A celebrated theorem of Friedgut says that every function f : {0, 1}n → {0, 1} can be approximated by a function g : {0, 1}n → {0, 1} with , which depends only on eO(If / ε) variables, where If is the sum of the influences of the variables of f. Dinur and Friedgut later showed that this statement also holds if we replace the discrete domain {0, 1}n with the continuous domain [0, 1]n, under the extra assumption that f is increasing. They conjectured that the condition of monotonicity is unnecessary and can be removed.

We show that certain constant-depth decision trees provide counter-examples to the Dinur–Friedgut conjecture. This suggests a reformulation of the conjecture in which the function g : [0, 1]n → {0, 1}, instead of depending on a small number of variables, has a decision tree of small depth. In fact we prove this reformulation by showing that the depth of the decision tree of g can be bounded by eO(If / ε2).

Furthermore, we consider a second notion of the influence of a variable, and study the functions that have bounded total influence in this sense. We use a theorem of Bourgain to show that these functions have certain properties. We also study the relation between the two different notions of influence.

This article describes the influence of tool and task design on student interaction in language learning at a distance. Interaction in a multimodal desktop video conferencing environment, FlashMeeting, is analyzed from an ecological perspective with two main foci: participation rates and conversational feedback strategies. The quantitative analysis of participation rates shows that as far as verbal interaction is concerned, multimodality did not have an equalizing effect in this context, contradicting previous research on multimodal student interaction. Additionally, the qualitative analysis of conversational feedback strategies shows that whereas some multimodal strategies were employed, the students did not manage to fully act upon the communicative affordances of the tool, as the feedback ratio during and after the often long broadcasts was relatively low. These findings are related to task and tool design and the article discusses how design improvements in these areas might result in a more constructive language learning ecology.

Let r ≥ 3 and (c/rr)r log n ≥ 1. If G is a graph of order n and its largest eigenvalue μ(G) satisfiesthen G contains a complete r-partite subgraph with r − 1 parts of size ⌊(c/rr)r log n⌋ and one part of size greater than n1−cr−1.

This result implies the Erdős–Stone–Bollobás theorem, the essential quantitative form of the Erdős–Stone theorem. Another easy consequence is that if F1, F2, . . . are r-chromatic graphs satisfying v(Fn) = o(log n), then

Space robotic systems are expected to play an increasingly important role in the future. Unlike on the earth, space operations require the ability to work in the unstructured environment. Some autonomous behaviors are necessary to perform complex and difficult tasks in space. This level of autonomy relies not only on vision, force, torque, and tactile sensors, but also the advanced planning and decision capabilities. In this paper, the authors study the autonomous target capturing from the issues of theory and experiments. Firstly, we deduce the kinematic and dynamic equations of space robotic system. Secondly, the visual measurement model of hand–eye camera is created, and the image processing algorithms to extract the target features are introduced. Thirdly, we propose an autonomous trajectory planning method, directly using the 2D image features. The method predicts the target motion, plans the end-effector's velocities and solves the inverse kinematic equations using practical approach to avoid the dynamic singularities. At last, numeric simulation and experiment results are given. The ground experiment system is set up based on the concept of dynamic simulation and kinematic equivalence. With the system, the experiments of autonomous capturing a target by a free-floating space robot, composed of a 6-DOF manipulator and a satellite as its base, are conducted, and the results validate the proposed algorithm.

This paper describes a study of the computer essay-scoring program BETSY. While the use of computers in rating written scripts has been criticised in some quarters for lacking transparency or lack of fit with how human raters rate written scripts, a number of essay rating programs are available commercially, many of which claim to offer comparable reliability with human raters. Much of the validation of such programs has focused on native-speaking tertiary-level students writing in subject content areas. Instead of content areas with native-speakers, the data for this study is drawn from a representative sample of scripts from an English as a second language (ESL) Year 11 public examination in Hong Kong. The scripts (900 in total) are taken from a writing test consisting of three topics (300 scripts per topic), each representing a different genre. Results in the study show good correlations between human raters’ scores and the program BETSY. A rater discrepancy rate, where scripts need to be re-marked because of disagreement between two raters, emerged at levels broadly comparable with those derived from discrepancies between paired human raters. Little difference was apparent in the ratings of test takers on the three genres. The paper concludes that while computer essay-scoring programs may appear to rate inside a ‘black box’ with concomitant lack of transparency, they do have potential to act as a third rater, time-saving assessment tool. And as technology develops and rating becomes more transparent, so will their acceptability.

This paper describes the development of a desktop robotic system that enables the plug-and-play function through the USB (universal serial bus) port of a personal computer (PC). Thus a new kind of desktop PC peripheral is invented that has programmable manipulability. The robotic system is realized on an internally distributed control structure that facilitates higher system reliability. A PID control algorithm is implemented on a prototype of the proposed system, to demonstrate the system's ability to implement feedback control. Experimental results show the performance and properties of the proposed system.

Let k3reg(n, d) be the minimum number of triangles in d-regular graphs with n vertices. We find the exact value of k3reg(n, d) for d between and n/2. In addition, we identify the structure of the extremal graphs.

The inverse kinematics of a 12 degrees-of-freedom (DOFs) biped robot is formulated in terms of certain parameters. The biped walking gaits are developed using the parameters. The walking gaits are optimized using genetic algorithm (GA). The optimization is carried out considering relative importance of stability margin and walking speed. The stability margin depends on the position of zero-moment-point (ZMP) while walking speed varies with step-size. The ZMP is computed by an approximation-based method which does not require system dynamics. The optimal walking gaits are experimentally realized on a biped robot.

Expressions for the distribution, density, and percentiles of weighted sums of Rayleigh random variables are given, including the tilted Edgeworth expansion.

We introduce and investigate a new type of decision problem related to multiclass fluid networks. Optimization problems arising from fluid networks with known parameters have been studied extensively in the queueing, scheduling, and optimization literature. In this article, we explore the makespan problem in fluid networks, with the assumption that the parameters are known only through a probability distribution. Thus, the decision maker does not have complete knowledge of the parameters in advance. This problem can be formulated as a stochastic nonlinear program. We provide necessary and sufficient feasibility conditions for this class of problems. We also derive a number of other structural results that can be used in developing effective computational procedures for solving stochastic fluid makespan problems.

In this article we study the joint optimization of finished goods inventory and pricing in a make-to-stock production system with long-run average profit criterion. The production time is random with controllable rate and the demand is Markovian with rate depending on the sale price. The objective is to dynamically adjust the production rate and the sale price to maximize the long-run average profit. We obtain the optimal dynamic pricing and production control policy and present an efficient bisection algorithm for computing the policy parameters.

We consider order statistics corresponding to X1, …, Xn, where , i = 1, …, n, ℰ1, …, ℰn are independent and identically distributed exponentials with mean 1, and λ1, …, λn are possibly dependent, possibly nonidentically distributed, positive random variables, with . Thus, λ1, …, λn, can be interpreted as random failure rates, and their dependency might be due to common environmental factors.

Congestion and its uncertainty are big factors affecting customers’ decision to join a queue or balk. In a queueing system, congestion itself is resulted from the aggregate joining behavior of other customers. Therefore, the property of the whole group of arriving customers affects the equilibrium behavior of the queue. In this paper, we assume each individual customer has a utility function which includes a basic cost function, common to all customers, and a customer-specific weight measuring sensitivity to delay. We investigate the impacts on the average customer utility and the throughput of the queueing system of different cost functions and weight distributions. Specifically, we compare systems where these parameters are related by various stochastic orders, under different information scenarios. We also explore the relationship between customer characteristics and the value of information.

We study the value of multistage advance demand information (MADI) in a production system in which customers place an order in advance of their actual need, and each order goes through multiple stages before it becomes due. Any order that is not immediately filled at its due date will be backordered. The producer must decide whether or not to produce based on real-time information regarding current and future orders. We formulate the problem as a Markov decision process and analyze the impact of the demand information on the production policy and the cost. We show that the optimal production policy is a state-dependent base-stock policy, and we show that it has certain monotonicity properties. We also introduce a simple heuristic policy that is significantly easier to compute and that inherits the structural properties of the optimal policy. In addition, we show that its base-stock levels bound those of the socially optimal policy. Numerical study identifies the conditions under which MADI is most beneficial and shows that the heuristic performs almost as well as the optimal policy when MADI is most beneficial.

In this article we study Markov-modulated queues with and without jumps. These queuing models arise naturally in production-inventory systems with and without an external supplier. We show an interesting decomposition property that relates the equilibrium state distributions in these two systems and present an integrated warranty-inventory management model as an application.

This paper presents a new approach to the management of the environmental map for mobile robots in dynamic environments. The environmental map is built of primitive features, such as lines, points, and even circles, extracted from ambiguous data captured by the robot's sonar sensor ring. The feature map must be managed because the indoor surroundings where mobile robots operate are continuously changing due to nonstationary objects, such as wastebaskets, tables, and people. The features are processed by trimming, division, or removal, depending on the dynamic circumstances. All processing refers to the occupancy probabilities of grid squares generated for the map features. The occupancy probabilities of the squares are updated using the Bayesian updating model with the sonar sensor data. Experimental results demonstrate the validity of the proposed method.

This paper studies the parameters contained in the truncated Fourier series (TFS) formulation for bipedal walking balance control. Using the TFS generated lateral motion reference, 3D bipedal walking can be directly achieved without any parameter adjustment. Furthermore, the potential of this TFS formulation for motion balance control has also been investigated. One more motion balance strategy is developed through the reinforcement learning, which adjusts the motion's reference trajectory according to the selected dynamic feedback in real time. Dynamic simulation results of the presented balance control method show that the resulting motion can be constrained periodical and long-distance 3D bipedal walking motions are achievable.