Global first-passage times of fractal lattices

The global first passage time density of a network is the probability that a random walker released at a random site arrives at an absorbing trap at time T. We find simple expressions for the mean global first passage time for five fractals: the d-dimensional Sierpinski gasket, T fractal, hierarchical percolation model, Mandelbrot-Given curve, and a deterministic tree. We also find an exact expression for the second moment and show that the variance of the first passage time, Var(T), scales with the number of nodes within the fractal N such that Var(T)similar to N(4/d), where d is the spectral dimension

Tissue-specific expression of high-voltage-activated dihydropyridine-sensitive L-type calcium channels

The cloning of the cDNA for the α1 subunit of L-type calcium channels revealed that at least two genes (CaCh1 and CaCh2) exist which give rise to several splice variants. The expression of mRNA for these α1 subunits and the skeletal muscle α2/δ, β and γ subunits was studied in rabbit tissues and BC3H1 cells. Nucleic-acid-hybridization studies showed that the mRNA of all subunits are expressed in skeletal muscle, brain, heart and aorta. However, the α1-, β- and γ-specific transcripts had different sizes in these tissues. Smooth muscle and heart contain different splice variants of the CaCh2 gene. The α1, β and γ mRNA are expressed together in differentiated but not in proliferating BC3H1 cells. A probe specific for the skeletal muscle α2/δ subunit did not hybridize to poly(A)-rich RNA from BC3H1 cells. These results suggest that different splice variants of the genes for the α1, β and γ subunits exist in tissues containing L-type calcium channels, and that their expression is regulated in a coordinate manner

Photogenerated Carriers in SrTiO3 Probed by Mid-Infrared Absorption

Infrared absorption spectra of SrTiO$_3$ have been measured under above-band-gap photoexcitations to study the properties of photogenerated carriers, which should play important roles in previously reported photoinduced phenomena in SrTiO$_3$. A broad absorption band appears over the entire mid-infrared region under photoexcitation. Detailed energy, temperature, and excitation power dependences of the photoinduced absorption are reported. This photo-induced absorption is attributed to the intragap excitations of the photogenerated carriers. The data show the existence of a high density of in-gap states for the photocarriers, which extends over a wide energy range starting from the conduction and valence band edges.Comment: 5 pages, 5 figures, submitted to J. Phys. Soc. Jp

Long-Term Visual Object Tracking Benchmark

We propose a new long video dataset (called Track Long and Prosper - TLP) and benchmark for single object tracking. The dataset consists of 50 HD videos from real world scenarios, encompassing a duration of over 400 minutes (676K frames), making it more than 20 folds larger in average duration per sequence and more than 8 folds larger in terms of total covered duration, as compared to existing generic datasets for visual tracking. The proposed dataset paves a way to suitably assess long term tracking performance and train better deep learning architectures (avoiding/reducing augmentation, which may not reflect real world behaviour). We benchmark the dataset on 17 state of the art trackers and rank them according to tracking accuracy and run time speeds. We further present thorough qualitative and quantitative evaluation highlighting the importance of long term aspect of tracking. Our most interesting observations are (a) existing short sequence benchmarks fail to bring out the inherent differences in tracking algorithms which widen up while tracking on long sequences and (b) the accuracy of trackers abruptly drops on challenging long sequences, suggesting the potential need of research efforts in the direction of long-term tracking.Comment: ACCV 2018 (Oral

Online, Real-Time Tracking Using a Category-to-Individual Detector

A method for online, real-time tracking of objects is presented. Tracking is treated as a repeated detection problem where potential target objects are identified with a pre-trained category detector and object identity across frames is established by individual-specific detectors. The individual detectors are (re-)trained online from a single positive example whenever there is a coincident category detection. This ensures that the tracker is robust to drift. Real-time operation is possible since an individual-object detector is obtained through elementary manipulations of the thresholds of the category detector and therefore only minimal additional computations are required. Our tracking algorithm is benchmarked against nine state-of-the-art trackers on two large, publicly available and challenging video datasets. We find that our algorithm is 10% more accurate and nearly as fast as the fastest of the competing algorithms, and it is as accurate but 20 times faster than the most accurate of the competing algorithms

Average distances on self-similar sets and higher order average distances of self-similar measures

The purpose of this paper is twofold: (1) we study different notions of the average distance between two points of a self-similar subset of ℝ, and (2) we investigate the asymptotic behaviour of higher order average moments of self-similar measures on self-similar subsets of ℝ

The synaptic ribbon is critical for sound encoding at high rates and with temporal precision.

We studied the role of the synaptic ribbon for sound encoding at the synapses between inner hair cells (IHCs) and spiral ganglion neurons (SGNs) in mice lacking RIBEYE (RBEKO/KO). Electron and immunofluorescence microscopy revealed a lack of synaptic ribbons and an assembly of several small active zones (AZs) at each synaptic contact. Spontaneous and sound-evoked firing rates of SGNs and their compound action potential were reduced, indicating impaired transmission at ribbonless IHC-SGN synapses. The temporal precision of sound encoding was impaired and the recovery of SGN-firing from adaptation indicated slowed synaptic vesicle (SV) replenishment. Activation of Ca2+-channels was shifted to more depolarized potentials and exocytosis was reduced for weak depolarizations. Presynaptic Ca2+-signals showed a broader spread, compatible with the altered Ca2+-channel clustering observed by super-resolution immunofluorescence microscopy. We postulate that RIBEYE disruption is partially compensated by multi-AZ organization. The remaining synaptic deficit indicates ribbon function in SV-replenishment and Ca2+-channel regulation

Laplace Operators on Fractals and Related Functional Equations

We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those used in the euclidean situation. Furthermore, we use the obtained information on the spectral zeta function to define the Casimir energy of fractals. We give numerical values for this energy for the Sierpi\'nski gasket