Characterization of Quasi L∞/L2 Hankel Norms of Sampled-Data Systems

This paper is concerned with the Hankel operator of sampled-data systems. The Hankel operator is usually defined as a mapping from the past input to the future output and its norm plays an important role in evaluating the performance of systems. Since the continuous-time mapping between the input and output is periodically time-varying (h -periodic, where h denotes the sampling period) in sampled-data systems, it matters when to take the time instant separating the past and the future when we define the Hankel operator for sampled-data systems. This paper takes an arbitrary Θ ϵ [0,h) as such an instant, and considers the quasi L∞/L2 Hankel operator defined as the mapping from the past input in L2(-∞ Θ) to the future output in L∞Θ ∞). The norm of this operator, which we call the quasi L∞/L2 Hankel norm at Θ is then characterized in such a way that its numerical computation becomes possible. Then, regarding the computation of the L∞L2 Hankel norm defined as the supremum of the quasi L∞L2 Hankel norms over Θ ϵ [0,h), some relationship is discussed between the arguments through such characterization and an alternative method developed in an earlier paper that is free from the computations of quasi L∞/L2 Hankel norms. A numerical example is studied to confirm the validity of the arguments in this paper. © 201711Ysciescopu

Direct observation of spin-quadrupolar excitations in Sr2_2CoGe2_2O7_7 by high field ESR

Exotic spin-multipolar ordering in spin transition metal insulators has so far eluded unambiguous experimental observation. A less studied, but perhaps more feasible fingerprint of multipole character emerges in the excitation spectrum in the form of quadrupolar transitions. Such multipolar excitations are desirable as they can be manipulated with the use of light or electric field and can be captured by means of conventional experimental techniques. Here we study single crystals of multiferroic Sr$_2$CoGe$_2$O$_7$, and show that due to its nearly isotropic nature a purely quadrupolar bimagnon mode appears in the electron spin resonance (ESR) spectra. This non-magnetic spin-excitation couples to the electric field of the light and becomes observable for a specific experimental configuration, in full agreement with a theoretical analysis of the selection rules.Comment: 19 pages, 13 figures, , accepted for publication in Phys. Rev.

Evaluation of contrast visual acuity in patients with retinitis pigmentosa

Kazumi Oomachi1, Kazuha Ogata2, Takeshi Sugawara2, Akira Hagiwara2, Akira Hata1, Shuichi Yamamoto21Department of Public Health; 2Department of Ophthalmology, Chiba University Graduate School of Medicine, Chiba, JapanBackground: The purpose of this study was to determine visual acuity at different contrast levels under photopic and mesopic conditions in patients with retinitis pigmentosa.Methods: Sixty eyes of 31 normal controls, 92 eyes of 52 patients with retinitis pigmentosa without other ocular disorders (RP-1 group), and 20 eyes of 14 patients with retinitis pigmentosa with cataracts and without other ocular disorders (RP-2 group) were studied. Conventional visual acuity was measured using a conventional Landolt ring chart with 100% contrast and luminance of 150 cd/m2. All of the patients with retinitis pigmentosa had a decimal visual acuity better than 1.0. Contrast visual acuity was measured with the same Landolt ring chart with contrasts of 100% and 10% and under photopic (200 cd/m2) and mesopic (10 cd/m2) conditions. Decimal visual acuities were converted to logMAR units for the analyses.Results: The 100% contrast visual acuity and the 10% contrast visual acuity determined under both photopic and mesopic conditions were significantly poorer in both the RP-1 and RP-2 groups than in the controls. The differences between the conventional visual acuity and the 100% contrast visual acuity were significantly greater in the RP-1 and RP-2 groups than in the controls under both photopic and mesopic conditions. The differences between the 100% contrast visual acuity and the 10% contrast visual acuity were not significant among the three groups under photopic and mesopic conditions.Conclusion: Contrast visual acuities were greatly reduced in patients with retinitis pigmentosa with relatively well preserved conventional visual acuity, and the contrast visual acuity was largely influenced by ambient light levels in patients with retinitis pigmentosa. Although a longitudinal study for confirmation has to be performed, our findings indicate that contrast visual acuity is a better test to follow changes in visual function in patients with retinitis pigmentosa.Keywords: retinitis pigmentosa, contrast visual acuity, photopic vision, mesopic visio

Experimental variable effects on laser heating of inclusions during Raman spectroscopic analysis

Raman spectroscopy for fluid, melt, and mineral inclusions provides direct insight into the physicochemical conditions of the environment surrounding the host mineral at the time of trapping. However, the obtained Raman spectral characteristics such as peak position are modified because of local temperature enhancement of the inclusions by the excitation laser, which might engender systematic errors and incorrect conclusions if the effect is not corrected. Despite the potentially non-negligible effects of laser heating, the laser heating coefficient (B) (°C/mW) of inclusions has remained unsolved. For this study, we found B from experiments and heat transport simulation to evaluate how various parameters such as experimental conditions, mineral properties, and inclusion geometry affect B of inclusions. To assess the parameters influencing laser heating, we measured B of a total of 19 CO2-rich fluid inclusions hosted in olivine, orthopyroxene, clinopyroxene, spinel, and quartz. Our results revealed that the measured B of fluid inclusions in spinel is highest (approx. 6 °C/mW) and that of quartz is lowest (approx. 1 × 10−2 °C/mW), consistent with earlier inferences. Our simulation results show that the absorption coefficient of the host mineral is correlated linearly with B. It is the most influential parameter when the absorption coefficient of the host mineral (αh) is larger than that of an inclusion (αinc). Furthermore, although our results indicate that both the inclusion size and depth have little effect on B if αh > αinc, the thickness and radius of the host mineral slightly influence B. These results suggest that the choice of inclusion size and depth to be analyzed in a given sample do not cause any systematic error in the Raman data because of laser heating, but the host radius and thickness, which can be adjusted to some degree at the time of sample preparation, can cause systematic errors between samples.Our results demonstrate that, even with laser power of 10 mW, which is typical for inclusion analysis, the inclusion temperature rises to tens or hundreds of degrees during the analysis, depending especially on the host mineral geometry and optical properties. Therefore, correction of the heating effects will be necessary to obtain reliable data from Raman spectroscopic analysis of inclusions. This paper presents some correction methods for non-negligible effects of laser heating

Symbol emergence as interpersonal cross-situational learning: the emergence of lexical knowledge with combinatoriality

We present a computational model for a symbol emergence system that enables the emergence of lexical knowledge with combinatoriality among agents through a Metropolis-Hastings naming game and cross-situational learning. Many computational models have been proposed to investigate combinatoriality in emergent communication and symbol emergence in cognitive and developmental robotics. However, existing models do not sufficiently address category formation based on sensory-motor information and semiotic communication through the exchange of word sequences within a single integrated model. Our proposed model facilitates the emergence of lexical knowledge with combinatoriality by performing category formation using multimodal sensory-motor information and enabling semiotic communication through the exchange of word sequences among agents in a unified model. Furthermore, the model enables an agent to predict sensory-motor information for unobserved situations by combining words associated with categories in each modality. We conducted two experiments with two humanoid robots in a simulated environment to evaluate our proposed model. The results demonstrated that the agents can acquire lexical knowledge with combinatoriality through interpersonal cross-situational learning based on the Metropolis-Hastings naming game and cross-situational learning. Furthermore, our results indicate that the lexical knowledge developed using our proposed model exhibits generalization performance for novel situations through interpersonal cross-modal inference