Neighbor Bootstrap Research Articles

A nonstationary stochastic simulator for clustered regional hydroclimatic extremes to characterize compound flood risk

Traditional approaches to flood risk management assume flood events follow an independent, identically distributed (i.i.d.) random process from which static risk measures are computed. Modern risk accounting strategies also consider nonstationarity or long-term trends in the mean and moments of the associated flood probability distributions. However, few approaches consider how extreme hydroclimatic events cluster in both space and time, compounding damage risks. Here we introduce a compound flood risk simulator that models and conditionally forecasts future variability in regional flooding events that cluster in time, given trends and oscillations in a variable climate signal. A modular, novel integration of wavelet signal processing, nonstationary time series forecasting, k-nearest neighbor (KNN) bootstrapping, multivariate copulas, and modified Neyman-Scott (NS) event clustering process provides users the ability to model interannual and sub-annual clustering of flood risk. Our semi-parametric flood generator specifically targets the clustered temporal dynamics of jointly modeled flood intensity, duration, and frequency over a finite future period of a decade or more, thereby providing a foundation for adaptation approaches that integrate temporally clustered flood risk into planning, response and recovery.

Assessment of Impacts of Climate Change on Indian Riverine Thermal Regimes Using Hybrid Deep Learning Methods

AbstractUnderstanding the riverine thermal regimes is challenging due to sparse spatiotemporal data of river water temperatures (RWTs). The development of systematic models combined with machine learning models under data‐limited context has not been intensively studied for the prediction of RWT. The present study developed hybrid models using long short‐term memory (LSTM), integrated with (a) k‐nearest neighbor (k‐NN) bootstrap resampling algorithms (kNN‐LSTM) to address the data limitations of RWT prediction and (b) discrete wavelet transform (WT) approach (WT‐LSTM) to address the time–frequency localized features of RWT prediction. The study assessed the climate change impacts on RWT using an ensemble of National Aeronautics Space Administration Earth Exchange Global Daily Downscaled Projections of air temperature with Representative Concentration Pathway scenarios 4.5 and 8.5 for seven major polluted river catchments of India. The hybrid kNN‐LSTM has effectively predicted RWT at monthly time scales under data limitations and outperformed the standalone LSTM, WT‐LSTM, and hybrid three‐parameter version air2stream models. The RWT increase for Tunga‐Bhadra, Musi, Ganga, and Narmada basins is predicted as 3.0, 4.0, 4.6, and 4.7°C, respectively, for 2071–2100.

Impact of climate change on river water temperature and dissolved oxygen: Indian riverine thermal regimes

The impact of climate change on the oxygen saturation content of the world’s surface waters is a significant topic for future water quality in a warming environment. While increasing river water temperatures (RWTs) with climate change signals have been the subject of several recent research, how climate change affects Dissolved Oxygen (DO) saturation levels have not been intensively studied. This study examined the direct effect of rising RWTs on saturated DO concentrations. For this, a hybrid deep learning model using Long Short-Term Memory integrated with k-nearest neighbor bootstrap resampling algorithm is developed for RWT prediction addressing sparse spatiotemporal RWT data for seven major polluted river catchments of India at a monthly scale. The summer RWT increase for Tunga-Bhadra, Sabarmati, Musi, Ganga, and Narmada basins are predicted as 3.1, 3.8, 5.8, 7.3, 7.8 °C, respectively, for 2071–2100 with ensemble of NASA Earth Exchange Global Daily Downscaled Projections of air temperature with Representative Concentration Pathway 8.5 scenario. The RWT increases up to7 °C for summer, reaching close to 35 °C, and decreases DO saturation capacity by 2–12% for 2071–2100. Overall, for every 1 °C RWT increase, there will be about 2.3% decrease in DO saturation level concentrations over Indian catchments under climate signals.

Phylogenetic analysis of the genus Conringia Heist. Ex Fabr. (Brassicaceae) in Turkey based on nuclear (nrITS) and chloroplast (trnL-F) DNA sequences

In this study, phylogenetic analysis of Turkish Conringia (Brassicaceae) species was conducted based on nuclear ribosomal DNA (nrITS) and chloroplast DNA (trnL-F) sequences. In addition, the relationships between the sequences of some Brassicaceae family species retrieved from NCBI, and Conringia species were documented. All of the plant specimens were collected at their flowering and vegetation periods from different regions of Turkey, and brought to the laboratory. Total genomic DNA was extracted using the GeneMark kit. In PCR analyses, ITS4 and ITS5A primers were used for the amplification of the nrITS region, while the trnLe and trnLf primers were used for the cpDNA trnL-F region. The DNA sequences obtained were then edited using BioEdit and FinchTV, and analyzed using MEGA 6.0 software. Neighbor joining (NJ) and bootstrap trees were constructed in order to identify the relationships among Conringia taxa. The nrITS sequences ranged between 573 and 672 nucleotides, while the trnL-F sequences ranged between 346 and 764 nucleotides. The divergence values of nrITS sequences differed between 0.177 and 0.00 and divergence values of trnL-F sequences differed between 0.902 and 0.00. NJ tree generated using nrITS and trnL-F sequences consisted of two clades. In trees generated with both the nrITS and trnL-F sequences, C. orientalis, C. grandiflora and C. austriaca appeared within the same group. In addition, according to the phylogenetic analysis results obtained with other Brassicaceae species, it is revealed that the Conringia genus is polyphyletic.

Application of the decomposition-prediction-reconstruction framework to medium- and long-term runoff forecasting

Abstract Medium- and long-term runoff forecasting has always been a problem, especially in the wet season. Forecasting performance can be improved using complementary ensemble empirical mode decomposition (CEEMD) to produce clearer signals as model inputs. In the forecasting models based on CEEMD, the entire time series is decomposed into several sub-series, each sub-series is divided into training and validation datasets and forecasted by some common models, such as least squares support vector machine (LSSVM), and finally an ensemble forecasting result is obtained by summing the forecasted results of each sub-series. This model was applied to forecast the inflow runoff of the Shitouxia Reservoir (STX Reservoir). The forecasting results show that the Nash efficiency coefficient of the LSSVM model is 0.815, and the Nash efficiency coefficient of the CEEMD-LSSVM model is 0.954, an increase of 13.9%. The root mean square error value is reduced from 20.654 to 10.235, a decrease of 50.4%. The runoff forecasting performance can be effectively improved by applying the CEEMD-LSSVM model. When analyzing the annual runoff forecasting results month by month, it was found that the forecasting results for November to April were unsatisfactory compared results from the nearest neighbor bootstrapping regressive (NNBR) model, which was more suitable for the dry season, but the forecasting results for May to October improved significantly. This also proves that the CEEMD-LSSVM model has a great advantage in the forecasting of inflow runoff during the wet season. In the optimized operation of reservoirs, the forecasting result of inflow runoff in the wet season is more important than in the dry season. Therefore, when forecasting annual runoff month by month, the CEEMD-LSSVM model is recommended for the wet season combined with the NNBR model for the dry season.

Smallest Percolating Sets in Bootstrap Percolation on Grids

In this paper we fill in a fundamental gap in the extremal bootstrap percolation literature, by providing the first proof of the fact that for all $d \geq 1$, the size of the smallest percolating sets in $d$-neighbour bootstrap percolation on $[n]^d$, the $d$-dimensional grid of size $n$, is $n^{d-1}$. Additionally, we prove that such sets percolate in time at most $c_d n^2$, for some constant $c_d >0 $ depending on $d$ only.

Minimum Degree Conditions for Small Percolating Sets in Bootstrap Percolation

The $r$-neighbour bootstrap process is an update rule for the states of vertices in which `uninfected' vertices with at least $r$ `infected' neighbours become infected and a set of initially infected vertices is said to percolate if eventually all vertices are infected. For every $r \geq 3$, a sharp condition is given for the minimum degree of a sufficiently large graph that guarantees the existence of a percolating set of size $r$. In the case $r=3$, for $n$ large enough, any graph on $n$ vertices with minimum degree $\lfloor n/2 \rfloor +1$ has a percolating set of size $3$ and for $r \geq 4$ and $n$ large enough (in terms of $r$), every graph on $n$ vertices with minimum degree $\lfloor n/2 \rfloor + (r-3)$ has a percolating set of size $r$. A class of examples are given to show the sharpness of these results.

Nearest neighbor time series bootstrap for generating influent water quality scenarios

Understanding influent water quality variability is essential for the long-term planning of potable water systems. To quantify variability and generate realistic influent scenarios, we propose a nonparametric time series approach based on k-nearest neighbor (k-NN) bootstrap resampling. The k-NN approach resamples historical data conditioned on a “feature vector” at a given time to generate values at subsequent times. We modified this algorithm by adding random perturbations to the resampled values to generate realistic extremes unobserved in the historical record. k-NN is widely used in stochastic hydrology and hydroclimatology; however, it is adapted here for the multivariate, data-limited context of water treatment. To examine the performance of the algorithm, we applied it to an eleven-year, monthly water quality dataset of alkalinity, temperature, total organic carbon, and pH from the Cache la Poudre River in Colorado. We found that the k-NN simulations captured the relevant distributional statistics of the historical record, which suggests that the algorithm produces realistic and varied scenarios. When used in conjunction with modeling and optimization, these scenarios have the potential to improve the sustainability, resilience, and efficiency of potable water systems.

The second term for two-neighbour bootstrap percolation in two dimensions

In the $r$-neighbour bootstrap process on a graph $G$, vertices are infected (in each time step) if they have at least $r$ already-infected neighbours. Motivated by its close connections to models from statistical physics, such as the Ising model of ferromagnetism, and kinetically constrained spin models of the liquid-glass transition, the most extensively-studied case is the two-neighbour bootstrap process on the two-dimensional grid $[n]^2$. Around 15 years ago, in a major breakthrough, Holroyd determined the sharp threshold for percolation in this model, and his bounds were subsequently sharpened further by Gravner and Holroyd, and by Gravner, Holroyd and Morris. In this paper we strengthen the lower bound of Gravner, Holroyd and Morris by proving that the critical probability $p_c\big( [n]^2,2 \big)$ for percolation in the two-neighbour model on $[n]^2$ satisfies \[p_c\big( [n]^2,2 \big) = \frac{\pi^2}{18\log n} - \frac{\Theta(1)}{(\log n)^{3/2}}\,.\] The proof of this result requires a very precise understanding of the typical growth of a critical droplet, and involves a number of technical innovations. We expect these to have other applications, for example, to the study of more general two-dimensional cellular automata, and to the $r$-neighbour process in higher dimensions.

Maximal Bootstrap Percolation Time on the Hypercube via Generalised Snake-in-the-Box

In $r$-neighbour bootstrap percolation, vertices (sites) of a graph $G$ become "infected" in each round of the process if they have $r$ neighbours already infected. Once infected, they remain such. An initial set of infected sites is said to percolate if every site is eventually infected. We determine the maximal percolation time for $r$-neighbour bootstrap percolation on the hypercube for all $r \geq 3$ as the dimension $d$ goes to infinity up to a logarithmic factor. Surprisingly, it turns out to be $\frac{2^d}{d}$, which is in great contrast with the value for $r=2$, which is quadratic in $d$, as established by Przykucki (2012). Furthermore, we discover a link between this problem and a generalisation of the well-known Snake-in-the-Box problem.

A new hybrid model for nonlinear and non-stationary runoff prediction at annual and monthly time scales

Due to the effects of frequent anthropogenic activities and climate change, the natural annual runoff series presents typical nonlinear, non-stationary and multiple-scale characteristics, which triggers the common problem of low accuracy for long-term runoff predictions. Therefore, the main goal of this study was to improve the long-term prediction accuracy for the nonlinear and non-stationary runoff series by introducing a new hybrid approach based on improved ensemble intrinsic time-scale decomposition (IEITD) and improved nearest neighbor bootstrapping regressive (INNBR) methods. First, the Brock-Dechert-Scheinkman (BDS) test and Augmented Dickey-Fuller (ADF) test were used to identify the nonlinear and non-stationary characteristics of annual runoff series, respectively, and the Modified Mann–Kendall (MM-K) test and Mann–Kendall (M-K) abrupt change test methods were applied to explore the drivers of non-stationarity. On this basis, the IEITD was used to decompose the original annual runoff series into several proper rotation components (PRCs) and a monotonic residual trend term to make the non-stationary runoff time series stationary. Then, the INNBR model was applied to predict the respective PRCs. The residual series was predicted by the polynomial fitting method. Finally, the predictive results of each PRC and residual series were summed to obtain an ensemble forecast for the runoff series. The performance of the new hybrid approach was tested by the annual (nine hydrological stations) and monthly (three hydrological stations) runoff data covering 1956–2011 in the Luanhe River basin in China. Results suggested: (1) the annual runoff time series of nine hydrological stations presented obviously dependent nonlinear structure; (2) the annual runoff series of nine hydrological stations were all non-stationary; (3) human activity, rather than change in precipitation, was the major driving factor of runoff decline in the Luanhe River basin; (4) For the performance evaluation criteria of Nash-Sutcliffe efficiency coefficient (NSEC), compared with Nearest Neighbor Bootstrapping Regressive (NNBR) and INNBR, the precision of IEITD-INNBR model almost increase by 227% and 37% on the average of nine hydrological stations; (5) the new hybrid approach of combining the IEITD and INNBR models outperformed the other two models (NNBR and INNBR) tested, and it is capable of capturing the nonlinear, non-stationary and multiple-scale characteristics of complex runoff time series and obtaining higher predictive precision.

Platelet gene expression profile in acute myocardial infarction

Acute myocardial infarction is a sudden event that is fatal in around one-third of patients. It is primarily due to coronary atherosclerotic plaque rupture with subsequent platelet (PLT) activation/aggregation and thrombus formation. PLTs have a key role in the genesis and progression of atherosclerosis and in thrombus formation1. PLTs are anucleated cells which retain mRNA from their megakaryocyte precursor, therefore PLT mRNA is unique in representing a nearly fixed transcriptome2. We tested the hypothesis that platelet transcriptome acts as a fingerprint indicating the development of a future myocardial infarction, with the final goal of identifying a specific STEMI gene-signature, able to discriminate patients with acute event from healthy donors (HD) and from patients affected by stable coronary artery disease (sCAD), the phenotypically closest clinical condition to STEMI. Peripheral blood samples (50mL) were collected in Na-citrate tubes from 20 myocardial infarction patients (MI), 20 sCAD and 20 HD. Highly purified platelets were obtained by leukocyte depletion as previously described3. Platelet RNA extraction were performed by TRIzolTM reagent according to the manufacturer’s protocol. Gene expression profile was analyzed using an Affymetrix GeneChip system (Cancer Genomics and Bioinformatics Laboratory Facility, Kimmel Cancer Center, Jefferson University. Philadelphia, US). The exploratory analysis of PLT transcriptome confirmed differences in gene expression between STEMI, sCAD and HD. Hence, the common differentially expressed genes (DEGs) derived from the STEMI vs sCAD and STEMI vs HD comparisons were obtained and tested by k-nearest neighbor classification and bootstrap. A set of 17 STEMI-related DEGs was identified, showing good sensitivity and specificity for the discrimination of STEMI patients. Overall, we described a STEMI-specific gene expression patterns, suggesting that PLT transcriptome allows to characterize a powerful fingerprint of STEMI theoretically able to predict a future acute event.

Wavelet‐based time series bootstrap model for multidecadal streamflow simulation using climate indicators

AbstractA model to generate stochastic streamflow projections conditioned on quasi‐oscillatory climate indices such as Pacific Decadal Oscillation (PDO) and Atlantic Multi‐decadal Oscillation (AMO) is presented. Recognizing that each climate index has underlying band‐limited components that contribute most of the energy of the signals, we first pursue a wavelet decomposition of the signals to identify and reconstruct these features from annually resolved historical data and proxy based paleoreconstructions of each climate index covering the period from 1650 to 2012. A K‐Nearest Neighbor block bootstrap approach is then developed to simulate the total signal of each of these climate index series while preserving its time‐frequency structure and marginal distributions. Finally, given the simulated climate signal time series, a K‐Nearest Neighbor bootstrap is used to simulate annual streamflow series conditional on the joint state space defined by the simulated climate index for each year. We demonstrate this method by applying it to simulation of streamflow at Lees Ferry gauge on the Colorado River using indices of two large scale climate forcings: Pacific Decadal Oscillation (PDO) and Atlantic Multi‐decadal Oscillation (AMO), which are known to modulate the Colorado River Basin (CRB) hydrology at multidecadal time scales. Skill in stochastic simulation of multidecadal projections of flow using this approach is demonstrated.

Wavelet Network Model Based on Multiple Criteria Decision Making for Forecasting Temperature Time Series

Due to nonlinear and multiscale characteristics of temperature time series, a new model called wavelet network model based on multiple criteria decision making (WNMCDM) has been proposed, which combines the advantage of wavelet analysis, multiple criteria decision making, and artificial neural network. One case for forecasting extreme monthly maximum temperature of Miyun Reservoir has been conducted to examine the performance of WNMCDM model. Compared with nearest neighbor bootstrapping regression (NNBR), the probability of relative error smaller than 10% increases from 65.79% to 84.21% (forecast periodT=1) and from 51.35% to 91.89%(T=2)by WNMCDM model. Similarly, the probability of relative error smaller than 20% increases from 84.21% to 97.37%(T=1)and from 81.08% to 91.89%(T=2)by WNMCDM model. Therefore, WNMCDM model is superior to NNBR model in forecasting temperature time series.

Hydrologic Variations and Stochastic Modeling of Runoff in Zoige Wetland in the Eastern Tibetan Plateau

Hydrological time series data (1988–2008) of the Hei River, the main water source to Zoige wetland in the Eastern Tibetan Plateau, were investigated. Results showed that the runoff distribution of Hei River varies with the relative change in amplitude (Cm=15.9) and the absolute change in amplitude (ΔQ=37.1 m3/s) during the year. There was a significant decreasing trend since 1988 with annual runoff of 20.0 m3/s (1988–1994), 19.0 m3/s (1995–2000), and 15.2 m3/s (2001–2008). There were double peaks in runoff during the water year: the highest peak in the period of 1988–2000 occurred in July while in the period of 2001–2008 it occurred in October. Shifting peak flow means less water quantity in wetland during growing season. Nearest neighbor bootstrapping regressive method was used to predict daily runoff of the Hei River. Model results show that it was fitted with 94.23% ofR2for daily time series, which can provide a basis for the development and utilization of regional water resources.

The time of bootstrap percolation with dense initial sets

Let r∈N . In r -neighbour bootstrap percolation on the vertex set of a graph G , vertices are initially infected independently with some probability p . At each time step, the infected set expands by infecting all uninfected vertices that have at least r infected neighbours. When p is close to 1, we study the distribution of the time at which all vertices become infected. Given t=t(n)=o(logn/loglogn) , we prove a sharp threshold result for the probability that percolation occurs by time t in d -neighbour bootstrap percolation on the d -dimensional discrete torus T d n . Moreover, we show that for certain ranges of p=p(n) , the time at which percolation occurs is concentrated either on a single value or on two consecutive values. We also prove corresponding results for the modified d -neighbour rule

Bootstrap percolation on Galton-Watson trees

Bootstrap percolation is a type of cellular automaton which has been used to model various physical phenomena, such as ferromagnetism. For each natural number $r$, the $r$-neighbour bootstrap process is an update rule for vertices of a graph in one of two states: `infected' or `healthy'. In consecutive rounds, each healthy vertex with at least $r$ infected neighbours becomes itself infected. Percolation is said to occur if every vertex is eventually infected. Usually, the starting set of infected vertices is chosen at random, with all vertices initially infected independently with probability $p$. In that case, given a graph $G$ and infection threshold $r$, a quantity of interest is the critical probability, $p_c(G,r)$, at which percolation becomes likely to occur. In this paper, we look at infinite trees and, answering a problem posed by Balogh, Peres and Pete, we show that for any $b \geq r$ and for any $\epsilon > 0$ there exists a tree $T$ with branching number $\operatorname{br}(T) = b$ and critical probability $p_c(T,r) 0$ such that if $T$ is a Galton- Watson tree with branching number $\operatorname{br}(T) = b \geq r$ then $$p_c(T,r) > \frac{c_r}{b} e^{-\frac{b}{r-1}}.$$ We also show that this bound is sharp up to a factor of $O(b)$ by giving an explicit family of Galton--Watson trees with critical probability bounded from above by $C_r e^{-\frac{b}{r-1}}$ for some constant $C_r>0$.

On Slowly Percolating Sets of Minimal Size in Bootstrap Percolation

Bootstrap percolation, one of the simplest cellular automata, can be seen as a model of the spread of infection. In $r$-neighbour bootstrap percolation on a graph $G$ we assign a state, infected or healthy, to every vertex of $G$ and then update these states in successive rounds, according to the following simple local update rule: infected vertices of $G$ remain infected forever and a healthy vertex becomes infected if it has at least $r$ already infected neighbours. We say that percolation occurs if eventually every vertex of $G$ becomes infected. A well known and celebrated fact about the classical model of $2$-neighbour bootstrap percolation on the $n \times n$ square grid is that the smallest size of an initially infected set which percolates in this process is $n$. In this paper we consider the problem of finding the maximum time a $2$-neighbour bootstrap process on $[n]^2$ with $n$ initially infected vertices can take to eventually infect the entire vertex set. Answering a question posed by Bollobás we compute the exact value for this maximum showing that, for $n \ge 4$, it is equal to the integer nearest to $(5n^2-2n)/8$.

中长期水文预报的最优组合模型研究

本文建立了径流中长期预报的自回归、季节性自回归、门限自回归、最近邻抽样回归、人工神经网络、支持向量机等六种模型，并对这些模型结果进行综合，开展最优组合预报。以飞来峡水库为研究实例，选取平均绝对误差和均方误差作为评价指标，发现人工神经网络模型模拟精度较高；支持向量机模型模拟精度高、且具有最好的预报性能；最优组合预报模型综合各单一预报模型的优点，结果稳健、通用性强。 This paper applies six models, including the autoregressive model, the seasonal autoregressive model, the threshold autoregressive model, the nearest neighbor bootstrap regressive model, the artificial neural network model and the support vector machine model into the mid and long-term hydrological forecasting. Based on Feilaixia reservoir project, the results show that the artificial neural network model is able to time series very well. The support vector machine model has the powerful ability of not only the simulation but also the forecasting. The results of those models were combined by the optimal combined forecasting model. The mean absolute error and the mean square error are selected as the measurements. Relying on the merits of each single model, the results of the optimal combined forecasting model work very well and are very well in robustness.

The sharp threshold for bootstrap percolation in all dimensions

In $r$-neighbour bootstrap percolation on a graph $G$, a (typically random) set $A$ of initially ‘infected’ vertices spreads by infecting (at each time step) vertices with at least $r$ already-infected neighbours. This process may be viewed as a monotone version of the Glauber dynamics of the Ising model, and has been extensively studied on the $d$-dimensional grid $[n]^d$. The elements of the set $A$ are usually chosen independently, with some density $p$, and the main question is to determine $p_c([n]^d,r)$, the density at which percolation (infection of the entire vertex set) becomes likely. In this paper we prove, for every pair $d,r \in \mathbb {N}$ with $d \geqslant r \geqslant 2$, that \[ p_c\big ( [n]^d,r \big ) = \left ( \frac {\lambda (d,r) + o(1)}{\log _{(r-1)} (n)} \right )^{d-r+1}\] as $n \to \infty$, for some constant $\lambda (d,r) > 0$, and thus prove the existence of a sharp threshold for percolation in any (fixed) number of dimensions. We moreover determine $\lambda (d,r)$ for every $d \geqslant r \geqslant 2$.