Data-driven Wasserstein distributionally robust chance-constrained optimization for crude oil scheduling under uncertainty

Crude oil scheduling optimization is an effective method to enhance the economic benefits of oil refining.But uncertainties,including uncertain demands of crude distillation units(CDUs),might make the production plans made by the traditional deterministic optimization models infeasible.A data-driven Wasserstein distributionally robust chance-constrained(WDRCC)optimization approach is proposed in this paper to deal with demand uncertainty in crude oil scheduling.First,a new deterministic crude oil scheduling optimization model is developed as the basis of this approach.The Wasserstein distance is then used to build ambiguity sets from historical data to describe the possible realizations of probability distributions of uncertain demands.A cross-validation method is advanced to choose suitable radii for these ambiguity sets.The deterministic model is reformulated as a WDRCC optimization model for crude oil scheduling to guarantee the demand constraints hold with a desired high probability even in the worst situation in ambiguity sets.The proposed WDRCC model is transferred into an equivalent conditional value-at-risk representation and further derived as a mixed-integer nonlinear programming counterpart.Industrial case studies from a real-world refinery are conducted to show the effectiveness of the proposed method.Out-of-sample tests demonstrate that the solution of the WDRCC model is more robust than those of the deterministic model and the chance-constrained model.

Distributional Chaoticity of the Minimal Subshift of Shift Operators

This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, distributional chaotic of type k ( k∈{ 1,2,2 1 2 ,3 } ), and ( 0,1 ) -distribution.

Web Page Recommendation Using Distributional Recurrent Neural Network

In the data retrieval process of the Data recommendation system,the matching prediction and similarity identification take place a major role in the ontology.In that,there are several methods to improve the retrieving process with improved accuracy and to reduce the searching time.Since,in the data recommendation system,this type of data searching becomes complex to search for the best matching for given query data and fails in the accuracy of the query recommendation process.To improve the performance of data validation,this paper proposed a novel model of data similarity estimation and clustering method to retrieve the relevant data with the best matching in the big data processing.In this paper advanced model of the Logarithmic Directionality Texture Pattern(LDTP)method with a Metaheuristic Pattern Searching(MPS)system was used to estimate the similarity between the query data in the entire database.The overall work was implemented for the application of the data recommendation process.These are all indexed and grouped as a cluster to form a paged format of database structure which can reduce the computation time while at the searching period.Also,with the help of a neural network,the relevancies of feature attributes in the database are predicted,and the matching index was sorted to provide the recommended data for given query data.This was achieved by using the Distributional Recurrent Neural Network(DRNN).This is an enhanced model of Neural Network technology to find the relevancy based on the correlation factor of the feature set.The training process of the DRNN classifier was carried out by estimating the correlation factor of the attributes of the dataset.These are formed as clusters and paged with proper indexing based on the MPS parameter of similarity metric.The overall performance of the proposed work can be evaluated by varying the size of the training database by 60%,70%,and 80%.The parameters that are considered for performance analysis are Precision,Recall,F1-score and the accuracy of data retrieval,the query recommendation output,and comparison with other state-of-art methods.

Distributional dynamic and trend evolution of China's agricultural carbon emissions-an analysis on panel data of 31 provinces from 2002 to 2011

Researching the dynamic distribution characteristics and trend evolution of agricultural carbon emissions is of considerable significance in formulating an effective agricultural carbon reduction policy.Based on measurement of agricultural carbon emissions of 31 provinces over the period 2002-2011,the study observed regional differences and the dynamic evolution of distribution of agricultural carbon emissions using agricultural carbon intensity as the indicator,accompanied by Gini coefficients and the kernel density estimation method.The results demonstrate first that agricultural carbon emissions for China show an obvious nonequilibrium nature in regard to spatial distribution.According to the differences in agricultural carbon emissions dynamic trends,we divided the 31 regions into four types- continuous decline,fluctuating decline,continuous increase,and fluctuating increase.Further,agricultural carbon emissions intensity showed a downward trend with significant differences in the research areas.Second,the gap in spatial distribution of national agricultural carbon emissions is gradually expanding based on the results calculated by Gini coefficient.From the perception of regional differences in agricultural carbon emissions,the eastern region showed an average level,the gap was more obvious in the central region,while western region showed a trend of fluctuating downward.Third,according to estimation by kernel density,the regional disparity in agricultural carbon emissions had a downward,but limited,trend.In regard to agricultural carbon emissions over the three areas,the regional gap not only tended to decrease but also showed a "four way" differentiation phenomenon in the eastern region.The difference in the central region difference was narrower.On the whole,the gap for the western region reduced steadily over a small range.

Second Order Periodic Boundary Value Problems Involving the Distributional Henstock-Kurzweil Integral

We apply the distributional derivative to study the existence of solutions of the second order periodic boundary value problems involving the distributional Henstock-Kurzweil integral. The distributional Henstock-Kurzweil integral is a general intergral, which contains the Lebesgue and Henstock-Kurzweil integrals. And the distributional derivative includes ordinary derivatives and approximate derivatives. By using the method of upper and lower solutions and a fixed point theorem, we achieve some results which are the generalizations of some previous results in the literatures.

Distributional features of temperature and salinity in the southern Taiwan Strait and its adjacent sea areas in late summer, 1994

Based on the CTD data obtained in the southern Taiwan Strait and its adjacent areas in August and September of 1994, the distributional features of the temperature and salinity in the studied area have been analyzed in detail. The results are as follows: (1) There are two low temperature and high salinity regions in the nearshore area between Dongshan and Shantou and in the southeastern Taiwan Shoal, respectively, which may be caused by upwellings. (2) There exists a cold eddy in the northwestern sea area and a warm eddy with two high temperature cores in the eastern sea area of the Dongsha Islands, which are related to the anti-cyclonic turning of the seawater near the Dongsha Islands. (3) A westward high temperature and high salinity water tongue extends through the northern Luzon Strait and reaches the sea areas near the Dengsha Islands and southern Taiwan Strait.

Some Remarks on Distributional Chaos for Linear Operators

In this paper, we consider some properties for bounded linear operators concerning distributional chaos. Norm-unimodality of bounded linear operators im- plies distributional chaos. Some properties such as similarity and spectra description for norm-unimodal operators are considered. The existence of distributional chaos in nest algebra is also proved. In addition, we obtain a sufficient and necessary condition of distributional chaos for a class of operators, which contains unilateral backward weighted shift operators.

Distributional characteristics of planktonic Amphipoda（Hyperiidea） in the South Huanghai Sea and East China Sea

In this paper the distributional characteristics of species composition, ecological nature and specific numberof planktonic Amphipoda (Hyperiidea) in the South Huanghai Sea and East China Sea are analyzed and their relation withthe environmental factors is also discussed. It is shown from the results that 71 species of planktonic Amphipoda (Hyperi idea)have been recorded, and the horizontal distribution of species number presents higher in the south and east,lower inthe south and west but the highest is in the southeast part of the study area.The higher abundance zone occurred in thenorthern margin of the study area and in the southeastern waters off the Changjiang Estuary respectively with evident dif ference in the two zones in composition of species number and ecological nature.The unique species Parathemistogandichaudi or Hyperiodes sibaginis was the dominant species distributed in the north and in the south of the ChangjiangEstuary respectively. The distribution of planktonic Amphipoda was controlled by the movement of many distinct watersystems within the study area and their reciprocal displacement.The distribution of Amphipoda (Hyperiidea) of differentecological characters showed evidence of the dynamics of the various water systems.

Research on the Distributional Features of and Interrelationships Between the Dissolved Oxygen, Salinity, pH Value and Nutrient Salts in the Honghai Bay Waters

In this paper, the environmental factors are surveyed of the mariculture waters of the Honghai Bay from the late spring to the early summer (June) in 1998. The distributional features and variation laws of dissolved oxygen, salinity, pH value and nutrient salts in the sea water are expounded. Also discussed are their relationships between each other. The results show that the contents of dissolved oxygen and pH value in the sea water increase with the increasing temperature from north (except for No.15~17 stations) to south (expect for No.6 station). At the same time it is affirmed that photosynthesis is the major cause of the high contents of dissolved oxygen and pH value. And the nutrient salt shows a negative correlation with salinity. The total content of phytoplankton obviously increased with the reduction of nutrient salts from north to south.

THE DISTRIBUTIONAL DIMENSION OF FRACTALS

In the book [1] H.Triebel introduces the distributional dimension of fractals in an analytical form and proves that： for Г as a non-empty set in R^n with Lebesgue measure ｜Г｜ = 0, one has dimH Г = dimD Г, where dimD Г and dimH Г are the Hausdorff dimension and distributional dimension, respectively. Thus we might say that the distributional dimension is an analytical definition for Hausdorff dimension. Therefore we can study Hausdorff dimension through the distributional dimension analytically. By discussing the distributional dimension, this paper intends to set up a criterion for estimating the upper and lower bounds of Hausdorff dimension analytically. Examples illustrating the criterion are included in the end.

ON DISTRIBUTIONAL n-CHAOS

Let （X, f ） be a topological dynamical system, where X is a nonempty compact and metrizable space with the metric d and f ：X →X is a continuous map. For any integer n≥2, denote the product space by X（n）=X · · · × X｜ {z }n times . We say a system （X, f ） is generally distributionally n-chaotic if there exists a residual set D ？X（n） such that for any point x=（x1, · · · , xn）∈D, lim inf k→∞#（{i：0≤i≤k-1, min{d（fi（xj）, fi（xl））：1≤j 6=l≤n}〈δ0}） k=0 for some real numberδ0〉0 and lim sup k→∞#（{i：0≤i≤k-1, max{d（fi（xj）, fi（xl））：1≤j 6=l≤n}〈δ}） k=1 for any real number δ 〉 0, where #（·） means the cardinality of a set. In this paper, we show that for each integer n ≥ 2, there exists a system （X,σ） which satisfies the following conditions： （1） （X,σ） is transitive;（2） （X,σ） is generally distributionally n-chaotic, but has no distributionally （n＋1）-tuples;（3） the topological entropy of （X,σ） is zero and it has an IT-tuple.

Distributional Reinforcement Learning with Quantum Neural Networks

Traditional reinforcement learning (RL) uses the return, also known as the expected value of cumulative random rewards, for training an agent to learn an optimal policy. However, recent research indicates that learning the distribution over returns has distinct advantages over learning their expected value as seen in different RL tasks. The shift from using the expectation of returns in traditional RL to the distribution over returns in distributional RL has provided new insights into the dynamics of RL. This paper builds on our recent work investigating the quantum approach towards RL. Our work implements the quantile regression (QR) distributional Q learning with a quantum neural network. This quantum network is evaluated in a grid world environment with a different number of quantiles, illustrating its detailed influence on the learning of the algorithm. It is also compared to the standard quantum Q learning in a Markov Decision Process (MDP) chain, which demonstrates that the quantum QR distributional Q learning can explore the environment more efficiently than the standard quantum Q learning. Efficient exploration and balancing of exploitation and exploration are major challenges in RL. Previous work has shown that more informative actions can be taken with a distributional perspective. Our findings suggest another cause for its success: the enhanced performance of distributional RL can be partially attributed to its superior ability to efficiently explore the environment.

Was Polchinski Wrong? Colombeau Distributional Rindler Space-Time with Distributional Levi-CivitàConnection Induced Vacuum Dominance. Unruh Effect Revisited

The vacuum energy density of free scalar quantum field in a Rindler distributional space-time with distributional Levi-Cività connection is considered. It has been widely believed that, except in very extreme situations, the influence of acceleration on quantum fields should amount to just small, sub-dominant contributions. Here we argue that this belief is wrong by showing that in a Rindler distributional background space-time with distributional Levi-Cività connection the vacuum energy of free quantum fields is forced, by the very same background distributional space-time such a Rindler distributional background space-time, to become dominant over any classical energy density component. This semiclassical gravity effect finds its roots in the singular behavior of quantum fields on a Rindler distributional space-times with distributional Levi-Cività connection. In particular we obtain that the vacuum fluctuations have a singular behavior at a Rindler horizon . Therefore sufficiently strongly accelerated observer burns up near the Rindler horizon. Thus Polchinski’s account doesn’t violate the Einstein equivalence principle.

Distributional Effects of Transport Taxes： An Incidence Analysis

Wider use of economic instruments in the field of environmental and energy policy provides several benefits. These instruments not only create market-based incentives for environmentally friendly behaviors but also represent effective opportunities to collect revenues. In this context, energy and transport-related taxes play a major role, even if their extensive use has raised several concerns over equity issues. The main objective of the paper is to investigate the redistributive burden of existing transport taxes on Italian households. An incidence analysis is carried out on a sample of more than 23,000 Italian families for the year 2009. Some alternative policy options are also analyzed to provide some suggestions on how to countervail the potential negative regressive effects that might arise. We find that vehicle ownership taxes, if properly set, can represent a promising opportunity to blend together budget and equity needs. To obtain a better indication of the progressivity or regressivity of certain policy designs, we rely on some summary indexes, such as the Kakwani measure of progressivity and the Reynolds-Smolensky measure of redistributive capacity of a tax.

Distributional expansion of maximum from logarithmic general error distribution

Logarithmic general error distribution is an extension of lognormal distribution. In this paper, with optimal norming constants the higher-order expansion of distribution of partial maximum of logarithmic general error distribution is derived.

Potential distributional shifts in North America of allelopathic invasive plant species under climate change models

Predictive studies play a crucial role in the study of biological invasions of terrestrial plants under possible climate change scenarios.Invasive species are recognized for their ability to modify soil microbial communities and influence ecosystem dynamics.Here,we focused on six species of allelopathic flowering plants-Ailanthus altissima,Casuarina equisetifolia,Centaurea stoebe ssp.micranthos,Dioscorea bulbifera,Lantana camara,and Schinus terebinthifolia-Xhat are invasive in North America and examined their potential to spread further during projected climate change.We used Species Distribution Models(SDMs)to predict future suitable areas for these species in North America under several proposed future climate models.ENMEval and Maxent were used to develop SDMs,estimate current distributions,and predict future areas of suitable climate for each species.Areas with the greatest predicted suitable climate in the future include the northeastern and the coastal northwestern regions of North America.Range size estimations demonstrate the possibility of extreme range loss for these invasives in the southeastern United States,while new areas may become suitable in the northeastern United States and southeastern Canada.These findings show an overall northward shift of suitable climate during the next few decades,given projected changes in temperature and precipitation.Our results can be utilized to analyze potential shifts in the distribution of these invasive species and may aid in the development of conservation and management plans to target and control dissemination in areas at higher risk for potential future invasion by these allelopathic species.

Study on distributional characteristics of phytoplankton population in the Bohai Sea and the Yellow Sea in the summer 2015

Marine phytoplankton plays a very important role in marine ecology,environment and global climate change,and it is an indicative organism for measuring water quality.The Bohai Sea and the Yellow Sea in China have unique geographical locations.Therefore,the characteristics of phytoplankton population distribution in the Bohai Sea and the Yellow Sea are of great significance to the study of marine ecology in China.In this work,the pigment data obtained from the Yellow Sea and Bohai Sea in August 2015 were analyzed by HPLC(High-Performance Liquid Chromatography).Then the pigment data were analyzed statistically by the CHEMTAX software,so that the phytoplankton community structure information was obtained.Results show that in summer 2015,from the perspective of sea area,the biomass of phytoplankton in the surface of Bohai Sea is higher than that in the Yellow Sea,while the phytoplankton biomass in the surface of North Yellow Sea is higher than that in the South.From the perspective of dominant species of phytoplankton,the surface waters of the Yellow Sea and Bohai Sea were dominated by diatoms,prymnesiophytes and chlorophytes,accounting for 55.76%,14.56%and 14.55%respectively.Among them,diatoms accounted for the absolute advantage.

The Homogeneity of Distributional Patterns of the Global Terrestrial Animal,Plant and Microorganism under the Influence of Ecological Conditions

The world animal geographical regionalization scheme and the plant geographical regionalization scheme have been formulated by zoologists and botanists respectively since the biogeography has been established.This research team initially confirmed the homogeneity of Chinese animal and plant geography.To explore the relationship between the distribution pattern of global animals,plants,and microorganisms,global 141,814 genera of terrestrial animals,17,526 genera of plants,21,321 genera of microorganisms,and their major taxa were analyzed using their proposed SGF(Similarity General Formula)and a new multivariate similarity clustering analysis method.Almost identical analytical results were obtained,meeting the requirements of statistics,geography,ecology and biology respectively.The expected consistency of their distribution pattern was achieved for the first time.We prove that the earth’s ecological conditions affect the homogeneity and accumulation of the distribution of animals,plants and microorganisms.Homogeneity determines the distribution pattern of global kinds of biological consistency,accumulation determines the impact of the evolutionary period on the breadth of distribution,microorganisms appear earliest,plants second,animals later,and their average distribution domain decreases in turn,reflecting these differences.Therefore,this study not only provides a theoretical basis and quantitative basis for the establishment of geographical regionalization scheme but also advances the development of biogeography to a new stage and raises the theory of biogeographic analysis to a new height.

Clustering Analysis of Distributional Patterns of Global Terrestrial Mammal

In this study,the world’s land(except Antarctica)is divided into 67 basic geographical units according to ecological types.Using our newly proposed MSCA(Multivariate Similarity Clustering Analysis)method,7,591 species of modern terrestrial mammals belonging to 1,374 genera in 162 families and 2,378 species of mammals in the Wallace era before 1876 are quantitatively analyzed,and almost the same clustering results are obtained,with clear levels and reasonable clustering,which conform to the principles of geography,statistics,ecology and biology.It not only affirms and supports the reasonable kernel of Wallace’s scheme,but also puts forward suggestions that should be revised and improved.The large or small differences between the clustering results and the mammalian geographical zoning schemes of contemporary scholars are caused by different analysis methods,and they are highly consistent with the analysis results of chordates,angiosperms and insects in the world analyzed by the same method.Once again,it confirms the homogeneity of the global biological distribution pattern of major groups,and the possibility of building a unified biogeographic zoning system in the world.

Description of a new species and new distributional data for two species of Aphytis (Hymenoptera: Aphelinidae) from China

Aphytis tridentatus Gao and Li sp. nov. is described and illustrated from southwest China, and A. bangalorensis Rosen and DeBach is newly recorded from China. New distributional data for A. chionaspis Ren are also provided.