499 research outputs found
Construction of Barrier in a Fishing Game With Point Capture
This paper addresses a particular pursuit-evasion game, called as “fishing game” where a faster evader attempts to pass the gap between two pursuers. We are concerned with the conditions under which the evader or pursuers can win the game. This is a game of kind in which an essential aspect, barrier, separates the state space into disjoint parts associated with each player's winning region. We present a method of explicit policy to construct the barrier. This method divides the fishing game into two subgames related to the included angle and the relative distances between the evader and the pursuers, respectively, and then analyzes the possibility of capture or escape for each subgame to ascertain the analytical forms of the barrier. Furthermore, we fuse the games of kind and degree by solving the optimal control strategies in the minimum time for each player when the initial state lies in their winning regions. Along with the optimal strategies, the trajectories of the players are delineated and the upper bounds of their winning times are also derived
Unveiling the nucleon tensor charge at Jefferson Lab: A study of the SoLID case
Future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the
Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in
the region where the partonic structure of the nucleon is dominated by the
valence quarks. One of the main goals is to constrain the quark transversity
distributions. We apply recent theoretical advances of the global QCD
extraction of the transversity distributions to study the impact of future
experimental data from the SoLID experiments. Especially, we develop a simple
strategy based on the Hessian matrix analysis that allows one to estimate the
uncertainties of the transversity quark distributions and their tensor charges
extracted from SoLID data simulation. We find that the SoLID measurements with
the proton and the effective neutron targets can improve the precision of the
u- and d-quark transversity distributions up to one order of magnitude in the
range 0.05 < x < 0.6.Comment: 11 pages, 3 figures, published on Physics Letters
An edge-based matching kernel through discrete-time quantum walks
In this paper, we propose a new edge-based matching kernel for graphs by using discrete-time quantum walks. To this end, we commence by transforming a graph into a directed line graph. The reasons of using the line graph structure are twofold. First, for a graph, its directed line graph is a dual representation and each vertex of the line graph represents a corresponding edge in the original graph. Second, we show that the discrete-time quantum walk can be seen as a walk on the line graph and the state space of the walk is the vertex set of the line graph, i.e., the state space of the walk is the edges of the original graph. As a result, the directed line graph provides an elegant way of developing new edge-based matching kernel based on discrete-time quantum walks. For a pair of graphs, we compute the h-layer depth-based representation for each vertex of their directed line graphs by computing entropic signatures (computed from discrete-time quantum walks on the line graphs) on the family of K-layer expansion subgraphs rooted at the vertex, i.e., we compute the depth-based representations for edges of the original graphs through their directed line graphs. Based on the new representations, we define an edge-based matching method for the pair of graphs by aligning the h-layer depth-based representations computed through the directed line graphs. The new edge-based matching kernel is thus computed by counting the number of matched vertices identified by the matching method on the directed line graphs. Experiments on standard graph datasets demonstrate the effectiveness of our new kernel
A quantum Jensen-Shannon graph kernel using discrete-time quantum walks
In this paper, we develop a new graph kernel by using the quantum Jensen-Shannon divergence and the discrete-time quantum walk. To this end, we commence by performing a discrete-time quantum walk to compute a density matrix over each graph being compared. For a pair of graphs, we compare the mixed quantum states represented by their density matrices using the quantum Jensen-Shannon divergence. With the density matrices for a pair of graphs to hand, the quantum graph kernel between the pair of graphs is defined by exponentiating the negative quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets, and demonstrate the effectiveness of the new kernel
Room-temperature Tunable Fano Resonance by Chemical Doping in Few-layer Graphene Synthesized by Chemical Vapor Deposition
A Fano-like phonon resonance is observed in few-layer (~3) graphene at room
temperature using infrared Fourier transform spectroscopy. This Fano resonance
is the manifestation of a strong electron-phonon interaction between the
discrete in-plane lattice vibrational mode and continuum electronic excitations
in graphene. By employing ammonia chemical doping, we have obtained different
Fano line shapes ranging from anti-resonance in hole-doped graphene to
phonon-dominated in n-type graphene. The Fano resonance shows the strongest
interference feature when the Fermi level is located near the Dirac point. The
charged phonon exhibits much-enhanced oscillator strength and experiences a
continuous red shift in frequency as electron density increases. It is
suggested that the phonon couples to different electronic transitions as Fermi
level is tuned by chemical doping.Comment: 14 pages, 4 figure
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