For a $t$ -nomial $f(x)=\sum _{i=1}^{t}c_{i}x^{a_{i}}\in \mathbb{F}_{q}[x]$ , we show that the number of distinct, nonzero roots of $f$ is bounded above by $2(q-1)^{1-\unicode[STIX]{x1D700}}C^{\unicode[STIX]{x1D700}}$ , where $\unicode[STIX]{x1D700}=1/(t-1)$ and $C$ is the size of the largest coset in $\mathbb{F}_{q}^{\ast }$ on which $f$ vanishes completely. Additionally, we describe a number-theoretic parameter depending only on $q$ and the exponents $a_{i}$ which provides a general and easily computable upper bound for  $C$ . We thus obtain a strict improvement over an earlier bound of Canetti et al. which is related to the uniformity of the Diffie–Hellman distribution. Finally, we conjecture that $t$ -nomials over prime fields have only $O(t\log p)$ roots in $\mathbb{F}_{p}^{\ast }$ when $C=1$ .

We prove that triangular configurations are plentiful in large subsets of Cartesian squares of finite quasirandom groups from classes having the quasirandom ultraproduct property, for example the class of finite simple groups. This is deduced from a strong double recurrence theorem for two commuting measure-preserving actions of a minimally almost periodic (not necessarily amenable or locally compact) group on a (not necessarily separable) probability space.

This paper proposes an interval-based approach in order to obtain the obstacle-free workspace of parallel mechanisms containing one prismatic actuated joint per limb, which connects the base to the end-effector. This approach is represented through two cases studies, namely a 3-RPR planar parallel mechanism and the so-called 6-DOF Gough–Stewart platform. Three main features of the obstacle-free workspace are taken into account: mechanical stroke of actuators, collision between limbs and obstacles and limb interference. In this paper, a circle(planar case)/spherical(spatial case) shaped obstacle is considered and its mechanical interference with limbs and edges of the end-effector is analyzed. It should be noted that considering a circle/spherical shape would not degrade the generality of the problem, since any kind of obstacle could be replaced by its circumscribed circle/sphere. Two illustrative examples are given to highlight the contributions of the paper.

This paper (Wu 2016), which was published in AI EDAM online on August 22, 2016, has been retracted by Cambridge University Press as it is very similar in content to a published ASME Conference Proceedings paper. The article in question and the ASME Conference Proceedings paper were submitted for review with AI EDAM and the ASME at similar times, but copyright was assigned to ASME before the paper was accepted in AI EDAM and therefore the article in AI EDAM is being retracted. (In recent years, industrial nations around the globe have invested heavily in new technologies, software, and services to advance digital design and manufacturing using cyber-physical systems, data analytics, and high-performance computing. Many of these initiatives, such as cloud-based design and manufacturing, fall under the umbrella of what has become known as Industry 4.0 or Industrial Internet and are often hailed as pillars of a new industrial revolution. While an increasing number of companies are developing or already offer commercial cloud-based software packages and services for digital design and manufacturing, little work has been reported on providing a review of the state of the art of these commercial software and services as well as identifying research gaps in this field. The objective of this paper is to present a state-of-the-art review of digital design and manufacturing software and services that are currently available on the cloud. The focus of this paper is on assessing to what extent engineering design, engineering analysis, manufacturing, and production across all phases of the product development lifecycles can already be performed based on the software and services accessed through the cloud. In addition, the key capabilities and benefits of these software packages and services are discussed. Based on the assessment of the core features of commercial software and services, it can be concluded that almost all phases of product realization can be conducted through digital design and manufacturing software and services on the cloud. Finally, existing research gaps and related challenges to overcome are identified. The state-of-the-art review serves to provide a technology guide for decision makers in their efforts to select suitable cloud-based software and services as alternatives to existing in-house resources as well as to recommend new research areas.)

Admissible rules are shown to be conservatively preserved by the meet-combination of a wide class of logics. A basis is obtained for the resulting logic from bases given for the component logics, under mild conditions. A weak form of structural completeness is proved to be preserved by the combination. Decidability of the set of admissible rules is also shown to be preserved, with no penalty on the time complexity. Examples are provided for the meet-combination of intermediate and modal logics.

A multimodal actuator was proposed to achieve a more agile power-assisted exoskeleton in uncertain complex walking environments. A power-assisted knee exoskeleton prototype based on a multimodal actuator was constructed. With this multimodal actuator, several modes of operation in the power-assisted knee exoskeleton during a motion cycle are actuated, including series elastic actuation, stiff position control, and energy storage and release. Also, a control strategy for power-assisted knee exoskeleton motion control based on a state machine is developed. The ability of the power-assisted knee exoskeleton to follow human motion was tested, and the results showed that the angle error of the knee exoskeleton followed the human motion is not more than 0.4˚, and the response time error of the knee exoskeleton followed the human motion is not more than 0.2 s.

In the real practice of multi-AUV (Autonomous Underwater Vehicle) cooperative systems, tasks or malfunctions will change the topology. The process of mutative topology structure will affect the reliability of multi-AUV cooperative system. The interactive Markov chains model, which is an intercurrent model of functional action and capability index, is selected to reflect the reliability of topology-changed multi-AUV cooperative systems. In this model, multi-AUV cooperative systems are described by the conception—“Action”. The concept of “action transfer” is used to describe the topology-changed multi-AUV cooperative system, and model checking is used to solve the interactive Markov chains, giving the probability of reliability within a certain time for the system. The result shows that the method proposed in this paper has a practical value.

We study the lower tail large deviation problem for subgraph counts in a random graph. Let X H denote the number of copies of H in an Erdős–Rényi random graph $\mathcal{G}(n,p)$ . We are interested in estimating the lower tail probability $\mathbb{P}(X_H \le (1-\delta) \mathbb{E} X_H)$ for fixed 0 < δ < 1.

Thanks to the results of Chatterjee, Dembo and Varadhan, this large deviation problem has been reduced to a natural variational problem over graphons, at least for p ≥ n −α H (and conjecturally for a larger range of p). We study this variational problem and provide a partial characterization of the so-called ‘replica symmetric’ phase. Informally, our main result says that for every H, and 0 < δ < δH for some δH > 0, as p → 0 slowly, the main contribution to the lower tail probability comes from Erdős–Rényi random graphs with a uniformly tilted edge density. On the other hand, this is false for non-bipartite H and δ close to 1.

Judicious partitioning problems on graphs and hypergraphs ask for partitions that optimize several quantities simultaneously. Let k ≥ 2 be an integer and let G be a hypergraph with m i edges of size i for i=1,2. Bollobás and Scott conjectured that G has a partition into k classes, each of which contains at most $m_1/k+m_2/k^2+O(\sqrt{m_1+m_2})$ edges. In this paper, we confirm the conjecture affirmatively by showing that G has a partition into k classes, each of which contains at most

$$m_1/k+m_2/k^2+\ffrac{k-1}{2k^2}\sqrt{2(km_1+m_2)}+O(1)$$.

When the end-effector of a robotic arm grasps different payload masses, the output of joint motion will vary. By using a model reference adaptive control approach, the payload variation effect can be solved. This paper describes the design for a hybrid controller for serial robotic manipulators by combining a PID controller and a model reference adaptive controller (MRAC) in order to further improve the accuracy and joint convergence speed performance. The convergence performance of the PID controller, the MRAC and the PID+MRAC hybrid controller for 1-DOF, 2-DOF and subsequently 3-DOF manipulators is compared. The comparison results show that the convergence speed and its performance for the MRAC and the PID+ MRAC controllers is better than that of the PID controller, and the convergence performance for the hybrid control is better than that of the MRAC control.

A new motion-free iterative closest point (ICP) algorithm is proposed for building a two-dimensional (2D) map for mobile robot navigation. A laser range finder (LRF) sensor is installed on a mobile robot to scan and measure the depth data of the environment to form a 2D map during mobile robot navigation. Because the scanning and navigation motions are performed independently, the scanned data contain distortions from the motions of the mobile robot. To compensate for the distortions, the proposed motion-free ICP algorithm estimates the effects of the dynamic motions of the robot on the scanning process. That is, the motion-free algorithm compensates for the distance measurement errors related to the dynamic changes in the mobile robot's velocity. Experiments were performed with actual velocity changes of a mobile robot to demonstrate and verify the effective performance of the proposed algorithm.

We prove that any equational basis that defines representable relation algebras (RRA) over weakly representable relation algebras (wRRA) must contain infinitely many variables. The proof uses a construction of arbitrarily large finite weakly representable but not representable relation algebras whose “small” subalgebras are representable.

Modelling and simulation have long been dominated by equation-based approaches, until the recent advent of agent-based approaches. To curb the resulting complexity of models, Axelrod promoted the KISS principle: ‘Keep It Simple, Stupid’. But the community is divided and a new principle appeared: KIDS, ‘Keep It Descriptive, Stupid’. Richer models were thus developed for a variety of phenomena, while agent cognition still tends to be modelled with simple reactive particle-like agents. This is not always appropriate, in particular in the social sciences trying to account for the complexity of human behaviour. One solution is to model humans as belief, desire and intention (BDI) agents, an expressive paradigm using concepts from folk psychology, making it easier for modellers and users to understand the simulation. This paper provides a methodological guide to the use of BDI agents in social simulations, and an overview of existing methodologies and tools for using them.

Programming languages which are capable of interpreting themselves have been fascinating computer scientists. Indeed, if this is possible then a ‘strange loop’ (in the sense of Hofstadter, 1979) is involved. Nevertheless, the phenomenon is a direct consequence of the existence of universal languages. Indeed, if all computable functions can be captured by a language, then so can the particular job of interpreting the code of a program of that language. Self-interpretation will be shown here to be possible in lambda calculus.

The set of λ-terms, notation Λ, is defined by the following abstract syntax

where

is the set {v, v′, v″, v′″,…} of variables. Arbitrary variables are usually denoted by x, y,z,… and λ-terms by M,N,L,…. A redex is a λ-term of the form

that is, the result of substituting N for (the free occurrences of) x in M. Stylistically, it can be said that λ-terms represent functional programs including their input. A reduction machine executes such terms by trying to reduce them to normal form; that is, redexes are continuously replaced by their contracta until hopefully no more redexes are present. If such a normal form can be reached, then this is the output of the functional program; otherwise, the program diverges.

This paper presents an application of functional programming: searching a domain for elements which satisfy certain constraints. We give a very general formulation of the problem and describe ‘generate and test’, ‘backtracking’ and ‘forward checking’ algorithms. We then introduce the concept of domain generating functions to capture a common optimization during the search process: using partial solutions to reduce the size of the search space. We compare the efficiency of the original algorithms and those using domain generating functions first with the ‘classical’ n-queens example, and then with a problem having larger domains to search which was inspired by an application in macromolecular structure determination. Using algorithms coded in Miranda, Haskell and Common Lisp, we show that a high order (lazy) functional language is a useful and efficient tool for prototyping search methods in large complex domains.

Polymorphic types are labels classifying both (a) defined components in a library and (b) contexts of free variables in partially written programs. It is proposed to help programmers make better use of software libraries by providing a system that, given (b), identifies candidates from (a) with matching types. Assuming at first that matching means unifying (i.e. having a common instance), efficient ways of implementing such a retrieval system are discussed and its likely effectiveness based on a quantitative study of currently available libraries is indicated. The applicative instance relation between types, which captures some intuitions about generalization/specialization is then introduced, and its use as the basis of a more flexible system is discussed.

Programming languages often come with type systems. Some of these are simple, others are sophisticated. As a stylistic representation of types in programming languages several versions of typed lambda calculus are studied. During the last 20 years many of these systems have appeared, so there is some need of classification. Working towards a taxonomy, Barendregt (1991) gives a fine-structure of the theory of constructions (Coquand and Huet 1988) in the form of a canonical cube of eight type systems ordered by inclusion. Berardi (1988) and Terlouw (1988) have independently generalized the method of constructing systems in the λ-cube. Moreover, Berardi (1988, 1990) showed that the generalized type systems are flexible enough to describe many logical systems. In that way the well-known propositions-as-types interpretation obtains a nice canonical form.

We present a modular proof of strong normalization for the Calculus of Constructions of Coquand and Huet (1985, 1988). This result was first proved by Coquand (1986), but our proof is more perspicious. The method consists of a little juggling with some systems in the cube of Barendregt (1989), which provides a fine structure of the calculus of constructions. It is proved that the strong normalization of the calculus of constructions is equivalent with the strong normalization of Fω.

In order to give the proof, we first establish some properties of various type systems. Therefore, we present a general framework of typed lambda calculi, including many well-known ones.