Maximizing spectral radii of uniform hypergraphs with few edges

In this paper we investigate the hypergraphs whose spectral radii attain the maximum among all uniform hypergraphs with given number of edges. In particular we characterize the hypergraph(s) with maximum spectral radius over all unicyclic hypergraphs, linear or power unicyclic hypergraphs with given girth, linear or power bicyclic hypergraphs, respectively

Thermodynamics of SU(2) bosons in one dimension

On the basis of Bethe ansatz solution of two-component bosons with SU(2) symmetry and $\delta$-function interaction in one dimension, we study the thermodynamics of the system at finite temperature by using the strategy of thermodynamic Bethe ansatz (TBA). It is shown that the ground state is an isospin "ferromagnetic" state by the method of TBA, and at high temperature the magnetic property is dominated by Curie's law. We obtain the exact result of specific heat and entropy in strong coupling limit which scales like $T$ at low temperature. While in weak coupling limit, it is found there is still no Bose-Einstein Condensation (BEC) in such 1D system.Comment: 7 page

Spectral coarse graining for random walk in bipartite networks

Many real-world networks display a natural bipartite structure, while analyzing or visualizing large bipartite networks is one of the most challenges. As a result, it is necessary to reduce the complexity of large bipartite systems and preserve the functionality at the same time. We observe, however, the existing coarse graining methods for binary networks fail to work in the bipartite networks. In this paper, we use the spectral analysis to design a coarse graining scheme specifically for bipartite networks and keep their random walk properties unchanged. Numerical analysis on artificial and real-world bipartite networks indicates that our coarse graining scheme could obtain much smaller networks from large ones, keeping most of the relevant spectral properties. Finally, we further validate the coarse graining method by directly comparing the mean first passage time between the original network and the reduced one.Comment: 7 pages, 3 figure

Anticipating Daily Intention using On-Wrist Motion Triggered Sensing

Anticipating human intention by observing one's actions has many applications. For instance, picking up a cellphone, then a charger (actions) implies that one wants to charge the cellphone (intention). By anticipating the intention, an intelligent system can guide the user to the closest power outlet. We propose an on-wrist motion triggered sensing system for anticipating daily intentions, where the on-wrist sensors help us to persistently observe one's actions. The core of the system is a novel Recurrent Neural Network (RNN) and Policy Network (PN), where the RNN encodes visual and motion observation to anticipate intention, and the PN parsimoniously triggers the process of visual observation to reduce computation requirement. We jointly trained the whole network using policy gradient and cross-entropy loss. To evaluate, we collect the first daily "intention" dataset consisting of 2379 videos with 34 intentions and 164 unique action sequences. Our method achieves 92.68%, 90.85%, 97.56% accuracy on three users while processing only 29% of the visual observation on average

Charmless B(s)→VVB_{(s)}\to VV Decays in Factorization-Assisted Topological-Amplitude Approach

Within the factorization-assisted topological-amplitude approach, we studied the 33 charmless $B_{(s)} \to VV$ decays, where $V$ stands for a light vector meson. According to the flavor flows, the amplitude of each process can be decomposed into 8 different topologies. In contrast to the conventional flavor diagrammatic approach, we further factorize each topological amplitude into decay constant, form factors and unknown universal parameters. By $\chi^2$ fitting 46 experimental observables, we extracted 10 theoretical parameters with $\chi^2$ per degree of freedom around 2. Using the fitted parameters, we calculated the branching fractions, polarization fractions, CP asymmetries and relative phases between polarization amplitudes of each decay mode. The decay channels dominated by tree diagram have large branching fractions and large longitudinal polarization fraction. The branching fractions and longitudinal polarization fractions of color-suppressed decays become smaller. Current experimental data of large transverse polarization fractions in the penguin dominant decay channels can be explained by only one transverse amplitude of penguin annihilation diagram. Our predictions of those not yet measured channels can be tested in the ongoing LHCb experiment and the Belle-II experiment in future.Comment: 22 pages, 2 figure