On the k-tuple domination of generalized de Brujin and Kautz digraphs

A vertex u in a digraph G = (V, A) is said to dominate itself and vertices v such that (u, v) ∈ A. For a positive integer k, a k-tuple dominating set of G is a subset D of vertices such that every vertex in G is dominated by at least k vertices in D. The k-tuple domination number of G is the minimum cardinality of a k-tuple dominating set of G. This paper deals with the k-tuple domination problem on generalized de Bruijn and Kautz digraphs. We establish bounds on the k-tuple domination number for the generalized de Bruijn and Kautz digraphs and we obtain some conditions for the k-tuple domination number attaining the bounds.     

RCC8 binary constraint network can be consistently extended

The RCC8 constraint language developed by Randell et al. has been popularly adopted by the Qualitative Spatial Reasoning and GIS communities. The recent observation that RCC8 composition table describes only weak composition instead of composition raises questions about Renz and Nebel's maximality results about the computational complexity of reasoning with RCC8.This paper shows that any consistent RCC8 binary constraint network (RCC8 network for short) can be consistently extended. Given Θ, an RCC8 network, and z, a fresh variable, suppose xTy∈Θ and T is contained in the weak composition of R and S. This means that we can add two new constraints xRz and zSy to Θ without changing the consistency of the network. The result guarantees the applicability to RCC8 of one key technique, (Theorem 5) of [J. Renz, B. Nebel, On the complexity of qualitative spatial reasoning: A maximal tractable fragment of the Region Connection Calculus. Artificial Intelligence 108 (1999) 69-123], which allows the transfer of tractability of a set of RCC8 relations to its closure under composition, intersection, and converse.     

Characterizations of regular ordered semigroups in terms of (α, β)-fuzzy generalized bi-ideals

In this paper, the concept of an (α, β)-fuzzy generalized bi-ideal in an ordered semigroup is introduced, which is a generalization of the concept of a fuzzy generalized bi-ideal in an ordered semigroup. Using this concept, some characterization theorems are provided. The upper/lower parts of an (∈, ∈ ∨ q)-fuzzy generalized bi-ideal are introduced and some characterizations of regular ordered semigroups are given. Also, we consider the concept of implication-based fuzzy generalized bi-ideals in an ordered semigroup. In particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed.     

A (4n − 9)/3 diagnosis algorithm on n-dimensional cube network

As a generalization of the precise and pessimistic diagnosis strategies of system-level diagnosis of multicomputers, the t/k diagnosis strategy can significantly improve the self-diagnosing capability of a system at the expense of no more than k fault-free processors (nodes) being mistakenly diagnosed as faulty. In the case k ? 2, to our knowledge, there is no known t/k diagnosis algorithm for general diagnosable system or for any specific system. Hypercube is a popular topology for interconnecting processors of multicomputers. It is known that an n-dimensional cube is (4n − 9)/3-diagnosable. This paper addresses the (4n − 9)/3 diagnosis of n-dimensional cube. By exploring the relationship between a largest connected component of the 0-test subgraph of a faulty hypercube and the distribution of the faulty nodes over the network, the fault diagnosis of an n-dimensional cube can be reduced to those of two constituent (n − 1)-dimensional cubes. On this basis, a diagnosis algorithm is presented. Given that there are no more than 4n − 9 faulty nodes, this algorithm can isolate all faulty nodes to within a set in which at most three nodes are fault-free. The proposed algorithm can operate in O(N log₂ N) time, where N = 2ⁿ is the total number of nodes of the hypercube. The work of this paper provides insight into developing efficient t/k diagnosis algorithms for larger k value and for other types of interconnection networks.     

The use of waveform lidar to measure northern temperate mixed conifer and deciduous forest structure in New Hampshire

The direct retrieval of canopy height and the estimation of aboveground biomass are two important measures of forest structure that can be quantified by airborne laser scanning at landscape scales. These and other metrics are central to studies attempting to quantify global carbon cycles and to improve understanding of the spatial variation in forest structure evident within differing biomes. Data acquired using NASA's Laser Vegetation Imaging Sensor (LVIS) over the Bartlett Experimental Forest (BEF) in central New Hampshire (USA) was used to assess the performance of waveform lidar in a northern temperate mixed conifer and deciduous forest.Using coincident plots established for this study, we found strong agreement between field and lidar measurements of height (r² = 0.80, p < 0.000) at the footprint level. Allometric calculations of aboveground biomass (AGBM) and LVIS metrics (AGBM: r² = 0.61, PRESS RMSE = 58.0 Mg ha^− 1, p < 0.000) and quadratic mean stem diameter (QMSD) and LVIS metrics (r² = 0.54, p = 0.002) also showed good agreement at the footprint level. Application of a generalized equation for determining AGBM proposed by Lefsky et al. (2002a) to footprint-level field data from Bartlett resulted in a coefficient of determination of 0.55; RMSE = 64.4 Mg ha^− 1; p = 0.002. This is slightly weaker than the strongest relationship found with the best-fit single term regression model.Relationships between a permanent grid of USDA Forest Service inventory plots and the mean values of aggregated LVIS metrics, however, were not as strong. This discrepancy suggests that validation efforts must be cautious in using pre-existing field data networks as a sole means of calibrating and verifying such remote sensing data. Stratification based on land-use or species composition, however, did provide the means to improve regression relationships at this scale. Regression models established at the footprint level for AGBM and QMSD were applied to LVIS data to generate predicted values for the whole of Bartlett. The accuracy of these models was assessed using varying subsets of the USFS NERS plot data. Coefficient of determinations ranged from fair to strong with aspects of land-use history and species composition influencing both the fit and the level of error seen in the predicted relationships.     

The pancyclicity and the Hamiltonian-connectivity of the generalized base-b hypercube

The interconnection network considered in this paper is the generalized base-b hypercube that is an attractive variance of the well-known hypercube. The generalized base-b hypercube is superior to the hypercube in many criteria, such as diameter, connectivity and fault diameter. In this paper, we study the Hamiltonian-connectivity and pancyclicity of the generalized base-b hypercube by the algorithmic approach. We show that a generalized base-b hypercube is Hamiltonian-connected for b ? 3. That is, there exists a Hamiltonian path joining each pair of vertices in a generalized base-b hypercube for b ? 3. We also show that a generalized base-b hypercube is pancyclic for b ? 3. That is, it embeds cycles of all lengths ranging from 3 to the order of the graph for b ? 3.     

The panpositionable panconnectedness of augmented cubes

A graph G is panconnected if, for any two distinct vertices x and y of G, it contains an [x, y]-path of length l for each integer l satisfying d_G(x, y) ? l ? ∣V(G)∣ − 1, where d_G(x, y) denotes the distance between vertices x and y in G, and V(G) denotes the vertex set of G. For insight into the concept of panconnectedness, we propose a more refined property, namely panpositionable panconnectedness. Let x, y, and z be any three distinct vertices in a graph G. Then G is said to be panpositionably panconnected if for any d_G(x, z) ? l₁ ? ∣V(G)∣ − d_G(y, z) − 1, it contains a path P such that x is the beginning vertex of P, z is the (l₁ + 1)th vertex of P, and y is the (l₁ + l₂ + 1)th vertex of P for any integer l₂ satisfying d_G(y, z) ? l₂ ? ∣V(G)∣ − l₁ − 1. The augmented cube, proposed by Choudum and Sunitha [6] to be an enhancement of the n-cube Q_n, not only retains some attractive characteristics of Q_n but also possesses many distinguishing properties of which Q_n lacks. In this paper, we investigate the panpositionable panconnectedness with respect to the class of augmented cubes. As a consequence, many topological properties related to cycle and path embedding in augmented cubes, such as pancyclicity, panconnectedness, and panpositionable Hamiltonicity, can be drawn from our results.     

A Note on Z-numbers

Decisions are based on information. To be useful, information must be reliable. Basically, the concept of a Z-number relates to the issue of reliability of information. A Z-number, Z, has two components, Z = (A, B). The first component, A, is a restriction (constraint) on the values which a real-valued uncertain variable, X, is allowed to take. The second component, B, is a measure of reliability (certainty) of the first component. Typically, A and B are described in a natural language. Example: (about 45 min, very sure). An important issue relates to computation with Z-numbers. Examples: What is the sum of (about 45 min, very sure) and (about 30 min, sure)? What is the square root of (approximately 100, likely)? Computation with Z-numbers falls within the province of Computing with Words (CW or CWW). In this note, the concept of a Z-number is introduced and methods of computation with Z-numbers are outlined. The concept of a Z-number has a potential for many applications, especially in the realms of economics, decision analysis, risk assessment, prediction, anticipation and rule-based characterization of imprecise functions and relations.     

Regional evaporation estimates from flux tower and MODIS satellite data

Two models were evaluated for their ability to estimate land surface evaporation at 16-day intervals using MODIS remote sensing data and surface meteorology as inputs. The first was the aerodynamic resistance-surface energy balance model, and the second was the Penman-Monteith (P-M) equation, where the required surface conductance is estimated from remotely-sensed leaf area index. The models were tested using 3 years of evaporation and meteorological measurements from two contrasting Australian ecosystems, a cool temperate, evergreen Eucalyptus forest and a wet/dry, tropical savanna. The aerodynamic resistance-surface energy balance approach failed because small errors in the radiative surface temperature translate into large errors in sensible heat, and hence into estimates of evaporation. The P-M model adequately estimated the magnitude and seasonal variation in evaporation in both ecosystems (RMSE = 27 W m^− 2, R² = 0.74), demonstrating the validity of the proposed surface conductance algorithm. This, and the ability to constrain evaporation estimates via the energy balance, demonstrates the superiority of the P-M equation over the surface temperature-based model. There was no degradation in the performance of the P-M model when gridded meteorological data at coarser spatial (0.05°) and temporal (daily) resolution were substituted for locally-measured inputs.The P-M approach was used to generate a monthly evaporation climatology for Australia from 2001 to 2004 to demonstrate the potential of this approach for monitoring land surface evaporation and constructing monthly water budgets from 1-km to continental spatial scales.     

On the structure of generalized rough sets

In this paper we consider some fundamental properties of generalized rough sets induced by binary relations on algebras and show that

1.

Any reflexive binary relation determines a topology.

2.

If θ is a reflexive and symmetric relation on a set X, then O={A⊆X|θ_-(A)=A} is a topology such that A is open if and only if it is closed.

3.

Conversely, for every topological space (X,O) satisfying the condition that A is open if and only if it is closed, there exists a reflexive and symmetric relation R such that O={A⊆X|R_-(A)=A}.

4.

Let θ be an equivalence relation on X. For any pseudo ω-closed subset A of X, θ₋(A) is an ω-closed set if and only if ω(x, x, … , x) ∈ θ₋(A) for any x ∈ X.

Moreover we consider properties of generalized rough sets.     

Computer usage questionnaire: Structure, correlates, and gender differences

Computer usage, computer experience, computer familiarity, and computer anxiety are often discussed as constructs potentially compromising computer-based ability assessment. After presenting and discussing these constructs and associated measures we introduce a brief new questionnaire assessing computer usage. The self-report measure consists of 18 questions asking for the frequency of different computer activities and software usage. Participants were N = 976 high school students who completed the questionnaire and several covariates. Based on theoretical considerations and data driven adjustments a model with a general computer usage factor and three nested content factors (Office, Internet, and Games) is established for a subsample (n = 379) and cross-validated with the remaining sample (n = 597). Weak measurement invariance across gender groups could be established using multi-group confirmatory factor analysis. Differential relations between the questionnaire factors and self-report scales of computer usage, self-concept, and evaluation are reported separately for females and males. It is concluded that computer usage is distinct from other behavior oriented measurement approaches and that it shows a diverging, gender-specific pattern of relations with fluid and crystallized intelligence.     

Neural network estimation of LAI, fAPAR, fCover and LAI×Cab, from top of canopy MERIS reflectance data: Principles and validation

A neural network is developed to operationally estimate biophysical variables over land surfaces from the observations of the ENVISAT-MERIS instrument: the leaf area index (LAI), the fraction of absorbed photosynthetically active radiation (fAPAR), the fraction of vegetation cover (fCover), and the canopy chlorophyll content (LAI×C_ab). The neural network requires as input the geometry of observation and the top of canopy reflectances, corrected from the atmospheric effects, in eleven spectral bands. It is trained on a reflectance database made of radiative transfer model simulations. The principles underlying the generation of the database and the design of the network are first presented. The estimated variables are then compared to other existing products, LAI- and fAPAR-MODIS and MGVI-MERIS, and validated against ground measurements performed in the framework of the VALERI project. Results show remarkable consistency of the temporal dynamics between the several products with however some differences in the range of variation. When compared to actual VALERI ground measurements, the proposed algorithm shows the best performances for LAI (RMSE = 0.47) and fAPAR (RMSE = 0.09).     

The design and analysis of an efficient load balancing algorithm employing the symmetric balanced incomplete block design

In order to maintain load balancing in a distributed network, each node should obtain workload information from all the nodes in the network. To accomplish this, this processing requires O(v²) communication complexity, where v is the number of nodes. First, we present a new synchronous dynamic distributed load balancing algorithm on a (v, k + 1, 1)-configured network applying a symmetric balanced incomplete block design, where v = k² + k + 1. Our algorithm designs a special adjacency matrix and then transforms it to (v, k + 1, 1)-configured network for an efficient communication. It requires only communication complexity and each node receives workload information from all the nodes without redundancy since each link has the same amount of traffic for transferring workload information. Later, this algorithm is revised for distributed networks and is analyzed in terms of efficiency of load balancing.     

Constraint Networks of Topological Relations and Convexity

This paper studies the expressivity and computational complexity of networks of constraints of topological relations together with convexity. We consider constraint networks whose nodes are regular regions (a regular region is one equal to the closure of its interior) and whose constraints have the following forms: (i) the eight base relations of [12], which describe binary topological relations of containment and adjacency between regions; (ii) the predicate, X is convex. We establish tight bounds on the computational complexity of this language: Determining whether such a constraint network is consistent is decidable, but essentially as hard as determining whether a set of comparable size of algebraic constraints over the real numbers is consistent. We also show an important expressivity result for this language: If r and s are bounded, regular regions that are not related by an affine transformation, then they can be distinguished by a constraint network. That is, there is a constraint network and a particular node in that network such that there is a solution where the node is equal to r, but no solution where the node is equal to s.     

The m-pancycle-connectivity of a WK-Recursive network

In this paper, we study the m-pancycle-connectivity of a WK-Recursive network. We show that a WK-Recursive network with amplitude W and level L is strictly (5 × 2^L−1 − 2)-pancycle-connected for W ? 3. That is, each pair of vertices in a WK-recursive network with amplitude greater than or equal to 3 resides in a common cycle of every length ranging from 5 × 2^L−1 − 2 to N, where N is the size of the interconnection network; and the value 5 × 2^L−1 − 2 reaches the lower bound of the problem.     

Enhancing a leaf radiative transfer model to estimate concentrations and in vivo specific absorption coefficients of total carotenoids and chlorophylls a and b from single-needle reflectance and transmittance

The relative concentrations of different pigments within a leaf have significant physiological and spectral consequences. Photosynthesis, light use efficiency, mass and energy exchange, and stress response are dependent on relationships among an ensemble of pigments. This ensemble also determines the visible characteristics of a leaf, which can be measured remotely and used to quantify leaf biochemistry and structure. But current remote sensing approaches are limited in their ability to resolve individual pigments. This paper focuses on the incorporation of three pigments—chlorophyll a, chlorophyll b, and total carotenoids—into the LIBERTY leaf radiative transfer model to better understand relationships between leaf biochemical, biophysical, and spectral properties.Pinus ponderosa and Pinus jeffreyi needles were collected from three sites in the California Sierra Nevada. Hemispheric single-leaf visible reflectance and transmittance and concentrations of chlorophylls a and b and total carotenoids of fresh needles were measured. These data were input to the enhanced LIBERTY model to estimate optical and biochemical properties of pine needles. The enhanced model successfully estimated reflectance (RMSE = 0.0255, BIAS = 0.00477, RMS%E = 16.7%), had variable success estimating transmittance (RMSE = 0.0442, BIAS = 0.0294, RMS%E = 181%), and generated very good estimates of carotenoid concentrations (RMSE = 2.48 µg/cm², BIAS = 0.143 µg/cm², RMS%E = 20.4%), good estimates of chlorophyll a concentrations (RMSE = 10.7 µg/cm², BIAS = − 0.992 µg/cm², RMS%E = 21.1%), and fair estimates of chlorophyll b concentrations (RMSE = 7.49 µg/cm², BIAS = − 2.12 µg/cm², RMS%E = 43.7%). Overall root mean squared errors of reflectance, transmittance, and pigment concentration estimates were lower for the three-pigment model than for the single-pigment model. The algorithm to estimate three in vivo specific absorption coefficients is robust, although estimated values are distorted by inconsistencies in model biophysics. The capacity to invert the model from single-leaf reflectance and transmittance was added to the model so it could be coupled with vegetation canopy models to estimate canopy biochemistry from remotely sensed data.     

(?, T)-fuzzy rough approximation operators and the TL-fuzzy rough ideals on a ring

In this paper, we consider a ring as a universal set and study (?, T)-fuzzy rough approximation operators with respect to a TL-fuzzy ideal of a ring. First, some new properties of generalized (?, T)-fuzzy rough approximation operators are obtained. Then, a new fuzzy algebraic structure - TL-fuzzy rough ideal is defined and its properties investigated. And finally, the homomorphism of (?, T)-fuzzy rough approximation operators is studied.     

A dynamic programming algorithm for simulation of a multi-dimensional torus in a crossed cube

The torus is a popular interconnection topology and several commercial multicomputers use a torus as the basis of their communication network. Moreover, there are many parallel algorithms with torus-structured and mesh-structured task graphs have been developed. If one network can embed a mesh or torus network, the algorithms with mesh-structured or torus-structured can also be used in this network. Thus, the problem of embedding meshes or tori into networks is meaningful for parallel computing. In this paper, we prove that for n ? 6 and 1 ? m ? ⌈n/2⌉ − 1, a family of 2^m disjoint k-dimensional tori of size 2^s₁×2^s₂×?×2^s_k each can be embedded in an n-dimensional crossed cube with unit dilation, where each s_i ? 2, , and max_1?i?k{s_i} ? 3 if n is odd and ; otherwise, max_1?i?k{s_i} ? n − 2m − 1. A new concept, cycle skeleton, is proposed to construct a dynamic programming algorithm for embedding a desired torus into the crossed cube. Furthermore, the time complexity of the algorithm is linear with respect to the size of desired torus. As a consequence, a family of disjoint tori can be simulated on the same crossed cube efficiently and in parallel.     

Comments on “Generalised finite Radon transform for N × N images”

In Kingston and Svalbe [1], a generalized finite Radon transform (FRT) that applied to square arrays of arbitrary size N × N was defined and the Fourier slice theorem was established for the FRT. Kingston and Svalbe asserted that “the original definition by Matúš and Flusser was restricted to apply only to square arrays of prime size,” and “Hsung, Lun and Siu developed an FRT that also applied to dyadic square arrays,” and “Kingston further extended this to define an FRT that applies to prime-adic arrays”. It should be said that the presented generalized FRT together with the above FRT definitions repeated the known concept of tensor representation, or tensor transform of images of size N × N which was published earlier by Artyom Grigoryan in 1984-1991 in the USSR. The above mentioned “Fourier slice theorem” repeated the known tensor transform-based algorithm of 2-D DFT [5-11], which was developed for any order N₁ × N₂ of the transformation, including the cases of N × N, when N = 2^r, (r > 1), and N = L^r, (r ≥ 1), where L is an odd prime. The problem of “over-representation” of the two-dimensional discrete Fourier transform in tensor representation was also solved by means of the paired representation in Grigoryan [6-9].