A d-simplex is a collection of d + 1 sets such that every d of them has non-empty intersection and the intersection of all of them is empty. Fix k ≥ d + 2 ≥ 3 and let be a family of k-element subsets of an n-element set that contains no d-simplex. We prove that if , then there is a vertex x of such that the number of sets in omitting x is o(nk−1) (here o(1)→ 0 and n → ∞). A similar result when n/k is bounded from above was recently proved in [10].

Our main result is actually stronger, and implies that if for any ϵ < 0 and n sufficiently large, then contains d + 2 sets A, A1, . . . ,Ad+1 such that the Ais form a d-simplex, and A contains an element of ∩j≠iAj for each i. This generalizes, in asymptotic form, a recent result of Vestraëte and the first author [18], who proved it for d = 1, ϵ = 0 and n ≥ 2k.

An instance of a size-n stable marriage problem involves n men and n women, each individually ranking all members of opposite sex in order of preference as a potential marriage partner. A complete matching, a set of n marriages, is called stable if no unmatched man and woman prefer each other to their partners in the matching. It is known that, for every instance of marriage partner preferences, there exists at least one stable matching, and that there are instances with exponentially many stable matchings. Our focus is on a random instance chosen uniformly from among all (n!)2n possible instances. The second author had proved that the expected number of stable marriages is of order nlnn, while its likely value is of order n1/2−o(1) at least. In this paper the second moment of that number is shown to be of order (nlnn)2. The combination of the two moment estimates implies that the fraction of problem instances with roughly cnlnn solutions is at least 0.84. Whether this fraction is asymptotic to 1 remains an open question.

This paper presents a distributed multiple mobile robots framework which allows programming and control of virtual and real mobile robots. The system provides the map building, path planning, robot task planning, simulation, and actual robot control functions in an indoor environment. Users can program the virtual robots in a customized simulation environment and check the performance of execution, i.e., if the simulation result is satisfying, users can download the code to a real robot. The paper focuses on the distributed architecture and key technologies of virtual robots simulation and control of real robots. A method for construction and transfer of a key index value (which stores the robot configuration) is proposed. Using this method, only the robot key configuration index is needed to build the robot in the virtual environment. This results in reduced network load and improved real time performance of the distributed system. Experiments were conducted to compare the performance of the proposed system with the performance of a centralized system. The results show that the distributed system uses less system resources and has better real time performance. What is more, this framework has been applied to Yaskawa's robot “SmartPal.” The simulation and experiment results show that our robotic framework can simulate and control the robot to perform complex tasks.

This paper demonstrates how numerical optimization techniques can efficiently be used to create self-stable running motions for a human-like robot model. Exploitation of self-stability is considered to be a crucial factor for biological running and might be the key for success to make bipedal and humanoid robots run in the future. We investigate a two-dimensional simulation model of running with nine bodies (trunk, thighs, shanks, feet, and arms) powered by external moments at all internal joints. Using efficient optimal control techniques and stability optimization, we were able to determine model parameters and actuator inputs that lead to fully open-loop stable running motions.

A collection of permutation classes is exhibited whose growth rates form a perfect set, thereby refuting some conjectures of Balogh, Bollobás and Morris.

This paper describes a complete laser-based approach for tracking the pose of a robot in a dynamic environment. The main novelty of this approach is that the matching between consecutively acquired scans is achieved using their associated curvature-based representations. The proposed scan matching algorithm consists of three stages. Firstly, the whole raw laser data is segmented into groups of consecutive range readings using a distance-based criterion and the curvature function for each group is computed. Then, this set of curvature functions is matched to the set of curvature functions associated to the previously acquired laser scan. Finally, characteristic points of pairwise curvature functions are matched and used to correctly obtain the best local alignment between consecutive scans. A closed form solution is employed for computing the optimal transformation and minimizing the robot pose shift error without iterations. Thus, the system is outstanding in terms of accuracy and computation time. The implemented algorithm is evaluated and compared to three state of the art scan matching approaches.

The Stewart platform manipulator is a fully kinematic linkage system that has major mechanical differences from typical serial link robots. It is a six-axis parallel robot manipulator with a high force-to-weight ratio and good positioning accuracy that exceeds that of a conventional serial link robot arm. This study examines the dynamic equations and control methodology for a Stewart platform. Because manual symbolic expansion of Stewart platform robot dynamic equations is tedious, time-consuming, and prone to errors, an automated derivation process is highly desired. The main goal of this work is to present an efficient procedure for computer generation of dynamic equations for a Stewart platform manipulator. As MATLAB has a powerful signal processing toolbox along with symbolic processing capabilities and is widely used as a common technical computing environment in many universities and research laboratories, the objective of this study was to develop a MATLAB-based approach for symbolic computation for a parallel linked robot. Additionally, a computed-torque control methodology is utilized for such a structure. Simulation results demonstrate the effectiveness of the proposed control methodology.

This paper develops a logical language for representing probabilistic causal laws. Our interest in such a language is two-fold. First, it can be motivated as a fundamental study of the representation of causal knowledge. Causality has an inherent dynamic aspect, which has been studied at the semantical level by Shafer in his framework of probability trees. In such a dynamic context, where the evolution of a domain over time is considered, the idea of a causal law as something which guides this evolution is quite natural. In our formalization, a set of probabilistic causal laws can be used to represent a class of probability trees in a concise, flexible and modular way. In this way, our work extends Shafer's by offering a convenient logical representation for his semantical objects. Second, this language also has relevance for the area of probabilistic logic programming. In particular, we prove that the formal semantics of a theory in our language can be equivalently defined as a probability distribution over the well-founded models of certain logic programs, rendering it formally quite similar to existing languages such as ICL or PRISM. Because we can motivate and explain our language in a completely self-contained way as a representation of probabilistic causal laws, this provides a new way of explaining the intuitions behind such probabilistic logic programs: we can say precisely which knowledge such a program expresses, in terms that are equally understandable by a non-logician. Moreover, we also obtain an additional piece of knowledge representation methodology for probabilistic logic programs, by showing how they can express probabilistic causal laws.

The use of mobile phones and other portable devices is beginning to have an impact on how learning takes place in many disciplines and contexts, including language learning. Learners who are not dependent on access to fixed computers can engage in activities that relate more closely to their current surroundings, sometimes crossing the border between formal and informal learning. This creates the potential for significant change in teaching and learning practices. Taking the broader field of mobile learning as the setting within which developments in mobile-assisted language learning may be understood, the paper argues that an emphasis on mobility can lead to new perspectives and practices. The paper offers reflections on what mobile learning has to offer and considers whether it is likely to change how languages are taught and learnt. ‘Mobile learning’ is not a stable concept; therefore its current interpretations need to be made explicit. Examples of current projects and practices show an affinity between mobile and games-based learning, and can further illuminate what is distinctive and worthwhile about mobile learning.

Using various results from extremal set theory (interpreted in the language of additive combinatorics), we prove an asymptotically sharp version of Freiman's theorem in : if is a set for which |A + A| ≤ K|A| then A is contained in a subspace of size ; except for the error, this is best possible. If in addition we assume that A is a downset, then we can also cover A by O(K46) translates of a coordinate subspace of size at most |A|, thereby verifying the so-called polynomial Freiman–Ruzsa conjecture in this case. A common theme in the arguments is the use of compression techniques. These have long been familiar in extremal set theory, but have been used only rarely in the additive combinatorics literature.

Let q be a power of a prime p, and let n, d, ℓ be integers such that 1 ≤ n, 1 ≤ ℓ < q. Consider the modulo q complete ℓ-wide family:

We describe a Gröbner basis of the vanishing ideal I() of the set of characteristic vectors of over fields of characteristic p. It turns out that this set of polynomials is a Gröbner basis for all term orderings ≺, for which the order of the variables is xn ≺ xn−1 ≺ ⋅⋅⋅ ≺ x1.

We compute the Hilbert function of I(), which yields formulae for the modulo p rank of certain inclusion matrices related to .

We apply our results to problems from extremal set theory. We prove a sharp upper bound of the cardinality of a modulo q ℓ-wide family, which shatters only small sets. This is closely related to a conjecture of Frankl [13] on certain ℓ-antichains. The formula of the Hilbert function also allows us to obtain an upper bound on the size of a set system with certain restricted intersections, generalizing a bound proposed by Babai and Frankl [6].

The paper generalizes and extends the results of [15], [16] and [17].

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.