Algorithmic Aspects of Acyclic Edge Colorings

Abstract. A proper coloring of the edges of a graph G is called acyclic if there is no two-colored cycle in G . The acyclic edge chromatic number of G , denoted by a'(G) , is the least number of colors in an acyclic edge coloring of G . For certain graphs G , a'(G)\geq Δ(G)+2 where Δ(G) is the maximum degree in G . It is known that a'(G)≤ Δ + 2 for almost all Δ -regular graphs, including all Δ -regular graphs whose girth is at least cΔ log Δ . We prove that determining the acyclic edge chromatic number of an arbitrary graph is an NP-complete problem. For graphs G with sufficiently large girth in terms of Δ(G) , we present deterministic polynomial-time algorithms that color the edges of G acyclically using at most Δ(G)+2 colors.     

The educational electronic book as a tool for supporting children’s emergent literacy in low versus middle SES groups

The effects of an educational electronic book (e-book) on 149 five- to six-year-old kindergarteners’ emergent literacy levels were researched in two SES groups: low (LSES) (79 children) vs. middle (MSES) (70 children). In each SES group, children were randomly assigned to four groups. Three groups were assigned to work individually in one of three e-book activity modes: “Read story only”, “Read with dictionary”, or “Read and play” during three similar activity sessions and the fourth group served as a control which received the regular program of the kindergarten. Pre- and post-intervention emergent literacy measures included word meaning, word recognition, and phonological awareness. Results show that word meaning of children from both middle and low SES improved following the educational e-book activity, regardless of mode. Second, LSES children’s emergent literacy levels showed relatively greater improvement rates than did those of the MSES children. Third, children in the “Read with dictionary” and “Read and play” activity modes showed more improvement in their emergent literacy levels than did those in the “Read story only” mode. Implications for future research and for education are discussed.     

Evaluation of Face Datasets as Tools for Assessing the Performance of Face Recognition Methods

Face datasets are considered a primary tool for evaluating the efficacy of face recognition methods. Here we show that in many of the commonly used face datasets, face images can be recognized accurately at a rate significantly higher than random even when no face, hair or clothes features appear in the image. The experiments were done by cutting a small background area from each face image, so that each face dataset provided a new image dataset which included only seemingly blank images. Then, an image classification method was used in order to check the classification accuracy. Experimental results show that the classification accuracy ranged between 13.5% (color FERET) to 99% (YaleB). These results indicate that the performance of face recognition methods measured using face image datasets may be biased. Compilable source code used for this experiment is freely available for download via the Internet.     

Adaptive pattern recognition with rotation, scale, and shift invariance

Mutually orthogonal pattern distortions are handled by an adaptive optical recognition system. A double-channel system is presented that implements pattern recognition with rotation, scale, and shift invariance. The recognition process is based on a two-stage operation: An object-independent determination of one distortion parameter (the scale, in the example presented here) is performed, and then the recognition is completed by a shift- and rotation-invariant optical correlator that is adapted to the measured parameter. Thus, complete invariance to three distortion parameters is achieved by the combination of two channels. The overall process is performed efficiently and can be executed in real time.     

Derandomized graph products

Berman and Schnitger gave a randomized reduction from approximating MAX-SNP problems within constant factors arbitrarily close to 1 to approximating clique within a factor ofn (for some ). This reduction was further studied by Blum, who gave it the namerandomized graph products. We show that this reduction can be made deterministic (derandomized), using random walks on expander graphs. The main technical contribution of this paper is in proving a lower bound for the probability that all steps of a random walk stay within a specified set of vertices of a graph. (Previous work was mainly concerned with upper bounds for this probability.) This lower bound extends also to the case where different sets of vertices are specified for different time steps of the walk.     

Design of UDE‐based controllers from their two‐degree‐of‐freedom nature

The control algorithm based on the uncertainty and disturbance estimator (UDE) is a robust control strategy and has received wide attention in recent years. In this paper, the two‐degree‐of‐freedom nature of UDE‐based controllers is revealed. The set‐point tracking response is determined by the reference model, whereas the disturbance response and robustness are determined by the error feedback gain and the filter introduced to estimate the uncertainty and disturbances. It is also revealed that the error dynamics of the system is determined by two filters, of which one is determined by the error feedback gain and the other is determined by the filter introduced to estimate the uncertainty and disturbances. The design of these two filters are decoupled in the frequency domain. Moreover, after introducing the UDE‐based control, the Laplace transform can be applied to some time‐varying systems for analysis and design because all the time‐varying parts are lumped into a signal. It has been shown that, in addition to the known advantages over the time‐delay control, the UDE‐based control also brings better performance than the time‐delay control under the same conditions. Design examples and simulation results are given to demonstrate the findings. Copyright © 2010 John Wiley & Sons, Ltd.     

Context‐Dependent Crowd Evaluation

Many times, even if a crowd simulation looks good in general, there could be some specific individual behaviors which do not seem correct. Spotting such problems manually can become tedious, but ignoring them may harm the simulation's credibility. In this paper we present a data‐driven approach for evaluating the behaviors of individuals within a simulated crowd. Based on video‐footage of a real crowd, a database of behavior examples is generated. Given a simulation of a crowd, an analog analysis is performed on it, defining a set of queries, which are matched by a similarity function to the database examples. The results offer a possible objective answer to the question of how similar are the simulated individual behaviors to real observed behaviors. Moreover, by changing the video input one can change the context of evaluation. We show several examples of evaluating simulated crowds produced using different techniques and comprising of dense crowds, sparse crowds and flocks.     

Matching with don't-cares and a small number of mismatches

In matching with don't-cares and k mismatches we are given a pattern of length m and a text of length n, both of which may contain don't-cares (a symbol that matches all symbols), and the goal is to find all locations in the text that match the pattern with at most k mismatches, where k is a parameter. We present new algorithms that solve this problem using a combination of convolutions and a dynamic programming procedure. We give randomized and deterministic solutions that run in time O(nk²logm) and O(nk³logm), respectively, and are faster than the most efficient extant methods for small values of k. Our deterministic algorithm is the first to obtain an O(polylog(k)⋅nlogm) running time.     

The Meteor metric for automatic evaluation of machine translation

The Meteor Automatic Metric for Machine Translation evaluation, originally developed and released in 2004, was designed with the explicit goal of producing sentence-level scores which correlate well with human judgments of translation quality. Several key design decisions were incorporated into Meteor in support of this goal. In contrast with IBM’s Bleu, which uses only precision-based features, Meteor uses and emphasizes recall in addition to precision, a property that has been confirmed by several metrics as being critical for high correlation with human judgments. Meteor also addresses the problem of reference translation variability by utilizing flexible word matching, allowing for morphological variants and synonyms to be taken into account as legitimate correspondences. Furthermore, the feature ingredients within Meteor are parameterized, allowing for the tuning of the metric’s free parameters in search of values that result in optimal correlation with human judgments. Optimal parameters can be separately tuned for different types of human judgments and for different languages. We discuss the initial design of the Meteor metric, subsequent improvements, and performance in several independent evaluations in recent years.     

Guaranteeing the Diversity of Number Generators

A major problem in using iterative number generators of the form x_i=f(x_i−1) is that they can enter unexpectedly short cycles. This is hard to analyze when the generator is designed, hard to detect in real time when the generator is used, and can have devastating cryptanalytic implications. In this paper we define a measure of security, called sequence diversity, which generalizes the notion of cycle-length for noniterative generators. We then introduce the class of counter-assisted generators and show how to turn any iterative generator (even a bad one designed or seeded by an adversary) into a counter-assisted generator with a provably high diversity, without reducing the quality of generators which are already cryptographically strong.