Combinatorial Configuration Research Articles

Generic constructions for partitioned difference families with applications: a unified combinatorial approach

Partitioned difference families are an interesting class of discrete structures which can be used to derive optimal constant composition codes. There have been intensive researches on the construction of partitioned difference families. In this paper, we consider the combinatorial approach. We introduce a new combinatorial configuration named partitioned relative difference family, which proves to be very powerful in the construction of partitioned difference families. In particular, we present two general recursive constructions, which not only include some existing constructions as special cases, but also generate many new series of partitioned difference families. As an application, we use these partitioned difference families to construct several new classes of optimal constant composition codes.

Danzer’s configuration revisited

Abstract We revisit the configuration DCD(4) of Danzer, a great inspiration for our work. This configuration of type (354) falls into an in_nite series of geometric point-line configurations DCD(n). Each DCD(n) is characterized combinatorially by having the Kronecker cover over the Odd graph On as its Levi graph. Danzer’s configuration is deeply rooted in Pascal’s Hexagrammum Mysticum. Although the combinatorial configuration is highly symmetric, we conjecture that there are no geometric point-line realizations with 7- or 5-fold rotational symmetry; on the other hand, we found a point-circle realization having the symmetry group D7, the dihedral group of order 14.

Research on thermal protection mechanism of forward-facing cavity and opposing jet combinatorial thermal protection system

Validated by the correlated experiments, a nose-tip with forward-facing cavity/opposing jet/the combinatorial configuration of forward-facing cavity and opposing jet thermal protection system (TPS) are investigated numerically. The physical mechanism of these TPS is discussed, and the cooling efficiency of them is compared. The combinatorial system is more suitable to be the TPS for the high speed vehicles which need fly under various flow conditions with long-range and long time.

Investigation of thermal protection system by forward-facing cavity and opposing jet combinatorial configuration

This paper focuses on the usage of the forward-facing cavity and opposing jet combinatorial configuration as the thermal protection system (TPS) for hypersonic vehicles. A hemisphere-cone nose-tip with the combinatorial configuration is investigated numerically in hypersonic free stream. Some numerical results are validated by experiments. The flow field parameters, aerodynamic force and surface heat flux distribution are obtained. The influence of the opposing jet stagnation pressure on cooling efficiency of the combinatorial TPS is discussed. The detailed numerical results show that the aerodynamic heating is reduced remarkably by the combinatorial system. The recirculation region plays a pivotal role for the reduction of heat flux. The larger the stagnation pressure of opposing jet is, the more the heating reduction is. This kind of combinatorial system is suitable to be the TPS for the high-speed vehicles which need long-range and long time flight.

Patterns and pathways of packing circles into a square

Seeking an improbable, but globally optimum, state is useful in many scientific and engineering endeavours. To handle a larger data size, computational techniques are often employed. Yet, they are bound by the inherent combinatorial complexity. This paper employs the examples of packing a set of circles into a square to verify the existence of the pathways between the global optimisations based on the hypothesis that hopping from one known optimum to an unknown optimum in a global landscape is feasible. Twenty seven proven optimal circle packing configurations are investigated and eleven pathways are identified. These pathways lead to other optimal configurations which conform to the best known results. These pathways are beneficial to obtaining the optimum since it does not require going through the combinatorial many intermediate configuration before reaching the optimum.

Linear spaces and transversal designs: k-anonymous combinatorial configurations for anonymous database search notes

Anonymous database search protocols allow users to query a database anonymously. This can be achieved by letting the users form a peer-to-peer community and post queries on behalf of each other. In this article we discuss an application of combinatorial configurations (also known as regular and uniform partial linear spaces) to a protocol for anonymous database search, as defining the key-distribution within the user community that implements the protocol. The degree of anonymity that can be provided by the protocol is determined by properties of the neighborhoods and the closed neighborhoods of the points in the combinatorial configuration that is used. Combinatorial configurations with unique neighborhoods or unique closed neighborhoods are described and we show how to attack the protocol if such configurations are used. We apply k-anonymity arguments and present the combinatorial configurations with k-anonymous neighborhoods and with k-anonymous closed neighborhoods. The transversal designs and the linear spaces are presented as optimal configurations among the configurations with k-anonymous neighborhoods and k-anonymous closed neighborhoods, respectively.

Cooling efficiency investigation of forward-facing cavity and opposing jet combinatorial thermal protection system

The cooling efficiency of a forward-facing cavity and opposing jet combinatorial thermal protection system is investigated, by which the flow field parameters, the aerodynamic force, and the surface heat flux distribution are obtained. The numerical simulation method is validated by experiment with no opposing jet model. The analysis of the numerical simulation results shows that this kind of combinatorial thermal protection system has an excellent effect on cooling the outer body surface of the nose-tip. By introducing an opposing jet with a small total pressure (total pressure ratio PR is 0.1), the cooling effect of combinatorial configuration can be much better than that of a single cavity. With the opposing jet speed increasing, the cooling efficiency is improved and the aerodynamic resistance is reduced. The combinatorial system is suited for the thermal protection of hypersonic aircraft that needs a long-distance and long-time flight.

Left sections and the left part of an artin algebra

Let A be an artin algebra. We are interested in studying the representation theory of A, thus the category modA of finitely generated right A-modules. For this purpose, we fix a full subcategory indA of modA having as objects exactly one representative from each isomorphism class of indecomposable modules. Following Happel, Reiten and Smalo [19], we define the left part LA to be the full subcategory of indA with objects those modules whose predecessors have projective dimension at most one. The right part is defined dually. These classes, whose definition suggests the interplay between homological properties of an algebra and representation theoretic ones, were heavily investigated and applied (see, for instance, the survey [4]). The initial motivation for this paper comes from the observations, made in [5, 2, 1], that the left part of an arbitrary artin algebra closely resembles that of a tilted algebra. Tilted algebras, introduced by Happel and Ringel in [20], are among the most important and best understood classes of algebras. Many criteria allow to recognise whether a given algebra is tilted or not. Most of them revolve around the existence of a combinatorial configuration, called “complete slice” or “section” inside the module category, see [20, 15, 22, 13, 28, 29, 7]. Perhaps the most efficient is the Liu-Skowronski criterion: they define (combinatorially) a so-called section in an Auslander-Reiten component and prove that, if there exists a section satisfying reasonable algebraic conditions, then the algebra is tilted (see [26, 30] or [9, (Chapter VIII)]). Surprisingly, however, as is shown in [1], none of the known criteria seems to apply directly to the tilted algebras arising from the study of the left part. The first aim of this paper is to derive a more suitable version of the Liu-Skowronski criterion, easier to apply in our case. For this purpose, we define a notion of left section in a translation quiver by weakening one of the Liu-Skowronski axioms for section (see (2.1)). Several known results for sections carry over to left sections, sometimes in a restricted form (see, for instance, (2.2) and (3.2)). We thus obtain our first main theorem.

Cluster-tilted algebras and slices

We give a criterion allowing to verify whether or not two tilted algebras have the same relation-extension (thus correspond to the same cluster-tilted algebra). This criterion is in terms of a combinatorial configuration in the Auslander–Reiten quiver of the cluster-tilted algebra, which we call local slice.

Lie algebras associated with triangular configurations

A new class of Lie algebras of finite dimension, those which are associated with a certain combinatorial configuration made up by triangles of weighted and non-directed edges, is introduced and a characterization theorem for them is proved. Moreover, some subclasses of such Lie algebras are classified.

Product configuration optimization for disassembly planning: A differential approach

Product configuration immensely influences the suitability of a product for end-of-life (EOL) disassembly. The product configuration is the relative spatial and logical arrangement of the different parts/sub-assemblies of the product with respect to each other. The complexity involved in studying the influence of configuration design on EOL disassembly has limited the scope of the current design for disassembly (DfD) approaches to guideline-based prescriptive methods and index-based evaluation techniques. The application of these approaches has primarily been limited to specific case studies of product redesign. Many of the current methods do not provide the necessary rigor that will lead to the creation of a theoretical base for addressing product configuration issues which is indispensable during product redesign. Though fraught with obstacles, studying the effects of product configuration on DfD will be useful to develop automated configuration optimization methods for EOL disassembly. To this end, a model to study the combinatorial configuration design optimization problem from a disassembly perspective is described in this study. The different structural principles of the design space derived in this study provide insights into the possibilities and the natural shortcomings of automated optimization of a product by relating the effects of design constraints and disassembly requirements on product redesign. A hierarchical evolutionary programming based algorithm is also developed to test the design solutions generated by the proposed model.

Pooling, lattice square, and union jack designs

Simplified pooling designs employ rows, columns, and principal diagonals from square and rectangular plates. The requirement that every two samples be tested together in exactly one pool leads to a novel combinatorial configuration: The union jack design. Existence of union jack designs is settled affirmatively whenever the ordern is a prime andn≡3 (mod 4).

Parallel genetic simulated annealing: a massively parallel SIMD algorithm

Many significant engineering and scientific problems involve optimization of some criteria over a combinatorial configuration space. The two methods most often used to solve these problems effectively-simulated annealing (SA) and genetic algorithms (GA)-do not easily lend themselves to massive parallel implementations. Simulated annealing is a naturally serial algorithm, while GA involves a selection process that requires global coordination. This paper introduces a new hybrid algorithm that inherits those aspects of GA that lend themselves to parallelization, and avoids serial bottle-necks of GA approaches by incorporating elements of SA to provide a completely parallel, easily scalable hybrid GA/SA method. This new method, called Genetic Simulated Annealing, does not require parallelization of any problem specific portions of a serial implementation-existing serial implementations can be incorporated as is. Results of a study on two difficult combinatorial optimization problems, a 100 city traveling salesperson problem and a 24 word, 12 bit error correcting code design problem, performed on a 16 K PE MasPar MP-1, indicate advantages over previous parallel GA and SA approaches. One of the key results is that the performance of the algorithm scales up linearly with the increase of processing elements, a feature not demonstrated by any previous parallel GA or SA approaches, which enables the new algorithm to utilize massive parallel architecture with maximum effectiveness. Additionally, the algorithm does not require careful choice of control parameters, a significant advantage over SA and GA.

Bipartite distance-regular interconnection topology for fault-tolerant multiprocessor systems

In the paper we propose a bipartite, distance-regular topology for interconnection networks to build large multiprocessor systems. The network consists of 2(2m+1[2]) nodes, with diameter 2m+1 and degree m+1. The connectivity for these networks is the best possible and their average internodal distance is roughly equal to half the diameter. These features show that the proposed networks have relatively high densities, and are capable of maximal fault-tolerance. The topology allows efficient self-routing for both the non-faulty and faulty network. For these networks we propose a semi-distributed fault-diagnosis algorithm which requires a relatively small computation overhead and generates considerably lower network traffic. The self-diagnostic scheme is in turn shown to be fault-tolerant. The most remarkable property of this topology is its symmetric partitioning capability, which is based on a combinatorial configuration known as the Hadamard matrix. On the basis of this partitioning property, we propose another semidistributed self-diagnosis algorithm which considerably improves the diagnosability of the partitioned network over the non-partitioned network

An interpolative PCM CODEC with multiplexed digital filters

An LSI CODEC, an LSI multiplexed digital filter, and an LSI compandor are developed for telephone PCM AD/DA conversion. The total chip count is 1.56 chips per channel. The single-chip interpolative CODEC operates at a 32 kHz sampling rate with a 12-bit linear code input/output, and is implemented in a phosphorus buried emitter IIL process without the need for component value trimming. The digital filter is four-channel multiplexed for both transmitting and receiving directions. It is compactly fabricated with a combinatorial configuration in a 5 /spl mu/m NMOS process. A new word length extension technique was devised to realize an 87 dB dynamic range with the digital filter. The compandor, also fabricated in 5 /spl mu/m NMOS, is 16-channel multiplexed for both directions. All measured characteristics meet CCITT recommendations with sufficient margins. They demonstrate the inherent stability and noise immunity that can be achieved with the interpolation technique of the CODEC and the digital signal processing of the digital filter.

A combinatorial configuration associated with the Higman-Sims simple group

A combinatorial configuration associated with the Higman-Sims simple group