities.

Litter Decomposition Is Not Affected by Perfluorobutane Sulfonate (PFBS) in Experimental Soil Microcosms

Perfluorobutane sulfonate (PFBS) has been found in increasing concentrations in the environment. However, its effect on litter decomposition in soils is still unclear. Therefore, the effect of PFBS on the decomposition of various litter types was tested, as well as on selected aspects of soil quality. Soil samples were treated with different concentrations of PFBS (0, 1, and 10 µg g–1) and five organic litter materials were used with various C:N ratios. A soil microcosm experiment was performed at 20 °C for 6 weeks. Litter decomposition, soil respiration, enzyme activities, soil pH, water-stable aggregates (WSA), and soil total C and N contents were measured. PFBS treatments were observed to have negligible effects on litter decomposition as well as on other soil properties. This means that in the concentration range examined, this substance has no observable effects on the key soil parameters examined. The present result was inconsistent with the findings of a previous study with similar experimental microcosms but different soils. This study suggests that the effects of PFBS may be less pronounced in the tested soil, but it cannot be concluded that PFBS is harmless in soil ecosystems. A wider range of soil types and PFBS levels should be tested in future studies.

Effect of Sludge Content on the Decomposition of Different Types of Food Waste

Food waste, which is the second largest component in landfills, generates excessive amounts of leachate and greenhouse gas. As a result, it has recently become a severe concern, mostly in the developing countries for its adverse impact on the environment. The addition of nutrients to organic waste limits the accumulation of volatile fatty acid (VFA) and accelerates the production of energy from food waste. The objective of the current study is to find out the effects of sludge addition on the decomposition and gas generation of separate components of food waste. This study was conducted for four combinations of reactors: two pairs containing meat and grain with the addition of a sludge content of 20% and 30%, respectively, as inoculum; another two pairs of reactors containing fruits and vegetables with a sludge content of 20% and 30%, respectively. Over the operation period, pH, volume, COD, and VFA tests were conducted for leachate while composition and volume measurements were done for the generated gas. Based on the results, it is observed that addition of sludge accelerated the decomposition of fruit and vegetable waste due to limited VFA accumulation compared to meat and grain. The maximum methane production was found in fruits and vegetable reactors at a rate of 6.7 L of methane per pound of food waste. For fruit and vegetable reactors, the CH4:CO2 ratio increased to as high as 8.5. On the other hand, for the meat and grain reactors, the increase in CH4:CO2 ratio was insignificant as they were in the lag phase.

Seasonal decomposition of different types of rivers in Slovakia: Implications for water management and agriculture

This study conducts an analysis of the seasonal decomposition of various river types in Slovakia in order to enhance the understanding of hydrological time series analysis and its potential implications for water management and agriculture. A comprehensive statistical methodology including decomposition of time series and correlation analysis was applied to the data collected from multiple river gauging stations across Slovakia. The results of the study indicate distinct seasonal variations in the hydrological characteristics of different river types, with a clear differentiation between lowland and mountain rivers. These findings have crucial implications for water management and agriculture as they suggest that a deeper understanding of seasonal patterns in river flow can lead to more efficient and effective utilization of water resources. Overall, this study highlights the significance of hydrological time series analysis in gaining a better comprehension of water resources and their management in Slovakia.

Dynamics of fouling of plastic waste fragments by microorganisms in the Gulf of Finland

In recent years, the problem of the aquatic environment pollution with synthetic polymers - plastic and microplastics - has become more urgent than ever, which causes an increasing interest of the scientific community in this topic, both in our country and abroad. The development of organic synthesis chemistry at the beginning of the last century led to the emergence of synthetic polymers – plastics; the chemical properties of plastic, making it an inexpensive, durable, and useful material, led to its widespread, mass distribution, but they are also the cause of difficulties with its disposal – the decay, decomposition, and disposal of many types of plastic takes decades, which much lower than the production rate of new plastic. As it is known, plastics are materials that are synthetic or natural high-molecular compounds (polymers); the term “microplastic” refers to particles of synthetic polymers or plastic copolymers (less than 5 microns), they are insoluble in water and non-degradable. Such characteristics of microplastic components as the area, the particle surface relief, the type of polymer will affect the biofilm formation rate. This indicator also is influenced by the flow rate, the bio-productivity of the waters, and the position of the particles in the water column.

Bayesian hierarchical modeling on covariance valued data

Analysis of structural and functional connectivity (FC) of human brains is of pivotal importance for diagnosis of cognitive ability. The Human Connectome Project (HCP) provides an excellent source of neural data across different regions of interest (ROIs) of the living human brain. Individual specific data were available in the form of time varying covariance matrices representing the brain activity as the subjects perform a specific task. As a preliminary objective of studying the heterogeneity of brain connectomics across the population, we develop a probabilistic model for a sample of covariance matrices using a scaled Wishart distribution. We stress here that our data units are available in the form of covariance matrices, and we use the Wishart distribution to create our likelihood function rather than its more common usage as a prior on covariance matrices. Based on empirical explorations suggesting the data matrices to have a low effective rank, we further model the center of the Wishart distribution using an orthogonal factor model type decomposition. We encourage shrinkage toward a low rank structure through a novel shrinkage prior and discuss strategies to sample from the posterior distribution using a combination of Gibbs and slice sampling. The efficacy of the approach is explored in various simulation settings and exemplified on several case studies including our motivating HCP data. We extend our modeling framework to a dynamic setting to detect change points.

New insight into abiotic or biotic gas in deep reservoirs of the CL-I gas field in Songliao Basin (China) by light hydrocarbons associated with natural gas

Abiotic synthesis through carbon dioxide (CO2) reduction may provide the prebiotic organic compounds needed for the emergence of life, whereas petroleum geologists pay more attention to whether abiotic gas generated by purely chemical reactions plays a prominent role in the formation of industrial gas pools like biotic gas. The Cretaceous reservoir associated with volcanic rocks of the Songliao Basin in northeastern China is suspected of possessing abiotic gas due to some abnormal geochemical characteristics, such as abundant 13C-enriched CO2, 13C-enriched CH4, 13C-depleted C2H6, and an isotopic trend of decreasing 13C content with growing carbon number. To understand further the genesis of deep natural gas, we examined the molecular and isotopic compositions of C1–C4 alkanes, CO2, and light hydrocarbons (LHs) of equal number (four) of gas samples collected from the Yingcheng (K1yc) volcanic and Denglouku (K1d) clastic reservoirs in the Changling (CL-I) gas field. Compared with the products of abiotic polymerization composed of 13C-depleted straight-chain alkanes, various 13C-enriched LH isomers that are highly compatible with the molecular and isotopic compositions of coal-derived thermogenic gas are confirmed in our samples, such as 2-methylhexane (2-MH), 2,3-dimethylpentane (2,3-DMP), cyclohexane (CH), methylcyclohexane (MCH), and other branched-chain alkanes or cycloalkanes. The striking invariable K1 ratio and resemblance of isotopic curves of LHs further indicate that the natural gas in different reservoirs is derived from underlying homologous source rocks, regardless of the variation of CO2 content (K1yc > 15% and K1d < 1%). Combining geological conditions, we propose that C1–C4 and LHs that have no inherent correlation with the concentration of CO2, which is predominantly derived from mantle degassing, are generated from the thermal decomposition of 13C-enriched type III organic matter during burial and diagenesis rather than sourced from mantle degassing, abiotic polymerization, or mixing of thermogenic gas. In addition, we also suggest that the geochemical anomalies consisting of 13C-enriched methane and 13C-depleted ethane are the products of the chemical mechanisms controlled by high temperature, and mantle-derived non-hydrocarbon gas (e.g., CO2 and He) are simply added to thermogenic gas.

Equivariant self-homotopy equivalences of product spaces

Let G be a finite group. We study the group of G-equivariant self-homotopy equivalences of product of G-spaces. For a product of n number of G-spaces, we represent it as product of n number of subgroups under the assumption of equivariant reducibility. Further we describe each factor as a split short exact sequence. Also we obtain another kind of factorisation, called LU type decomposition, as product of two subgroups.

Modeling of the Assessment System of the Main Risks of Investing in Engineering Enterprises in the Conditions of the Development of the Knowledge Economy

The main purpose of the study is to form a theoretical and methodological model for assessing the risks of investing in engineering enterprises in the context of the development of the knowledge economy. To achieve this purpose, it was necessary to apply the modeling methodology through the use of elements of functional processes that are aimed at achieving the goals and objectives. The relevance of the research topic is given by the fact that today engineering enterprises are extremely sensitive to changes in the operating environment and require a high level of investment. According to the results of the study, we have formed a theoretical and methodological decomposition of a two-variant type of modeling of both external (those that do not directly relate to the enterprise but come from outside) and internal risks (those that arise within the enterprise). The study has limitations and, first of all, they relate to the narrow level of the practical application of the model. Its current state implies a theoretical presentation of the possibilities of informing investors about the state of external and internal risks in the activities of engineering enterprises. Further research will include expanding the modeling process and tasks.

Estimation of soil enzyme activity with respect to decomposition of leaf litter types

Estimation of soil enzyme activity with respect to decomposition of leaf litter types

Fine-root biomass production and its contribution to organic matter accumulation in sedge fens under changing climate

Climate change may affect the carbon sink function of peatlands through warming and drying. Fine-root biomass production (FRBP) of sedge fens, a widespread peatland habitat, is important in this context, since most of the biomass is below ground in these ecosystems.We examined the response of fine-root biomass production, depth distribution (10 cm intervals down to 60 cm), chemical characteristics, and decomposition along with other main litter types (sedge leaves, Sphagnum moss shoots) to an average May-to-October warming of 1.7 °C above ambient daily mean temperature and drying of 2–8 cm below ambient soil water-table level (WL) in two sedge fens situated in Northern and Southern Boreal zones. Warming was induced with open top chambers and drying with shallow ditching. Finally, we simulated short-term organic matter (OM) accumulation using net primary production and mass loss data.Total FRBP, and FRBP in deeper layers, was clearly higher in southern than northern fen. Drying significantly increased, and warming marginally increased, total FRBP, while warming significantly increased, and drying marginally increased, the proportional share of FRBP in deeper layers. Drying, especially, modified root chemistry as the relative proportions of fats, wax, lipids, lignin and other aromatics increased while the proportion of polysaccharides decreased. Warming did not affect the decomposition of any litter types, while drying reduced the decomposition of sedge leaf litter. Although drying increased OM accumulation from root litter at both fens, total OM accumulation decreased at the southern fen, while the northern fen with overall lower values showed no such pattern.Our results suggest that in warmer and/or modestly drier conditions, sedge fen FRBP will increase and/or be allocated to deeper soil layers. These changes along with the altered litter inputs may sustain the soil carbon sink function through OM accumulation, unless the WL falls below a tipping point.

Differences in leaf and root litter decomposition in tropical montane rainforests are mediated by soil microorganisms not by decomposer microarthropods.

Plant litter decomposition is a key process in carbon and nutrient cycling. Among the factors determining litter decomposition rates, the role of soil biota in the decomposition of different plant litter types and its modification by variations in climatic conditions is not well understood. In this study, we used litterbags with different mesh sizes (45 µm, 1 mm and 4 mm) to investigate the effect of microorganisms and decomposer microarthropods on leaf and root litter decomposition along an altitudinal gradient of tropical montane rainforests in Ecuador. We examined decomposition rates, litter C and N concentrations, microbial biomass and activity, as well as decomposer microarthropod abundance over one year of exposure at three different altitudes (1,000, 2,000 and 3,000 m). Leaf litter mass loss did not differ between the 1,000 and 2,000 m sites, while root litter mass loss decreased with increasing altitude. Changes in microbial biomass and activity paralleled the changes in litter decomposition rates. Access of microarthropods to litterbags only increased root litter mass loss significantly at 3,000 m. The results suggest that the impacts of climatic conditions differentially affect the decomposition of leaf and root litter, and these modifications are modulated by the quality of the local litter material. The findings also highlight litter quality as the dominant force structuring detritivore communities. Overall, the results support the view that microorganisms mostly drive decomposition processes in tropical montane rainforests with soil microarthropods playing a more important role in decomposing low-quality litter material.

Characterizing the composition of iPSC derived cells from bulk transcriptomics data with CellMap

Induced pluripotent stem cell (iPSC) derived cell types are increasingly employed as in vitro model systems for drug discovery. For these studies to be meaningful, it is important to understand the reproducibility of the iPSC-derived cultures and their similarity to equivalent endogenous cell types. Single-cell and single-nucleus RNA sequencing (RNA-seq) are useful to gain such understanding, but they are expensive and time consuming, while bulk RNA-seq data can be generated quicker and at lower cost. In silico cell type decomposition is an efficient, inexpensive, and convenient alternative that can leverage bulk RNA-seq to derive more fine-grained information about these cultures. We developed CellMap, a computational tool that derives cell type profiles from publicly available single-cell and single-nucleus datasets to infer cell types in bulk RNA-seq data from iPSC-derived cell lines.

Asymptotic properties for compressions of two-isometries

The bounded linear operators T on a Hilbert space which have 2-isometric liftings S on are investigated in this paper. We refer to the structure of those operators in the case of general liftings, as well as for a more special type of such liftings S, namely for which is invariant to the orthogonal projection onto the kernel of S∗S − I. In this special case we describe the canonical triangulation of T induced by S, with entries expressed by operators close to contractions or isometries. Also, in this case we refer to some asymptotic properties of T and of its adjoint T∗ obtained by means of asymptotic limits associated to T∗ and T, relative to a lifting S for T. The canonical triangulations of T in this setting are described in detail, and as an application, the Wold type decomposition of a concave operator is obtained.

Solving 3D fractional Schrödinger systems on the basis of Phragmén–Lindelöf methods

Our aim in this article is to study the existence and uniqueness of time periodic solutions to 3D fractional Schrödinger systems. The techniques in this work are based on Phragmén–Lindelöf method (Liess, Necessary conditions in Phragmén–Lindelöf type estimates and decomposition for non-divergence type elliptic equations and mixed boundary conditions. Math Nachr 290(8–9):1328–1346, 2017) and Matsaev’s theory (Sukochev, Ferleger, Matsaev’s theorem for symmetric spaces of measurable operators. Math Notes 56(5–6):1185–1189, 1995). Particularly, the fractional maximal effects and the potential nonlinear equation are taken into account which play a key role in the Green–Schrödinger growth properties, especially in the selection of the Schrödinger norm.

On Energy Laws and Stability of Runge--Kutta Methods for Linear Seminegative Problems

This paper presents a systematic theoretical framework to derive the energy identities of general implicit and explicit Runge--Kutta (RK) methods for linear seminegative systems. It generalizes the stability analysis of explicit RK methods in [Z. Sun and C.-W. Shu, SIAM J. Numer. Anal., 57 (2019), pp. 1158-1182]. The established energy identities provide a precise characterization on whether and how the energy dissipates in the RK discretization, thereby leading to weak and strong stability criteria of RK methods. Furthermore, we discover a unified energy identity for all the diagonal Pade approximations, based on an analytical Cholesky type decomposition of a class of symmetric matrices. The structure of the matrices is very complicated, rendering the discovery of the unified energy identity and the proof of the decomposition highly challenging. Our proofs involve the construction of technical combinatorial identities and novel techniques from the theory of hypergeometric series. Our framework is motivated by a discrete analogue of integration by parts technique and a series expansion of the continuous energy law. In some special cases, our analyses establish a close connection between the continuous and discrete energy laws, enhancing our understanding of their intrinsic mechanisms. Several specific examples of implicit methods are given to illustrate the discrete energy laws. A few numerical examples further confirm the theoretical properties.

Coordinating transportation and pricing policies for perishable products

We study the joint pricing and transportation problem in a perishable product supply chain where products with different levels of quality are substitutable depending on the pricing policy and the customers’ quality sensitivity. We propose two frameworks to study this problem under sequential and integrated systems. Pricing and transportation decisions are made separately and then coordinated through an iterative process in the sequential model, but jointly optimized in the integrated system. The integration of transportation and pricing leads to a challenging mixed-integer quadratic programming (MIQP) formulation which is intractable for the current state-of-the-art commercial solvers. We exploit the special structure of this formulation and develop a Benders type decomposition method with a transportation master problem and a collection of pricing subproblems. To evaluate the proposed models and algorithms, we perform numerical experiments on an illustrative case study. We show that the performance of the sequential model is noticeably inferior to the integrated optimization model on two key metrics: profit and product waste. We observe, counter-intuitively, that the presence of customers with lower quality sensitivity who tolerate imperfect products increases the waste to sales ratio. Moreover, due to the interrelationship between pricing and transportation policies, the waste to sales ratio is not monotone in the cost of the freshness keeping efforts. Finally, we show the practical efficiency of our proposed decomposition-based algorithm in solving the MIQP compared to the state-of-the-art solver.

Lebesgue type decompositions and Radon–Nikodym derivatives for pairs of bounded linear operators

For a pair of bounded linear Hilbert space operators A and Bone considers the Lebesgue type decompositions of B with respect toA into an almost dominated part and a singular part, analogous to theLebesgue decomposition for a pair of measures in which case one speaks ofan absolutely continuous and a singular part. A complete parametrizationof all Lebesgue type decompositions will be given, and the uniqueness ofsuch decompositions will be characterized. In addition, it will be shownthat the almost dominated part of B in a Lebesgue type decomposition hasan abstract Radon–Nikodym derivative with respect to the operator A.

A parallel type decomposition scheme for quasi-linear abstract hyperbolic equation

Abstract The Cauchy problem for an abstract hyperbolic equation with the Lipschitz continuous operator is considered in the Hilbert space. The operator corresponding to the elliptic part of the equation is the sum of operators A 1 , A 2 , … , A m {A_{1},A_{2},\ldots,A_{m}} . Each summand is a self-adjoint and positive definite operator. A parallel type decomposition scheme for an approximate solution of the stated problem is constructed. The main idea of the scheme is that on each local interval the classical difference problems are solved in parallel (independently from each other) with the operators A 1 , A 2 , … , A m {A_{1},A_{2},\ldots,A_{m}} . The weighted average of the obtained solutions is announced as an approximate solution at the right end of the local interval. The convergence of the proposed scheme is proved and the approximate solution error is estimated, as well as the error of the difference analogue for the first-order derivative for the case when the initial problem data satisfy the natural sufficient conditions for solution existence.