Nontrivial Component Research Articles

On the question of 3D seed reconstruction in prostate brachytherapy: the determination of x-ray source and film locations

Inaccuracy in seed placement during permanent prostate implants may lead to significant dosimetric deviations from the intended plan. In two recent publications (Todor et al 2002 Phys. Med. Biol. 47 2031–48, Todor et al 2003 Phys. Med. Biol. 48 1153–71), methodology was described for identifying intraoperatively the positions of seeds already implanted, thus allowing re-optimization of the treatment plan and correcting for such seed misplacement. Seed reconstruction is performed using fluoroscopic images and an important (and non-trivial) component of this approach is the ability to accurately determine the position of the gantry relative to the treatment volume. We describe the methodology for acquiring this information, based on the known geometry of six markers attached to the ultrasound probe. This method does not require the C-arm unit to be isocentric and films can be taken with the gantry set at any arbitrary position. This is significant because the patient positioning on the operating table (in the lithotomy position) restricts the range of angles at which films can be taken to a quite narrow (typically ±10°) interval and, as a general rule, the closer the angles the larger the uncertainty in the seed location reconstruction along the direction from the x-ray source to the film.

Probing dark energy perturbations: The dark energy equation of state and speed of sound as measured by WMAP

We review the implications of having a nontrivial matter component in the Universe and the potential for detecting such a component through the matter power spectrum and integrated Sachs-Wolfe effect. We adopt a phenomenological approach and consider the mysterious dark energy to be a cosmic fluid. It is thus fully characterized, up to linear order, by its equation of state and its speed of sound. Whereas the equation of state has been widely studied in the literature, less interest has been devoted to the speed of sound. Its observational consequences come predominantly from very large scale modes of dark matter perturbations $(kl0.01h{\mathrm{Mpc}}^{\ensuremath{-}1}).$ Since these modes have hardly been probed so far by large scale galaxy surveys, we investigate whether joint constraints can be placed on those two quantities using the recent cosmic microwave background (CMB) fluctuations measurements by the Wilkinson Microwave Anisotropy Probe as well as the recently measured CMB large scale structure cross correlation. We find only a tentative 1 sigma detection of the speed of sound, from CMB alone, ${c}_{s}^{2}l0.04$ at this low significance level. Furthermore, the current uncertainties in bias in the matter power spectrum preclude any constraints being placed using the cross correlation of CMB with the NRAO VLA Sky Survey radio survey.

The temporal prior in bioelectromagnetic source imaging problems.

The multiplicity of temporal priors proposed for regularization of the bioelectromagnetic source imaging problems [e.g., the inverse electrocardiogram (ECG) and inverse electroencephalogram (EEG) problems], is discordant with the fact that fundamental statistical principles sharply limit the choice. Thus, our objective is to derive the form of the prior consistent with the general unavailability of temporal constraints. Writing linear formulations of the inverse ECG and inverse EEG problems as H = FG + N (where the ith columns of matrices H, G, and N, are data, signal, and noise vectors at time step i, and F is the transfer matrix), and using the noninformative principle that features of the spatiotemporal prior not supplied a posteriori should be invariant under temporal transformations, we show that the implied spatiotemporal signal autocovariance matrix (of the vector formed by the entries of G) is given in block matrix form [equation in text] where Cg is a matrix of unit trace proportional to the autocovariance matrix of any column of G (representing supplied information regarding the spatial prior), epsilon[.] denotes expectation, superscript ' indicates transpose, [symbol in text] is the Kronecker product, [symbol in text] is Frobenius norm, and the "matrix scalar product" [symbol in text] indicates the inner product of the two vectors formed by the entries of the two adjacent matrices (i.e., A [symbol in text] B [triple bond] trace[A'B]). This result eliminates some uncertainties and ambiguities that have characterized spatiotemporal regularization methods--including eight methods previously introduced in this transactions. Ultimately, the result derives from an implied symmetry principle under which the form of a nontrivial noninformative temporal component of the prior can be identified. Among other things, separability of the spatiotemporal prior in terms of the above Kronecker product can be thought of as the expression of the lack of "entanglement" of the spatial and temporal contributions (a consequence of noninformativity). The approach is generalized to the important cases of non-Gaussian spatial priors, and signal and noise that are not independent (transfer matrix noise). We also demonstrate a means for computational complexity reduction, related to the application of a particular orthogonal transformation, having features dependent on whether or not the transfer matrix represents a surjective mapping.

Z-transformation graphs of maximum matchings of plane bipartite graphs

Let G be a plane bipartite graph. The Z-transformation graph Z(G) and its orientation Z→(G) on the maximum matchings of G are defined. If G has a perfect matching, Z(G) and Z→(G) are the usual Z-transformation graph and digraph. If G has neither isolated vertices nor perfect matching, then Z(G) is not connected. This paper mainly shows that some basic results for Z-transformation graph (digraph) of a plane elementary bipartite graph still hold for every nontrivial component of Z(G)(Z→(G)). In particular, by obtaining a result that every shortest path of Z(G) from a source of Z→(G) corresponds to a directed path of Z→(G), we show that every nontrivial component of Z→(G) has exactly one source and one sink. Accordingly, it follows that the block graph of every nontrivial component of Z(G) is a path. In addition, we give a simple characterization for a maximum matching of G being a cut-vertex of Z(G).

Super Edge Least-Magic Graphs

Abstract A (p, q)-graph G = (V, E) is said to be super edge—magic if there exists a bijection f fromV ∪ E to {1, 2, 3,…, p + q } with vertices maps to {1, 2, 3,…, p} such that for all edges uv of G, f(u) + f(v) + f(uv) is a constant and bijection so denned is called a super edge— magic labeling of G, For any super edge—magic labeling of G, there is a constant c(f) such that for all edges uv of G, f(u) + f(v) + f(uv) = c(f) and its range is p + q + 3 ≤ c(f) ≤ 3p. In this paper we study super edge—magic graphs with constant c(f) = p+q +3 for at least one f and such graphs are denned as super edge least—magic(SEL—magic) graphs. We investigate the following general results on the structure of SEL—magic graphs including a result, which determines all the regular SEL—magic graphs. (1) A SEL—magic graph is either a forest with exactly one nontrivial component, which is a star or has a triangle. (2) If an eulerian (p,q)-graph G = (V, E) is SEL—magic then q ≡ 0, 3(mod4). (3) The minimum vertex degree δ of any SEL—monograph is at most 3. (4) There are exactly three nontrivial regular graphs K2,K3 and K2 × K3 which are SEL—magic. Also we define level joined planar grid graph L J : P m × P n and prove that it is SEL—magic. Also we give a general method of constructing new SEL—magic graphs from any given SEL—magic graph.

Right Inverses of Nonsymmetric Lévy Processes

We analyze the existence and properties of right inverses $K$ for nonsymmetric Lévy processes $X$, extending recent work of Evans in the symmetric setting. First, both $X$ and $-X$ have right inverses if and only if $X$ is recurrent and has a nontrivial Gaussian component. Our main result is then a description of the excursion measure $n^Z$ of the strong Markov process $Z=X-L$ (reflected process) where $L_t=\inf\{x>0:K_x>t\}$. Specifically, $n^Z$ is essentially the restriction of $n^X$ to the ``excursions starting negative.'' Second, when only asking for right inverses of $X$, a certain ``strength of asymmetry'' is needed. Millar's notion of creeping turns out necessary but not sufficient for the existence of right inverses. We analyze this both in the bounded and unbounded variation case with a particular emphasis on results in terms of the Lévy–Khintchine characteristics.

Global direct radiative forcing due to multicomponent anthropogenic and natural aerosols

Global simulations of the composition of and direct forcing due to aerosols containing natural and/or anthropogenic sulfate, nitrate, chloride, carbonate, ammonium, sodium, calcium, magnesium, potassium, black carbon, organic matter, silica, ferrous oxide, and aluminum oxide were carried out. Chloride and natural sulfate were found to be the most important natural aerosol constituents in the atmosphere in terms of solar plus thermal‐infrared forcing. Sea spray was the most important natural aerosol type, indicating that it should be accounted for in weather and climate calculations. Ammonium was found to have a positive direct forcing, since it reduces water uptake in sulfate‐containing solutions; thus, anthropogenic ammonium contributes to global warming. The magnitudes of ammonium and nitrate forcing were smaller than those of chloride or sulfate forcing. When organics were divided into three groups with different assumed UV absorption characteristics, total aerosol direct forcing at the tropopause increased by about +0.03 to +0.05 W m−2 (direct forcing by organics remained negative), suggesting that UV absorption by organics is a nontrivial component of the global energy balance. Gypsum [CaSO4‐2H2O], sal ammoniac [NH4Cl], halite [NaCl], halite, and nitrum [KNO3] were estimated to be the most common sulfate‐, ammonium‐, sodium‐, chloride‐, and nitrate‐containing solid‐phase aerosol constituents, respectively, in the global atmosphere. Solid formation in aerosols was found to increase total‐aerosol direct forcing by +0.03 to +0.05 W m−2. Spatial and vertical forcing estimates, sensitivities of forcing to relative humidity and concentration, and estimates of global aerosol liquid water content are given. Modeled aerosol optical properties are compared with satellite and field measurements.

Association and linkage for age at onset of a common oligogenic disease using genetic variance component models.

The aims of our analysis were: (1) to investigate association of single nucleotide polymorphisms (SNPs) and other covariates with age at onset in the simulated Genetic Analysis Workshop (GAW) 12 general population data, and (2) to use the polygenic random effects estimated during model fitting (sigma squared A random effects) as input to a Haseman-Elston linkage analysis. The association analyses used genetic variance component models in a generalized linear mixed models framework and were fitted using Gibbs sampling. This method successfully detected the only three sequenced genes that were also major genes. The single-point linkage analysis used all markers provided. Regions of linkage were found close to all four of the sites of major genes that explained a non-trivial component of the variance of age at onset. In all four cases the linkage peak fell within 5 cM of the true location. In three cases the peak significance was p < 0.01.

Right inverses of Lévy processes and stationary stopped local times

If X is a symmetric Lévy process on the line, then there exists a non-decreasing, càdlàg process H such that X(H(x)) = x for all x≥ 0 if and only if X is recurrent and has a non-trivial Gaussian component. The minimal such H is a subordinator K. The law of K is identified and shown to be the same as that of a linear time change of the inverse local time at 0 of X. When X is Brownian motion, K is just the usual ladder times process and this result extends the classical result of Lévy that the maximum process has the same law as the local time at 0. Write G t for last point in the range of K prior to t. In a parallel with classical fluctuation theory, the process Z := (X t −X Gt ) t ≥0 is Markov with local time at 0 given by (X Gt ) t ≥0. The transition kernel and excursion measure of Z are identified. A similar programme is outlined for Lévy processes on the circle. This leads to the construction of a stopping time such that the stopped local times constitute a stationary process indexed by the circle.

On Form-Sum Approximations of Singularly Perturbed Positive Self-adjoint Operators

We discuss singular perturbations of a self-adjoint positive operator A in Hilbert space H formally given by AT=A+T, where T is a singular positive operator (singularity means that KerT is dense in H). We prove the following result: if T is strongly singular with respect to A in the sense that KerT is dense in the Hilbert space H1(A)=D(A1/2) equipped by the graph-norm, then any suitable approximation by positive operators, Tn→T, gives a trivial result, i.e., ATn→A in the strong resolvent sense, where ATn is defined as a form-sum of A and Tn. A corresponding statement is true for operators T, Tn of finite rank which are not necessarily positive. This can be considered as an abstract version of the well known result for the perturbation by a point interaction of the Laplace operator in L2(R3). In the more general case, where the singular operator T has a nontrivial regular component Tr in H1(A), we prove that ATn→ATr in the strong resolvent sense. We give applications to the case of perturbations of the Laplace operator by a positive Radon measure with a nontrivial singular component.

On the abelian inner permutation groups of loops

Let Q be a loop such that the inner permutation group I(Q) of Q is finite and abelian. The aim of the present note is to show that Q is then centrally nilpotent and no non-trivial primary component of I(Q) is cyclic. Notice that this is a generalization of [5, 2.1,2.4] and [7, 6.2,6.4], where the mentioned results are proved for finite loops.

Self-Adjoint Fredholm Operators And Spectral Flow

AbstractWe study the topology of the nontrivial component, , of self-adjoint Fredholm operators on a separable Hilbert space. In particular, if {Bt} is a path of such operators, we can associate to {Bt} an integer, sf({Bt}), called the spectral flow of the path. This notion, due to M. Atiyah and G. Lusztig, assigns to the path {Bt} the net number of eigenvalues (counted with multiplicities) which pass through 0 in the positive direction. There are difficulties in making this precise — the usual argument involves looking at the graph of the spectrum of the family (after a suitable perturbation) and then counting intersection numbers with y = 0.We present a completely different approach using the functional calculus to obtain continuous paths of eigenprojections (at least locally) of the form . The spectral flow is then defined as the dimension of the nonnegative eigenspace at the end of this path minus the dimension of the nonnegative eigenspace at the beginning. This leads to an easy proof that spectral flow is a well-defined homomorphism from the homotopy groupoid of onto Z. For the sake of completeness we also outline the seldom-mentioned proof that the restriction of spectral flow to is an isomorphism onto Z.

Gas diffusivity and production of CO2 in deep soils of the eastern Amazon

The rate of gaseous diffusion in soils affects the exchange of gases between the soil and the atmosphere, thereby affecting rates of soil respiration and other soil microbial processes. Understanding the causes of spatial and temporal variation in soil diffusivity will help explain controls of soil sources and sinks of atmospheric gases. In a study of sources of CO 2 in deep soils of forests and pastures of the eastern Amazon, we estimated gaseous diffusivity from bulk density and volumetric water content using published equations that assume the soil to be either an aggregated or nonaggregated medium. The aggregated model requires differentiation of interand intra-aggregate pore space; we estimated intra-aggregate pore space from volumetric water content at field capacity. Steady state 222 Rn profiles were predicted from a 1-D model using the diffusivities generated by both aggregated and nonaggregated models. Predicted values were compared with 222 Rn activities measured to 5 m depth. While the models predict similar radon activities below about 1 m, large differences are predicted for the top 1 m of soil. The nonaggregated model underestimated diffusivity and overestimated 222 Rn activities at 1 m and above, which is not surprising given that surface soils are usually well aggregated. Having validated the aggregated media model using the 222 Rn profiles, estimates of diffusivity were combined with measured profiles of CO 2 concentrations to estimate CO 2 production by depth. About 70-80% of the measured CO 2 flux from the soil surface was produced in the top 1 m of soil (including litter in the forest). The 20-30% produced below 1 m results from root respiration and microbial decay of root inputs at depth, indicating that deep soil processes are a non-trivial component of carbon cycling in these deep-rooting ecosystems. About 1% of the 20 kg C m -2 stock of soil C found between 1 m and 8 m depths turns over annually, indicating that land-use changes that affect rooting depth could significantly affect deep soil C stocks over decades to centuries. Fully understanding the role of land-use change on the global carbon cycle will require consideration of these deep soil processes. DOI: 10.1034/j.1600-0889.47.issue5.3.x

The edge reconstruction number of a disconnected graph

AbstractThe edge reconstruction number of a graph G, RN(G), is the minimum number of edge deleted subgraphs required to determine G up to isomorphism. We prove the following results for a disconnected graph G with at least two nontrivial components. If G has a pair of nontrivial nonisomorphic components then RN(G) ≤ 3. If G has a pair of nontrivial nonisomorphic components, is not a forest, and contains a nontrivial component other than K3 or K1,3 then RN(G) ≤ 2. Finally, if all nontrivial components of G are isomorphic to a graph with k edges, then RN(G) ≤ k + 2. The edge reconstruction results in this paper are similar to the vertex reconstruction results stated by Myrvold (“The Ally‐Reconstruction Number of a Disconnected Graph,” Ars Combinatoria, Vol. 28 [1989] pp. 123‐127), but a significant difference is that the edge reconstruction number of a disconnected graph is often two, while the vertex reconstruction number of a graph is always three or more. © 1995 John Wiley &amp; Sons, Inc.

Strongly indexable graphs

A ( p, q)-graph G = ( V, E) is said to be strongly k-indexable if it admits a strong k-indexer viz., an injective function ƒ:V→{0, 1, 2, …, p − 1} such that ƒ(x)+ƒ(y)=ƒ +(xy)ϵ⨍ +(E)={k, k + 1, k + 2, …, k + q − 1} . In the terms defined here, k will be omitted if it happens to be unity. We find that a strongly indexable graph has exactly one nontrivial component which is either a star or has a traingle. In any strongly k-indexable graph the minimum point degree is at most 3. Using this fact we show that there are exactly three strongly indexable regular graphs, viz. K 2, K 3 and K 2x K 3. If an eulerian ( p, q)-graph is strongly indexable then q ϵ 0, 3( mod4).

Quantium dynamics of an extended object in Bogolyubov's group variables

Bogolyubov's method of group variables is used to consider the dynamics of a quantum-field Fermi-Bose systems in the neighborhood of a nontrivial classical component in the form of an extended object of the type of a kink. It is shown how the quantum corrections are calculated in the framework of the method. A study is made of the kind dynamics with allowance for the quantum fluctuations that arise when it interacts with the fundamental particles of the fields; the effects due to them and related questions are discussed.

Anderson localization for Bernoulli and other singular potentials

We prove exponential localization in the Anderson model under very weak assumptions on the potential distribution. In one dimension we allow any measure which is not concentrated on a single point and possesses some finite moment. In particular this solves the longstanding problem of localization for Bernoulli potentials (i.e., potentials that take only two values). In dimensions greater than one we prove localization at high disorder for potentials with Holder continuous distributions and for bounded potentials whose distribution is a convex combination of a Holder continuous distribution with high disorder and an arbitrary distribution. These include potentials with singular distributions. We also show that for certain Bernoulli potentials in one dimension the integrated density of states has a nontrivial singular component.

Development of the ability to perceive ambiguities: evidence for the task specificity of a linguistic skill.

This study asked whether children's ability to perceive linguistic ambiguities was correlated with that of perceiving pictorial ambiguities. A total of 48 ambiguous sentences and 24 ambiguous pictures were selected for comprehensibility. Half the sentences and pictures were symbolic ambiguities (i.e., they contained symbols that stood for two different objects) and half were structural ambiguities (i.e., the structures of the sentences or pictures could be broken up two different ways). No significant correlations were found between the linguistic and pictorial modes. In both modes, correct performance on the symbolic ambiguities was better and was observed earlier than that for structural ambiguities. After taking into account certain methodological problems with nonsignificant correlations and ambiguous sentences, it was concluded that at least some nontrivial component of the linguistic ambiguity detector was task specific to language.

Closed Hulls in Infinite Symmetric Groups

Let $\operatorname {Sym} M$ be the symmetric group of an infinite set $M$. What is the smallest subgroup of $\operatorname {Sym} M$ containing a given element if the subgroup is subject to the further condition that it is also the automorphism group of some finitary algebra on $M$? The structures of such closed hulls are related to the disjoint-cycle decompositions of the given elements. If the closed hull is not just the cyclic subgroup on the given element then it is nonminimal as a closed hull and is represented as a subdirect product of finite cyclic groups as well as by a quotient group of a group of infinite sequences. We determine the conditions under which it has a nontrivial primary component for a given prime $p$ and show that such components must be bounded abelian groups.

Closed hulls in infinite symmetric groups

Let Sym ⁡ M \operatorname {Sym} M be the symmetric group of an infinite set M M . What is the smallest subgroup of Sym ⁡ M \operatorname {Sym} M containing a given element if the subgroup is subject to the further condition that it is also the automorphism group of some finitary algebra on M M ? The structures of such closed hulls are related to the disjoint-cycle decompositions of the given elements. If the closed hull is not just the cyclic subgroup on the given element then it is nonminimal as a closed hull and is represented as a subdirect product of finite cyclic groups as well as by a quotient group of a group of infinite sequences. We determine the conditions under which it has a nontrivial primary component for a given prime p p and show that such components must be bounded abelian groups.