Multi-Objective Optimal Allocation of River Basin Water Resources under Full Probability Scenarios Considering Wet–Dry Encounters: A Case Study of Yellow River Basin

Wet–dry encounters between basins and regions have an important impact on the allocation of water resources. This study proposes a multi-objective allocation model for basin water resources under full probability scenarios considering wet–dry encounters (FPS-MOWAM) to solve the problem of basin water resource allocation. In the FPS-MOWAM model, the sub-regions were merged by precipitation correlation analysis. Next, the joint probability distribution of basin runoff and region precipitation was constructed using copula functions. The possible wet–dry encounter scenarios and their probabilities were then acquired. Finally, the multi-objective allocation model of water resources was constructed using the full probability scenario for wet–dry encounters in each region. The FPS-MOWAM is calculated by the NSGA-II algorithm and the optimal water resource allocation scheme was selected using the fuzzy comprehensive evaluation method. Using the Yellow River Basin as an example, the following conclusions were obtained: (1) the Yellow River Basin can be divided into four sub-regions based on precipitation correlations: Qh-Sc (Qinghai, Sichuan), Sg-Nx-Nmg (Gansu, Ningxia, Inner Mongolia), Sxq-Sxj (Shaanxi, Shanxi), and Hn-Sd (Henan, Shandong), (2) the inconsistencies in synchronous–asynchronous encounter probabilities in the Yellow River Basin were significant (the asynchronous probabilities were 0.763), whereas the asynchronous probabilities among the four regions were 0.632, 0.932, and 0.763 under the high, medium, and low flow conditions in the Yellow River Basin respectively, and (3) the allocation of water resources tends to increase with time, allocating the most during dry years. In 2035, the expected economic benefits are between 11,982.7 billion CNY and 12,499.6 billion CNY, while the expected water shortage rate is between 2.02% and 3.43%. In 2050, the expected economic benefits are between 21,291.4 billion CNY and 21,781.3 billion CNY, while the expected water shortage rate is between 1.28% and 6.05%.

Site Pattern Probabilities Under the Multispecies Coalescent and a Relaxed Molecular Clock: Theory and Applications

The first step in statistical inference of the evolutionary histories of species is developing a probability model that describes the mutation process as accurately and realistically as possible. A major complication of this inference is that different loci on the genome can have histories that diverge from the common species history and each other. The multispecies coalescent process is commonly used to model one source of this divergence, incomplete lineage sorting, or ILS. Chifman and Kubatko (2015) computed the site pattern probabilities for four taxa under a full probability model based on the Jukes-Cantor substitution model when the molecular clock holds. This paper generalizes that work to a relaxed clock model, allowing for mutation rates to differ among species. This will enable better phylogentic inference in cases where the molecular clock does not hold.

Taking unknown risks based on positive and negative information

Many decisions have to be made under partial ambiguity where information is notavailable about the full probability distribution of risks. To decide in a principled way,one would have to make some assumption(s) about hidden risks. We examined howpeople may balance between the valence of the available information and the potentialinformation concealed by the ambiguity. Under partial ambiguity, people showedflexible skepticism towards the valence of the partially observable probabilisticinformation. When ambiguity size was small, risk taking was sensitive to valence: if theinformation was promising, ambiguity aversion increased, skeptically balancing thepromising prospects of available positive evidence against the hazards of what mightbe hidden from the view. Conversely, when the available information wasdisappointing, ambiguity tolerance increased, cautiously anticipating more than whatthe available information promised. This flexible skepticism was not a trivially reflexiveresponse to valence: when ambiguity was large (i.e., available information wasunreliable), the valence of available information did not impact risk attitudes.

An ALMA survey of the SCUBA-2 Cosmology Legacy Survey UKIDSS/UDS field: Halo Masses for Submillimetre Galaxies

We present an analysis of the spatial clustering of a large sample of high-resolution, interferometically identified, submillimetre galaxies (SMGs). We measure the projected cross-correlation function of ∼ 350 SMGs in the UKIDSS Ultra Deep-Survey Field across a redshift range of z = 1.5–3 utilising a method that incorporates the uncertainties in the redshift measurements for both the SMGs and cross-correlated galaxies through sampling their full probability distribution functions. By measuring the absolute linear bias of the SMGs we derive halo masses of $\log _{10}(M_{\rm halo}[{h^{-1}\, \rm M_{\odot }}])$ ∼ 12.8 with no evidence of evolution in the halo masses with redshift, contrary to some previous work. From considering models of halo mass growth rates we predict that the SMGs will reside in haloes of mass $\log _{10}(M_{\rm halo}[{h^{-1}\, \rm M_{\odot }}])$ ∼ 13.2 at z = 0, consistent with the expectation that the majority of z = 1.5–3 SMGs will evolve into present-day spheroidal galaxies. Finally, comparing to models of stellar-to-halo mass ratios, we show that SMGs may correspond to systems that are maximally efficient at converting their gas reservoirs into stars. We compare them to a simple model for gas cooling in halos that suggests that the unique properties of the SMG population, including their high levels of star-formation and their redshift distribution, are a result of the SMGs being the most massive galaxies that are still able to accrete cool gas from their surrounding intragalactic medium.

Eliciting Beliefs as Distributions in Online Surveys

Citizens’ beliefs about uncertain events are fundamental variables in many areas of political science. While beliefs are often conceptualized in the form of distributions, obtaining reliable measures in terms of full probability densities is a difficult task. In this letter, we ask if there is an effective way of eliciting beliefs as distributions in the context of online surveys. Relying on experimental evidence, we evaluate the performance of five different elicitation methods designed to capture citizens’ uncertain expectations. Our results suggest that an elicitation method originally proposed by Manski (2009) performs well. It measures average citizens’ subjective belief distributions reliably and is easily implemented in the context of regular (online) surveys. We expect that a wider use of this method will lead to considerable improvements in the study of citizens’ expectations and beliefs.

Information Geometry of the Probability Simplex: A Short Course

This set of notes is intended for a short course aiming to provide an (almost) self-contained and (almost) elementary introduction to the topic of Information Geometry (IG) of the probability simplex. Such a course can be considered an introduction to the original monograph by Amari and Nagaoka [1], and to the recent monographs by Amari [2] and by Ay, Jost, Lê, and Schwachhöfer [3]. The focus is on a non-parametric approach, that is, I consider the geometry of the full probability simplex and compare the IG formalism with what is classically done in Statistical Physics.

Global Convergence of the (1 + 1) Evolution Strategy to a Critical Point

We establish global convergence of the (1 + 1) evolution strategy, that is, convergence to a critical point independent of the initial state. More precisely, we show the existence of a critical limit point, using a suitable extension of the notion of a critical point to measurable functions. At its core, the analysis is based on a novel progress guarantee for elitist, rank-based evolutionary algorithms. By applying it to the (1 + 1) evolution strategy we are able to provide an accurate characterization of whether global convergence is guaranteed with full probability, or whether premature convergence is possible. We illustrate our results on a number of example applications ranging from smooth (non-convex) cases over different types of saddle points and ridge functions to discontinuous and extremely rugged problems.

Assessing the Level of Enterprise Reengineering in the Context of Global Digitalization

A simulation of the level of re-engineering organization is presented on the example of a selected group of four enterprises. It is assumed that in the conditions of the experiment there is an occurrence of an event of effective re-engineering in the field of financial relations of enterprises forming a complete group of independent events - incompatible hypotheses of quantitative and qualitative measurement of the statistical likelihood of relevant indicators of experimental events in the organization of enterprise re-engineering. The probabilities of full group events were determined using an expert evaluation matrix by the principle of pairwise comparison of the importance of each event using a 5-point scale of intensity of significance of the items in the hypothesis group. The conditional probabilities of quantitative and qualitative measurement of the statistical probability of relevant indicators in the plane of action of the factors of influence on the organization of re-engineering of the enterprise are established. The formula of full probability presents the visualization of the dynamics of the level of organization of reengineering in financial relations of enterprises in the conditions of global digitization in four time intervals since 2012. by 2019. It has been proven that the reengineering process remains an effective tool for companies seeking to operate in a competitive world; companies are required to re-engineer their business processes to deliver breakthrough results and a long-term strategy for company development