Type Of Partition Research Articles

Time-Dependent Multiconfiguration Theory and Its Application to Ultrafast Electronic Dynamics of Molecules in an Intense Laser Field

(spin-orbitals) as Φ(t )= P I CI (t)ΦI (t). The equations of motion (EOMs) for spin-orbitals in coordinate representation are derived together with the EOMs for configuration interaction coefficients CI (t). As an example of application to molecules, we presented the results of investigation of the ionization dynamics of H2 interacting with a near-infrared intense laser filed. By extending the concept of Hartree-Fock orbital energy to multiconfiguration theory, we newly introduced the molecular orbital of natural spin-orbitals (NSOs) {j} of a many-electron system and defined the orbital potentialsj(t) and correlation energies V c j (t) of NSOs. The total energy E(t) is decomposed into individual components as E(t )= P j ωj(t)¯ � j(t )a s in thermodynamics, whereωj(t) are the occupation numbers of {j} .W e proved that this type of partition of the total energy is interpreted as the time-dependent chemical potential for the two-electron system. The newly defined correlation energy V c j (t) associated with the j th NSO, involved inj(t), reflects dynamical electron correlations on the attosecond timescale. We also compared the energy ζj(t) directly supplied by the applied field with the net energy gain Δ¯ j (t) for respective natural orbitals. The responses of natural orbitals can be classified into three: Δ¯ j (t )= ζj (t) (spectator orbital); Δ¯ j(t) ζ j(t) (energy acceptor orbital). We found that ionization of H2 most efficiently occurs from a time-developing energy acceptor NSO 2σg for the case of the present applied field. We concluded that energy acceptor natural orbitals play a key role in ionization processes.

Double Star Embedded Clustering Algorithm for Wireless Ad Hoc Networks Using Ranking

Clustering of mobile ad hoc network (MANET) is an important concept, which partitions node set into many classes such that each class has some structural property. In literature, there are many papers available, which are due to star topology clusters. In this paper, a new concept of k-hop double star embedded clustering is introduced, in which each cluster has a master, a proxy and two types of slaves. The slaves in the cluster are adjacent to either the master or the proxy or both and themselves. Clearly, this type of partition of the network will induce less number of clusters than the star clustering. Extending the concept of ranking of nodes done by authors in T.N. Janakiraman and J. Janet Lourds Rani, An efficient k-hop weighted domination clustering algorithm for mobile ad hoc networks using ranking, IEEE Proceedings of the International Conference on Computational Intelligence and Multimedia Applications 2007 (ICCIMA ’07) based on the signal strength, in this paper, the edges are also ranked based on reliability of having more number of common nodes and four-con-cyclic neighbours to the end vertices of the edges. Comparing to star clusters, it is clear that this procedure produces lesser number of clusters and also with increasing reliability. Clearly, the double star embedded cluster of the given network must have a sub graph, which is a double star having a master and a proxy as a central pair of nodes.

On application of input data partitioning to Bayesian weighted averaging of biomedical signals

AbstractAveraging in the time domain may be used for noise attenuation in case of biomedical signals with a quasi‐cyclical character. Traditional arithmetic averaging technique assumes the constancy of the noise power cycle‐wise, however, most types of noise are not stationary and the variability of noise power is observed. It constitutes a motivation for using methods of weighted averaging, in particular Bayesian weighted averaging. This paper presents the computational study of Bayesian weighted averaging with traditional (sharp) and fuzzy partition of the input data in the presence of non‐stationary noise. There is presented the known empirical Bayesian weighted averaging method (EBWA), with the parameter p describing the probabilistic model, and its modification NBWA which eliminates the parameter. Both methods can be extended by partitioning of the input data. The performance of presented methods is experimentally evaluated for an analytical signal as well as a real ECG signal and compared with traditional arithmetic averaging method. However, the methods can be applied to any signal with a quasi‐cyclical character. The aim of the paper is to show the influence of the type of partition as well as the number of parts on the quality of the averaged signal.

Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions

In this paper we study the relation between pyramid partitions with a general empty room configuration (ERC) and the BPS states of D-branes on the resolved conifold. We find that the generating function for pyramid partitions with a length n ERC is exactly the same as the D6/D2/D0 BPS partition function on the resolved conifold in particular Kahler chambers. We define a new type of pyramid partition with a finite ERC that counts the BPS degeneracies in certain other chambers.

SIMPLIFIED FUZZY INFERENCE RULE-BASED GENETICALLY OPTIMIZED HYBRID FUZZY NEURAL NETWORKS

In this study, we introduce an advanced architecture of genetically optimized Hybrid Fuzzy Neural Networks (gHFNN) and develop a comprehensive design methodology supporting their construction. A series of numeric experiments is included to illustrate the performance of the networks. The construction of gHFNN exploits fundamental technologies of Computational Intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms (GAs). The architecture of the gHFNNs results from a synergistic usage of the genetic optimization-driven hybrid system generated by combining Fuzzy Neural Networks (FNN) with Polynomial Neural Networks (PNN). In this tandem, a FNN supports the formation of the condition part of the rule-based structure of the gHFNN. The conclusion part of the gHFNN is designed using PNNs. We distinguish between two types of the simplified fuzzy inference rule-based FNN structures showing how this taxonomy depends upon the type of a fuzzy partition of input variables. As to the conclusion part of the gHFNN, the development of the PNN dwells on two general optimization mechanisms: the structural optimization is realized via GAs whereas in case of the parametric optimization we proceed with a standard least square method-based learning. To evaluate the performance of the gHFNN, we experimented with three representative numerical examples. A comparative analysis demonstrates that the proposed gHFNN come with higher accuracy as well as superb predictive capabilities when compared with other neurofuzzy models.

THERMAL ENTANGLEMENT IN SPIN SYSTEMS

We examine the entanglement of thermal states of n spins interacting through an XYZ type Heisenberg coupling in the presence of a uniform magnetic field, by evaluating the negativities of bipartite partitions of the whole system and subsystems. The corresponding limit temperatures for entanglement are also examined. Results indicate that limit temperatures for global entanglement depend on the type of partition and are higher than those limiting pairwise entanglement, and that their behavior with anisotropy and applied magnetic field may differ significantly from that of the corresponding mean field critical temperature.

Enumeration of M-partitions

An M-partition of a positive integer m is a partition of m with as few parts as possible such that every positive integer less than m can be written as a sum of parts taken from the partition. This type of partition is a variation of MacMahon's perfect partition, and was recently introduced and studied by O’Shea, who showed that for half the numbers m , the number of M-partitions of m is equal to the number of binary partitions of 2 n + 1 - 1 - m , where n = ⌊ log 2 m ⌋ . In this note we extend O’Shea's result to cover all numbers m .

An Optimal Adaptive Finite Element Method

Although existing adaptive finite element methods for solving second order elliptic equations often perform better in practical computations than nonadaptive ones, usually they are not even proven to converge. Only recently in the work of Dörfler [SIAM J. Numer. Anal., 33 (1996), pp. 1106--1124] and that of Morin, Nochetto, and Siebert [SIAM J. Numer. Anal., 38 (2000), pp. 466--488], adaptive methods were constructed for which convergence could be demonstrated. However, convergence alone does not imply that the method is more efficient than its nonadaptive counterpart. In [ Numer. Math.}, 97 (2004), pp. 219--268], Binev, Dahmen, and DeVore added a coarsening step to the routine of Morin, Nochetto, and Siebert, and proved that the resulting method is quasi-optimal in the following sense: If the solution is such that for some s > 0, the error in energy norm of the best continuous piecewise linear approximations subordinate to any partition with n triangles is $\mathcal{O}(n^{-s})$, then given an $\eps>0$, the adaptive method produces an approximation with an error less than $\eps$ subordinate to a partition with $\mathcal{O}(\eps^{-1/s})$ triangles, in only $\mathcal{O}(\eps^{-1/s})$ operations. In this paper, employing a different type of adaptive partition, we develop an adaptive method with properties similar to those of Binev, Dahmen, and DeVore's method, but unlike their method, our coarsening routine will be based on a transformation to a wavelet basis, and we expect it to have better quantitative properties. Furthermore, all our results are valid uniformly in the size of possible jumps of the diffusion coefficients. Since the algorithm uses solely approximations of the right-hand side, we can even allow right-hand sides in $H^{-1}(\Omega)$ that lie outside $L_2(\Omega)$, at least when they can be sufficiently well approximated by piecewise constants. In our final adaptive algorithm, all tolerances depend on an a posteriori estimate of the current error instead of an a priori one; this can be expected to provide quantitative advantages.

Variable dimension range and domain block-based fractal image coding

Proposes some variable-dimension block-based fractal image-coding schemes which employ encoding of fixed and variable-dimension range blocks with fixed and variable-dimension domain blocks. The first decision to be made in a variable-dimension fractal coding scheme is in the choice of the type of image partition used for the range blocks. We propose a partition based on a rate-distortion criterion such that the range block sizes and domain block sizes are selected adaptively by the algorithm itself based on the complexity of the image region that is being encoded. Variable domain blocks address the nonuniformity of fractal scaling across the image as manifested by different resampling ratios across the image. Variable range blocks address the nonstationarity of the image. So, this algorithm provides a general framework of variable range, variable domain fractal encoding. All fixed-dimension fractal coding schemes are constrained variation of this generalized version.

Morphology of the hallux sesamoids

Recognition of congenital variations in the shape, size and partition of the hallux sesamoids is important, in order to distinguish these developmental anomalies from acquired pathologies such as fractures, osteomyelitis and osteonecrosis. There are, however, controversies regarding the shape and the incidence of partition of these bones. Kewenter [Acta Orthop Scand (1936)], who reviewed radiographs of 800 patients found partition in 33% whereas Inge and Ferguson [Arch Surg 27 (1933) 466], found only 10% partition in 560 patients. We reviewed 1025 patients, (1242 feet) the largest number in the literature to date and found that in 19% of them the sesamoids showed some type of partition. We also found four cases with one absent sesamoid and we also described some new types of partition. We confirmed that there are no differences between sexes in the incidence and type of partition, and that there is often asymmetry in the appearance of the sesamoids in the two feet of one individual.

Classification des difféomorphismes de Smale des surfaces : types géométriques réalisables

Geometrical types of Markov partitions are the main tools of the classification of Smale diffeomorphisms of surfaces, i.e., C 1 -structurally stable diffeomorphisms of surfaces. In this paper, we solve the realisability problem: we give an effective criterion to decide whether an abstract combinatorial object is, or is not, the geometrical type of a Markov partition of a basic piece of a Smale diffeomorphism on a compact surface.

Geometry dependence of the dimension of spaces of piecewise polynomials on rectilinear partitions

We consider the vector space of piecewise polynomials of total degree d and global smoothness order r on a certain type of rectilinear partition. The dimension of the space is shown to depend on the geometric relationship of a set of edges that are not all attached to one vertex. The geometric dependence persists even when d is large relative to r. This resultcontrasts with earlier results for spaces of piecewise polynomials on triangulations where, for d ⩾ 3 r + 2, the dimension of the space is a function of the graph of the partition and the number of edges with different slopes attached to each interior vertex.

Work Space Adjustability, Storage, And Enclosure As Predictors Of Employee Reactions And Performance

This study develops and tests a conceptual model of the relationships between work space adjustability, storage, and enclosure characteristics, mediating psychosocial perceptions of privacy, distractions, and communication, and outcome measures of satisfaction and performance. Building design and job level variables are also included in the model. A total of 541 managerial and nonmanagerial workers in 14 office buildings located across the United States provided data. Regression and path analyses reveal overall support for the relationships hypothesized by the model. The analyses show that adjustability and storage contribute directly to satisfaction and performance, and indirectly to these outcomes through mediating perceptions of the psychosocial environment. Enclosure played only a minor role in predicting mediating and outcome variables. One aspect of enclosure, type of partition surrounding the work space, predicts communication and privacy, but is only indirectly related to outcome measures. There is a negative relationship between number of floors and density of workers, and some psychosocial perceptions and satisfaction. A positive relationship was found between job level and satisfaction. The study illustrates the value of a multivariate approach to understanding the relative contributions of design variables to worker perceptions and behavior.

On optimal guillotine partitions approximating optimal d-box partitions

Given a set of n points, P, in E d (the plane when d = 2) that lie inside a d-box (rectangle when d = 2) R, we study the problem of partitioning R into d-boxes by introducing a set of orthogonal hyperplane segments (line segments when d = 2) whose total ( d − 1)-volume (length when d = 2) is the least possible. In a valid d-box partition, each point in P must be included in at least one partitioning orthogonal hyperplane segment. Since this minimization problem is NP-hard and thus likely to be computationally intractable, we present an approximation algorithm to generate a suboptimal solution. This solution is obtained by finding an optimal guillotine partition, i.e., a special type of rectangular partition, which can be generated in O( dn 2 d+1 ) time. We present a simple proof that the ( d − 1)-volume of an optimal guillotine partition is not greater than 2 d − 4 + 4/ d times the ( d − 1)-volume of an optimal d-box partition.

Extracting dynamic parameters from speech movement data

A quantitative characterization of articulatory movements, using the parameter values of a linear second-order dynamical system, was developed in order to compare classes of movements, in particular, classes defined by linguistic factors such as syllable position, stress, and vowel quality. Movements of the lower lip in utterances such as ['bibebib] and [babe'bab] were partitioned into sections ("windows") in two ways: at successive displacement peaks and valleys, and at the right edge of plateau regions around such extreme values. The linguistic factors affected natural frequency in similar ways regardless of whether damping ratio was permitted to vary or held fixed at one of several different values. Damping ratio was generally unaffected by the linguistic factors. For the most part, the type of partition or window did not affect the patterns of the results, with the exception of the closing gesture out of the reduced syllable.

A new type of Littlewood-Paley partition

We define a partition of Z into intervals {I j} and prove the Littlewood-Paley inequality ‖f‖ p ≦C p‖Sf‖ p , 2≦p<∞. Heref is a function on [o, 2π) and\(Sf = (\sum |\Delta _j |^2 )^{1/2} , \hat \Delta j = \hat f\chi _{Ij} \). This is a new example of a partition having the Littlewood-Paley property since the {I j} are not of the type obtained by iterating lacunary partitions finitely many times.

MEASUREMENT AND IMPACT OF OUTDOOR AIR SUPPLIED TO INDIVIDUAL OFFICE BUILDING OCCUPANTS ON INDOOR AIR QUALITY

A novel procedure has been developed to measure, under field conditions, the portion of outdoor air that is supplied to individual building occupants. The method is simpler to use than measurement of ventilation efficiency and ventilation effectiveness procedures. This method also takes into consideration factors associated with office design that can have a significant effect on this parameter. The method is based on the constant release of tracer gas into the outdoor air introduced into a ventilation system and its measurement, at steady state, at individual work stations. The values obtained are called outdoor air supply indexes (OASls) to differentiate them from those found with the measurement of ventilation efficiency or effectiveness, which refer to the performance of a mechanical ventilation and air-distribution system. The results indicate that the type of diffuser, office, partition, and return air inlet and their position relative to each other can have a dramatic effect on the amount of outdoo...

FREQUENCY DISTRIBUTIONS OF LENGTHS OF POSSIBLE NETWORKS FROM A DATA MATRIX.

Abstract- It is common practice to attempt to find the minimum length tree (also known as the Wagner tree) for a given data matrix on a group of OTUs (taxa). However, little study has been made of the pattern of frequency distributions when the lengths of all possible networks (unrooted trees) are taken into consideration. A published real data matrix with eight OTUs was compared with randomly generated data, when the former showed a much larger variance and very marked skewness. A number of published data matrices with a larger number of OTUs were studied by random selection of 10240 out of the possible trees: these were compared with 32 randomly generated data sets with 13 OTUs, using the same program. An algorithm has been found for calculation of the expected mean, variance and skewness for random binary data with up to 13 OTUs, based on the number of characters representing each type of partition of the OTUs. The calculation requires listing of the possible topologies and their relative weighting, which are tabulated.

Bonding and stability of the Cr + ion in octahedral fluoride lattices: Results of approximate Hartree-Fock-Roothaan calculations

Frozen-core Hartree-Fock-Roothaan calculations at several values of the metal-fluoride distance have been performed for the (CrF 6) 5− cluster in an attempt to study the stability of the Cr +F − bond in fluoride lattices. The separate effects on the 6 A 1 g ground state of the 3 d basis set and the type of corevalence partition have been analyzed. Whereas inclusion of the 3 s and 3 p metallic AO's in the valence shell seems to be unnecessary for obtaining a stable cluster ground state, the diffuse 4 s and 4 p AO's play a significant role in describing the equilibrium geometry of this complex ion. The metal-ligand covalency is examined and related to the information deduced from the curvature of the 6 A 1 g nuclear potential and the orbital energies of the valence MO's. Consideration of the point-charge lattice potential of the NaF leaves the cluster electron density almost unchanged but noticeably decreases the cluster valence energy. It also reduces the size of the cluster by nearly 0.2 Å. As an alternative stabilizing mechanism, a ligand-to-lattice charge transfer has been explored. At the cluster- in-vacuo level it produces electron-deficient clusters more stable than the (CrF 6) 5− unit. As an example, the 7 T 1 u state of the neutral CrF 6 cluster (a system in which the oxidation state of the metal is nominally +1) has been computed and compared with the 6 A 1 g state. This CrF 6 unit turns out to be smaller and more strongly bonded than the (CrF 6) 5− ion but the latter becomes more stable when the point-charge potential of the NaF is taken into account.

Polyman — A system for polynomials

An M-partition of a positive integer m is a partition of m with as few parts as possible such that every positive integer less than m can be written as a sum of parts taken from the partition. This type of partition is a variation of MacMahon's perfect partition, and was recently introduced and studied by O’Shea, who showed that for half the numbers m, the number of M-partitions of m is equal to the number of binary partitions of 2n+1-1-m, where n=⌊log2m⌋. In this note we extend O’Shea's result to cover all numbers m.