Input Array Research Articles

Group 3 Innate Lymphoid Cells: Communications Hubs of the Intestinal Immune System.

The maintenance of mammalian health requires the generation of appropriate immune responses against a broad range of environmental and microbial challenges, which are continually encountered at barrier tissue sites including the skin, lung, and gastrointestinal tract. Dysregulated barrier immune responses result in inflammation, both locally and systemically in peripheral organs. Group 3 innate lymphoid cells (ILC3) are constitutively present at barrier sites and appear to be highly specialized in their ability to sense a range of environmental and host-derived signals. Under homeostatic conditions, ILC3 respond to local cues to maintain tissue homeostasis and restrict inflammatory responses. In contrast, perturbations in the tissue microenvironment resulting from disease, infection, or tissue damage can drive dysregulated pro-inflammatory ILC3 responses and contribute to immunopathology. The tone of the ILC3 response is dictated by a balance of “exogenous” signals, such as dietary metabolites and commensal microbes, and “endogenous” host-derived signals from stromal cells, immune cells, and the nervous system. ILC3 must therefore have the capacity to simultaneously integrate a wide array of complex and dynamic inputs in order to regulate barrier function and tissue health. In this review, we discuss the concept of ILC3 as a “communications hub” in the intestinal tract and associated lymphoid tissues and address the variety of signals, derived from multiple biological systems, which are interpreted by ILC3 to modulate the release of downstream effector molecules and regulate cell–cell crosstalk. Successful integration of environmental cues by ILC3 and downstream propagation to the broader immune system is required to maintain a tolerogenic and anti-inflammatory tone and reinforce barrier function, whereas dysregulation of ILC3 responses can contribute to the onset or progression of clinically relevant chronic inflammatory diseases.

Gradual synthesis for static parallelization of single-pass array-processing programs

Parallelizing of software improves its effectiveness and productivity. To guarantee correctness, the parallel and serial versions of the same code must be formally verified to be equivalent. We present a novel approach, called GRASSP, that automatically synthesizes parallel single-pass array-processing programs by treating the given serial versions as specifications. Given arbitrary segmentation of the input array, GRASSP synthesizes a code to determine a new segmentation of the array that allows computing partial results for each segment and merging them. In contrast to other parallelizers, GRASSP gradually considers several parallelization scenarios and certifies the results using constrained Horn solving. For several classes of programs, we show that such parallelization can be performed efficiently. The C++ translations of the GRASSP solutions sped performance by up to 5X relative to serial code on an 8-thread machine and Hadoop translations by up to 10X on a 10-node Amazon EMR cluster.

Creating a Business Value while Transforming Data Assets using Machine Learning

Machine learning enables computers to learn from large amounts of data without specific programming. Besides its commercial application, companies are starting to recognize machine learning importance and possibilities in order to transform their data assets into business value. This study explores integration of machine learning into business core processes, while enabling predictive analytics that can increase business values and provide competitive advantage. It proposes machine learning algorithm based on regression analysis for a business solution in large enterprise company in Macedonia, while predicting real-value outcome from a given array of business inputs. The results show that most of the machine learning predictive values for the desired process output deviated from 0 to 15% of actual employees' decision. Hence, it verifies the appropriateness of the chosen approach, with predictive accuracy that can be meaningful in practice. As a machine learning case study in business context, it contains valuable information that can help companies understand the significance of machine learning for enterprise computing. It also points out some potential pitfalls of machine learning misuse.

Benchmarking Cycling and Walking in Six New Zealand Cities: Pilot Study 2015

Benchmarking cities to compare active transport is established internationally, with varying approaches used. It can be a useful tool for planners, policy makers, advocates and researchers to determine how well cities are doing at promoting active transport, making it safe for people and reaping the environmental, health and economic rewards of this approach. New Zealand is a car-dominated society with high per-capita carbon emissions. While there has been a recent, modest, policy push to develop urban cycling, overall the policy environment remains unsupportive of active travel. Despite this, there are well-known differences between New Zealand cities in active transport patterns, although this has never been looked at systematically. We undertook a project to benchmark cycling and walking in the six largest New Zealand cities (Auckland, Tauranga, Hamilton, Wellington, Christchurch and Dunedin). This work used (with permission) the same format as the successful Alliance for Biking and Walking biennial Benchmarking report in the United States, but was modified to the New Zealand context. Using existing data sources and new survey data we reported on an extensive array of inputs (for example policies, extent of infrastructure, level of investment, programmes and personnel) and outcomes (including levels of cycling and walking, health outcomes such as physical activity, obesity, and safety for cyclists and pedestrians). Where possible we also reported gender, ethnic and socio-economic differences in outcomes. In this presentation we discuss some of the key findings- the full report is published here: http://sustainablecities.org.nz/resilient-urban-futures/benchmarking/ . We will also discuss some of the lessons learned from this first attempt at Benchmarking. These include issues with engaging local government, dealing with discrepancies in geographic boundaries, limitations of routinely collected datasets, a lack of shared understanding of infrastructure, the funding and sustainability of benchmarking, and who should undertake benchmarking. Benchmarking cities can potentially be a powerful tool to encourage active transport, this preliminary experience in New Zealand contains useful lessons for other researchers or practitioners interested in this approach.

Validation of parallelizing transformations of sequential programs

SummaryTransformations for high‐performance superscalar, vector, and parallel processors maximize parallelism and memory locality. Often parallelizing compilers apply transformations, such as loop parallelization and loop vectorization, to convert a sequential array‐handling program into a parallel program. Validation of such transformations is extremely useful in the prevalent high‐performance computing environment. This paper proposes a novel algorithm for construction of the dependence graph of the generated parallel programs. These transformations are validated by checking equivalence of the dependence graphs of the original sequential program and the transformed parallel program using a standard algorithm reported in the literature. The above equivalence checker works even when the above parallelizing transformations are preceded by various enabling transformations except for loop collapsing transformation that changes the dimensions of the arrays. In the present paper, the scope of the equivalence checker has been expanded to handle this special case by informing it of the correspondence between the index spaces of the corresponding of input and output arrays in the sequential and the parallel programs. The proposed methods are implemented and tested against a set of available benchmark programs that are parallelized by the polyhedral auto‐parallelizer LooPo and the auto‐vectorizer Scout.

Time–space trade-offs for triangulations and Voronoi diagrams

Let S be a planar n-point set. A triangulation for S is a maximal plane straight-line graph with vertex set S. The Voronoi diagram for S is the subdivision of the plane into cells such that all points in a cell have the same nearest neighbor in S. Classically, both structures can be computed in O(nlog⁡n) time and O(n) space. We study the situation when the available workspace is limited: given a parameter s∈{1,…,n}, an s-workspace algorithm has read-only access to an input array with the points from S in arbitrary order, and it may use only O(s) additional words of Θ(log⁡n) bits for reading and writing intermediate data. The output should then be written to a write-only structure. We describe a deterministic s-workspace algorithm for computing an arbitrary triangulation of S in time O(n2/s+nlog⁡nlog⁡s) and a randomized s-workspace algorithm for finding the Voronoi diagram of S in expected time O((n2/s)log⁡s+nlog⁡slog⁎⁡s).

Two-dimensional double jumping finite automata

In this paper, we extend the concept of double jumping automata for string languages recently introduced in the literature to two-dimensional languages, also called as picture languages. The paper is a modification and study of jumping finite automata for two-dimensional languages already introduced in the literature, where they always perform two simultaneous row-jumps over a row of an input array according to the same rule which is defined. The direction of either of the two simultaneous row-jumps is: 1) left; 2) right or 3) in either direction. Based on the directions of the two simultaneous jumps, we give the classification of the jumping finite automata for two-dimensional languages. The mutual relationship between the families of languages accepted by the two-dimensional jumping finite automata performing the jumps in the ways as mentioned above are investigated. We also give the comparison of these families with that of local and recognisable families of languages and families of Siromoney matrix languages.

Efficient Algorithms for Stream Compaction on GPUs

Stream compaction, also known as stream filtering or selection, produces a smaller output array which contains the indices of the only wanted elements from the input array for further processing. With the tremendous amount of data elements to be filtered, the performance of selection is of great concern. Recently, modern Graphics Processing Units (GPUs) have been increasingly used to accelerate the execution of massively large, data parallel applications. In this paper, we designed and implemented two new algorithms for stream compaction on GPU. The first algorithm, which can preserve the relative order of the input elements, uses a multi-level prefix-sum approach. The second algorithm, which is non-order-preserving, is based the hybrid use of the prefix-sum and the atomics approaches. We compared their performance with other parallel selection algorithms on the current generation of NVIDIA GPUs. The experimental results show that both algorithms run faster than Thrust, an open-source parallel algorithms library. Furthermore, the hybrid method performs the best among all existing selection algorithms on GPU and can be two orders of magnitude faster than the sequential selection on CPU, especially when the data size is large.

Informing vaccine decision-making: A strategic multi-attribute ranking tool for vaccines—SMART Vaccines 2.0

SMART Vaccines 2.0 software is being developed to support decision-making among multiple stakeholders in the process of prioritizing investments to optimize the outcomes of vaccine development and deployment. Vaccines and associated vaccination programs are one of the most successful and effective public health interventions to prevent communicable diseases and vaccine researchers are continually working towards expanding targets for communicable and non-communicable diseases through preventive and therapeutic modes. A growing body of evidence on emerging vaccine technologies, trends in disease burden, costs associated with vaccine development and deployment, and benefits derived from disease prevention through vaccination and a range of other factors can inform decision-making and investment in new and improved vaccines and targeted utilization of already existing vaccines. Recognizing that an array of inputs influences these decisions, the strategic multi-attribute ranking method for vaccines (SMART Vaccines 2.0) is in development as a web-based tool—modified from a U.S. Institute of Medicine Committee effort (IOM, 2015)—to highlight data needs and create transparency to facilitate dialogue and information-sharing among decision-makers and to optimize the investment of resources leading to improved health outcomes. Current development efforts of the SMART Vaccines 2.0 framework seek to generate a weighted recommendation on vaccine development or vaccination priorities based on population, disease, economic, and vaccine-specific data in combination with individual preference and weights of user-selected attributes incorporating valuations of health, economics, demographics, public concern, scientific and business, programmatic, and political considerations.Further development of the design and utility of the tool is being carried out by the National Vaccine Program Office of the Department of Health and Human Services and the Fogarty International Center of the National Institutes of Health. We aim to demonstrate the utility of SMART Vaccines 2.0 through the engagement of a community of relevant stakeholders and to identify a limited number of pilot projects to determine explicitly defined attribute preferences and the related data and model requirements that are responsive to user needs and able to improve the use of evidence for vaccine-related decision-making and consequential priorities of vaccination options.

The GATOR1 Complex Regulates Metabolic Homeostasis and the Response to Nutrient Stress in Drosophila melanogaster.

TORC1 regulates metabolism and growth in response to a large array of upstream inputs. The evolutionarily conserved trimeric GATOR1 complex inhibits TORC1 activity in response to amino acid limitation. In humans, the GATOR1 complex has been implicated in a wide array of pathologies including cancer and hereditary forms of epilepsy. However, the precise role of GATOR1 in animal physiology remains largely undefined. Here, we characterize null mutants of the GATOR1 components nprl2, nprl3, and iml1 in Drosophila melanogaster. We demonstrate that all three mutants have inappropriately high baseline levels of TORC1 activity and decreased adult viability. Consistent with increased TORC1 activity, GATOR1 mutants exhibit a cell autonomous increase in cell growth. Notably, escaper nprl2 and nprl3 mutant adults have a profound locomotion defect. In line with a nonautonomous role in the regulation of systemic metabolism, expressing the Nprl3 protein in the fat body, a nutrient storage organ, and hemocytes but not muscles and neurons rescues the motility of nprl3 mutants. Finally, we show that nprl2 and nprl3 mutants fail to activate autophagy in response to amino acid limitation and are extremely sensitive to both amino acid and complete starvation. Thus, in Drosophila, in addition to maintaining baseline levels of TORC1 activity, the GATOR1 complex has retained a critical role in the response to nutrient stress. In summary, the TORC1 inhibitor GATOR1 contributes to multiple aspects of the development and physiology of Drosophila.

Nonlinear ultrasonic phased array for closed crack imaging

In nondestructive ultrasonic inspection, closed cracks can lead to the underestimation or overlook, resulting in the catastrophic accidents. To solve this problem, nonlinear ultrasonics has been expected as a most promising approach. In nonlinear ultrasonics, by irradiating large amplitude, the nonlinear interaction between closed cracks and ultrasonics generates nonlinear components. Among them, we found that subharmonics has a higher selectivity than the others including higher harmonics. We also found that the subharmonics has higher temporal resolution, providing the high spatial resolution in ultrasonic imaging. Based on these findings, we have developed a novel imaging method, subharmonic phased array for crack evaluation (SPACE), based on the subharmonic generation at closed cracks due to large-amplitude short burst waves input and phased array imaging with frequency filtering. As a result of applying SPACE to closed-crack specimens, SPACE visualized the closed part of cracks, which were not observed in the conventional methods. It was substantiated that SPACE is useful in accurately measuring closed-crack depths.

A.1D-C: A novel fast automatic heuristic to handle large-scale one-dimensional clustering

The one-dimensional clustering aims to group real-values of an input array into identified number of clusters. Some of the current algorithms, such as the k-means, need the number of clusters in advance, and use a goal function based on minimizing the sum of squared Euclidean distances to the mean of each group. This paper shows why this goal function is not efficient, even for one-dimensional case, then proposes an O (n×log n) efficient algorithm for the one-dimensional clustering purposes. The proposed algorithm can automatically detect the number of clusters. The performance of the proposed algorithm is approved across several experiments. In addition, results of experiments show why the goal function used in some current algorithms like the k-means is not suitable for the one-dimensional clustering.

Toward a Unified Socio-Cognitive Framework for Salience in Language.

To begin with, consider the following four statements, one by one: The word seemed salient because it was the first word that came to my mind. The word seemed salient because it was the first word that came to my mind in this context. The word seemed salient because I had not expected to hear it in this context. The word seemed salient because I had never heard it before. It is not unlikely that all four statements seem plausible, although 1 and 2 are actually opposed to 4 and 3 respectively. Apparently, then, words can be considered salient because they are… highly familiar and strongly entrenched, highly expected in a given context, highly unexpected in a given context, or totally unfamiliar. Surprisingly, linguists have actually relied on at least three of these four scenarios for defining the notion of salience (see also Bowman et al., 2013, for a psychological perspective). Scenario (1) lies at the heart of Giora's idea of salience as what is “foremost on one's mind […] stored and coded in the mental lexicon” (Giora, 2003, p. 15). Scenario (2) accords with Geeraerts' view of onomasiological salience in terms of “the relative frequency with which a signifiant is associated with a given signifie” (Geeraerts, forthcoming), i.e., the frequency with which a word is used to denote a given piece of experience. Scenario (3) corresponds to understanding salience in terms of surprisal, as, e.g., proposed by Racz: “A segment is cognitively salient if it has a large surprisal value when compared to an array of language input” (Racz, 2013, p. 37; see also Friston, 2010; Clark, 2013; Fine et al., 2013; Divjak, 2016). Scenario (4) represents an extreme variant of type (3) which builds on memory-based novelty rather than context-based surprise (see Barto et al., 2013, for this distinction). The four scenarios can be summarized systematically by a cross-tabulation of two types of sources of expectations, viz. long-term memory and current context, with two types of mechanisms of salience, viz. confirmation and violation of expectations: Salience by context-free entrenchment: confirmation of expectations based on knowledge stored in long-term memory. Salience by contexual entrenchment: confirmation of expectations derived from the probability of occurrence in the current context. Salience by surprisal: violation of expectations derived from the probability of occurrence in the current context. Salience by novelty: violation of expectations based on lack of stored knowledge. In this paper we propose a unified framework for salience which reconciles these opposing conceptions by showing that they focus on different aspects of the interaction between knowledge, context, expectation, and external input.

Rectilinear path problems in restricted memory setup

We study the rectilinear path problem in the presence of disjoint axis parallel rectangular obstacles in the read-only and in-place setup. The input to the problem is a set R of n axis-parallel rectangular obstacles in R2. The objective is to answer the following query efficiently. Path-Query(p,q):Given a pair of points p and q, report an axis-parallel path from p to q avoiding the obstacles in R. In the read-only setup, we show that Path-Query(p,q) problem can be solved in O(n2s+nlogs) time using O(s) extra space. We also show that the existence of an x-monotone path and reporting it, if it exists, can be done with the same asymptotic time complexity. If the objective is to test the existence of an xy-monotone path between the given pair of points p and q avoiding the obstacles, and report it if exists, then our proposed algorithm needs O(n2s+nlogs+Mslogn) time with O(s) extra space, where Ms is the time complexity for computing the median of n elements in the read-only setup using O(s) extra space. Finally, we show that when the obstacles are unit squares instead of rectangles of arbitrary size, then there always exists a path of O(n) links between a pair of query points, and the path can be reported in O(nn) time using O(1) extra work-space. It is also shown that there is an instance where the minimum number of links in a path between a pair of specified points is O(n).The objective of the Path-Query(p,q) in the in-place setup is to preprocess the input rectangles in a data structure in the input array itself such that for any pair of query points p and q, a rectilinear path can be reported efficiently. Here we propose an algorithm with O(nlogn) preprocessing time and O(n3/4+χ) query time, where χ is the number of links (bends) in the path. Both the preprocessing and query answering need O(1) extra space.

Target-specific modulation of the descending prefrontal cortex inputs to the dorsal raphe nucleus by cannabinoids

Serotonin (5-HT) neurons located in the raphe nuclei modulate a wide range of behaviors by means of an expansive innervation pattern. In turn, the raphe receives a vast array of synaptic inputs, and a remaining challenge lies in understanding how these individual inputs are organized, processed, and modulated in this nucleus to contribute ultimately to the core coding features of 5-HT neurons. The details of the long-range, top-down control exerted by the medial prefrontal cortex (mPFC) in the dorsal raphe nucleus (DRN) are of particular interest, in part, because of its purported role in stress processing and mood regulation. Here, we found that the mPFC provides a direct monosynaptic, glutamatergic drive to both DRN 5-HT and GABA neurons and that this architecture was conducive to a robust feed-forward inhibition. Remarkably, activation of cannabinoid (CB) receptors differentially modulated the mPFC inputs onto these cell types in the DRN, in effect regulating the synaptic excitatory/inhibitory balance governing the excitability of 5-HT neurons. Thus, the CB system dynamically reconfigures the processing features of the DRN, a mood-related circuit believed to provide a concerted and distributed regulation of the excitability of large ensembles of brain networks.

Synthetic Genetic Array Analysis.

Genetic interaction studies have been used to characterize unknown genes, assign membership in pathway and complex, and build a comprehensive functional map of a eukaryotic cell. Synthetic genetic array (SGA) methodology automates yeast genetic analysis and enables systematic mapping of genetic interactions. In its simplest form, SGA consists of a series of replica pinning steps that enable construction of haploid double mutants through automated mating and meiotic recombination. Using this method, a strain carrying a query mutation, such as a deletion allele of a nonessential gene or a conditional temperature-sensitive allele of an essential gene, can be crossed to an input array of yeast mutants, such as the complete set of approximately 5000 viable deletion mutants. The resulting output array of double mutants can be scored for genetic interactions based on estimates of cellular fitness derived from colony-size measurements. The SGA score method can be used to analyze large-scale data sets, whereas small-scale data sets can be analyzed using SGAtools, a simple web-based interface that includes all the necessary analysis steps for quantifying genetic interactions.

Synthetic Genetic Arrays: Automation of Yeast Genetics.

Genome-sequencing efforts have led to great strides in the annotation of protein-coding genes and other genomic elements. The current challenge is to understand the functional role of each gene and how genes work together to modulate cellular processes. Genetic interactions define phenotypic relationships between genes and reveal the functional organization of a cell. Synthetic genetic array (SGA) methodology automates yeast genetics and enables large-scale and systematic mapping of genetic interaction networks in the budding yeast,Saccharomyces cerevisiae SGA facilitates construction of an output array of double mutants from an input array of single mutants through a series of replica pinning steps. Subsequent analysis of genetic interactions from SGA-derived mutants relies on accurate quantification of colony size, which serves as a proxy for fitness. Since its development, SGA has given rise to a variety of other experimental approaches for functional profiling of the yeast genome and has been applied in a multitude of other contexts, such as genome-wide screens for synthetic dosage lethality and integration with high-content screening for systematic assessment of morphology defects. SGA-like strategies can also be implemented similarly in a number of other cell types and organisms, includingSchizosaccharomyces pombe,Escherichia coli, Caenorhabditis elegans, and human cancer cell lines. The genetic networks emerging from these studies not only generate functional wiring diagrams but may also play a key role in our understanding of the complex relationship between genotype and phenotype.

RELIABILITY ASSESSMENT OF STRINGERS SPACINGS IN BRIDGES AS FUNCTION OF TIMBER PROPERTIES

This presentation accounts for established functions of stringer spacing of major Nigerian woods when used as bridge decks. It entails stochastic evaluation of bridge wood decks with absolute regards to the spacing of supporting stringers. A timber bridge deck is modelled on timber stringers in accordance with current specifications as outline in AASHTO LRFD (2010), to represent real life experiment in order to depict the structural behaviour of Nigerian timbers when used for bridge decks. This model is then subjected to some degree of entropy using Advance Second Moment Reliability Assessment (ASMRA) method, which is subsequently analysed using JAVA library with the help of Flanagan polynomial. The concept of ASMRA with Flanagan polynomial returns optimum output values for any input array of data along the input normal distribution curve. Taking Lophira alata (EKKI), Afzelia bipindensis (APA),Chlorophora exceisa (IROKO) and Mitragyna ciliate (ABURA) to represent N 1 , N 2 , N 3 , and N 4 classes of Nigerian timber suitable for bridge decks, convincingly, it was established that, stringer spacing, strength classes, timber thicknesses and width are some of the major factors among others influencing the structural behaviour of Nigerian timber species used for bridge decks. These data are treated as random variables to generate relative optimum values which, are used to predict the relationship between stringer spacing as a dependent variable on other variables using Analysis of Variance (ANOVA) and multiple Regression line analysis. For the considered timber species, it was observed that large percentages, (R 2 ≌ 1 that is 100% for EKKI, APA, IROKO and ABURA of the variation in the dependent variable (stringer spacing) is explained by the independent variables (strength classes, timber thicknesses, timber width, plank deck unit weight, unit weight of surfacing material, lane load, thickness of surfacing material and reliability indices) which are all good fit. Also all the predicted regression lines are reliable and statistically significant as the significance F, (3.59709E-05 for EKKI, 5.58768E-05 for APA, 3.59709E-05 for IROKO and 8.55563E-05 for ABURA) are all less than 0.05. Thus, these established relationships will help in future forecast of stringer spacing for bridge deck design and analysis within acceptable structural reliability indices which are statistically significant (and are all within acceptable values ≤0.05) http://dx.doi.org/10.4314/njt.v35i2.10

Parallel Partition and Merge QuickSort (PPMQSort) on Multicore CPUs

An explosive amount of data has tremendous impacts on sorting, searching, indexing, and so on. Sorting is one of the basic Computer Science problems needed to be fast and efficient to serve Big Data. This paper presents an efficient and scalable algorithm called Parallel Partition and Merge QuickSort (PPMQSort) running on any shared memory/multicore/multi-socket systems. Together with OpenMP 3.0 library, the PPMQSort is developed to be compatible and benchmarked with the fastest C/C++ Stdlib qsort(). The PPMQSort recursively divides an unsorted input array into partially sorted partitions up to Cutoff length using nested multithreading. Finally, those independent partitions are qsort() (conquered) such that no synchronizations are needed. The resulting Speedup of 12.29$$\times $$× on a dual-socket 8-core Xeon E5520 can be achieved for sorting random 200 M 32-bit integer data at 16 threads. With the same configuration, a 4-core AMD A6-3600 CPU (non-HyperThread) can reach up to 4.67$$\times $$×, a superlinear Speedup. It has been proved that the proposed PPMQSort can exploit all available cache levels and HyperThread CPU cores well thus utilizing up to 83 % and 96 % of CPU on E5520 and A6-3600, respectively.

Simultaneous encodings for range and next/previous larger/smaller value queries

Given an array of n elements from a total order, we propose encodings that support various range queries (range minimum, range maximum and their variants), and previous and next smaller/larger value queries. When query time is not of concern, we obtain a 4.088n+o(n)-bit encoding that supports all these queries. For the case when we need to support all these queries in constant time, we give an encoding that takes 4.585n+o(n) bits, where n is the length of input array. This improves the 5.08n+o(n)-bit encoding obtained by encoding the colored 2d-Min and Max heaps proposed by Fischer [11]. We first extend the original DFUDS [8] encoding of the colored 2d-Min (Max) heap that supports the queries in constant time. Then, we combine the extended DFUDS of 2d-Min heap and 2d-Max heap using the Min–Max encoding of Gawrychowski and Nicholson [15] with some modifications. We also obtain encodings that take lesser space and support a subset of these queries.