Drought Severity Assessment Based on Bivariate Probability Analysis

Conventionally drought severity is assessed based on drought indices. Recently the Reconnaissance Drought Index (RDI) was proposed to assess drought severity based on the precipitation to potential evapotranspiration ratio (P/PET). In this paper RDI is studied as a bivariate index under a set of assumptions and simplifications. The paper presents a simple computational procedure for estimating the P/PET ratio for selected reference periods varying from 3 to 12 months, for any return period of drought. Alternatively, based on this procedure, the severity of any drought episode is rationally assessed. A bivariate probability analysis is employed based on the assumption that P and PET values are normally distributed and often negatively correlated. Examples for the application of the proposed procedure are presented using data from several meteorological stations in Greece. It is shown that the assumption of normality of both P and PET holds for long periods at all examined stations.     

Autobiographical Accounts of Students' Experiences Learning Mathematics: A Review

ABSTRACT

In this article, we review published literature that draws on autobiographical accounts of students' experiences learning mathematics. We summarize the main findings of the target literature and present recommendations for further research that will extend this field. Our review indicates that autobiographical and narrative methodological approaches have the potential to occasion important advances in our knowledge of students' experiences learning mathematics. However, relative to accounts of preservice teacher learning, there is a paucity of published research that documents the mathematics learning experiences of kindergarten to Grade 12 students.     

Integrating job parallelism in real-time scheduling theory

We investigate the global scheduling of sporadic, implicit deadline, real-time task systems on multiprocessor platforms. We provide a task model which integrates job parallelism. We prove that the time-complexity of the feasibility problem of these systems is linear relatively to the number of (sporadic) tasks for a fixed number of processors. We propose a scheduling algorithm theoretically optimal (i.e., preemptions and migrations neglected). Moreover, we provide an exact feasibility utilization bound. Lastly, we propose a technique to limit the number of migrations and preemptions.     

Optimally Adaptive Integration of Univariate Lipschitz Functions

We consider the problem of approximately integrating a Lipschitz function f (with a known Lipschitz constant) over an interval. The goal is to achieve an additive error of at most ε using as few samples of f as possible. We use the adaptive framework: on all problem instances an adaptive algorithm should perform almost as well as the best possible algorithm tuned for the particular problem instance. We distinguish between and , the performances of the best possible deterministic and randomized algorithms, respectively. We give a deterministic algorithm that uses samples and show that an asymptotically better algorithm is impossible. However, any deterministic algorithm requires samples on some problem instance. By combining a deterministic adaptive algorithm and Monte Carlo sampling with variance reduction, we give an algorithm that uses at most samples. We also show that any algorithm requires samples in expectation on some problem instance (f,ε), which proves that our algorithm is optimal.     

Path Hitting in Acyclic Graphs

An instance of the path hitting problem consists of two families of paths, and ℋ, in a common undirected graph, where each path in ℋ is associated with a non-negative cost. We refer to and ℋ as the sets of demand and hitting paths, respectively. When p∈ℋ and share at least one mutual edge, we say that p hits q. The objective is to find a minimum cost subset of ℋ whose members collectively hit those of . In this paper we provide constant factor approximation algorithms for path hitting, confined to instances in which the underlying graph is a tree, a spider, or a star. Although such restricted settings may appear to be very simple, we demonstrate that they still capture some of the most basic covering problems in graphs. Our approach combines several novel ideas: We extend the algorithm of Garg, Vazirani and Yannakakis (Algorithmica, 18:3–20, 1997) for approximate multicuts and multicommodity flows in trees to prove new integrality properties; we present a reduction that involves multiple calls to this extended algorithm; and we introduce a polynomial-time solvable variant of the edge cover problem, which may be of independent interest. An extended abstract of this paper appeared in Proceedings of the 14th Annual European Symposium on Algorithms, 2006. This work is part of D. Segev’s Ph.D. thesis prepared at Tel-Aviv University under the supervision of Prof. Refael Hassin.     

Measuring ranked list robustness for query performance prediction

We introduce the notion of ranking robustness, which refers to a property of a ranked list of documents that indicates how stable the ranking is in the presence of uncertainty in the ranked documents. We propose a statistical measure called the robustness score to quantify this notion. Our initial motivation for measuring ranking robustness is to predict topic difficulty for content-based queries in the ad-hoc retrieval task. Our results demonstrate that the robustness score is positively and consistently correlation with average precision of content-based queries across a variety of TREC test collections. Though our focus is on prediction under the ad-hoc retrieval task, we observe an interesting negative correlation with query performance when our technique is applied to named-page finding queries, which are a fundamentally different kind of queries. A side effect of this different behavior of the robustness score between the two types of queries is that the robustness score is also found to be a good feature for query classification.      

A scalable algorithm for mining maximal frequent sequences using a sample

In this paper, we propose an efficient scalable algorithm for mining Maximal Sequential Patterns using Sampling (MSPS). The MSPS algorithm reduces much more search space than other algorithms because both the subsequence infrequency-based pruning and the supersequence frequency-based pruning are applied. In MSPS, a sampling technique is used to identify long frequent sequences earlier, instead of enumerating all their subsequences. We propose how to adjust the user-specified minimum support level for mining a sample of the database to achieve better overall performance. This method makes sampling more efficient when the minimum support is small. A signature-based method and a hash-based method are developed for the subsequence infrequency-based pruning when the seed set of frequent sequences for the candidate generation is too big to be loaded into memory. A prefix tree structure is developed to count the candidate sequences of different sizes during the database scanning, and it also facilitates the customer sequence trimming. Our experiments showed MSPS has very good performance and better scalability than other algorithms. Congnan Luo received the B.E. degree in Computer Science from Tsinghua University, Beijing, P.R. China, in 1997, the M.S. degree in Computer Science from the Institute of Software, Chinese Academy of Sciences, Beijing, P.R. China, in 2000, and the Ph.D. degree in Computer Science and Engineering from Wright State University, Dayton, OH, in 2006. Currently he is a technical staff at the Teradata division of NCR in San Diego, CA, and his research interests include data mining, machine learning, and databases. Soon M. Chung received the B.S. degree in Electronic Engineering from Seoul National University, Korea, in 1979, the M.S. degree in Electrical Engineering from Korea Advanced Institute of Science and Technology, Korea, in 1981, and the Ph.D. degree in Computer Engineering from Syracuse University, Syracuse, New York, in 1990. He is currently a Professor in the Department of Computer Science and Engineering at Wright State University, Dayton, OH. His research interests include database, data mining, Grid computing, text mining, XML, and parallel and distributed processing.     

A survey on algorithms for mining frequent itemsets over data streams

The increasing prominence of data streams arising in a wide range of advanced applications such as fraud detection and trend learning has led to the study of online mining of frequent itemsets (FIs). Unlike mining static databases, mining data streams poses many new challenges. In addition to the one-scan nature, the unbounded memory requirement and the high data arrival rate of data streams, the combinatorial explosion of itemsets exacerbates the mining task. The high complexity of the FI mining problem hinders the application of the stream mining techniques. We recognize that a critical review of existing techniques is needed in order to design and develop efficient mining algorithms and data structures that are able to match the processing rate of the mining with the high arrival rate of data streams. Within a unifying set of notations and terminologies, we describe in this paper the efforts and main techniques for mining data streams and present a comprehensive survey of a number of the state-of-the-art algorithms on mining frequent itemsets over data streams. We classify the stream-mining techniques into two categories based on the window model that they adopt in order to provide insights into how and why the techniques are useful. Then, we further analyze the algorithms according to whether they are exact or approximate and, for approximate approaches, whether they are false-positive or false-negative. We also discuss various interesting issues, including the merits and limitations in existing research and substantive areas for future research.     

Non-negative matrix factorization for semi-supervised data clustering

Traditional clustering algorithms are inapplicable to many real-world problems where limited knowledge from domain experts is available. Incorporating the domain knowledge can guide a clustering algorithm, consequently improving the quality of clustering. In this paper, we propose SS-NMF: a semi-supervised non-negative matrix factorization framework for data clustering. In SS-NMF, users are able to provide supervision for clustering in terms of pairwise constraints on a few data objects specifying whether they “must” or “cannot” be clustered together. Through an iterative algorithm, we perform symmetric tri-factorization of the data similarity matrix to infer the clusters. Theoretically, we show the correctness and convergence of SS-NMF. Moveover, we show that SS-NMF provides a general framework for semi-supervised clustering. Existing approaches can be considered as special cases of it. Through extensive experiments conducted on publicly available datasets, we demonstrate the superior performance of SS-NMF for clustering.

Fixed-Parameter Complexity of Minimum Profile Problems

The profile of a graph is an integer-valued parameter defined via vertex orderings; it is known that the profile of a graph equals the smallest number of edges of an interval supergraph. Since computing the profile of a graph is an NP-hard problem, we consider parameterized versions of the problem. Namely, we study the problem of deciding whether the profile of a connected graph of order n is at most n−1+k, considering k as the parameter; this is a parameterization above guaranteed value, since n−1 is a tight lower bound for the profile. We present two fixed-parameter algorithms for this problem. The first algorithm is based on a forbidden subgraph characterization of interval graphs. The second algorithm is based on two simple kernelization rules which allow us to produce a kernel with linear number of vertices and edges. For showing the correctness of the second algorithm we need to establish structural properties of graphs with small profile which are of independent interest. A preliminary version of the paper is published in Proc. IWPEC 2006, LNCS vol. 4169, 60–71.