Partitioning Theory Research Articles

Shrubland biomass and root-shoot allocation along a climate gradient in China

Background – Shrublands are receiving increasing attention because of climate change. However, knowledge about biomass allocation of shrublands at the community level and how this is regulated by climate is of limited availability but critical for accurately estimating carbon stocks and predicting global carbon cycles. Methods – We sampled 50 typical shrublands along a climate gradient in China and investigated the biomass allocation of shrubland at the community level and the effect of climate on biomass allocation. Shrub biomass was estimated using species-specific allometric relationships and the biomass of understory herbs was collected by excavating the whole plant. Regression analysis was used to examine the relationships between the biomass and the climate factors. RMA were conducted to establish the allometric relationships between the root and the shoot biomass at the community level.Key results – Shoot, root, and total biomass of shrub communities across different sites were estimated with median values of 206.5, 145.8, and 344.5 g/m2, respectively. Shoot, root, and total biomass of herb communities were estimated at 68.2, 58.9, and 117.2 g/m2, respectively. The median value of the R/S ratio of shrub communities was 0.58 and that of herb communities was 0.84. The R/S ratio of the shrub community showed a negative relationship with mean annual temperature and mean annual precipitation and a positive relationship with total annual sunshine and the aridity index. The R/S ratio of the herb community however showed a weak relationship with climate factors. Shoot biomass of the shrub community was nearly proportional to root biomass with a scaling exponent of 1.17, whereas shoot biomass of the herb community was disproportional to root biomass with a scaling exponent of 2.1.Conclusions – In shrublands, root biomass was more affected than shoot biomass by climate factors and this is related to water availability as a result of biomass allocation change of the shrub community. The understory herb community was less affected by climate due to the modification of the overstory–understory interaction to the climate-induced biomass allocation pattern. Shoot biomass of shrubs scales isometrically with root biomass at the community level, which supports the isometric theory of above-ground and below-ground biomass partitioning.

Advancing prediction of polycyclic aromatic hydrocarbon bioaccumulation in plants for historically contaminated soils using Lolium multiflorum and simple chemical in-vitro methodologies

This study compared chemical extraction methods for the prediction of PAH bioaccumulation in ryegrass (Lolium multiflorum) roots in four Manufactured Gas Plant (MGP) historically (>50 years) contaminated soils. The in-vitro methods compared were butanol (BuOH), non-buffered and buffered 2-hydroxypropyl-β-cyclodextrin extractions (HPCD, Buf-HPCD), potassium persulfate oxidation (KPS), solid phase extraction using Tenax resin (Tenax), and polyoxymethylene solid-phase extraction (POM). Extractions were directly compared with bioaccumulation and modelled using equilibrium partitioning theory (EqPT) with a combination of different partitioning parameters (KOC and KOW values) that aimed to improve predictions. The PAH accumulation in plant roots showed good correlation with concentrations in soils, and higher concentrations of the 4–6 ring PAHs compared with 2–3 ring PAHs. Plant accumulation of 16 PAHs in L. multiflorum was estimated within a factor of 5 using direct comparison for all bioaccessibility extraction methods. Accumulation values predicted using the calculation approach depended on the combination of KOC, KOW parameters and root components (total lipid vs total dry weight) used in calculations. Using KOC values derived from historically contaminated soils improved accuracy of predicted total root accumulation although precision was low. The combined contribution of PAH in lipid and carbohydrate root components (total dry weight) overestimated accumulation and a lipid only approach using generic partitioning parameters provided more accurate and precise approximation of bioaccumulation in roots of L. multiflorum in the soils. Overall, Tenax, POM and HPCD-based extractions showed promising results for predicting L. multiflorum root accumulation using the different approaches. This work significantly extends current knowledge for integrating simple chemical extractions into ecological risk assessment frameworks for the prediction of plant PAH bioavailability in historically contaminated soils.

Excess protein enabled dog domestication during severe Ice Age winters

Dogs (Canis familiaris) are the first animals to be domesticated by humans and the only ones domesticated by mobile hunter-gatherers. Wolves and humans were both persistent, pack hunters of large prey. They were species competing over resources in partially overlapping ecological niches and capable of killing each other. How could humans possibly have domesticated a competitive species? Here we present a new hypothesis based on food/resource partitioning between humans and incipient domesticated wolves/dogs. Humans are not fully adapted to a carnivorous diet; human consumption of meat is limited by the liver’s capacity to metabolize protein. Contrary to humans, wolves can thrive on lean meat for months. We present here data showing that all the Pleistocene archeological sites with dog or incipient dog remains are from areas that were analogous to subarctic and arctic environments. Our calculations show that during harsh winters, when game is lean and devoid of fat, Late Pleistocene hunters-gatherers in Eurasia would have a surplus of animal derived protein that could have been shared with incipient dogs. Our partitioning theory explains how competition may have been ameliorated during the initial phase of dog domestication. Following this initial period, incipient dogs would have become docile, being utilized in a multitude of ways such as hunting companions, beasts of burden and guards as well as going through many similar evolutionary changes as humans.

PAEs and PBDEs in plastic fragments and wetland sediments in Yangtze estuary

Phthalates (PAEs) and polybrominated diphenyl ethers (PBDEs) are widely used as additives in various plastic products. Because of their ubiquity and potential hazards to the environment, they have attracted widespread attention. This research supports the addition critical data of the concentration and distribution of PAEs and PBDEs in the plastic fragments and wetland sediments in Yangtze Estuary. The concentrations of Σ7PAEs and Σ9PBDEs in the plastic samples in Yangtze Estuary wetlands were 26.8–4241.8 μg/g and n.d. (no detectable) to 250.1 μg/g, respectively. The sixteen PAEs and eight PBDEs varied from 35.9 to 36225.2 ng/g and 3.9–253.0 ng/g in sediment samples. The dominant types of these chemicals in plastic and sediment samples were diisobutyl phthalate (DIBP), dibutyl phthalate (DBP), dioctyl phthalate (DEHP) and BDE-209. According to correlation analysis and principal component analysis, the major sources of additives in sediment were associated with the leak from plastic fragment and microplastic. Based on the equilibrium partitioning theory and Sediment Quality Guidelines (SeQGs), the ecological risk of PAEs (high risk) and PBDEs (moderate risk) were evaluated. Overall, the investigated area has been moderately polluted by additives and microplastics; therefore, it is necessary to strengthen the control of environmental input of plastic waste.

Allometry rather than abiotic drivers explains biomass allocation among leaves, stems and roots of Artemisia across a large environmental gradient in China

Abstract Biomass allocation patterns reflect the adaptive strategies of plants growing in different environments, which is a central issue in comparative plant ecology and evolution. However, the factors underpinning specific allocation patterns across organs and the existence of general rules governing allocation remain contentious. Optimal partitioning theory (OPT) states that plants can respond to resource availability by allocating relatively more biomass to the organ that captures the most limiting resources to optimize growth. In contrast, allometric partitioning theory (APT) postulates that biomass allocation among organs is a power function of plant size independently of environmental variation. As phylogenetic and growth form constraints (e.g. formation of inert heartwood in tree clades) may also affect biomass allocation, comparison among and within closely related taxa of rather similar growth form may enable a more direct testing of which of these two theories prevails. To test whether OPT or APT was prevalent at wide geographical scale, we investigated biomass allocation patterns among leaves, stems and roots of 1,022 plants of 62 Artemisia species (Asteraceae) collected along broad climate (annual mean temperature range: −4.9 to 18.0°C, annual mean precipitation range: 193–1,668 mm) and soil gradients (soil carbon content range: 1.6–15.4 kg C m−2) in central and eastern China. There were strong allometric relationships among leaf mass (ML), stem mass (MS) and root mass (MR) at both interspecific and intraspecific levels. Moreover, the interspecific and intraspecific patterns were not different from general patterns for pooled plants, that is, ML/MR and ML/MS, but not MS/MR, generally decreased with plant size. However, the three organ mass ratios were not responsive to broad climatic or soil gradients after the effect of plant size was removed. Synthesis. Our results generally support APT instead of OPT, suggesting that Artemisia plants have evolved an allometric strategy rather than relying on adjustment of allocation among organs to adapt to the broadly varying environments at the regional scale. For follow‐up research, we hypothesize that the strong allometric constraints on biomass allocation should depend on strong physiological adaptive responses of the different organs of Artemisia to environmental gradients.

Global patterns of biomass allocation in woody species with different tolerances of shade and drought: evidence for multiple strategies.

The optimal partitioning theory predicts that plants of a given species acclimate to different environments by allocating a larger proportion of biomass to the organs acquiring the most limiting resource. Are similar patterns found across species adapted to environments with contrasting levels of abiotic stress? We tested the optimal partitioning theory by analysing how fractional biomass allocation to leaves, stems and roots differed between woody species with different tolerances of shade and drought in plants of different age and size (seedlings to mature trees) using a global dataset including 604 species. No overarching biomass allocation patterns at different tolerance values across species were found. Biomass allocation varied among functional types as a result of phenological (deciduous vs evergreen broad-leaved species) and broad phylogenetical (angiosperms vs gymnosperms) differences. Furthermore, the direction of biomass allocation responses between tolerant and intolerant species was often opposite to that predicted by the optimal partitioning theory. We conclude that plant functional type is the major determinant of biomass allocation in woody species. We propose that interactions between plant functional type, ontogeny and species-specific stress tolerance adaptations allow woody species with different shade and drought tolerances to display multiple biomass partitioning strategies.

Contrasting biomass allocation responses across ontogeny and stress gradients reveal plant adaptations to drought and cold

Abstract How plants allocate their biomass to different organs is essential to understanding plant adaptations and distributions. Overall, biomass allocation may follow fixed rules across taxa. They are also likely to exhibit substantial departure from these rules during ontogeny and in response to particular limiting factors to optimize their growth and maximize their survival. However, how plants adjust their allocation priorities depending on size and age across stress gradients remain largely unknown in wild populations. We examined ontogenetic variation in biomass allocation in Himalayan forb Potentilla pamirica across its 5,250–5,900‐m elevation range, between populations from dry steppe, wet alpine and cold subnival zone. We evaluated whether biomass allocation followed optimal partitioning or fixed allometric rules using organ mass in 1,019 individuals spanning 1–73 years. We found shifting biomass fractions with plant size and age, supporting the optimal partitioning theory. Young plants (<10 years) allocated similar proportions of biomass to leaves, stems and roots, intermediate‐aged plants (10–30 years) allocated more biomass to roots, while the oldest plants had 90% biomass in below‐ground stems. Major developmental processes including secondary thickening, branching and flowering begin 10–15 years earlier under more thermally favourable steppe conditions. Young steppe plants are larger than alpine and subnival plants, but these differences disappear in plants aged ~30, and the oldest alpine and subnival plants are larger than steppe plants. Plant age exerted significant control over biomass allocation after controlling for plant size. While in steppe plants the preference for stem biomass allocation increases with both size and age, for large alpine and subnival plants the stem prioritization decreases with age in favour of root and leaf mass fractions. We interpret root and leaf prioritization in older plants as a way to reduce carbon imbalances and the risk of frost damage to secure long life. Our analyses rejected ontogenetically fixed allometry and instead found high variation in biomass allocation depending on age, size and environment, supporting optimal partitioning theory. The uneven allocation of resources to different structures and functions during ontogenesis reflects plant adaptations to different levels of low‐temperature and water stress across species elevation range. A free Plain Language Summary can be found within the Supporting Information of this article.

Gas-particle partitioning of carbonyls and its influencing factors in the urban atmosphere of Zhengzhou, China

Despite their profound roles in atmospheric chemistry and health concerns, the gas-particle partitioning of carbonyl compounds and its influencing factors in the ambient atmosphere are poorly elucidated. In this work, a reliable method using a denuder/filter-pack system coated with the derivative reagent, O-(2,3,4,5,6-pentafluorobenzyl)hydroxylamine (PFBHA) was developed for the simultaneous collection of gaseous and particulate carbonyls. Sampling campaigns were performed at an urban site in Zhengzhou, China. The average field-derived partitioning coefficients (Kpf) of the six most abundant carbonyls (formaldehyde, acetaldehyde, acetone, propionaldehyde, glyoxal, and methylglyoxal) were in the range of 10−5–10−4 m3·μg−1, and their effective Henry's law coefficients (eff. KH) ranged from 107 to 109 M·atm−1. Comparisons revealed that their Kpf and eff. KH were 104–106 times and 102–107 times higher than theoretically predicted, respectively. Given that the aerosol liquid water is a concentrated salt solution, these six carbonyls very clearly salted in to three atmospherically relevant aqueous salts, following the order of sulfate > ammonium > nitrate. However, even taking salting-in effects into account, the Pankow's absorptive partitioning theory and effective Henry's law both failed to explain the unexpected highly particulate carbonyls. In regard to the influencing factors, the negative correlations between Kpf and temperature indicate that lower temperature is conducive to carbonyls partitioning. As for the strong relative humidity (RH) dependence of KPf, high partitioning coefficients were observed under low and high RH conditions. Partitioning is considered to be dominated by the carbonyl-oligomer formation when RH increases from <10% to 50%, and driven by the abundant aerosol liquid water content when RH exceeds 50%. The presence of particulate inorganic components and the transition of particle phase state may also impact the partitioning process, especially in the urban atmosphere.

Shifting biomass allocation determines community water use efficiency under climate warming

Understanding how net primary production (NPP) and its allocation respond to climate warming is of fundamental importance in predicting ecosystem carbon (C) cycle and C-climate feedback. Especially, the optimal partitioning theory suggests that plants preferentially allocate photosynthates toward the above- or below-ground parts to acquire the limiting resources to maximize their growth rate and optimize resource use under environmental change. However, it remains elusive on how NPP allocation changes and regulates community water-use efficiency (WUEc) under climate warming. In this study, we conducted a manipulative warming experiment with three levels of warming treatments (control, + 1.5 °C and + 2.5 °C) to explore the response of NPP allocation and its regulation on WUEc in an alpine meadow. Results showed that above-ground NPP (ANPP) and below-ground NPP (BNPP) responded differently to warming. On average, W1.5 (+ 1.5 °C) and W2.5 (+ 2.5 °C) treatments increased BNPP by 28.98% and 33.28% and increased NPP by 20.05% and 38.70%, respectively, across 4 years. Whereas no consistent warming effect on ANPP was observed across years. The fraction of BNPP to total NPP (fBNPP) responded positively to warming under low ambient temperature and community biomass while it responded negatively under high ambient temperature and community biomass. Notably warming-induced changes in fBNPP negatively correlated with warming-induced changes in WUEc. These results suggested that warming effect on NPP allocation was largely contextually dependent and implied important biological regulation on WUEc. The emerging trade-offs between NPP allocation and WUEc reflect adaptation strategy of plant community under climate change.

The Effect of Micro Entrants on Generalists' Performance

Resource partitioning theory and market entry research provide tremendous clarity on specialists, generalists and entrant-incumbent dynamics, but such scholarship overlooks micro enterprises—a distinct strategic group of firms who are very small in terms of scale, scope, and/or capability yet they are often seen as specialists. This is a serious oversight because unlike specialists who erode incumbent positions one at a time, micro entrants not only act differently, they often ride on top of multisided platforms (e.g., Airbnb, Uber, Etsy, Facebook, etc.) and gain market access almost overnight. In addition, while extant research focuses on adversarial entrant- incumbent relations, our study redirects attention to why and how the entry of micro enterprises augment the performance of generalists. Using panel data on entrants who provide dwelling capacity via the Airbnb platform from 2010 to 2015, we show that micro entrants enhance the performance of large incumbents (i.e., four-star hotels). We also find that an influx of micro entrants has even a stronger positive effect on generalists’ performance when the generalists’ market is more concentrated, and the activity of the multisided platforms is regulated. All in all, we show that when resource partitioning theory recognizes micro enterprises it provides new and greater clarity on entrant-incumbent relations.

A hierarchical parallel fusion framework for egocentric ADL recognition based on discernment frame partitioning and belief coarsening

Recently, egocentric activity recognition has become a major research area in pattern recognition and artificial intelligence due to its high significance in potential applications in medical care, rehabilitation, smart home/office, etc. In this study, we develop a hierarchical parallel multimodal fusion framework for the recognition of egocentric activities in daily living (ADL). This framework uses the Dezert–Smarandache theory and is constructed around three modalities: location, motion and vision data from a wearable hybrid sensor system. The reciprocal distance and a trained support vector machine classifier are used to form the basic belief assignments (BBA) of location and motion. For vision data composed of egocentric photo streams, a well-trained convolutional neural network is utilized to produce a set of textual tags and the entropy-based statistics for these tags are used to construct the vision BBA. Discernment partitioning and belief coarsening theory are adopted for the hierarchical fusion of the three BBA functions from different ADL levels. Experimental results show that the recognition accuracy of the proposed fusion method was significantly higher than that of the methods based on single modality or modality combinations when our method was applied to real-life multimodal egocentric activity datasets. In addition, our method also achieved higher adaptability and scalability.

Phthalates: Relationships between Air, Dust, Electronic Devices, and Hands with Implications for Exposure.

Exposure to phthalates is pervasive and is of concern due to associations with adverse health effects. Exposures and exposure pathways of six phthalates were investigated for 51 women aged 18-44 years in Ontario, Canada, based on measured phthalate concentrations in hand wipes and indoor media in their residences. All six phthalates had detection frequencies of 100% in air (∑6670 ng m-3 geomean) and floor dust (∑6630 μg g-1), nearly 100% detection frequencies for hand palms and backs that were significantly correlated and concentrations were repeatable over a 3 week interval. Phthalates on hands were significantly correlated with levels in air and dust, as expected according to partitioning theory. Total exposure was estimated as 4860 ng kg bw-1 day-1 (5th and 95th percentiles 1980-16 950 ng kg bw-1 day-1), with dust ingestion, followed by hand-to-mouth transfer, as the dominant pathways. With the exception of diethyl phthalate (DEP), phthalates had over 50% detection frequencies in surface wipes of most electronic devices sampled, including devices in which the use of phthalates was not expected. Phthalate concentrations on surfaces of hand-held devices were ∼10 times higher than on non-hand-held devices and were correlated with levels on hands. The data are consistent with phthalate emissions from sources such as laminate flooring and personal care products (e.g., scented candles), followed by partitioning among air, dust, and surface films that accumulate on electronic devices and skin, including hands. We hypothesize that hands transfer phthalates from emission sources and dust to hand-held electronic devices, which accumulate phthalates due to infrequent washing and which act as a sink and then a secondary source of exposure. The findings support those of others that exposure can be mitigated by increasing ventilation, damp cloth cleaning, and minimizing the use of phthalate-containing products and materials.

Partitioning of hydrogen peroxide in gas-liquid and gas-aerosol phases

Abstract. Hydrogen peroxide (H2O2) is a vital oxidant in the atmosphere and plays critical roles in the oxidation chemistry of both liquid and aerosol phases. The partitioning of H2O2 between the gas and liquid phases, or the aerosol phase, could affect its abundance in these condensed phases and eventually the formation of secondary components. However, the partitioning processes of H2O2 in gas-liquid and gas-aerosol phases are still unclear, especially in the ambient atmosphere. In this study, field observations of gas-, liquid-, and aerosol-phase H2O2 were carried out in the urban atmosphere of Beijing during the summer and winter of 2018. The effective field-derived mean value of Henry's law constant (HAm, 2.1×105 M atm−1) was 2.5 times of the theoretical value in pure water (HAt, 8.4×104 M atm−1) at 298±2 K. The effective derived gas-aerosol partitioning coefficient (KPm, 3.8×10-3 m3 µg−1) was 4 orders of magnitude higher on average than the theoretical value (KPt, 2.8×10-7 m3 µg−1) at 270±4 K. Beyond following Henry's law or Pankow's absorptive partitioning theory, the partitioning of H2O2 in the gas-liquid and gas-aerosol phases in the ambient atmosphere was also influenced by certain physical and chemical reactions. The average concentration of liquid-phase H2O2 in rainwater during summer was 44.12±26.49 µM. In 69 % of the collected rain samples, the measured level of H2O2 was greater than the predicted value in pure water calculated by Henry's law. In these samples, 41 % of the measured H2O2 was from gas-phase partitioning, while most of the rest may be from residual H2O2 in raindrops. In winter, the level of aerosol-phase H2O2 was 0.093±0.085 ng µg−1, which was much higher than the predicted value based on Pankow's absorptive partitioning theory. The contribution of partitioning of the gas-phase H2O2 to the aerosol-phase H2O2 formation was negligible. The decomposition/hydrolysis rate of aerosol-phase organic peroxides could account for 11 %–74 % of the consumption rate of aerosol-phase H2O2, and the value depended on the composition of organic peroxides in the aerosol particles. Furthermore, the heterogeneous uptake of HO2 and H2O2 on aerosols contributed to 22 % and 2 % of the aerosol-phase H2O2 consumption, respectively.

Evaluating Sphagnum traits in the context of resource economics and optimal partitioning theories

Tradeoffs between key aspects of plant performance such as resource acquisition and allocation underpin several trait‐based theories that have been derived for vascular plants. However, due to difficulty in quantifying traits in nonvascular plants, our theoretical understanding of how traits govern the physiological and ecological preferences of nonvascular plant species is quite limited. Here, we used the resource economics theory (RET) and optimal partitioning theory (OPT) to evaluate functional traits in mosses. We evaluated aspects of these theories in two common but ecologically different Sphagnum moss species. We used a suite of morpho‐physiological traits across a range of environmental treatments to test whether Sphagnum is capable of functional tissue partitioning and whether the two Sphagnum species studied conform to a fast or slow strategy often observed in vascular plants. Consistent with the predictions of RET, the fast‐growing species maintained a faster growth rate and low biomass across treatments. However, some of the traits responded contrary to predictions for respiration and photosynthetic rates. Consistent with OPT, Sphagnum diverted biomass from branch to capitulum to connect with the primary source of moisture when under drought stress. Overall, this study showed that moss traits could be used to test ecological theories that were developed primarily for vascular plants.

Entity Shielding and the Rule of “Debt-Follow-Asset” in China: An Empirical Law and Economics Analysis

Legal personality has been regarded as one of the essential characteristics of modern corporations. Since a corporation is a legal entity separated from its shareholders, its assets are usually shielded from the creditors of its shareholders. Scholars refer to this arrangement as “entity shielding” and generally consider it as an efficient arrangement. China, however, has explicitly adopted the controversial rule of “debts-follow-assets” (the DFA rule), with which courts may hold a corporation liable for the debt of its shareholder under certain circumstances. This article presents an empirical study of how this rule is enforced in practice. It finds that courts often consider two important factors that are not stipulated in the DFA rule – the identity of the creditor raising the lawsuit and the number of outside investors in the corporation. These patterns can be explained with the theory of asset partitioning. China’s experience contributes to the literature of the law and economics of business forms and organizational law by showing for the first time that economic concerns shape the legal restrictions of entity shielding within a specific jurisdiction. The factors identified in this article as important may also be considered by policymakers in the legal design of rules that restrict entity shielding in other jurisdictions.

Construction of a generalized Voronoi diagram with optimal placement of generator points based on the theory of optimal set partitioning

The problem of construction of a generalized Voronoi diagram with optimal placement of a finite number of generator points in a bounded set of \textit{n}-dimensional Euclidean space is considered. A method is proposed for solving such a problem based on the formulation of the corresponding continuous problem of optimal partitioning of a set in \textit{n}-dimensional Euclidean space with a partition quality criterion that provides the corresponding form of the Voronoi diagram. Further, to solve such a problem, the developed mathematical and algorithmic apparatus is used, the part of which is Shor's \textit{r}-algorithm.

Current State of Atmospheric Aerosol Thermodynamics and Mass Transfer Modeling: A Review

A useful aerosol model must be able to adequately resolve the chemical complexity and phase state of the wide particle size range arising from the many different secondary aerosol growth processes to assess their environmental and health impacts. Over the past two decades, significant advances in understanding of gas-aerosol partitioning have occurred, particularly with respect to the role of organic compounds, yet aerosol representations have changed little in air quality and climate models since the late 1990s and early 2000s. The gas-aerosol partitioning models which are still commonly used in air quality models are separate inorganics-only thermodynamics and secondary organic aerosol (SOA) formation based on absorptive partitioning theory with an assumption of well-mixed liquid-like particles that continuously maintain equilibrium with the gas phase. These widely used approaches in air quality models for secondary aerosol composition and growth based on separated inorganic and organic processes are inadequate. This review summarizes some of the important developments during the past two decades in understanding of gas aerosol mass transfer processes. Substantial increases in computer performance in the last decade justify increasing the process detail in aerosol models. Organics play a central role during post-nucleation growth into the accumulation mode and change the hygroscopic properties of sulfate aerosol. At present, combined inorganic-organic aerosol thermodynamics models are too computationally expensive to be used online in 3-D simulations without high levels of aggregation of organics into a small number of functional surrogates. However, there has been progress in simplified modeling of liquid-liquid phase separation (LLPS) and distinct chemical regimes within organic-rich and inorganic-rich phases. Additional limitations of commonly used thermodynamics models are related to lack of surface tension data for various aerosol compositions in the small size limit, and lack of a comprehensive representation of surface interaction terms such as disjoining pressure in the Gibbs free energy which become significant in the small size limit and which affect both chemical composition and particle growth. As a result, there are significant errors in modeling of hygroscopic growth and phase transitions for particles in the nucleation and Aitken modes. There is also increasing evidence of reduced bulk diffusivity in viscous organic particles and, therefore, traditional secondary organic aerosol models, which are typically based on the assumption of instantaneous equilibrium gas-particle partitioning and neglect the kinetic effects, are no longer tenable.

Algorithm for Constructing Voronoi Diagrams with Optimal Placement of Generator Points Based on Theory of Optimal Set Partitioning

An algorithm is proposed for constructing a generalized Voronoi diagram with optimal placement of a finite number of generator points in a bounded set of n-dimensional Euclidean space. The algorithm is based on the formulation of the corresponding continuous problem of optimal set partitioning with a partition quality criterion providing the corresponding form of Voronoi diagram, and on the application of the apparatus of the optimal partitioning theory to solve this problem. Herewith, the efficient method of non-differentiable optimization is used for the numerical solution of an auxiliary finite-dimensional optimization problem arising in the development of the method for solving the mentioned infinite-dimensional problem of optimal set partitioning. Namely, that is one of the variants of the generalized gradient descent method with space expansion in the direction of the difference of two successive generalized antigradients (Shor's r-algorithm). The proposed algorithm for constructing a generalized Voronoi diagram with optimal placement of a finite number of generator points in a bounded set of n-dimensional Euclidean space has some advantages compared to those known in a scientific literature. It does not depend on a dimension of Euclidean space containing the initial bounded set; it is applicable for the large-scale problems (over 300 generator points); it works not only for Euclidean metrics, but also for Chebyshev, Manhattan and other ones; the complexity of the algorithm implementation for constructing Voronoi diagram based on the proposed approach does not increase with increasing number of generator points. The results of software implementation of the developed algorithm are presented for constructing a standard Voronoi diagram with an optimal placement of generator points as well as some of its generalizations such as additive, multiplicative and additive-multiplicative Voronoi diagrams with optimal placement of generator points.

APPLICATION OF THE THEORY OF OPTIMAL SET PARTITIONING BEFORE BUILDING MULTIPLICATIVELY WEIGHTED VORONOI DIAGRAM WITH FUZZY PARAMETERS

An algorithm for constructing a multiplicatively weighted Voronoi diagram involving fuzzy parameters with the optimal location of a finite number of generator points in a limited set of n-dimensional Euclidean space 𝐸𝑛 has been suggested in the paper. The algorithm has been developed based on the synthesis of methods of solving the problems of optimal set partitioning theory involving neurofuzzy technologies modifications of N.Z. Shor 𝑟 -algorithm for solving nonsmooth optimization problems.

Solving a two-step continuous-discrete optimal split-distribution problem with fuzzy parameters

The theory of optimal set partitioning from an n-dimensional Euclidean space En is an important part of infinite-dimensional mathematical programming. The mostly reason of high interest in development of the theory of optimal set partitioning is that its results can be applied to solving the classes of different theoretical and applied optimization problems, which are transferred into continuous optimal set partitioning problem. This paper investigates the further development of the theory of optimal set partitioning from En in the case of a two-stage continuous-discrete problem of optimal partitioningdistribution with non-determined input data, which is frequently appear in solving practical problems. The two-stage continuous-discrete problem of optimal partition-distribution under constraints in the form of equations and determined position of centers of subsets is generalized by proposed continuous-discrete problem of optimal partition-distribution in case if some parameters are presented in incomplete, inaccurate or unreliable form. These parameters can be represented as linguistic variables and the method of neurolinguistic identification of unknown complex, nonlinear dependencies can be used in purpose to recovery them. A method for solving the two-stage continuous-discrete optimal partitioning-distribution problem with fuzzy parameters in target functional which based on usage of neurolinguistic identification of unknown dependencies for recovering precise values of fuzzy parameters, methods of the theory of optimal set partitioning and the method of potentials for solving a transportation problem is proposed.