The paper by Woodbury and Burrow is examined using four criteria: completeness, discrimination, alternative approaches, and combining exploration in different problem domains. Although the paper covers significant aspects of the search space literature it leaves out some relevant aspects of the cognitive approach. It fares much better in terms of discriminating important concepts and alternative approaches to the modeling of the design search space. The structure–function–behavior model is suggested as an analogy for the central parameters of the search space paradigm. The Woodbury and Burrow paper reveals more than what has been accomplished up to now in the design search space area, but its task still remains incomplete.

The paper presents aspects of designer action that stress cognitive strategies for effective design problem solving, under the headings of exploration and representation. It proposes that links among design moves and shifts between design arguments are of prime importance in exploration and the design space should accommodate and expose them. The primacy of self-generated representations in the form of free-hand sketches and the role of arbitrary visual stimuli as supporting design reasoning is introduced. The expositions lead to the conclusion that the design space should be conceived as a multilevel and multifacet construct that supports on the spot experimentation and provides essential feedback not only regarding designs, but also concerning the process of designing.

Exploration with a generative formalism must necessarily account for the nature of interaction between humans and the design space explorer. Established accounts of design interaction are made complicated by two propositions in Woodbury and Burrow's Keynote on design space exploration. First, the emphasis on the primacy of the design space as an ordered collection of partial designs (version, alternatives, extensions). Few studies exist in the design interaction literature on working with multiple threads simultaneously. Second, the need to situate, aid, and amplify human design intentions using computational tools. Although specific research and practice tools on amplification (sketching, generation, variation) have had success, there is a lack of generic, flexible, interoperable, and extensible representation to support amplification. This paper addresses the above, working with design threads and computer-assisted design amplification through a theoretical model of dialogue based on Grice's model of rational conversation. Using the concept of mixed initiative, the paper presents a visual notation for representing dialogue between designer and design space formalism through abstract examples of exploration tasks and dialogue integration.

Design of balancing control and the stability analysis of a biped during disturbed standing are investigated. A PD-based switching state feedback control is used to stabilize the biped at the upright position while satisfying the constraints between the feet and the ground. The concept of Lyapunov exponents is used for the stability analysis, and a stability region is determined. Furthermore, the stability region is compared and agrees well with the one from the previous work that predicts the feasible movement during which balance of human standing can be maintained. This agreement shows the potential of the concept of Lyapunov exponents to be used as a measure of balancing of human standing. The work contributes to bipedal balancing control, which is important in the development of bipedal robots.

This article considers the optimization and optimality of single-item/location, infinite-horizon, (s,S) inventory models. Departing from the conventional approach, we do not assume the loss function describing holding and shortage costs per period to be quasiconvex. As the existing optimization algorithms have been established on the condition of quasiconvexity, our goal in this article is to develop a computational procedure for obtaining optimal (s,S) policies for models with general loss functions. Our algorithm is based on the parametric method commonly used in fractional programming and is intuitive, exact, and efficient. Moreover, this method allows us to extend the optimality of (s,S) policies to a broader class of loss functions that can be non-quasiconvex.

In a communication network, one might attempt to route calls from an origin to a destination through n paths that will be tried one by one, each having a success probability pi ∈ (0,1), i = 1,2,…,n. The order of trying is controlled by a routing table. The number of attempts made is defined as the cost of the routing table. Move-forward self-organizing rules are applied to the routing table and comparisons of expected equilibrium costs are performed when p2 = p3 = … = pn. Stationary distributions for a subset of f-swap rules are obtained for general pi's.

We consider the transformation T that takes a distribution F into the distribution of the length of the interval covering a fixed point in the stationary renewal process corresponding to F. This transformation has been referred to as size-biasing, length-biasing, the renewal length transformation, and the stationary lifetime operator. We review and develop properties of this transformation and apply it to diverse areas.

For a system in which arrivals occur according to a Poisson process, we give a new approach for using simulation to estimate the expected value of a random variable that is independent of the arrival process after some specified time t. We also give a new approach for using simulation to estimate the expected value of an increasing function of independent uniform random variables. Stratified sampling is a key technique in both cases.

We present an elementary proof that if $A$ is a finite set of numbers, and the sumset $A+_GA$ is small, $|A+_GA|\leq c|A|$, along a dense graph $G$, then $A$ contains $k$-term arithmetic progressions.

In the literature, most of the bounds for the renewal function U(x) corresponding to a lifetime distribution F are given in terms of the first two moments of F only. The best general upper bound of this type is the one given in Lorden (1970). In the present article, we show that improved bounds can be obtained if one exploits the specific form of the distribution F. We derive a bound that improves upon Lorden's, at least on an interval [0,a) with a ≤ ∞, and we give both sufficient and necessary conditions for this improvement to hold uniformly for x ≥ 0. Refined upper as well as lower bounds are given for the case where F belongs to a class of distributions with monotone aging or when the renewal density is monotone.

Three new notions of positive dependence (positive regression dependence, positive left-tail regression dependence, and positive right-tail regression dependence) are studied in this article. Consider a latent variable model where the manifest random variables T1,T2,…,Tn given latent random variable/vector (Θ1,…,Θm) are conditional independent. Conditions are identified under which T1,…,Tn possesses the new dependence notions for different types of latent variable model. Applications of the results are also provided.

We study a single-product periodic-review inventory model in which the ordering quantity is either zero or at least a minimum order size. The ordering cost is a linear function of the ordering quantity, and the demand in different time periods are independent random variables. The objective is to characterize the inventory policies that minimize the total discounted ordering, holding, and backorder penalty costs over a finite time horizon. We introduce the concept of an M-increasing function. These functions allow us to characterize the optimal inventory policies everywhere in the state space outside of an interval for each time period. Furthermore, we identify easily computable upper bounds and asymptotic lower bounds for these intervals. Finally, examples are given to demonstrate the complex structure of the optimal inventory policies.

We study a stochastic fluid EOQ-type model operating in a Markovian random environment of alternating good and bad periods determining the demand rate. We deal with the classical problem of “when to place an order” and “how big it should be,” leading to the trade-off between the setup cost and the holding cost. The key functionals are the steady-state mean of the content level, the expected cycle length (which is the time between two large orders), and the expected number of orders in a cycle. These performance measures are derived in closed form by using the level crossing approach in an intricate way. We also present numerical examples and carry out a sensitivity analysis.

We consider a scheduling problem with two interconnected queues and two flexible servers. It is assumed that all jobs are present at the beginning and that there are no further arrivals to the system at any time. For each job, there are waiting costs per unit of time until the job leaves the system. A job of queue 1, after being served, joins queue 2 with probability p and leaves the system with probability 1 − p. The objective is how to allocate the two servers to the queues such that the expected total holding costs until the system is empty are minimized. We give a sufficient condition such that for any number of jobs in queue 1 and queue 2, it is optimal to allocate both servers to queue 1 (resp. queue 2).

In the article published last year, three inequalities should be in the opposite direction.

In this article a Markov chain for the distribution of single atoms is suggested and studied. We explore a recursive model for the number of atoms present in a magneto-optical trap under a feedback regime with a Poisson-distributed load. Formulas for the stationary distribution of this process are derived. They can be used to adjust the loading rate of atoms to maximize the proportion of time that a single atom spends in the trap. The (approximate) optimal regime for the Poisson loading and loss processes is found.