On Degeneracy of Linear Reconstruction from Three Views: Linear Line Complex and Applications

This paper investigates the linear degeneracies of projective structure estimation from point and line features across three views. We show that the rank of the linear system of equations for recovering the trilinear tensor of three views reduces to 23 (instead of 26) in the case when the scene is a Linear Line Complex (set of lines in space intersecting at a common line) and is 21 when the scene is planar. The LLC situation is only linearly degenerate, and we show that one can obtain a unique solution when the admissibility constraints of the tensor are accounted for. The line configuration described by an LLC, rather than being some obscure case, is in fact quite typical. It includes, as a particular example, the case of a camera moving down a hallway in an office environment or down an urban street. Furthermore, an LLC situation may occur as an artifact such as in direct estimation from spatio-temporal derivatives of image brightness. Therefore, an investigation into degeneracies and their remedy is important also in practice.

A Note on Support Vector Machines Degeneracy

When training Support Vector Machines (SVMs) over non-separable data sets, one sets the threshold $b$ using any dual cost coefficient that is strictly between the bounds of $0$ and $C$. We show that there exist SVM training problems with dual optimal solutions with all coefficients at bounds, but that all such problems are degenerate in the sense that the "optimal separating hyperplane" is given by ${f w} = {f 0}$, and the resulting (degenerate) SVM will classify all future points identically (to the class that supplies more training data). We also derive necessary and sufficient conditions on the input data for this to occur. Finally, we show that an SVM training problem can always be made degenerate by the addition of a single data point belonging to a certain unboundedspolyhedron, which we characterize in terms of its extreme points and rays.

A hexadecanuclear copper(I)-copper(II) mixed-valence compound: structure, magnetic properties, intervalence charge transfer, EPR, and NMR

Hexadecanuclear copper mixed-valence complex 2 containing 10 Cu-II, centers and 6 Cu-I centers was isolated with N,O donor ligands. From the X-ray crystal structure, 2 was found to contain a centrosymmetric dimeric cation - each monomeric unit composed of eight copper centers. It displays a very broad and weak intervalence charge-transfer band around 1100 nm at room temperature in the solid state. Variable-temperature magnetic susceptibility measurements indicate an S = 1/2 ground state for half of 2, explicitly, each Cu-8 moiety has a g value around 2.26. Complex 2 was examined by NMR spectroscopy at room temperature in solution and by EPR at low temperature; the data indicates that the valence is delocalized in 2 at room temperature but localized at low temperature. ((C) Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)

Simultaneous bridge-localized and mixed-valence character in diruthenium radical cations featuring diethynylaromatic bridging ligands

A series of bimetallic ruthenium complexes [{Ru(dppe)Cp*}2(μ-C≡CArC≡C)] featuring diethynylaromatic bridging ligands (Ar = 1,4-phenylene, 1,4-naphthylene, 9,10-anthrylene) have been prepared and some representative molecular structures determined. A combination of UV–vis–NIR and IR spectroelectrochemical methods and density functional theory (DFT) have been used to demonstrate that one-electron oxidation of compounds [{Ru(dppe)Cp*}2(μ-C≡CArC≡C)](HC≡CArC≡CH = 1,4-diethynylbenzene; 1,4-diethynyl-2,5-dimethoxybenzene; 1,4-diethynylnaphthalene; 9,10-diethynylanthracene) yields solutions containing radical cations that exhibit characteristics of both oxidation of the diethynylaromatic portion of the bridge, and a mixed-valence state. The simultaneous population of bridge-oxidized and mixed-valence states is likely related to a number of factors, including orientation of the plane of the aromatic portion of the bridging ligand with respect to the metal d-orbitals of appropriate π-symmetry.

Beyond arousal and valence: the importance of the biological versus social relevance of emotional stimuli

The present study addressed the hypothesis that emotional stimuli relevant to survival or reproduction (biologically emotional stimuli) automatically affect cognitive processing (e.g., attention, memory), while those relevant to social life (socially emotional stimuli) require elaborative processing to modulate attention and memory. Results of our behavioral studies showed that (1) biologically emotional images hold attention more strongly than do socially emotional images, (2) memory for biologically emotional images was enhanced even with limited cognitive resources, but (3) memory for socially emotional images was enhanced only when people had sufficient cognitive resources at encoding. Neither images’ subjective arousal nor their valence modulated these patterns. A subsequent functional magnetic resonance imaging study revealed that biologically emotional images induced stronger activity in the visual cortex and greater functional connectivity between the amygdala and visual cortex than did socially emotional images. These results suggest that the interconnection between the amygdala and visual cortex supports enhanced attention allocation to biological stimuli. In contrast, socially emotional images evoked greater activity in the medial prefrontal cortex (MPFC) and yielded stronger functional connectivity between the amygdala and MPFC than did biological images. Thus, it appears that emotional processing of social stimuli involves elaborative processing requiring frontal lobe activity.

Allocation of spatial attention to emotional stimuli depends upon arousal and not valence

Attentional allocation to emotional stimuli is often proposed to be driven by valence and in particular by negativity. However, many negative stimuli are also arousing leaving the question whether valence or arousal accounts for this effect. The authors examined whether the valence or the arousal level of emotional stimuli influences the allocation of spatial attention using a modified spatial cueing task. Participants responded to targets that were preceded by cues consisting of emotional pictures varying on arousal and valence. Response latencies showed that disengagement of spatial attention was slower for stimuli high in arousal than for stimuli low in arousal. The effect was independent of the valence of the pictures and not gender-specific. The findings support the idea that arousal affects the allocation of attention.

Discovery of two distinct red clumps in NGC 419: a rare snapshot of a cluster at the onset of degeneracy

Colour-magnitude diagrams (CMDs) of the Small Magellanic Cloud (SMC) star cluster NGC 419, derived from Hubble Space Telescope (HST)/Advanced Camera for Surveys (ACS) data, reveal a well-delineated secondary clump located below the classical compact red clump typical of intermediate-age populations. We demonstrate that this feature belongs to the cluster itself, rather than to the underlying SMC field. Then, we use synthetic CMDs to show that it corresponds very well to the secondary clump predicted to appear as a result of He-ignition in stars just massive enough to avoid e(-)-degeneracy settling in their H-exhausted cores. The main red clump instead is made of the slightly less massive stars which passed through e(-) degeneracy and ignited He at the tip of the red giant branch. In other words, NGC 419 is the rare snapshot of a cluster while undergoing the fast transition from classical to degenerate H-exhausted cores. At this particular moment of a cluster`s life, the colour distance between the main-sequence turn-off and the red clump(s) depends sensitively on the amount of convective core overshooting, Lambda(c). By coupling measurements of this colour separation with fits to the red clump morphology, we are able to estimate simultaneously the cluster mean age (1.35(-0.04)(+0.11) Gyr) and overshooting efficiency (Lambda(c) = 0.47(-0.04)(+0.14)). Therefore, clusters like NGC 419 may constitute important marks in the age scale of intermediate-age populations. After eye inspection of other CMDs derived from HST/ACS data, we suggest that the same secondary clump may also be present in the Large Magellanic Cloud clusters NGC 1751, 1783, 1806, 1846, 1852 and 1917.

On an Electrode Modified by a Supramolecular Ruthenium Mixed Valence (Ru(II)/Ru(III)) Diphosphine-Porphyrin Assembly

Three novel polymetallic ruthenium (III) meso-tetra(4-pyridyl)porphyrins containing peripheral ""RuCl(3)(dppb)"" moieties have been prepared and characterized. The X-ray structure of the tetraruthenated {NiTPyP[RuCl(3)(dppb)](4)} porphyrin complex crystallizes in the triclinic space group FT. This structure is discussed and compared with the crystal data for the mer-[RuCl(3)(dppb)(py)]. The {TPyP[RuCl(3)(dppb)](4)} and {CoTPyP[RuCl(3)(dppb)](4)} porphyrins were used to obtain electrogenerated films on ITO and glass carbon electrode surfaces, respectively. Such tetraruthenated porphyrins form films of a mixed-valence species {TPyP[Ru(dppb)](4)(mu Cl(3))(2)}(2)(4n2+) and {CoTPyP[Ru(dppb)](4)(mu Cl(3))(2)}(2n)(4n2+) on the electrode surface. The modified electrode with {CoTPyP[RuCl(3)(dppb)](4)} is very stable and can be used to detect organic substrates such as catechol.

Study on the observation of Eu(2+) and Eu(3+) valence states in low silica calcium aluminosilicate glasses

The optical, magnetic and structural properties of Eu doped low silica calcium aluminosilicate glasses were investigated. The optical absorption coefficient presented two bands at 39 246 and 29 416 cm(-1), which were assigned respectively to the 4f(7) ((8)S(7/2)) -> 4f(6) (4F(J)) 5d (T(2g)), and 4f(7) ((8)S(7/2)) -> 4f(6) (4F(J)) 5d (E(g)) transitions of Eu(2+). The fluorescence measured at 300 K on a sample doped with 0.5 wt% of Eu(2)O(3) exhibited a broad band centered at 17 350 cm(-1), which is attributed to the 4f(6)5d -> 4f(7) transition of Eu(2+), whereas the additional peaks are due to the (5)D(0) -> (7)F(J) (J = 1, 2, 4) transitions of Eu(3+). From magnetization and XANES data it was possible to evaluate the fractions of Eu(2+) and Eu(3+) for the sample doped with 0.5 and 5.0 wt% of Eu(2)O(3), the values of which were approximately 30 and 70%, respectively.

An effective singular oscillator for Duffin-Kemmer-Petiau particles with a nonminimal vector coupling: a two-fold degeneracy

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X-ray powder data and bond valence of La0.65Sr0.35MnO3 after Rietveld refinement

Powder X-ray diffraction (XRD) data were collected for La0.65Sr0.35MnO3 prepared through an alternative method from a stoichiometric mixture of Mn2O3, La2O3, and SrO2, fired at 1300 degreesC for 16 h. XRD analysis using the Rietveld method was carried out and it was found that manganite has rhombohedral symmetry (space group R(3) over bar c). The lattice parameters are found to be a=5.5032 Angstrom and c=13.3674 Angstrom. The bond valence computation indicates that the initial inclusion of Sr occurs at higher temperature. (C) 2002 International Centre for Diffraction Data.

Resonant x-ray diffraction as a tool to calculate mixed valence ratios: Application to Prussian Blue materials

An approach is proposed here to calculate mixed valence ratios in molecular compounds. Synchrotron x-ray powder diffraction experiments were conducted to determine the Fe(+3)/Fe(+2) ratio in Prussian Blue compounds, which were elected as an example of the use of this approach. As a result, a resonant x-ray diffraction measurement provided direct evidence that the vacant [Fe(CN)(6)] group was randomly absent from similar to 31% of the structure, which was indicated by structural differences caused by variations in the anomalous dispersion term. These findings are very important for a deeper understanding of the changes occurring in properties during in situ compositional variations. (c) 2008 American Institute of Physics.

EPR linewidth of local magnetic moments diluted in Ce intermediate-valence compounds

Anomalous thermal behavior on the EPR linewidths has been observed for Gd impurities diluted in CexA1-xBn (A=La,Y, B=Ir,Os,Rh,Pd) intermediate-valence compounds. In this work we show that the exchange interaction between the local magnetic moments and the intermediate-valence host ions has an important contribution to the relaxation rates of the local moments. We calculated the relaxation, using the Redfield formalism and the ideas contained in the interconfigurational fluctuation model of Hirst. We show that the exchange interaction contribution has an exponential dependence on the excitation energy of the intermediate-valence ions. © 1992 The American Physical Society.

Local attractors, degeneracy and analyticity: Symmetry effects on the locally coupled Kuramoto model

In this work we study the local coupled Kuramoto model with periodic boundary conditions. Our main objective is to show how analytical solutions may be obtained from symmetry assumptions, and while we proceed on our endeavor we show apart from the existence of local attractors, some unexpected features resulting from the symmetry properties, such as intermittent and chaotic period phase slips, degeneracy of stable solutions and double bifurcation composition. As a result of our analysis, we show that stable fixed points in the synchronized region may be obtained with just a small amount of the existent solutions, and for a class of natural frequencies configuration we show analytical expressions for the critical synchronization coupling as a function of the number of oscillators, both exact and asymptotic. © 2013 Elsevier Ltd. All rights reserved.