Elements of analytical geometry; embracing the equations of the point, the straight line, the conic sections, and surfaces of the first and second order,

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First- and second-order stimulus length selectivity in New World monkey striate cortex

Motion is a powerful cue for figure-ground segregation, allowing the recognition of shapes even if the luminance and texture characteristics of the stimulus and background are matched. In order to investigate the neural processes underlying early stages of the cue-invariant processing of form, we compared the responses of neurons in the striate cortex (V1) of anaesthetized marmosets to two types of moving stimuli: bars defined by differences in luminance, and bars defined solely by the coherent motion of random patterns that matched the texture and temporal modulation of the background. A population of form-cue-invariant (FCI) neurons was identified, which demonstrated similar tuning to the length of contours defined by first- and second-order cues. FCI neurons were relatively common in the supragranular layers (where they corresponded to 28% of the recorded units), but were absent from layer 4. Most had complex receptive fields, which were significantly larger than those of other V1 neurons. The majority of FCI neurons demonstrated end-inhibition in response to long first- and second-order bars, and were strongly direction selective, Thus, even at the level of V1 there are cells whose variations in response level appear to be determined by the shape and motion of the entire second-order object, rather than by its parts (i.e. the individual textural components). These results are compatible with the existence of an output channel from V1 to the ventral stream of extrastriate areas, which already encodes the basic building blocks of the image in an invariant manner.

Discrimination between strain and temperature effects using first and second-order diffraction from a long period grating

We study the effects of temperature and strain on the spectra of the first and second-order diffraction attenuation bands of a single long-period grating (LPG) in step-index fibre. The primary and second-order attenuation bands had comparable strength with the second-order bands appearing in the visible and near-infra red parts of the spectrum. Using first and second-order diffraction to the eighth cladding mode a sensitivity matrix was obtained with limiting accuracy given by cross-sensitivity of ~1.19% of the measurement. The sensing scheme presented as a limiting temperature and strain resolution of ±0.7 °C and ~±25 µ.

Simultaneous measurement of strain and temperature using the first- and second-order diffraction wavelengths of Bragg gratings

A method of discriminating between temperature and strain effects in fibre sensing using a conventionally written, in-fibre Bragg grating is presented. The technique uses wavelength information from the first and second diffraction orders of the grating element to determine the wavelength dependent strain and temperature coefficients, from which independent temperature and strain measurements can be made. The authors present results that validate this matrix inversion technique and quantify the strain and temperature errors which can arise for a given uncertainty in the measurement of the reflected wavelength.

Simultaneous measurement of strain and temperature using the first- and second-order diffraction wavelengths of Bragg gratings

A method of discriminating between temperature and strain effects in fibre sensing using a conventionally written, in-fibre Bragg grating is presented. The technique uses wavelength information from the first and second diffraction orders of the grating element to determine the wavelength dependent strain and temperature coefficients, from which independent temperature and strain measurements can be made. The authors present results that validate this matrix inversion technique and quantify the strain and temperature errors which can arise for a given uncertainty in the measurement of the reflected wavelength.

Discrimination between strain and temperature effects using first and second-order diffraction from a long-period grating

We study the effects of temperature and strain on the spectra of the first and second-order diffraction attenuation bands of a single long-period grating (LPG) in step-index fibre. The primary and second-order attenuation bands had comparable strength with the second-order bands appearing in the visible and near-infra red parts of the spectrum. Using first and second-order diffraction to the eighth cladding mode a sensitivity matrix was obtained with limiting accuracy given by cross-sensitivity of ∼ 1.19% of the measurement. The sensing scheme presented as a limiting temperature and strain resolution of ± 0.7 °C and ∼ ± 25 με. © 2002 Elsevier Science B.V. All rights reserved.

Area summation of first- and second-order modulations of luminance

To extend our understanding of the early visual hierarchy, we investigated the long-range integration of first- and second-order signals in spatial vision. In our first experiment we performed a conventional area summation experiment where we varied the diameter of (a) luminance-modulated (LM) noise and (b) contrastmodulated (CM) noise. Results from the LM condition replicated previous findings with sine-wave gratings in the absence of noise, consistent with long-range integration of signal contrast over space. For CM, the summation function was much shallower than for LM suggesting, at first glance, that the signal integration process was spatially less extensive than for LM. However, an alternative possibility was that the high spatial frequency noise carrier for the CM signal was attenuated by peripheral retina (or cortex), thereby impeding our ability to observe area summation of CM in the conventional way. To test this, we developed the ''Swiss cheese'' stimulus of Meese and Summers (2007) in which signal area can be varied without changing the stimulus diameter, providing some protection against inhomogeneity of the retinal field. Using this technique and a two-component subthreshold summation paradigm we found that (a) CM is spatially integrated over at least five stimulus cycles (possibly more), (b) spatial integration follows square-law signal transduction for both LM and CM and (c) the summing device integrates over spatially-interdigitated LM and CM signals when they are co-oriented, but not when crossoriented. The spatial pooling mechanism that we have identified would be a good candidate component for amodule involved in representing visual textures, including their spatial extent.

Linear binocular combination of responses to contrast modulation:contrast-weighted summation in first- and second-order vision

Binocular combination for first-order (luminancedefined) stimuli has been widely studied, but we know rather little about this binocular process for spatial modulations of contrast (second-order stimuli). We used phase-matching and amplitude-matching tasks to assess binocular combination of second-order phase and modulation depth simultaneously. With fixed modulation in one eye, we found that binocularly perceived phase was shifted, and perceived amplitude increased almost linearly as modulation depth in the other eye increased. At larger disparities, the phase shift was larger and the amplitude change was smaller. The degree of interocular correlation of the carriers had no influence. These results can be explained by an initial extraction of the contrast envelopes before binocular combination (consistent with the lack of dependence on carrier correlation) followed by a weighted linear summation of second-order modulations in which the weights (gains) for each eye are driven by the first-order carrier contrasts as previously found for first-order binocular combination. Perceived modulation depth fell markedly with increasing phase disparity unlike previous findings that perceived first-order contrast was almost independent of phase disparity. We present a simple revision to a widely used interocular gain-control theory that unifies first- and second-order binocular summation with a single principle-contrast-weighted summation-and we further elaborate the model for first-order combination. Conclusion: Second-order combination is controlled by first-order contrast.

Second Order Optimality Conditions in Nonsmooth Unconstrained Optimization

AMS subject classification: 49J52, 90C30.

Foundational, First-Order, and Second-Order Classification Theory

Both basic and applied research on the construction, implementation, maintenance, and evaluation of classification schemes is called classification theory. If we employ Ritzer’s metatheoretical method of analysis on the over one-hundred year-old body of literature, we can see categories of theory emerge. This paper looks at one particular part of knowledge organization work, namely classification theory, and asks 1) what are the contours of this intellectual space, and, 2) what have we produced in the theoretical reflection on con- structing, implementing, and evaluating classification schemes? The preliminary findings from this work are that classification theory can be separated into three kinds: foundational classification theory, first-order classification theory, and second-order classification theory, each with its own concerns and objects of study.

I. Site effects and exciton structure in molecular crystals - Benzene. II. The first and second triplet states of solid benzene

The effect of intermolecular coupling in molecular energy levels (electronic and vibrational) has been investigated in neat and isotopic mixed crystals of benzene. In the isotopic mixed crystals of C₆H₆, C₆H₅D, m-C₆H₄D₂, p-C₆H₄D₂, sym-C₆H₃D₃, C₆D₅H, and C₆D₆ in either a C₆H₆ or C₆D₆ host, the following phenomena have been observed and interpreted in terms of a refined Frenkel exciton theory: a) Site shifts; b) site group splittings of the degenerate ground state vibrations of C₆H₆, C₆D₆, and sym-C₆H₃D₃; c) the orientational effect for the isotopes without a trigonal axis in both the ¹B_2u electronic state and the ground state vibrations; d) intrasite Fermi resonance between molecular fundamentals due to the reduced symmetry of the crystal site; and e) intermolecular or intersite Fermi resonance between nearly degenerate states of the host and guest molecules. In the neat crystal experiments on the ground state vibrations it was possible to observe many of these phenomena in conjunction with and in addition to the exciton structure.

To theoretically interpret these diverse experimental data, the concepts of interchange symmetry, the ideal mixed crystal, and site wave functions have been developed and are presented in detail. In the interpretation of the exciton data the relative signs of the intermolecular coupling constants have been emphasized, and in the limit of the ideal mixed crystal a technique is discussed for locating the exciton band center or unobserved exciton components. A differentiation between static and dynamic interactions is made in the Frenkel limit which enables the concepts of site effects and exciton coupling to be sharpened. It is thus possible to treat the crystal induced effects in such a fashion as to make their similarities and differences quite apparent.

A calculation of the ground state vibrational phenomena (site shifts and splittings, orientational effects, and exciton structure) and of the crystal lattice modes has been carried out for these systems. This calculation serves as a test of the approximations of first order Frenkel theory and the atom-atom, pair wise interaction model for the intermolecular potentials. The general form of the potential employed was V(r) = Be^-Cr - A/r⁶ ; the force constants were obtained from the potential by assuming the atoms were undergoing simple harmonic motion.

In part II the location and identification of the benzene first and second triplet states (³B_1u and ³E_1u) is given.

The curvature of the conical intersection seam: an approximate second-order analysis

We present a method for analyzing the curvature (second derivatives) of the conical intersection hyperline at an optimized critical point. Our method uses the projected Hessians of the degenerate states after elimination of the two branching space coordinates, and is equivalent to a frequency calculation on a single Born-Oppenheimer potential-energy surface. Based on the projected Hessians, we develop an equation for the energy as a function of a set of curvilinear coordinates where the degeneracy is preserved to second order (i.e., the conical intersection hyperline). The curvature of the potential-energy surface in these coordinates is the curvature of the conical intersection hyperline itself, and thus determines whether one has a minimum or saddle point on the hyperline. The equation used to classify optimized conical intersection points depends in a simple way on the first- and second-order degeneracy splittings calculated at these points. As an example, for fulvene, we show that the two optimized conical intersection points of C2v symmetry are saddle points on the intersection hyperline. Accordingly, there are further intersection points of lower energy, and one of C2 symmetry - presented here for the first time - is found to be the global minimum in the intersection space

Metal binding selectivity of oxa-aza macrocyclic ligand: a DFT study of first- and second-row transition metal for four coordination systems

A detailed theoretical study of the 1,7,1l,17-tetraoxa-2,6,12,16-tetraaza-cycloeicosane ligand ([20]AneN(4)O(4)) coordinated to Fe2+, Co2+, Ni2+, Ru2+, Rh2+, and Pd2+ transition metal ions was carried out with the B3LYP method. Two different cases were performed: when nitrogen is the donor atom (1a (q) ) and also with the oxygen as the donor atom (1b (q) ). For all the cases performed in this study 1a (q) structures were always more stable than the 1b (q) ones. Considering each row is possible to see that the energy increases with the increase of the atomic number. The M2+ cation binding energies for the 1a (q) complexes increase with the following order: Fe2+ < Ru2+ < Co2+ < Ni2+ < Rh2+ < Pd2+.

First- and second-row transition metal oxa-aza macrocyclic complexes: a DFT study of an octahedral conformation

A theoretical study of structures of the 1,7,1 l,17-tetraoxa-2,6,12,16-tetraaza-cycloeicosane ligand ([20]AneN(4)O(4)) coordinated to Fe2+, Co2+, Ni2+, Ru2+, Rh2+, and Pd2+ transition metals ions was carried out with the DFT/B3LYP method. Complexes were fully optimized in C-s symmetry with the metal ions coordinated either to nitrogen (1a) or oxygen atoms (1b). For all the cases performed in this work, 1a was always more stable than 1b. Considering each row it is possible to see that the binding energy increases with the atomic number. The M2+ cation binding energies increase in the following order: Fe2+ < Ru2+ < Co2+ < Ni2+ < Rh2+ < Pd2+. In addition, it was observed the preference of Pd2+ and Rh2+ complexes for a tetrahedral arrangement, while Fe2+, Ru2+, Co2+, Ni2+ complexes had a preference for the octahedral arrangement. From the orbital representation results, it was seen that 1b unsymmetrical orbitals may influence the susceptibility over metal ions orientation toward heteroatoms orbitals.

Methodological approach to the first and second lactate threshold in incremental cardiopulmonary exercise testing

Determination of an 'anaerobic threshold' plays an important role in the appreciation of an incremental cardiopulmonary exercise test and describes prominent changes of blood lactate accumulation with increasing workload. Two lactate thresholds are discerned during cardiopulmonary exercise testing and used for physical fitness estimation or training prescription. A multitude of different terms are, however, found in the literature describing the two thresholds. Furthermore, the term 'anaerobic threshold' is synonymously used for both, the 'first' and the 'second' lactate threshold, bearing a great potential of confusion. The aim of this review is therefore to order terms, present threshold concepts, and describe methods for lactate threshold determination using a three-phase model with reference to the historical and physiological background to facilitate the practical application of the term 'anaerobic threshold'.