Convergence of Weighted Averages of Martingales in Banach Function Spaces

AbstractLet f=(fn)n≥1 be a martingale and (wn)n≥1 a sequence of positive numbers such that Wn=∑nk=1wk→∞. Kazamaki and Tsuchikura proved that f converges in Lp (1<p<∞) if and only if the weighted average (σn(f))n≥1 of f converges in Lp, where σn(f) are given byσnf=1Wn∑k=1nwkfk,n=1,2,….We shall investigate the convergence of f and σn(f) in general Banach function spaces X. Our main result can be applied to the case where X is a rearrangement-invariant space, or X is a weighted Lp-space with a weight function satisfying the condition Ap introduced by Izumisawa and Kazamaki

Using Conservative Estimation for Conditional Probability instead of Ignoring Infrequent Case

There are several estimators of conditional probability from observed frequencies of features. In this paper, we propose using the lower limit of confidence interval on posterior distribution determined by the observed frequencies to ascertain conditional probability. In our experiments, this method outperformed other popular estimators.Comment: The 2016 International Conference on Advanced Informatics: Concepts, Theory and Application (ICAICTA2016

Conservative Likelihood Ratio Estimator for Infrequent Data Slightly above a Frequency Threshold

A naive likelihood ratio (LR) estimation using the observed frequencies of events can overestimate LRs for infrequent data. One approach to avoid this problem is to use a frequency threshold and set the estimates to zero for frequencies below the threshold. This approach eliminates the computation of some estimates, thereby making practical tasks using LRs more efficient. However, it still overestimates LRs for low frequencies near the threshold. This study proposes a conservative estimator for low frequencies, slightly above the threshold. Our experiment used LRs to predict the occurrence contexts of named entities from a corpus. The experimental results demonstrate that our estimator improves the prediction accuracy while maintaining efficiency in the context prediction task.Comment: The 9th International Conference on Advanced Informatics: Concepts, Theory and Applications (ICAICTA 2022

Effect of Visual Information on Active Touch During Mirror Visual Feedback

Several studies have demonstrated that observation of a dummy or mirror-reflected hand being stroked or moving at the same time as the hidden hand evokes a feeling that the dummy hand is one’s own, such as the rubber hand illusion (RHI) and mirror visual feedback (MVF). Under these conditions, participants also report sensing the tactile stimulation applied to the fake hands, suggesting that tactile perception is modulated by visual information during the RHI and MVF. Previous studies have utilized passive stimulation conditions; however, active touch is more common in real-world settings. Therefore, we investigated whether active touch is also modulated by visual information during an MVF scenario. Twenty-three participants (13 men and 10 women; mean age ± SD: 21.6 ± 2.0 years) were required to touch a polyurethane pad with both hands synchronously, and estimate the hardness of the pad while observing the mirror reflection. When participants observed the mirror reflection of the other hand pushing a softer or harder pad, perceived hardness estimates were significantly biased toward softer or harder, respectively, even though the physical hardness of the pad remained constant. Furthermore, perceived hardness exhibited a strong correlation with finger displacement of the mirrored, but not hidden, hand. The modulatory effects on perceived hardness diminished when participants touched the pad with both hands asynchronously or with their eyes closed. Moreover, participants experienced ownership of the mirrored hand when they touched the pad with both hands synchronously but not asynchronously. These results indicate that hardness estimates were modulated by observation of the mirrored hand during synchronous touch conditions. The present study demonstrates that, similar to passive touch, active touch is also modulated by visual input

New femoral remains of <i>Nacholapithecus kerioi</i>: Implications for intraspecific variation and Miocene hominoid evolution

The middle Miocene stem kenyapithecine Nacholapithecus kerioi (16-15 Ma; Nachola, Kenya) is represented by a large number of isolated fossil remains and one of the most complete skeletons in the hominoid fossil record (KNM-BG 35250). Multiple fieldwork seasons performed by Japanese-Kenyan teams during the last part of the 20th century resulted in the discovery of a large sample of Nacholapithecus fossils. Here, we describe the new femoral remains of Nacholapithecus. In well-preserved specimens, we evaluate sex differences and within-species variation using both qualitative and quantitative traits. We use these data to determine whether these specimens are morphologically similar to the species holotype KNM-BG 35250 (which shows some plastic deformation) and to compare Nacholapithecus with other Miocene hominoids and extant anthropoids to evaluate the distinctiveness of its femur. The new fossil evidence reaffirms previously reported descriptions of some distal femoral traits, namely the morphology of the patellar groove. However, results also show that relative femoral head size in Nacholapithecus is smaller, relative neck length is longer, and neck-shaft angle is lower than previously reported for KNM-BG 35250. These traits have a strong functional signal related to the hip joint kinematics, suggesting that the morphology of the proximal femur in Nacholapithecus might be functionally related to quadrupedal-like behaviors instead of more derived antipronograde locomotor modes. Results further demonstrate that other African Miocene apes (with the exception of Turkanapithecus kalakolensis) generally fall within the Nacholapithecus range of variation, whose overall femoral shape resembles that of Ekembo spp. and Equatorius africanus. Our results accord with the previously inferred locomotor repertoire of Nacholapithecus, indicating a combination of generalized arboreal quadrupedalism combined with other antipronograde behaviors (e.g., vertical climbing)