Dual Maps Research Articles

Quantitative dual energy CT measurements in rabbit VX2 liver tumors: Comparison to perfusion CT measurements and histopathological findings

PurposeTo evaluate the correlation between quantitative dual energy CT and perfusion CT measurements in rabbit VX2 liver tumors. Materials and methodsThis study was approved by the institutional animal care and use committee at our institution. Nine rabbits with VX2 liver tumors underwent contrast-enhanced dual energy CT and perfusion CT. CT attenuation for the tumors and normal liver parenchyma and tumor-to-liver ratio were obtained at the 140kVp, 80kVp, average weighted images and dual energy CT iodine maps. Quantitative parameters for the viable tumor and adjacent liver were measured with perfusion CT. The correlation between the enhancement values of the tumor in iodine maps and perfusion CT parameters of each tumor was analyzed. Radiation dose from dual energy CT and perfusion CT was measured. ResultsEnhancement values for the tumor were higher than that for normal liver parenchyma at the hepatic arterial phase (P<0.05). The highest tumor-to-liver ratio was obtained in hepatic arterial phase iodine map. Hepatic blood flow of the tumor was higher than that for adjacent liver (P<0.05). Enhancement values of hepatic tumors in the iodine maps positively correlated with permeability of capillary vessel surface (r=0.913, P<0.001), hepatic blood flow (r=0.512, P=0.010), and hepatic blood volume (r=0.464, P=0.022) at the hepatic arterial phases. The effective radiation dose from perfusion CT was higher than that from DECT (P<0.001). ConclusionsThe enhancement values for viable tumor tissues measured in iodine maps were well correlated to perfusion CT measurements in rabbit VX2 liver tumors. Compared with perfusion CT, dual energy CT of the liver required a lower radiation dose.

SELF-DUAL FORMULATIONS OF d = 3 GRAVITY THEORIES IN THE PATH-INTEGRAL FRAMEWORK

We study the connection, at the quantum level, between (d = 2+1)-dimensional self-dual models with actions of growing (from first to fourth) order, governing the dynamics of helicity ±2 massive excitations. We obtain identities between generating functionals of the different models using the path-integral framework, this allowing us to establish dual maps among relevant vacuum expectation values. We check consistency of these vacuum expectation values with the gauge invariance gained in each mapping.

Brun expansions of stepped surfaces

Dual maps have been introduced as a generalization to higher dimensions of word substitutions and free group morphisms. In this paper, we study the action of these dual maps on particular discrete planes and surfaces, namely stepped planes and stepped surfaces. We show that dual maps can be seen as discretizations of toral automorphisms. We then provide a connection between stepped planes and the Brun multi-dimensional continued fraction algorithm, based on a desubstitution process defined on local geometric configurations of stepped planes. By extending this connection to stepped surfaces, we obtain an effective characterization of stepped planes (more exactly, stepped quasi-planes) among stepped surfaces.

Duality of parity doublets of helicity±2inD=2+1dimensions

In $D=2+1$ dimensions there are two dual descriptions of parity singlets of helicity $\ifmmode\pm\else\textpm\fi{}1$, namely, the self-dual model of first order (in derivatives) and the Maxwell-Chern-Simons theory of second order. Correspondingly, for helicity $\ifmmode\pm\else\textpm\fi{}2$ there are four models ${S}_{\mathrm{SD}\ifmmode\pm\else\textpm\fi{}}^{(r)}$ describing parity singlets of helicities $\ifmmode\pm\else\textpm\fi{}2$. They are of first, second, third, and fourth order ($r=1$, 2, 3, 4), respectively. Here we show that the generalized soldering of the opposite helicity models ${S}_{\mathrm{SD}+}^{(4)}$ and ${S}_{\mathrm{SD}\ensuremath{-}}^{(4)}$ leads to the linearized form of the new massive gravity suggested by Bergshoeff, Hohm, and Townsend (BHT) similarly to the soldering of ${S}_{\mathrm{SD}+}^{(3)}$ and ${S}_{\mathrm{SD}\ensuremath{-}}^{(3)}$. We argue why in both cases we have the same result. We also find out a triple master action which interpolates between the three dual models: linearized BHT theory, ${S}_{\mathrm{SD}+}^{(3)}+{S}_{\mathrm{SD}\ensuremath{-}}^{(3)}$, and ${S}_{\mathrm{SD}+}^{(4)}+{S}_{\mathrm{SD}\ensuremath{-}}^{(4)}$. By comparing gauge invariant correlation functions we deduce dual maps between those models. In particular, we learn how to decompose the field of the linearized BHT theory in helicity eigenstates of the dual models up to gauge transformations.

Fuzzy transform and least-squares approximation: Analogies, differences, and generalizations

Investigating the relations between the least-squares approximation techniques and the Fuzzy Transform, in this paper we show that the Discrete Fuzzy Transform is invariant with respect to the interpolating and least-squares approximation. Additionally, the Fuzzy Transform is evaluated at any point by simply resampling the continuous approximation underlying the input data. Using numerical linear algebra, we also derive new properties (e.g., stability to noise, additivity with respect to the input data) and characterizations (e.g., radial and dual membership maps) of the Discrete Fuzzy Transform. Finally, we define the geometry- and confidence-driven Discrete Fuzzy Transforms, which take into account the intrinsic geometry and the confidence weights associated to the data.

Dual Source Dual-Energy Computed Tomography of Acute Myocardial Infarction

To evaluate the feasibility and value of dual-energy computed tomography myocardial iodine maps in the diagnosis of acute myocardial infarction. In 6 dogs, arterial-phase myocardial dual-energy computed tomography imaging were performed 1 day prior to and 3 hours after the surgical ligation of the left anterior descending artery to generate 100 kVp, 140 kVp, average weighted images, and dual energy myocardial iodine maps. For each of the 17 segments of the left ventricle (LV, 102 total segments), the presence or absence myocardial infarction was determined by histopathology and correlated to blinded reader determination of infarcted and noninfarcted myocardium at computed tomography (CT). Statistical analysis for diagnostic accuracy of aforementioned techniques and inter-reader agreement was performed. The LV myocardial contrast enhancement at the average weighted images and iodine maps were uniform in all 6 dogs before surgery. Following anterior descending artery ligation, histopathology showed 40 infarcted left ventricular segments and 62 noninfarcted segments. For the postligation CT scans, 100 kVp, 140 kVp, average weighted images, and myocardial iodine maps showed 33, 28, 33, 34 infarcted segments and 53, 56, 56, 52 noninfarcted segments for both readers; corresponding to per-segment sensitivities of 83%, 70%, 80%, 92% and specificities of 85%, 90%, 92%, 80% for detecting myocardial infarction. No statistical difference was found for diagnostic accuracy of 100 kV, 140 kV, weighted average images, and iodine maps to detect myocardial infarct segments (all P > 0.05 for both readers). Good inter-reader agreement was seen for myocardial infarct detection using iodine maps (kappa = 0.80). Myocardial single- and dual-energy CT imaging shows high per-segment sensitivity and moderate specificity for detecting acute myocardial infarction in a canine model with histopathology as the standard of reference.

Dual spatial maps of transcript and protein abundance in the mouse brain

Integrating quantitative proteomic and transcriptomic datasets promises valuable insights in unraveling the molecular mechanisms of the brain. We concentrate on recent studies using mass spectrometry and microarray data to investigate transcript and protein abundance in normal and diseased neural tissues. Highlighted are dual spatial maps of these molecules obtained using voxelation of the mouse brain. We demonstrate that the relationship between transcript and protein levels displays a specific anatomical distribution, with greatest fidelity in midline structures and the hypothalamus. Genes are also identified that have strong correlations between mRNA and protein abundance. In addition, transcriptomic and proteomic analysis of mouse models of Parkinson’s disease are discussed.

Oriented matroids and complete-graph embeddings on surfaces

We provide a link between topological graph theory and pseudoline arrangements from the theory of oriented matroids. We investigate and generalize a function f that assigns to each simple pseudoline arrangement with an even number of elements a pair of complete-graph embeddings on a surface. Each element of the pair keeps the information of the oriented matroid we started with. We call a simple pseudoline arrangement triangular, when the cells in the cell decomposition of the projective plane are 2-colorable and when one color class of cells consists of triangles only. Precisely for triangular pseudoline arrangements, one element of the image pair of f is a triangular complete-graph embedding on a surface. We obtain all triangular complete-graph embeddings on surfaces this way, when we extend the definition of triangular complete pseudoline arrangements in a natural way to that of triangular curve arrangements on surfaces in which each pair of curves has a point in common where they cross. Thus Ringel's results on the triangular complete-graph embeddings can be interpreted as results on curve arrangements on surfaces. Furthermore, we establish the relationship between 2-colorable curve arrangements and Petrie dual maps. A data structure, called intersection pattern is provided for the study of curve arrangements on surfaces. Finally we show that an orientable surface of genus g admits a complete curve arrangement with at most 2 g + 1 curves in contrast to the non-orientable surface where the number of curves is not bounded.

Geodesic and re–coupling–induced limits toS2ngroup invariants of uniform (k1⋯k2n) dual tensorial sets in spin physics, or NMR: SR dynamical structure on {ℍv} via polyhedral re–coupling and time–reversal invariance

ForSn–based,uniform auxiliarydual tensorial (UDT) sets, explicitly with even maximal all–alikeji(ki) overv≡ (j1⋯j2n), or (k1⋯k2n), sub–rank auxiliary labelling, the specific time–reversal invariance–dependentdual group invariantsand their independent cardinalities (|SI|(2n)) are fundamental to understanding simply reducible (SR) dynamical spin system structure over (Liouvillian) carrier space, a quantum physics property implicit in dual quasi–particle (QP) formalisms associated with, for example,uniform identical multiple spin NMR systems. Such UDT sets stand in total contrast to thedistinctji(ki) of (j1⋯j″n)((k1⋯k″n)) sub–rank orthogonal tensorial sets with theirZaa′graph invariants which for reasons discussed in the text are of restricted validity. For UDTs as operator bases related to the (spin) interaction network–based tensors of highSnpermutational NMR Hamiltonians (Liouvillians), the use of QP boson (superboson) formalisms and their dual projective maps (F. P. Temme 1993PhysicaA198, 245–261) prove invaluable. Once the independent cardinality of the multiple invariants of these UDTs (alias theSU(2) ×S2ngroup invariants) (here denoted |SI|(2n)) are known in terms of democratic re–coupling (DR) and polyhedral combinatorial (PC) sampling applied to the time–reversal invariance (TRI) properties of the uniform multiple spin (sub–)system, so theSR dual carrier spaces, ℍ˜, ℍ˜vfollow directly as well–defined entities. For UDTs of general (2n&gt; 6)–fold ensembles, the augmented models of TRI discussed here (i.e. beyond linear re–coupled Weyl forms) are essential, due to the presence of non–Abelian degeneracy. A regular geometric automorphic limit is established for sequential (2n)–based |SI|(2n)totalseries, specific to (higher) uniform (j1⋯ji), (k1⋯ki)–based dual tensors. By treating the |SI|(2n)obtained from the DR–based TRIs as group measures and invoking an automorphic geodesic augmentation, certain otherwise inaccessible, additional |SI|(2n′)(and hence UDTs) may be established; these are based on sporadic higher (regular) (2n≫ 12)–fold ensemble invariants and are obtained via finite group duality properties implicit in the concept of group measures. The PC DR–based views of general (2n) interacting spins of UDTs expressed here give specific insight into dynamic structure over (explicit TRI invariant–defined) Liouvillian carrier spaces. This lattice point (Erdösian) view of DR shows that UDT invariants are distinct and more contracted than predicted by the earlier linear–re–coupling–based |D0(U)|(⨷SU(2)) approach. The presence of degeneracy in general high (2n) UDTs as non–Abelian entities ensures that the homomorphic–based, |D0(U)| enumeration (with its implied linear graphical re–coupling) is invalid for high (2n) uniform (NMR) multi–spin systems whose TRI properties are governed by DR re–coupling. The prime focus of the report concerns the positive conceptual value of PC lattice–point–based DR, as applied to theS2n–invariants which define UDTs (of NMR) and their completeness. Brief contrasts with the earlier, more restrictedO(2k+ 1) (overall) invariants of (O(n) ⊃ ⋯ ⊃G)–based democratic re–coupled quantum systems are given for completeness.

Differential induction and decay curves of c-fos and zif268 revealed through dual activity maps

The use of inducible transcription factors for mapping neural activity is now a common procedure. We have previously developed a double-labelling technique that allows visualization of activated neurons after two different stimulation sequences. The technique exploits the differential time course of mRNA versus protein expression of transcription factors. However, the precise details of the differential time course remained unknown. Here, we provide a complete up- and downregulation profile for both the c-fos and zif268 genes, as determined through combined in situ hybridization and immunocytochemical detection of the mRNA and protein products in primary visual cortex. The data presented here can be used in the design of future studies employing double-label mapping of neural activation following a compound stimulus.

Quadratic rational rotations of the torus and dual lattice maps

We develop a general formalism for computer-assisted proofs concerning the orbit structure of certain nonergodic piecewise affine maps of the torus, whose eigenvalues are roots of unity. For a specific class of maps, we prove that if the trace is a quadratic irrational (the simplest nontrivial case, comprising eight maps), then the periodic orbits are organized into finitely many renormalizable families, with exponentially increasing period, plus a finite number of exceptional families. The proof is based on exact computations with algebraic numbers, where units play the role of scaling parameters. Exploiting a duality existing between these maps and lattice maps representing rounded-off planar rotations, we establish the global periodicity of the latter systems, for a set of orbits of full density.

Grouping and representation of odorant receptors in domains of the olfactory bulb sensory map.

Individual glomeruli in the mammalian main olfactory bulb represent a single or at most a few types of odorant receptors. Thus the physical arrangement of glomeruli at the surface of the olfactory bulb can be viewed as a sensory map representing approximately 1,000 types of odorant receptors. This review summarizes the recent advance of the knowledge regarding the spatial organization of the sensory map in the main olfactory bulb. Recent studies show that individual olfactory bulbs contain dual sensory maps, one in the lateral hemisphere and the other in the medial hemisphere of the bulb. The tracings of selective subsets of olfactory axons to their target glomeruli in the olfactory bulb show that glomeruli are parceled into large zones or bands. The spatial arrangement of these zones and bands are stereotypical and conserved across individual mice. Optical imaging studies show that glomeruli in the most rostrodosal zone, zone I, are further parceled into smaller functional domains, and suggest that odorant receptors having a common or similar molecular feature receptive site are grouped together and represented by glomeruli within the functional domain. The possible relation between the functional domain organization and the subjectively perceived odor quality (olfactory submodality) is reviewed.

A spherical model for orientation and spatial–frequency tuning in a cortical hypercolumn

A theory is presented of the way in which the hypercolumns in primary visual cortex (V1) are organized to detect important features of visual images, namely local orientation and spatial-frequency. Given the existence in V1 of dual maps for these features, both organized around orientation pinwheels, we constructed a model of a hypercolumn in which orientation and spatial-frequency preferences are represented by the two angular coordinates of a sphere. The two poles of this sphere are taken to correspond, respectively, to high and low spatial-frequency preferences. In Part I of the paper, we use mean-field methods to derive exact solutions for localized activity states on the sphere. We show how cortical amplification through recurrent interactions generates a sharply tuned, contrast-invariant population response to both local orientation and local spatial frequency, even in the case of a weakly biased input from the lateral geniculate nucleus (LGN). A major prediction of our model is that this response is non-separable with respect to the local orientation and spatial frequency of a stimulus. That is, orientation tuning is weaker around the pinwheels, and there is a shift in spatial-frequency tuning towards that of the closest pinwheel at non-optimal orientations. In Part II of the paper, we demonstrate that a simple feed-forward model of spatial-frequency preference, unlike that for orientation preference, does not generate a faithful representation when amplified by recurrent interactions in V1. We then introduce the idea that cortico-geniculate feedback modulates LGN activity to generate a faithful representation, thus providing a new functional interpretation of the role of this feedback pathway. Using linear filter theory, we show that if the feedback from a cortical cell is taken to be approximately equal to the reciprocal of the corresponding feed-forward receptive field (in the two-dimensional Fourier domain), then the mismatch between the feed-forward and cortical frequency representations is eliminated. We therefore predict that cortico-geniculate feedback connections innervate the LGN in a pattern determined by the orientation and spatial-frequency biases of feed-forward receptive fields. Finally, we show how recurrent cortical interactions can generate cross-orientation suppression.

Prediction of in-use emissions of heavy-duty diesel vehicles from engine testing.

A model of a heavy-duty vehicle driveline with automatic transmission has been developed for estimating engine speed and load from vehicle speed. The model has been validated using emissions tests conducted on three diesel vehicles on a chassis dynamometer and then on the engines removed from the vehicles tested on an engine dynamometer. Nitrogen oxide (NOx) emissions were proportional to work done by the engine. For two of the engines, the NOx/horsepower(HP) ratio was the same on the engine and on the chassis dynamometer tests. For the third engine NOx/HP was significantly higher from the chassis test, possibly due to the use of dual engine maps. The engine certification test generated consistently less particulate matter emissions on a gram per brake horsepower-hour basis than the Heavy Duty Transient and Central Business District chassis cycles. A good linear correlation (r2 = 0.97 and 0.91) was found between rates of HP increase integrated over the test cycle and PM emissions for both the chassis and the engine tests for two of the vehicles. The model also shows how small changes in vehicle speeds can lead to a doubling of load on the engine. Additionally, the model showed that it is impossible to drive a vehicle cycle equivalent to the heavy-duty engine federal test procedure on these vehicles.

Higher dimensional extensions of substitutions and their dual maps

Given a substitution σ ond letters, we define itsk-dimensional extension,E k (σ), for 0≤k≤d. Thek-dimensional extension acts on the set ofk-dimensional faces of unit cubes inR d with integer vertices. The extensions of a substitution satisfy a commutation relation with the natural boundary operator: the boundary of the image is the image of the boundary. We say that a substitution is unimodular (resp. hyperbolic) if the matrix associated to the substitution by abelianization is unimodular (resp. hyperbolic). In the case where the substitution is unimodular, we also define dual substitutions which satisfy a similar coboundary condition. We use these constructions to build self-similar sets on the expanding and contracting space for an hyperbolic substitution.

Duality and Exact Penalization for Vector Optimization via Augmented Lagrangian

In this paper, we introduce an augmented Lagrangian function for a multiobjective optimization problem with an extended vector-valued function. On the basis of this augmented Lagrangian, set-valued dual maps and dual optimization problems are constructed. Weak and strong duality results are obtained. Necessary and sufficient conditions for uniformly exact penalization and exact penalization are established. Finally, comparisons of saddle-point properties are made between a class of augmented Lagrangian functions and nonlinear Lagrangian functions for a constrained multiobjective optimization problem.

Formule d'homotopie entre les complexes de Hochschild et de De Rham

Let k be the field ℂ or ℝ let M be the space kn and let A be the algebra of polynomials over M. We know from Hochschild and co-workers that the Hochschild homology H·(A,A) is isomorphic to the de Rham differential forms over M: this means that the complexes (C·(A,A),b) and (Ω·(M), 0) are quasi-isomorphic. In this work, I produce a general explicit homotopy formula between those two complexes. This formula can be generalized when M is an open set in a complex manifold and A is the space of holomorphic functions over M. Then, by taking the dual maps, I find a new homotopy formula for the Hochschild cohomology of the algebra of smooth fonctions over M (when M is either a complex or a real manifold) different from the one given by De Wilde and Lecompte. I will finally show how this formula can be used to construct an homotopy for the cyclic homology.

Pisot substitutions and Rauzy fractals

We prove that the dynamical system generated by a primitive unimodular substitution of the Pisot type ond letters satisfying a combinatorial condition which is easy to check, is measurably isomorphic to a domain exchange in R d 1 , and is a nite extension of a translation on the torus T d 1 .I n the course of the proof, we introduce some potentially useful notions: the linear maps associated to a substitution and their dual maps, and the -structure for a dynamical system with respect to a pair of partitions.

On weighted centers for semidefinite programming

In this paper, we generalize the notion of weighted centers to semidefinite programming. Our analysis fits in the v-space framework, which is purely based on the symmetric primal–dual transformation and does not make use of barriers. Existence and scale invariance properties are proven for the weighted centers. Relations with other primal–dual maps are discussed.

Dual displays

The study examined whether the simultaneous presentation of different map displays can aid situational awareness in spatial tasks relying on ego-centred and world-centred reference frames. Two commonly used aircraft displays, track-up and north-up maps, were compared with a dual aircraft display consisting of both track-up and north-up maps. Participants took part in two tasks: one relied on an ego-centred reference frame (ERF) and the other on a world-centred reference frame (WRF). The ERF task involved left/right judgements with respect to the aircraft's current heading while in the WRF task participants were asked to identify the compass heading associated with a landmark. A moderate amount of training resulted in a significant improvement with the dual maps in both the WRF task (relative to track-up maps) and the ERF task (relative to north-up maps). The findings are discussed with reference to how attention is allocated to visual displays.