Academic literature on the topic 'Approximate counting'
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Journal articles on the topic "Approximate counting"
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BUSS, SAMUEL R., LESZEK ALEKSANDER KOŁODZIEJCZYK, and NEIL THAPEN. "FRAGMENTS OF APPROXIMATE COUNTING." Journal of Symbolic Logic 79, no. 2 (June 2014): 496–525. http://dx.doi.org/10.1017/jsl.2013.37.
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AbstractWe study the long-standing open problem of giving $\forall {\rm{\Sigma }}_1^b$ separations for fragments of bounded arithmetic in the relativized setting. Rather than considering the usual fragments defined by the amount of induction they allow, we study Jeřábek’s theories for approximate counting and their subtheories. We show that the $\forall {\rm{\Sigma }}_1^b$ Herbrandized ordering principle is unprovable in a fragment of bounded arithmetic that includes the injective weak pigeonhole principle for polynomial time functions, and also in a fragment that includes the surjective weak pigeonhole principle for FPNP functions. We further give new propositional translations, in terms of random resolution refutations, for the consequences of $T_2^1$ augmented with the surjective weak pigeonhole principle for polynomial time functions.
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Aronov, Boris, and Micha Sharir. "Approximate Halfspace Range Counting." SIAM Journal on Computing 39, no. 7 (January 2010): 2704–25. http://dx.doi.org/10.1137/080736600.
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Louchard, Guy, and Helmut Prodinger. "Generalized approximate counting revisited." Theoretical Computer Science 391, no. 1-2 (February 2008): 109–25. http://dx.doi.org/10.1016/j.tcs.2007.10.035.
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Jeřábek, Emil. "Approximate counting in bounded arithmetic." Journal of Symbolic Logic 72, no. 3 (September 2007): 959–93. http://dx.doi.org/10.2178/jsl/1191333850.
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AbstractWe develop approximate counting of sets definable by Boolean circuits in bounded arithmetic using the dual weak pigeonhole principle (dWPHP(PV)), as a generalization of results from [15]. We discuss applications to formalization of randomized complexity classes (such as BPP, APP, MA, AM) in PV1 + dWPHP(PV).
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Cichoń, Jacek, and Karol Gotfryd. "Average Counting via Approximate Histograms." ACM Transactions on Sensor Networks 14, no. 2 (July 21, 2018): 1–32. http://dx.doi.org/10.1145/3177922.
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Kirschenhofer, Peter, and Helmut Prodinger. "Approximate counting : an alternative approach." RAIRO - Theoretical Informatics and Applications 25, no. 1 (1991): 43–48. http://dx.doi.org/10.1051/ita/1991250100431.
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BORDEWICH, M., M. FREEDMAN, L. LOVÁSZ, and D. WELSH. "Approximate Counting and Quantum Computation." Combinatorics, Probability and Computing 14, no. 5-6 (October 11, 2005): 737. http://dx.doi.org/10.1017/s0963548305007005.
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Flajolet, Philippe. "Approximate counting: A detailed analysis." BIT 25, no. 1 (March 1985): 113–34. http://dx.doi.org/10.1007/bf01934993.
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Erdős, Péter L., Sándor Z. Kiss, István Miklós, and Lajos Soukup. "Approximate Counting of Graphical Realizations." PLOS ONE 10, no. 7 (July 10, 2015): e0131300. http://dx.doi.org/10.1371/journal.pone.0131300.
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Aldous, David. "Approximate Counting via Markov Chains." Statistical Science 8, no. 1 (February 1993): 16–19. http://dx.doi.org/10.1214/ss/1177011078.
Full textDissertations / Theses on the topic "Approximate counting"
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Ben, Mazziane Younes. "Analyse probabiliste pour le caching." Electronic Thesis or Diss., Université Côte d'Azur, 2024. http://www.theses.fr/2024COAZ4014.
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Les caches sont de petites mémoires qui accélèrent la récupération des données. L'un des objectifs des politiques de mise en cache est de sélectionner le contenu du cache afin de minimiser le temps de réponse aux requêtes d'objets. Un problème plus général permet de répondre approximativement à la requête d'un objet par un objet similaire mis en cache. Ce concept, appelé "mise en cache par similarité", s'avère utile pour les systèmes de recommandation. L'objectif est de minimiser le temps de latence tout en fournissant des réponses satisfaisantes. La compréhension théorique des algorithmes de gestion de la mémoire cache, sous des hypothèses spécifiques sur les requêtes, aide à choisir un algorithme approprié. Les politiques d'éviction du cache les plus répandues sont celles de l'utilisation la moins fréquente (LFU) et de l'utilisation la moins récente (LRU). LFU est efficace lorsque le processus requêtes est stationnaire, et LRU s'adapte aux changements dans les processus de requêtes. Les algorithmes d'apprentissage séquentiel, tels que l'algorithme aléatoire Follow-the-Perturbed Leader (FPL), appliqués à la mise en cache, bénéficient de garanties théoriques même dans le pire des cas.LFU et FPL s'appuient sur le nombre de requêtes d'objets. Cependant, le comptage est un défi dans les scénarios à mémoire limitée. Pour y remédier, les politiques de mise en cache utilisent des schémas de comptage approximatifs, tels que la structure de données Count-Min Sketch avec mises à jour conservatrices (CMS-CU), afin d'équilibrer la précision des comptages et l'utilisation de la mémoire. Dans le cadre de la mise en cache par similarité, RND-LRU est une stratégie LRU modifiée. Malheureusement, il reste difficile de quantifier théoriquement à la fois la performance d'un cache LFU utilisant CMS-CU, celle d'un cache FPL avec un algorithme de comptage approximatif, ainsi que celle de RND-LRU.Cette thèse explore trois algorithmes probabilistes : CMS-CU, FPL avec des estimations bruitées des nombres de requêtes d'objets (NFPL) et RND-LRU. Pour CMS-CU, nous proposons une approche novatrice pour trouver de nouvelles bornes supérieures sur l'espérance et le complémentaire de la fonction de répartition de l'erreur d'estimation sous un processus de requêtes i.i.d. De plus, nous démontrons que NFPL se comporte aussi bien que la politique de mise en cache statique, optimale et omnisciente, quelle que soit la séquence de requêtes (sous certaines conditions sur les comptages bruités). Enfin, nous introduisons une nouvelle politique de mise en cache qui est analytiquement résoluble. Nous montrons alors que cette politique approxime RND-LRUCaches are small memories that speed up data retrieval. Caching policies may aim to choose cache content to minimize latency in responding to item requests. A more general problem permits an item's request to be approximately answered by a similar cached item. This concept, referred to as "similarity caching," proves valuable for content-based image retrieval and recommendation systems. The objective is to further minimize latency while delivering satisfactory answers.Theoretical understanding of cache memory management algorithms under specific assumptions on the requests provides guidelines for choosing a suitable algorithm. The Least-Frequently-Used (LFU) and the Least-Recently-Used (LRU) are popular caching eviction policies. LFU is efficient when the requests process is stationary, while LRU adapts to changes in the patterns of the requests. Online learning algorithms, such as the randomized Follow-the-Perturbed Leader (FPL) algorithm, applied for caching, enjoy worst-case guarantees. Both LFU and FPL rely on items' request count. However, counting is challenging in memory-constrained scenarios. To overcome this problem, caching policies operate with approximate counting schemes, such as the Count-Min Sketch with Conservative Updates (CMS-CU), to balance counts' accuracy and memory usage. In the similarity caching setting, RND-LRU is a modified LRU where a request is probabilistically answered by the most similar cached item. Unfortunately, a theoretical analysis of an LFU cache utilizing CMS-CU, an FPL cache with an approximate counting algorithm, and RND-LRU remains difficult.This thesis investigates three randomized algorithms: CMS-CU, FPL with noisy items' request counts estimations (NFPL), and RND-LRU. For CMS-CU, we propose a novel approach to derive new upper bounds on the expected value and the complementary cumulative distribution function of the estimation error under a renewal request process. Additionally, we prove that NFPL behaves as well as the optimal omniscient static caching policy for any request sequence under specific conditions on the noisy counts. Finally, we introduce a new analytically tractable similarity caching policy and show that it can approximate RND-LRU
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Dreier, Jan [Verfasser], Peter [Akademischer Betreuer] Rossmanith, and Sebastian [Akademischer Betreuer] Siebertz. "Two new perspectives on algorithmic meta-theorems : evaluating approximate first-order counting queries on bounded expansion and first-order queries on random graphs / Jan Dreier ; Peter Rossmanith, Sebastian Siebertz." Aachen : Universitätsbibliothek der RWTH Aachen, 2020. http://d-nb.info/1228630380/34.
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Zou, Tingxiang. "Structures pseudo-finies et dimensions de comptage." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSE1083/document.
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Cette thèse porte sur la théorie des modèles des structures pseudo-finies en mettant l’accent sur les groupes et les corps. Le but est d'approfondir notre compréhension des interactions entre les dimensions de comptage pseudo-finies et les propriétés algébriques de leurs structures sous-jacentes, ainsi que de la classification de certaines classes de structures en fonction de leurs dimensions. Notre approche se fait par l'étude d'exemples. Nous avons examiné trois classes de structures. La première est la classe des H-structures, qui sont des expansions génériques. Nous avons donné une construction explicite de H-structures pseudo-finies comme ultraproduits de structures finies. Le deuxième exemple est la classe des corps aux différences finis. Nous avons étudié les propriétés de la dimension pseudo-finie grossière de cette classe. Nous avons montré qu'elle est définissable et prend des valeurs entières, et nous avons trouvé un lien partiel entre cette dimension et le degré de transcendance transformelle. Le troisième exemple est la classe des groupes de permutations primitifs pseudo-finis. Nous avons généralisé le théorème classique de classification de Hrushovski pour les groupes stables de permutations d'un ensemble fortement minimal au cas où une dimension abstraite existe, cas qui inclut à la fois les rangs classiques de la théorie des modèles et les dimensions de comptage pseudo-finies. Dans cette thèse, nous avons aussi généralisé le théorème de Schlichting aux sous-groupes approximatifs, en utilisant une notion de commensurabilitéThis thesis is about the model theory of pseudofinite structures with the focus on groups and fields. The aim is to deepen our understanding of how pseudofinite counting dimensions can interact with the algebraic properties of underlying structures and how we could classify certain classes of structures according to their counting dimensions. Our approach is by studying examples. We treat three classes of structures: The first one is the class of H-structures, which are generic expansions of existing structures. We give an explicit construction of pseudofinite H-structures as ultraproducts of finite structures. The second one is the class of finite difference fields. We study properties of coarse pseudofinite dimension in this class, show that it is definable and integer-valued and build a partial connection between this dimension and transformal transcendence degree. The third example is the class of pseudofinite primitive permutation groups. We generalise Hrushovski's classical classification theorem for stable permutation groups acting on a strongly minimal set to the case where there exists an abstract notion of dimension, which includes both the classical model theoretic ranks and pseudofinite counting dimensions. In this thesis, we also generalise Schlichting's theorem for groups to the case of approximate subgroups with a notion of commensurability
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Kelk, Steven M. "On the relative complexity of approximately counting H-colourings." Thesis, University of Warwick, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.398734.
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Sella, Francesco. "Typical and Atypical Development of Numerical Representation." Doctoral thesis, Università degli studi di Padova, 2013. http://hdl.handle.net/11577/3426396.
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How numerical information is represented? Recent studies have highlighted the prominent role of preverbal core knowledge systems for representing numerical quantities: the Object Tracking System (OTS) and the Approximate Number System (ANS; or analogue magnitude system). The former is general mechanism which allows individuals to track the spatio-temporal characteristics of the objects and its capacity is limited (3-4 items). The latter is a quantitative mechanism which entails the representation of each numerosity as a distribution of activation on the mental number line. In the present work we investigated several aspects of these two systems along with numerical and non-numerical estimation ability in typical and atypical development.
In Study 1.1, we implemented an imitation task to investigate the spontaneous focusing on numerosity in 2 ½ year-old children. The results suggest that most of the children employed the analogue magnitude system when spontaneously encoding numerosity. The use of the analogue magnitude system may be related to both its low demanding of attentional resources and to the availability of other (non-numerical) quantitative cues which covariate with numerosity.
In Study 1.2, 2 ½ year-old children completed a categorization task in order to investigate their ability in estimating numerical sets. Children’s estimations were independent from the visual characteristics of the stimuli (i.e. perimeter or density) within the OTS capacity. Conversely, the estimation of larger quantities (5-9 dots) was significantly affected by stimuli characteristics: in particular, the increase of perimeter with a constant density appears as the combination of visual characteristics which strongly increases the perceived numerosity.
In Study 2, Preschoolers, Grade 1 and Grade 3 pupils had to map continuous, discrete and symbolic quantities. The results indicated that different mechanisms are involved in the estimation of continuous quantities with respect to numerical (discrete and symbolic) quantities.
In Study 3, we devised a dual-task paradigm to investigate the relation between visual short term memory (VSTM) and subitizing. We found a striking correspondence between the number of elements retained in VSTM and the number of elements that can be subitized.
In Study 4.1, children with developmental dyscalculia (DD) in comorbidity with a profile of Non-Verbal syndrome (NVS) and typically developing (TD) children completed a numerical comparison task. We found a specific deficit in the comparison of numerical quantities in DD-NVS children with respect to TD. In particular, the OTS capacity seems to be reduced in the DD-NVS group as compared to TD.
In Study 4.2, children with developmental dyscalculia (DD) and typically developing (TD) children completed two number-line tasks. Children with DD displayed a less precise estimation of symbolic quantities, thereby suggesting a specific deficit in the number representation with respect to TD children.
In Study 5, individuals with Down Syndrome (DS) and typically developing children matched for both mental (MA) and chronological age (CA) completed two numerical tasks in order to evaluate their ability to compare non-symbolic quantities (i.e. dots) and counting process. Kids with DS showed a specific deficit in comparing small quantities, within OTS capacity, with respect to both MA and CA matched kids. For the comparison of larger quantities, kids with DS displayed a performance similar to MA matched controls but lower as compared to CA matched controls. Finally, the counting ability appears similar between kids with DS and MA matched children.Come viene rappresentata l’informazione numerica? Recenti ricerche hanno evidenziato il ruolo fondamentale dei sistemi cognitive preverbali nella rappresentazione numerica: l’Object Tracking System (OTS) e l’Approximate Number System (ANS; o Analogue Magnitude System). Il primo è un meccanismo generale che permette di conservare in memoria le caratteristiche spazio-temporali degli stimoli e la sua capacità è limitata (3-4 elementi). Il secondo è un meccanismo quantitativo che rappresenta ogni numerosità come una distribuzione d’attivazione su teorica linea numerica mentale. Nella presente lavoro di tesi, presenteremo diversi studi volti ad indagare il funzionamento di questi meccanismi in interazione con processi di stima numerica e non-numerica in contesto di sviluppo tipico ed atipico. Nello Studio 1.1, abbiamo utilizzato un compito di imitazione per indagare la capacità di concentrarsi spontaneamente sulla numerosità in bambini di 2 ½ anni. I risultati hanno evidenziato come la maggior parte dei bambini adotti un sistema analogico di quantità quando analizzano spontaneamente delle quantità numeriche. La selezione di questo meccanismo è probabilmente legata sia alla minor richiesta di risorse attentive, sia alla disponibilità di altri indizi quantitativi (non numerici) che covariano con la numerosità. Nello Studio 1.2, bambini di 2 ½ anni hanno svolto un compito di categorizzazione per investigare la loro capacità di stimare la grandezza numerica di insiemi. Le stime dei bambini erano indipendenti dalle caratteristiche visive degli elementi dell’insieme (i.e. perimetro o densità) per le quantità dentro il range di OTS (1-4 elementi). Le stime di quantità più grandi (5-9 elementi) erano invece influenzate dalle caratteristiche visive degli stimoli: in particolare, l’aumento del perimetro con densità costante sembra essere la combinazione di caratteristiche visive degli stimoli che fa aumentare maggiormente la percezione di numerosità. Nello Studio 2, bambini prescolari, di prima primaria e di terza primaria dovevano stimare quantità continue, discrete e simboliche. I risultati suggeriscono la presenza di differenti meccanismi coinvolti nella stima di quantità continue rispetto a quelle numeriche (discrete e simboliche). Nello Studio 3, abbiamo utilizzato il paradigma del doppio compito per studiare la relazione tra memoria visiva a breve termine e subitizing. Dai risultati emerge una marcata corrispondenza tra il numero di elementi memorizzati ed il numero di elementi che possono essere velocemente enumerati attraverso il subitizing. Nello Studio 4.1, bambini con diagnosi di Discalculia Evolutiva (DE) in comorbidità con sindrome non verbale (SNV) e bambini con sviluppo tipico hanno svolto un compito di confronto di quantità numeriche. Abbiamo riscontrato un deficit nella discriminazione di numerosità nel gruppo DE-SNV rispetto ai bambini a sviluppo tipico. In particolare, la capacità di OTS sembra essere ridotta nei bambini con DE-SNV rispetto ai bambini a sviluppo tipico. Nello Studio 4.2, bambini con diagnosi di Discalculia Evolutiva (DE) e bambini con sviluppo tipico hanno completato due compiti di stima sulla linea numerica. I bambini con DE hanno mostrato minor precisione nella stima di quantità simboliche suggerendo una rappresentazione numerica deficitaria rispetto al gruppo con sviluppo tipico. Nello Studio 5, ragazzi con sindrome di Down (SD) e bambini con sviluppo tipico pareggiati per età mentale (EM) ed età cronologica (EC) hanno svolto due compiti numerici per valutare le loro abilità di discriminazione numerica e di conteggio. I ragazzi con SD hanno mostrato un deficit nel discriminare piccole quantità, all’interno del range di OTS, rispetto ai bambini a sviluppo tipico pareggiati sia per EM che per EC. Nella comparazione di numerosità più grandi, i ragazzi con SD hanno ottenuto una performance simile ai bambini pareggiati per EM e minore rispetto ai ragazzi pareggiati per EC. Infine, l’abilità di conteggio appare simile tra i partecipanti con SD e i bambini pareggiati per EM.
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Schott, Sarah. "TPA: A New Method for Approximate Counting." Diss., 2012. http://hdl.handle.net/10161/5429.
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Many high dimensional integrals can be reduced to the problem of finding the relative measure of two sets. Often one set will be exponentially larger than the other. A standard method of dealing with this problem is to interpolate between the sets with a series of nested sets where neighboring nested sets have relative measures bounded above by a constant. Choosing these sets can be very difficult in practice. Here a new approach that creates a randomly drawn sequence of such sets is presented. This procedure gives faster approximation algorithms and a well-balanced set of nested sets that are essential to building effective tempering and annealing algorithms.
Dissertation
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Afshani, Peyman. "On Geometric Range Searching, Approximate Counting and Depth Problems." Thesis, 2008. http://hdl.handle.net/10012/4032.
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In this thesis we deal with problems connected to range searching,
which is one of the central areas of computational geometry.
The dominant problems in this area are
halfspace range searching, simplex range searching and orthogonal range searching and
research into these problems has spanned decades.
For many range searching problems, the best possible
data structures cannot offer fast (i.e., polylogarithmic) query
times if we limit ourselves to near linear storage.
Even worse, it is conjectured (and proved in some cases)
that only very small improvements to these might be possible.
This inefficiency has encouraged many researchers to seek alternatives through approximations.
In this thesis we continue this line of research and focus on
relative approximation of range counting problems.
One important problem where it is possible to achieve significant speedup
through approximation is halfspace range counting in 3D.
Here we continue the previous research done
and obtain the first optimal data structure for approximate halfspace range counting in 3D.
Our data structure has the slight advantage of being Las Vegas (the result is always correct) in contrast
to the previous methods that were Monte Carlo (the correctness holds with high probability).
Another series of problems where approximation can provide us with
substantial speedup comes from robust statistics.
We recognize three problems here:
approximate Tukey depth, regression depth and simplicial depth queries.
In 2D, we obtain an optimal data structure capable of approximating
the regression depth of a query hyperplane.
We also offer a linear space data structure which can answer approximate
Tukey depth queries efficiently in 3D.
These data structures are obtained by applying our ideas for the
approximate halfspace counting problem.
Approximating the simplicial depth turns out to be much more
difficult, however.
Computing the simplicial depth of a given point is more computationally
challenging than most other definitions of data depth.
In 2D we obtain the first data structure which uses near linear space
and can answer approximate simplicial depth queries in polylogarithmic time.
As applications of this result, we provide two non-trivial methods to
approximate the simplicial depth of a given point in higher dimension.
Along the way, we establish a tight combinatorial relationship between
the Tukey depth of any given point and its simplicial depth.
Another problem investigated in this thesis is the dominance reporting problem,
an important special case of orthogonal range reporting.
In three dimensions, we solve this
problem in the pointer machine model and the external memory model
by offering the first optimal data structures in these models of computation.
Also, in the RAM model and for points from
an integer grid we reduce the space complexity of the fastest
known data structure to optimal.
Using known techniques in the literature, we can use our
results to obtain solutions for the orthogonal range searching problem as well.
The query complexity offered by our orthogonal range reporting data structures
match the most efficient query complexities
known in the literature but our space bounds are lower than the previous methods in the external
memory model and RAM model where the input is a subset of an integer grid.
The results also yield improved orthogonal range searching in
higher dimensions (which shows the significance
of the dominance reporting problem).
Intersection searching is a generalization of range searching where
we deal with more complicated geometric objects instead of points.
We investigate the rectilinear disjoint polygon counting problem
which is a specialized intersection counting problem.
We provide a linear-size data structure capable of counting
the number of disjoint rectilinear polygons
intersecting any rectilinear polygon of constant size.
The query time (as well as some other properties of our data structure) resembles
the classical simplex range searching data structures.
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Wilkinson, Bryan T. "Adaptive Range Counting and Other Frequency-Based Range Query Problems." Thesis, 2012. http://hdl.handle.net/10012/6739.
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We consider variations of range searching in which, given a query range, our goal is to compute some function based on frequencies of points that lie in the range. The most basic such computation involves counting the number of points in a query range. Data structures that compute this function solve the well-studied range counting problem. We consider adaptive and approximate data structures for the 2-D orthogonal range counting problem under the w-bit word RAM model. The query time of an adaptive range counting data structure is sensitive to k, the number of points being counted. We give an adaptive data structure that requires O(n loglog n) space and O(loglog n + log_w k) query time. Non-adaptive data structures on the other hand require Ω(log_w n) query time (Pătraşcu, 2007). Our specific bounds are interesting for two reasons. First, when k=O(1), our bounds match the state of the art for the 2-D orthogonal range emptiness problem (Chan et al., 2011). Second, when k=Θ(n), our data structure is tight to the aforementioned Ω(log_w n) query time lower bound.
We also give approximate data structures for 2-D orthogonal range counting whose bounds match the state of the art for the 2-D orthogonal range emptiness problem. Our first data structure requires O(n loglog n) space and O(loglog n) query time. Our second data structure requires O(n) space and O(log^ε n) query time for any fixed constant ε>0. These data structures compute an approximation k' such that (1-δ)k≤k'≤(1+δ)k for any fixed constant δ>0.
The range selection query problem in an array involves finding the kth lowest element in a given subarray. Range selection in an array is very closely related to 3-sided 2-D orthogonal range counting. An extension of our technique for 3-sided 2-D range counting yields an efficient solution to adaptive range selection in an array. In particular, we present an adaptive data structure that requires O(n) space and O(log_w k) query time, exactly matching a recent lower bound (Jørgensen and Larsen, 2011).
We next consider a variety of frequency-based range query problems in arrays. We give efficient data structures for the range mode and least frequent element query problems and also exhibit the hardness of these problems by reducing Boolean matrix multiplication to the construction and use of a range mode or least frequent element data structure. We also give data structures for the range α-majority and α-minority query problems. An α-majority is an element whose frequency in a subarray is greater than an α fraction of the size of the subarray; any other element is an α-minority. Surprisingly, geometric insights prove to be useful even in the design of our 1-D range α-majority and α-minority data structures.
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Hamilton, Christopher. "Range Searching Data Structures with Cache Locality." 2011. http://hdl.handle.net/10222/13363.
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This thesis focuses on range searching data structures, an elementary problem in computational
geometry with research spanning decades. These problems often involve very large data sets.
Processor speeds increase faster than memory speeds, thus the gap between the rate at which CPUs can
process data and the rate at which it can be retrieved is increasing. To bridge this gap, various
levels of cache are used. Since cache misses are costly, algorithms should be cache-friendly.
The input-output (I/O) model was the first model for constructing cache-efficient algorithms,
focusing on a two-level memory hierarchy. Algorithms for this model require manual tuning to
determine optimal values for hardware dependent parameters, and are only optimal at a single level
of a memory hierarchy. Cache-oblivious (CO) algorithms are built without knowledge of the hierarchy,
allowing them to be optimal across all levels at once.
There exist strong theoretical and practical results for I/O-efficient range searching. Recently,
the CO model has received attention, but range searching remains poorly understood. This thesis
explores data structures for CO range counting and reporting. It presents the first space and
worst-case query-time optimal approximate range counting structure for a family of related problems,
and associated O(N log N)-space query-optimal reporting structures. The approximate counting
structure is the first of its kind in internal memory, I/O and CO models. Researchers have been
trying to create linear-space query-optimal CO reporting structures. This thesis shows that for a
variety of problems, linear space is in fact impossible.
Heuristics are also used for building cache-friendly algorithms. Space-filling curves are
continuous functions mapping multi-dimensional sets into one-dimensional ones. They are used to
build search structures in the hopes that objects that were close in the original space remain close
in the resulting ordering. This results in queries incurring fewer page swaps when traversing the
structure. The Hilbert curve is notably good at this, but often imposes a space or time penalty.
This thesis introduces compact Hilbert indices, which remove the ineffiency inherent for input point
sets with bounding boxes smaller than their bounding hypercubes.
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"Approximately Counting Perfect and General Matchings in Bipartite and General Graphs." Diss., 2009. http://hdl.handle.net/10161/1054.
Full textBooks on the topic "Approximate counting"
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Dyer, Martin. Approximately counting Hamilton cycles in dense graphs. Edinburgh: LFCS, Dept. of Computer Science, University of Edinburgh, 1993.
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Murphy, Stuart J. Coyotes All Around (Mathstart). HarperCollins Publishers, 2003.
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LeFevre, Jo-Anne, Emma Wells, and Carla Sowinski. Individual Differences in Basic Arithmetical Processes in Children and Adults. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.005.
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This chapter describes the four main sources of individual differences in arithmetic that have been identified through research with children and adults. Numerical quantitative knowledge invokes basic cognitive processes that are either numerically specific or are recruited to be used in quantitative tasks (e.g. subitizing, discrimination acuity for approximate quantities). Attentional skills, including executive attention and various aspects of working memory are important, especially for more complex procedures. Linguistic knowledge is used within arithmetic to learn number system rules and structures, specific number words, and in developing and executing counting processes. Strategic abilities, which may reflect general planning and awareness skills, are involved in selecting procedures and solving problems adaptively. Other important sources of individual differences include automaticity of knowledge related to practice, experiences outside school, and the specific language spoken. Suggestions are made for further research that would be helpful in establishing a full picture of individual differences in arithmetic.
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Uittenhove, Kim, and Patrick Lemaire. Numerical Cognition during Cognitive Aging. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.045.
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This chapter provides an overview of age-related changes and stabilities in numerical cognition. For each component (i.e. approximate and exact number system, quantification, and arithmetic) of numerical cognition, we review changes in participants’ performance during normal and pathological aging in a wide variety of tasks (e.g. number comparison, subitizing, counting, and simple or complex arithmetic problem-solving). We discuss both behavioral and neural mechanisms underlying these performance variations. Moreover, we highlight the importance of taking into account strategic variations. Indeed, investigating strategy repertoire (i.e. how young and older adults accomplish numerical cognitive tasks), selection (i.e. how participants choose strategies on each problem), execution (i.e. how strategies are implemented once selected), and distribution (i.e. how often participants use each available strategy) enables to determine sources of aging effects and individual differences in numerical cognition. Finally, we discuss potential future research to further our understanding of age-related changes in numerical cognition.
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Núñez, Rafael, and Tyler Marghetis. Cognitive Linguistics and the Concept(s) of Number. Edited by Roi Cohen Kadosh and Ann Dowker. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199642342.013.023.
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What is a ‘number,’ as studied within numerical cognition? The term is highly polysemous, and can refer to numerals, numerosity, and a diverse collection of mathematical objects, from natural numbers to infinitesimals. However, numerical cognition has focused primarily on prototypical counting numbers (PCNs) – numbers used regularly to count small collections of objects. Even these simple numbers are far more complex than apparent pre-conditions for numerical abilities like subitizing and approximate discrimination of large numerosity, which we share with other animals. We argue that the leap to number concepts proper relies, in part, on two embodied, domain-general cognitive mechanisms: conceptual metaphor and fictive motion. These mechanisms were first investigated within cognitive linguistics, a subdiscipline of cognitive science, but are now thought to subserve cognition more generally. We review the proposal that these mechanisms structure numerical cognition – including PCNs, but also the positive integers and arithmetic – and survey the supporting empirical evidence.
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The Bruce-Grey Plant Committee (Owen Sound Field Naturalists). Asters, Goldenrods and Fleabanes of Grey and Bruce Counties: Includes Approximately 50% of Ontario Species. Stan Brown Printers Ltd., 2000.
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Jucker, J., and G. J. Trinkaus. Design and Estimate of Approximate Cost of a Sanitary Sewer System for the Village of Barrington, Cook and Lake Counties, Illinois. Creative Media Partners, LLC, 2018.
Find full textBook chapters on the topic "Approximate counting"
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Bubley, Russ. "Approximate Counting." In Randomized Algorithms: Approximation, Generation and Counting, 29–36. London: Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-0695-1_3.
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Lipton, Richard J. "An Approximate Counting Method." In The P=NP Question and Gödel’s Lost Letter, 115–18. Boston, MA: Springer US, 2010. http://dx.doi.org/10.1007/978-1-4419-7155-5_25.
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Aaronson, Scott, and Patrick Rall. "Quantum Approximate Counting, Simplified." In Symposium on Simplicity in Algorithms, 24–32. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2020. http://dx.doi.org/10.1137/1.9781611976014.5.
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Tan, Yong Kiam, Jiong Yang, Mate Soos, Magnus O. Myreen, and Kuldeep S. Meel. "Formally Certified Approximate Model Counting." In Computer Aided Verification, 153–77. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-65627-9_8.
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AbstractApproximate model counting is the task of approximating the number of solutions to an input Boolean formula. The state-of-the-art approximate model counter for formulas in conjunctive normal form (CNF), $$\textsf{ApproxMC}$$ ApproxMC , provides a scalable means of obtaining model counts with probably approximately correct (PAC)-style guarantees. Nevertheless, the validity of $$\textsf{ApproxMC}$$ ApproxMC ’s approximation relies on a careful theoretical analysis of its randomized algorithm and the correctness of its highly optimized implementation, especially the latter’s stateful interactions with an incremental CNF satisfiability solver capable of natively handling parity (XOR) constraints.We present the first certification framework for approximate model counting with formally verified guarantees on the quality of its output approximation. Our approach combines: (i) a static, once-off, formal proof of the algorithm’s PAC guarantee in the Isabelle/HOL proof assistant; and (ii) dynamic, per-run, verification of $$\textsf{ApproxMC}$$ ApproxMC ’s calls to an external CNF-XOR solver using proof certificates. We detail our general approach to establish a rigorous connection between these two parts of the verification, including our blueprint for turning the formalized, randomized algorithm into a verified proof checker, and our design of proof certificates for both $$\textsf{ApproxMC}$$ ApproxMC and its internal CNF-XOR solving steps. Experimentally, we show that certificate generation adds little overhead to an approximate counter implementation, and that our certificate checker is able to fully certify $$84.7\%$$ 84.7 % of instances with generated certificates when given the same time and memory limits as the counter.
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Gao, Younan, and Meng He. "On Approximate Colored Path Counting." In Lecture Notes in Computer Science, 209–24. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-55598-5_14.
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Yang, Jiong, and Kuldeep S. Meel. "Rounding Meets Approximate Model Counting." In Computer Aided Verification, 132–62. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-37703-7_7.
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AbstractThe problem of model counting, also known as $$\#\textsf{SAT}$$ # SAT , is to compute the number of models or satisfying assignments of a given Boolean formula F. Model counting is a fundamental problem in computer science with a wide range of applications. In recent years, there has been a growing interest in using hashing-based techniques for approximate model counting that provide $$(\varepsilon , \delta )$$ ( ε , δ ) -guarantees: i.e., the count returned is within a $$(1+\varepsilon )$$ ( 1 + ε ) -factor of the exact count with confidence at least $$1-\delta $$ 1 - δ . While hashing-based techniques attain reasonable scalability for large enough values of $$\delta $$ δ , their scalability is severely impacted for smaller values of $$\delta $$ δ , thereby preventing their adoption in application domains that require estimates with high confidence.The primary contribution of this paper is to address the Achilles heel of hashing-based techniques: we propose a novel approach based on rounding that allows us to achieve a significant reduction in runtime for smaller values of $$\delta $$ δ . The resulting counter, called $$\textsf{ApproxMC6}$$ ApproxMC 6 (The resulting tool $$\textsf{ApproxMC6}$$ ApproxMC 6 is available open-source at https://github.com/meelgroup/approxmc), achieves a substantial runtime performance improvement over the current state-of-the-art counter, $$\textsf{ApproxMC}$$ ApproxMC . In particular, our extensive evaluation over a benchmark suite consisting of 1890 instances shows $$\textsf{ApproxMC6}$$ ApproxMC 6 solves 204 more instances than $$\textsf{ApproxMC}$$ ApproxMC , and achieves a $$4\times $$ 4 × speedup over $$\textsf{ApproxMC}$$ ApproxMC .
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Manjunath, Madhusudan, Kurt Mehlhorn, Konstantinos Panagiotou, and He Sun. "Approximate Counting of Cycles in Streams." In Algorithms – ESA 2011, 677–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23719-5_57.
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Bordewich, Magnus, Martin Dyer, and Marek Karpinski. "Stopping Times, Metrics and Approximate Counting." In Automata, Languages and Programming, 108–19. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11786986_11.
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Bendík, Jaroslav, and Kuldeep S. Meel. "Approximate Counting of Minimal Unsatisfiable Subsets." In Computer Aided Verification, 439–62. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-53288-8_21.
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Wang, Jinyan, Minghao Yin, and Jingli Wu. "Approximate Model Counting via Extension Rule." In Frontiers in Algorithmics, 229–40. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19647-3_22.
Full textConference papers on the topic "Approximate counting"
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Meng, Chang, Hanyu Wang, Yuqi Mai, Weikang Qian, and Giovanni De Micheli. "VACSEM: Verifying Average Errors in Approximate Circuits Using Simulation-Enhanced Model Counting." In 2024 Design, Automation & Test in Europe Conference & Exhibition (DATE), 1–6. IEEE, 2024. http://dx.doi.org/10.23919/date58400.2024.10546819.
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Mitchell, Scott A., and David M. Day. "Flexible approximate counting." In the 15th Symposium. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/2076623.2076655.
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Andrei, Stefan, Gabriel Manolache, Roland H. C. Yap, and Victor Felea. "Approximate Satisfiability Counting." In 2007 Ninth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing. IEEE, 2007. http://dx.doi.org/10.1109/synasc.2007.16.
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Dyer, Martin. "Approximate counting by dynamic programming." In the thirty-fifth ACM symposium. New York, New York, USA: ACM Press, 2003. http://dx.doi.org/10.1145/780542.780643.
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Nelson, Jelani, and Huacheng Yu. "Optimal Bounds for Approximate Counting." In SIGMOD/PODS '22: International Conference on Management of Data. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3517804.3526225.
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Slota, George M., and Kamesh Madduri. "Fast Approximate Subgraph Counting and Enumeration." In 2013 42nd International Conference on Parallel Processing (ICPP). IEEE, 2013. http://dx.doi.org/10.1109/icpp.2013.30.
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Huber, Mark. "Exact sampling and approximate counting techniques." In the thirtieth annual ACM symposium. New York, New York, USA: ACM Press, 1998. http://dx.doi.org/10.1145/276698.276709.
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Chan, Timothy M., and Bryan T. Wilkinson. "Adaptive and Approximate Orthogonal Range Counting." In Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2013. http://dx.doi.org/10.1137/1.9781611973105.18.
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Ting, Daniel. "Streamed approximate counting of distinct elements." In KDD '14: The 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York, NY, USA: ACM, 2014. http://dx.doi.org/10.1145/2623330.2623669.
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Afshani, Peyman, and Timothy M. Chan. "On approximate range counting and depth." In the twenty-third annual symposium. New York, New York, USA: ACM Press, 2007. http://dx.doi.org/10.1145/1247069.1247129.
Full textReports on the topic "Approximate counting"
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Rosenkrantz, Walter A. Approximate Counting. A Martingale Approach. Fort Belvoir, VA: Defense Technical Information Center, February 1986. http://dx.doi.org/10.21236/ada170229.
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Baader, Franz, Pavlos Marantidis, and Alexander Okhotin. Approximately Solving Set Equations. Technische Universität Dresden, 2016. http://dx.doi.org/10.25368/2022.227.
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Unification with constants modulo the theory ACUI of an associative (A), commutative (C) and idempotent (I) binary function symbol with a unit (U) corresponds to solving a very simple type of set equations. It is well-known that solvability of systems of such equations can be decided in polynomial time by reducing it to satisfiability of propositional Horn formulae. Here we introduce a modified version of this problem by no longer requiring all equations to be completely solved, but allowing for a certain number of violations of the equations. We introduce three different ways of counting the number of violations, and investigate the complexity of the respective decision problem, i.e., the problem of deciding whether there is an assignment that solves the system with at most l violations for a given threshold value l.
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Davis, James C., John Cromartie, Tracey Farrigan, Brandon Genetin, Austin Sanders, and Justin B. Winikoff. Rural America at a glance. Washington, D.C: United States Department of Agriculture, Economic Research Service, November 2023. http://dx.doi.org/10.32747/2023.8134362.ers.
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The U.S. rural population is growing again after a decade of overall population loss, with growth of approximately a quarter percent from 2020 to 2022. This growth occurred because rural in-migration was larger than declines in the natural rate (the number of births compared with the number of deaths) of population growth. The rural population is also experiencing declines in poverty. In 2021, 9.7 percent fewer nonmetropolitan counties experienced persistent poverty (20 percent or more of the population had poverty level household incomes in each of the last four decennial Census years) compared with a decade earlier. Still, more than half of extremely low-income nonmetropolitan renter households experienced housing insecurity. This issue was particularly acute for American Indian or Alaska Native and Hispanic households. This report examines recent issues such as rural population and migration trends, poverty, housing insecurity, employment, and clean energy jobs. The report finds that rural employment levels and annual growth rates nearly returned to those seen in the years prior to the Coronavirus (COVID-19) pandemic. Finally, highlighting an emerging employment area of interest, approximately 1 percent of nonmetropolitan workers hold clean energy jobs
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Connell, Sean D. Geologic map of the Albuquerque - Rio Rancho metropolitan area and vicinity, Bernalillo and Sandoval counties, New Mexico. New Mexico Bureau of Geology and Mineral Resources, 2008. http://dx.doi.org/10.58799/gm-78.
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This is the most comprehensive compilation of the geology of the Albuquerque Basin to be printed in 30 years. The area covered by this new compilation, though not as large as the earlier map, is presented at a scale nearly four times the detail (1:50,000 scale compared to the earlier map's 1:190,000 scale). This new geologic map is a compilation of sixteen 7.5-min USGS quadrangle maps and encompasses an area from Tijeras Arroyo on the south to Santa Ana Mesa north of Santa Ana and San Felipe Pueblos, and from the crest of the Sandia Mountains westward across the Rio Grande and onto the Llano de Albuquerque (West Mesa) west of the city limits of Albuquerque and Rio Rancho.This geologic map graphically displays information on the distribution, character, orientation, and stratigraphic relationships of rock and surficial units and structural features. The map and accompanying cross sections were compiled from geologic field mapping and additionally from available aerial photography, satellite imagery, and drill-hole data (many published and unpublished reports, examination of lithologic cuttings, and from the interpretation of borehole geophysical log data).The map and accompanying cross sections represent the most informed interpretations of the known faults in the Albuquerque-Rio Rancho area that are presently available. In addition to the positions of many faults, the cross sections show the approximate vertical extent of poorly consolidated earth materials that may pose liquefaction hazards. This map also contains derivative maps selected to portray geologically important features in the metropolitan area, such as elevations of ground water levels, and the mostly buried boundary between generally poorly consolidated and saturated aquifer materials and the more consolidated underlying materials. The gravity anomaly map is a geophysical dataset that shows major geological structures buried beneath the metropolitan area and vicinity.
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Arhin, Stephen, Babin Manandhar, Hamdiat Baba Adam, and Adam Gatiba. Predicting Bus Travel Times in Washington, DC Using Artificial Neural Networks (ANNs). Mineta Transportation Institute, April 2021. http://dx.doi.org/10.31979/mti.2021.1943.
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Washington, DC is ranked second among cities in terms of highest public transit commuters in the United States, with approximately 9% of the working population using the Washington Metropolitan Area Transit Authority (WMATA) Metrobuses to commute. Deducing accurate travel times of these metrobuses is an important task for transit authorities to provide reliable service to its patrons. This study, using Artificial Neural Networks (ANN), developed prediction models for transit buses to assist decision-makers to improve service quality and patronage. For this study, we used six months of Automatic Vehicle Location (AVL) and Automatic Passenger Counting (APC) data for six Washington Metropolitan Area Transit Authority (WMATA) bus routes operating in Washington, DC. We developed regression models and Artificial Neural Network (ANN) models for predicting travel times of buses for different peak periods (AM, Mid-Day and PM). Our analysis included variables such as number of served bus stops, length of route between bus stops, average number of passengers in the bus, average dwell time of buses, and number of intersections between bus stops. We obtained ANN models for travel times by using approximation technique incorporating two separate algorithms: Quasi-Newton and Levenberg-Marquardt. The training strategy for neural network models involved feed forward and errorback processes that minimized the generated errors. We also evaluated the models with a Comparison of the Normalized Squared Errors (NSE). From the results, we observed that the travel times of buses and the dwell times at bus stops generally increased over time of the day. We gathered travel time equations for buses for the AM, Mid-Day and PM Peaks. The lowest NSE for the AM, Mid-Day and PM Peak periods corresponded to training processes using Quasi-Newton algorithm, which had 3, 2 and 5 perceptron layers, respectively. These prediction models could be adapted by transit agencies to provide the patrons with accurate travel time information at bus stops or online.
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Ahn, Yushin, and Richard Poythress. Impervious Surfaces from High Resolution Aerial Imagery: Cities in Fresno County. Mineta Transportation Institute, May 2024. http://dx.doi.org/10.31979/mti.2024.2257.
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This study investigates impervious surfaces — areas covered by materials with restricted water permeability, such as pavement, sidewalks, and parking lots—due to their crucial role in influencing water dynamics within urban landscapes. The impermeability of these surfaces disrupts natural water absorption processes, resulting in adverse environmental consequences such as increased flooding, erosion, and water pollution. The research employs impervious surface analysis, a method involving the mapping and analysis of these surfaces within specified study areas, including cities, counties, and census tracts. Remote sensing techniques, specifically satellites and aerial imagery, are commonly utilized for the identification and classification of impervious surfaces. In the context of Fresno County, diverse classification methods, encompassing pixel-based, object-based, and deep learning approaches, are employed to classify and evaluate impervious surfaces. Significantly, the deep learning classification method exhibits exceptional performance, achieving an impressive overall accuracy ranging between 85-92%. The study reveals that the estimated percentage of impervious surfaces in Fresno County cities approximates 45%, comparable to the characteristics of medium density residential areas. Noteworthy is the observation in the Fresno/Clovis city area, where the percentage of impervious surfaces escalated from 53% in 2010 (per EnviroAtlas) to 63% in 2020. This 10% increase over a decade closely aligns with concurrent population growth trends in the region. In conclusion, this research underscores the critical significance of comprehending and monitoring impervious surfaces due to their pivotal role in shaping the environmental quality and resilience of urban areas. The insights gleaned from this study provide valuable guidance for the development of effective land use planning and management strategies, specifically tailored to mitigate the adverse impacts of impervious surfaces on the environment and human well-being.
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Pfisterer, Nathan, and Nathan Beane. Estimating present value cost of invasive Emerald Ash Borer (Agrilus planipennis) on USACE project lands. Engineer Research and Development Center (U.S.), February 2023. http://dx.doi.org/10.21079/11681/46475.
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The US Army Corps of Engineers (USACE) is responsible for stewardship of approximately 12.5 million acres across the United States. USACE’s Environmental Stewardship program mission is to protect, preserve, and restore significant ecological resources on USACE project lands. Since the early 2000s, non-native and invasive Emerald Ash Borer (EAB) has killed hundreds of millions of ash trees in the US, becoming the most destructive and costly invasive forest insect in North America. This research effort estimates the cost of managing EAB damage to USACE projects including treatment, removal, or removal and replacement of dying/dead ash trees. The results suggest potential impact to more than 122,800 USACE project acres in currently infested counties including 181,000 ash trees. While not all damaged trees require removal, many USACE recreation sites have ash trees that pose an increased risk to humans and structures thus requiring removal of EAB infected trees. The widespread and pervasive impacts of EAB will have significant costs associated with removal and replacement of ash trees that could be hazardous to recreational users at the projects. Data from the United States Department of Agriculture (USDA), Forest Inventory and Analysis (FIA) database, and methods developed by Kovacs et al. (2010) were utilized to calculate yearly present value costs of EAB to USACE projects from 2006-2026. Overall EAB impacts are estimated at $121.6 million across 201 USACE projects evaluated in this study. Increased efforts to limit EAB spread and perform measures of control are warranted to reduce potential cost to USACE.
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Anderson, Zachary W., Greg N. McDonald, Elizabeth A. Balgord, and W. Adolph Yonkee. Interim Geologic Map of the Browns Hole Quadrangle, Weber and Cache Counties, Utah. Utah Geological Survey, December 2023. http://dx.doi.org/10.34191/ofr-760.
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The Browns Hole quadrangle is in Weber and Cache Counties of northern Utah and covers the eastern part of Ogden Valley, a rapidly developing area of the Wasatch Range. The Middle and South Forks of the Ogden River bisect the quadrangle and are important watersheds and recreational areas to the communities of Ogden Valley and the Wasatch Front. The towns of Huntsville and Eden are just west of the quadrangle, unincorporated communities with year-round residents are present throughout the quadrangle, and numerous summer-cabin communities are present in the eastern part of the quadrangle. A portion of Powder Mountain ski resort, which draws year-round visitation and recreation, is present in the northwest corner of the quadrangle. The quadrangle contains the Willard thrust, a major thrust fault with approximately 30 mi (50 km) of eastward displacement that was active during the Cretaceous-Eocene Sevier orogeny (Yonkee and others, 2019). In the quadrangle, the Willard thrust places Neoproterozoic through Ordovician strata in the hanging wall over a fault-bounded lozenge of Cambrian strata and footwall Jurassic and Triassic strata (see cross section on Plate 2). Neoproterozoic strata comprise a succession of mostly clastic rocks deposited during rifting of western North America and breakup of the supercontinent Rodinia (Yonkee and others, 2014). These rocks include the Cryogenian-age Perry Canyon and Maple Canyon Formations, and the Ediacaran-age Kelley Canyon Formation, Papoose Creek Formation, Caddy Canyon Quartzite, Inkom Formation, Mutual Formation, and Browns Hole Formation. The Browns Hole Formation is a sequence of interbedded volcaniclastic rock and basalt lava flows that provides the only radiometric age control in the quadrangle. Provow and others (2021) reported a ~610 Ma detrital apatite U-Pb age from volcaniclastic sandstone at the base of the formation, Crittenden and Wallace (1973) reported a 580 ± 14 Ma K-Ar hornblende age for a volcanic clast, and Verdel (2009) reported a 609 ± 25 Ma U-Pb apatite age for a basalt flow near the top of the formation. Cambrian strata in the hanging wall include a thick basal clastic sequence (Geertsen Canyon Quartzite) overlain by a thick sequence of interbedded limestone, shale, and dolomite (Langston, Ute, and Blacksmith Formations). Hanging wall rocks are deformed by Willard thrust-related structures, including the Browns Hole anticline, Maple Canyon thrust, and numerous smaller folds and minor faults. Footwall rocks of the Willard thrust include highly deformed Cambrian strata within a fault-bounded lozenge exposed in the southern part of the quadrangle, and Jurassic and Triassic rocks exposed just south of the quadrangle. The Paleocene-Eocene Wasatch Formation unconformably overlies older rocks and was deposited over considerable paleotopography developed during late stages of the Sevier orogeny. The southwest part of the quadrangle is cut by a southwest-dipping normal fault system that bounds the east side of Ogden Valley. This fault is interpreted to have experienced an early phase of slip during local late Eocene to Oligocene collapse of the Sevier belt and deposition of volcanic and volcaniclastic rocks (Norwood Tuff) exposed west of the quadrangle (Sorensen and Crittenden, 1979), and a younger phase of slip during Neogene Basin and Range extension (Zoback, 1983). Lacustrine deposits and shorelines of Pleistocene-age Lake Bonneville are present in the southwest corner of the quadrangle near the mouth of the South Fork of the Ogden River and record the highstand of Lake Bonneville (Oviatt, 2015). Pleistocene glacial deposits, present in the northwest corner of the map, are likely related to the Pinedale glaciation, commonly expressed by two moraine building episodes in the Wasatch Range (Quirk and others, 2020). Numerous incised alluvial deposits and geomorphic surfaces are present along major drainages and record pre- and post-Lake Bonneville aggradational and degradational alluvial and colluvial sequences. Mass-movement deposits, including historically active landslides, are present throughout the quadrangle. Crittenden (1972) mapped the Browns Hole quadrangle at 1:24,000 scale, which provided an excellent foundation for the general stratigraphy and structure, but the 1972 map lacked important details of unconsolidated surficial units. As part of 1:62,500 scale mapping of the Ogden 30'x60' quadrangle, Coogan and King (2016) updated stratigraphic nomenclature, revised some contacts, and added more details for surficial units. For this map, we utilized new techniques for data acquisition and analysis to delineate surficial deposits, bedrock contacts, and faults more accurately and precisely. Mapping and field data collection were largely done in 2021–2022 using a combination of GPS-enabled tablets equipped with georectified aerial imagery (U.S. Department of Agriculture [USDA] National Agriculture Imagery Program [NAIP], 2009), orthoimagery (Utah Geospatial Resource Center [UGRC] State Geographic Information Database, 2018b, 2018c; 2021a, 2021b), and lidar data (UGRC State Geographic Information Database, 2006; 2011; 2013–2014; 2018a), previously published geologic maps, topographic maps, and applications for digital attitude collection. We also used hand-held GPS units, Brunton compasses, and field notebooks to collect geologic data. Field data were transferred to a Geographic Information System (GIS), where the map was compiled and completed.
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Pesis, Edna, Elizabeth J. Mitcham, Susan E. Ebeler, and Amnon Lers. Application of Pre-storage Short Anaerobiosis to Alleviate Superficial Scald and Bitter Pit in Granny Smith Apples. United States Department of Agriculture, January 2013. http://dx.doi.org/10.32747/2013.7593394.bard.
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There is increased demand for high quality fruit produced and marketed with reduced chemical inputs to minimize toxic effects on human health and the environment. Granny Smith (GS) apple quality is reduced by two major physiological disorders, superficial scald and bitter pit (BP). These disorders cause great loss to apple growers worldwide. Superficial scald is commonly controlled by chemical treatments, mainly the antioxidant diphenylamine (DPA) and/or the ethylene action inhibitor, 1-methylcyclopropene (1–MCP). Both chemicals are ineffective in controlling bitter pit incidence. We proposed to investigate the beneficial use of non-chemical, abiotic stress with low O2 (LO2) applied for 10d at 20°C on GS apple fruit. During the project we expanded the treatment to more apple cultivars, Golden Delicious (GD) and Starking Delicious (SD) and another pome fruit, the pear. Apple and pear have similar physiological disorders that develop during cold storage and we examined if the LO2 treatment would also be effective on pear. Application of 0.5% LO2 atmosphere for 10d at 20°C or 500ppb 1-MCP at 20°C prior to cold storage at 0°C, was effective in reducing superficial scald in GS apple. Moreover, LO2 pretreatment was also effective in reducing bitter pit (BP) development in California GS and Israeli GD and SD apples The BP symptoms in GS from California were much more prominent, so the effect of LO2 was more dramatic than the effect on the Israeli cvs. GD and SD, nevertheless the LO2 treatment showed the same trend in all cultivars in reducing BP. The LO2 and 1-MCP -treated fruit exhibited lower levels of ethylene, - farnesene and its oxidation product, 6-methyl-5-hepten-2-one (MHO), as determined by SPME/GC-MS analysis. In addition, LO2 pretreatment applied to California Bartlett or Israeli Spadona pears was effective in reducing superficial scald, senescent scald and internal breakdown after 4 m of cold storage at 0°C. For GS apple, low-temperature storage resulted in oxidative stress and chilling injury, caused by increased production of superoxide anions which in turn led to the generation of other dangerous reactive oxygen species (ROS). Using confocal laser-scanning microscopy and H2O2 measurements of apple peel, we observed ROS accumulation in control fruit, while negligible amounts were found in LO2 and 1-MCP treated fruit. Gene-expression levels of ROS-scavenging enzymes were induced by the various pretreatments: catalase was induced by LO2 treatment, whereas Mn superoxide dismutase was induced by 1-MCP treatment. We assume that LO2 and 1-MCP pretreated fruit remained healthier due to reduced production of ethylene and reactive oxygen substances, such as MHO, during cold storage. The LO2-treated apple exhibited greener peel and firmer fruit after 6 m of cold storage, and the fruit had high crispiness leading to high taste preference. In both pear cultivars, the LO2 treatment led to a reduction in internal breakdown and browning around the seed cavity. We tested the LO2 pre-storage treatment on a semi-commercial scale that would be applicable to a small organic grower by sealing the fruit within the plastic field bins. The treatment was most effective with a continuous flow of nitrogen through the bins; however, a single 6 hour flush of nitrogen was also fairly effective. In addition, we determined that it was very important to have the oxygen levels below 0.5% for approximately 10 days to achieve good scald control, not counting the time required to reduce the oxygen concentration. Our LO2 technology has been proven in this project to be effective in reducing several physiological disorders developed in pome fruit during cold storage. We hope that our non-chemical treatment which is friendly to the environment will be used in the near future for the organic apple and pear industry. The next step should be an analysis of the cost-benefits and commercial feasibility.