In this paper, we study birth/immigration-death processes under mild (binomial) catastrophes. We obtain explicit expressions for both the time-dependent (transient) and the limiting (equilibrium) factorial moments, which are then used to construct the transient and equilibrium distribution of the population size. We demonstrate that our approach is also applicable to multidimensional systems such as stochastic processes operating under a random environment and other variations of the model at hand. We also obtain various stochastic order results for the number of individuals with respect to the system parameters, as well as the relaxation time.

We consider a monotone binary system with ternary components. “Ternary” means that each component can be in one of three states: up, middle (mid) and down. Handling such systems is a hard task, even if a part of the components have no mid state. Nevertheless, the permutation Monte Carlo methods, that proved very useful for dealing with binary components, can be efficiently used also for ternary monotone systems. It turns out that for “ternary” system there also exists a combinatorial invariant by means of which it becomes possible to count the number C(r;x) of system failure sets which have a given number r and x of components in up and down states, respectively. This invariant is called ternary D-spectrum and it is an analogue of the D-spectrum (or signature) of a system with binary components. Its value is the knowledge of system failure or path set properties which do not depend on stochastic mechanism governing component failures. In case of independent and identical components, knowing D-spectrum makes it easy to calculate system UP or DOWN probability for a variety of UP/DOWN definitions suitable for systems of many types, like communication networks, flow and supply networks, etc.

Graphs are a powerful representation formalism that can be applied to a variety of aspects related to language processing. We provide an overview of how Natural Language Processing problems have been projected into the graph framework, focusing in particular on graph construction – a crucial step in modeling the data to emphasize the phenomena targeted.

Resources and their use and consumption form a central part of our life. Many branches of science and engineering are concerned with the question of which given resource objects can be converted into which target resource objects. For example, information theory studies the conversion of a noisy communication channel instance into an exchange of information. Inspired by work in quantum information theory, we develop a general mathematical toolbox for this type of question. The convertibility of resources into other ones and the possibility of combining resources is accurately captured by the mathematics of ordered commutative monoids. As an intuitive example, we consider chemistry, where chemical reaction equations such as

\mathrm{2H_2 + O_2} \lra \mathrm{2H_2O,}

While closely related to both Girard's linear logic and to Deutsch's constructor theory, our framework also produces results very reminiscent of the utility theorem of von Neumann and Morgenstern in decision theory and of a theorem of Lieb and Yngvason on the foundations of thermodynamics.

Concerning pure algebra, our observation is that some pieces of algebra can be developed in a context in which equality is not necessarily symmetric, i.e. in which the equality relation is replaced by an ordering relation. For example, notions like cancellativity or torsion-freeness are still sensible and very natural concepts in our ordered setting.

This paper studies optimal switching on and off of the entire service capacity of an M/M/∞ queue with holding, running and switching costs. The running costs depend only on whether the system is on or off, and the holding costs are linear. The goal is to minimize average costs per unit time. The main result is that an average-cost optimal policy either always runs the system or is an (M, N)-policy defined by two thresholds M and N, such that the system is switched on upon an arrival epoch when the system size accumulates to N and is switched off upon a departure epoch when the system size decreases to M. It is shown that this optimization problem can be reduced to a problem with a finite number of states and actions, and an average-cost optimal policy can be computed via linear programming. An example, in which the optimal (M, N)-policy outperforms the best (0, N)-policy, is provided. Thus, unlike the case of single-server queues studied in the literature, (0, N)-policies may not be average-cost optimal.

We analyze a continuous review inventory model with the marginal carrying cost of a unit of inventory given by an increasing function of its shelf age and the marginal delay cost of a backlogged demand unit by an increasing function of its delay duration. We show that, under a minor restriction, an (r, q)-policy is optimal when the demand process is a renewal process, and a state dependent (r, q)-policy is optimal when the demand is a Markov-modulated renewal process. We also derive various monotonicity properties for the optimal policy parameters r* and r* + q*.

Configuration and parameterization of optimization frameworks for the computational support of design exploration can become an exclusive barrier for the adoption of such systems by engineers. This work addresses the problem of defining the elements that constitute a multiple-objective design optimization problem, that is, design variables, constants, objective functions, and constraint functions. In light of this, contributions are reviewed from the field of evolutionary design optimization with respect to their concrete implementation for design exploration. Machine learning and natural language processing are supposed to facilitate feasible approaches to the support of configuration and parameterization. Hence, the authors further review promising machine learning and natural language processing methods for automatic knowledge elicitation and formalization with respect to their implementation for evolutionary design optimization. These methods come from the fields of product attribute extraction, clustering of design solutions, relationship discovery, computation of objective functions, metamodeling, and design pattern extraction.

This paper presents research in the development of heuristic evolutionary algorithms (EAs) for generating and exploring differentiated force-based structures. The algorithm is weighted toward design exploration of topological differentiation while including specific structural and material constraints. An embryological EA model is employed to “grow” networks of mass-spring elements achieving desired mesh densities that resolve themselves in tensile force (form-active) equilibrium. The primal quadrilateral quadrisection method serves as the foundation for a range of extensible subdivision methods. Unique to this research, the quad is addressed as a “cell” rather than a topological or geometric construct, allowing for the contents of the cell to vary in number of mass-spring elements and orientation. In this research, this approach has been termed the quadrilateral quadrisection with n variable topological transformation method. This research culminates with the introduction of a method for grafting meshes where emergent features from the evolved meshes can be transposed and replicated in an explicit yet informed manner. The EA and grafting methods function within a Java-based software called springFORM, developed in previous research, which utilizes a mass-spring based library for solving force equilibrium and allows for both active (manual) and algorithmic topology manipulation. In application to a specific complex tensile mesh, the design framework, which combines the generative EA and mesh grafting method, is shown to produce emergent and highly differentiated topological arrangements that negotiate the specific relationships among a desired maximal mesh density, geometric patterning, and equalized force distribution.

Nowadays, on the basis of significant work carried out, architectural adaption structures are considered to be intelligent entities, able to react to various internal or external influences. Their adaptive behavior can be examined in a digital or physical environment, generating a variety of alternative solutions or structural transformations. These are controlled through different computational approaches, ranging from interactive exploration ones, producing alternative emergent results, to automate optimization ones, resulting in acceptable fitting solutions. This paper examines the adaptive behavior of a kinetic structure, aiming to explore suitable solutions resulting in final appropriate shapes during the transformation process. A machine learning methodology that implements an artificial neural networks algorithm is integrated to the suggested structure. The latter is formed by units articulated together in a sequential composition consisting of primary soft mechanisms and secondary rigid components that are responsible for its reconfiguration and stiffness. A number of case studies that respond to unstructured environments are set as examples, to test the effectiveness of the proposed methodology to be used for handling a large number of input data and to optimize the complex and nonlinear transformation behavior of the kinetic system at the global level, as a result of the units’ local activation that influences nearby units in a chaotic and unpredictable manner.

A platform for experimenting with population-based design exploration algorithms is presented, called Dexen. The platform has been developed in order to address the needs of two distinct groups of users loosely labeled as researchers and designers. Whereas the researchers group focuses on creating and testing customized toolkits, the designers group focuses on applying these toolkits in the design process. A platform is required that is scalable and extensible: scalable to allow computationally demanding population-based exploration algorithms to be executed on distributed hardware within reasonable time frames, and extensible to allow researchers to easily implement their own customized toolkits consisting of specialized algorithms and user interfaces. In order to address these requirements, a three-tier client–server system architecture has been used that separates data storage, domain logic, and presentation. This separation allows customized toolkits to be created for Dexen without requiring any changes to the data or logic tiers. In the logic tier, Dexen uses a programming model in which tasks only communicate through data objects stored in a key-value database. The paper ends with a case study experiment that uses a multicriteria evolutionary algorithm toolkit to explore alternative configurations for the massing and façade design of a large residential development. The parametric models for developing and evaluating design variants are described in detail. A population of design variants are evolved, a number of which are selected for further analysis. The case study demonstrates how evolutionary exploration methods can be applied to a complex design scenario without requiring any scripting.

Building performance simulation and genetic algorithms are powerful techniques for helping designers make better design decisions in architectural design optimization. However, they are very time consuming and require a significant amount of computing power. More time is needed when two techniques work together. This has become the primary impediment in applying design optimization to real-world projects. This study focuses on reducing the computing time in genetic algorithms when building simulation techniques are involved. In this study, we combine two techniques (offline simulation and divide and conquer) to effectively improve the run time in these architectural design optimization problems, utilizing architecture-specific domain knowledge. The improved methods are evaluated with a case study of a nursing unit design to minimize the nurses’ travel distance and maximize daylighting performance in patient rooms. Results show the computing time can be saved significantly during the simulation and optimization process.