Heat kernel-based p-energy norms on metric measure spaces

We focus on heat kernel-based p-energy norms (1<p<\infty) on bounded and unbounded metric measure spaces, in particular, weak-monotonicity properties for different types of energies. Such properties are key to related studies, under which we generalise the convergence result of Bourgain-Brezis-Mironescu (BBM) for p\neq2. We establish the equivalence of various p-energy norms and weak-monotonicity properties when there admits a heat kernel satisfying the two-sided estimates. Using these equivalences, we verify various weak-monotonicity properties on nested fractals and their blowups. Immediate consequences are that, many classical results on p-energy norms hold for such bounded and unbounded fractals, including the BBM convergence and Gagliardo-Nirenberg inequality.Comment: 39 pages with 1 figur

A Prioritized Test Generation Method For Pair-wise Testing

The most sufficient test methods are based on a test case set which covers all combinations of parameters. However, the scale of test cases is always too large and their cost cannot be accepted. People will first consider the implementation of critical test cases. Even if the test is terminated suddenly, the test cases of high importance will have been executed. It improves the testing efficiency while securing the detection rate of defect. The contribution of this paper is how to generate pair-wise testing cases with a priority. Firstly, We design formulas to compute the weights of priorities. Secondly, we adopt a greed algorithm to solve the combined testing problems. Furthermore, we integrate the greed strategy into a genetic algorithm which makes the most efficient testing in critical parameters and their sets, and ensures its detection rate of defect under limited resources. DOI: http://dx.doi.org/10.11591/telkomnika.v11i1.188

Discrimination experiment of sound distance perception for a real source in near-field

International audienceThe ability of distance perception is quite important for our daily life. For the backward region where the vision cannot cover, listeners perceive objects only via binaural hearing, and the distance perception for a backward sound source is very important. It helps listeners to perceive an approaching sound source and avoid dangerous object especially when the sound source is in the rear. In the free field, the main acoustic distance perception cues for a nearby sound source include intensity variation with distance, binaural cues, dynamic cues, spectrum change and direct-to-reverberant energy ratio (Pavel Zahorik, 2005). Theoretically, all the above mentioned cues can be simulated via virtual auditory display (VAD), and realized by using a real sound source in an anechoic chamber. In comparison, the results based on a real sound source measurement should be more accurate. Previous researches have proved that the sound pressure has a giant influence on the ability of distance discrimination in both near field and far field when source is in front of head (Daniel H. Ashmead, 1990). However, few researches attempt to examine the binaural effect alone in distance perception. The theory was based on a fact that both the sound intensities and spectrums of a nearby sound will be different in two ears due to the head shadow, and these differences will change with distance when the sound source is lateral (PAUL D. COLEMAN, 1963). To verify the impact of binaural effect to distance discrimination, we conducted an experiment to exam the backward sound distance perception thresholds when the sound is presented from different azimuths in the horizontal plane. We used an automatic test system controlled by a computer in an anechoic room, eight listeners participated in the test. A loudness balanced band noise was used as test signals to remove the influence of sound level, and the signal was presented in 75 dBA. One signal was presented in the reference distance (50cm or 100cm), while the other one was presented in a closer distance, and sequence is random. The subjects need to do 2IFC (choose the closer one) between the signals presented in two different distances, and no feedback was given to subjects.The discrimination thresholds of two reference distances (0.5m and 1m) and five source azimuth (0°, 45°, 90°, 135°, 180°, right half plane of head) were examined in the experiment. The result show that subjects&#61602; distance discrimination thresholds are lower when the sound source is on the side of head (about 20%) compared with front and back (above 30%), distinguishing two signals become quite difficult for participants when signals are presented in azimuth 0° and 180°. Moreover, this phenomenon is more prominent in 50cm compared with 100cm, while the effect of head shadow is more significant in 50cm. The results obtained in this study are consistent with previous studies and reveal that the binaural effect indeed contributes to distance discrimination process of human in a degree. This work is supported by the National Natural Science Foundation of China (Grant No. 11574090) and the Natural Science Foundation of Guangdong Province (Grant No. 2018B030311025)

Weak monotonicity property of Korevaar-Schoen norms on nested fractals

In this paper, we study the weak monotonicity property of p-energy related Korevaar-Schoen norms on connected nested fractals for $1 < p < \infty$. Such property has many important applications on fractals and other metric measure spaces, such as constructing p-energies (when $p = 2$ this is basically a Dirichlet form), generalizing the classical Sobolev type inequalities and the celebrated Bourgain-Brezis-Mironescu convergence.Comment: 10 pages,1 figur