Entropy exchange, coherent information and concurrence

For a simple model we derive analytic expressions of entropy exchange and coherent information, from which relations between them and the concurrence are drawn. We find that in the quantum evolution the entropy exchange exhibits behavior \textsl{opposite} to that of the concurrence, whereas the coherent information shows features very similar to those of the concurrence. The meaning of this result for general systems is discussed.Comment: 4 pages, 8 figures v2: version accepted for publication in Phys. Rev.

Comment on ``Geometric phase of entangled spin pairs in a magnetic field''

The degree of entanglement between two spins may change due to interaction. About this we find that a wrong result in a recent work by Ge and Wadati [Phys. Rev. A {\bf72}, 052101(2005)] which breach the basic principle.Comment: 2 pages, comment on Phys. Rev. A {\bf72}, 052101(2005), and to appear in Phys. Rev.

Computer modeling and analysis of biological rhythms

Biological rhythms are an important phenomenon and feature of physiologic systems. Indirect means have to be employed for their description and exploration due to the unclear internal nature of the system. This study analyzed and developed several possible mathematical models using single or multidimensional nonlinear differential equations to approach the experimental circadian data. The numerical solutions of the models were obtained by computer simulation and the simulated and experimental acquired circadian data were analyzed in both the time and frequency domains. Phase plane plots, phase response curves and power spectrum analysis were employed to determine the nonlinearity of the system and its relation to the harmonic structure while bispectrum analysis showed the relation between the harmonics. Dynamic spectrum and frequency demodulation techniques were used to explore the dynamic transient process of the circadian rhythms when a stimulus is applied. The coherence function was examined to explore the frequency correlation between two different circadian rhythms: temperature and activity of the same subject. The study showed that a two dimensional coupled nonlinear oscillator model can be used to describe the circadian rhythm better and a model with relatively large nonlinearity closely approximated the experimental data. The research revealed the harmonic structure of circadian rhythms. This structure related to the nonlinearity of the system with the 2nd harmonic of experimental data representing bimodality in the time series. All the models developed in this research reflected this important feature. The effects of a nonperiodic stimulus to the circadian system were simulated in the model and an overshoot phenomenon was found during the frequency transient process. High values of coherence were found at the fundamental and third harmonics while no phase relation was found between harmonics of the experimental data using the bispectrum method

Enhancement of coherent energy transfer by disorder and temperature in light harvesting processes

We investigate the influence of static disorder and thermal excitations on excitonic energy transport in the light-harvesting apparatus of photosynthetic systems by solving the Schr\"{o}dinger equation and taking into account the coherent hoppings of excitons, the rates of exciton creation and annihilation in antennas and reaction centers, and the coupling to thermally excited phonons. The antennas and reaction centers are modeled, respectively, as the sources and drains which provide the channels for creation and annihilation of excitons. Phonon modes below a maximum frequency are coupled to the excitons that are continuously created in the antennas and depleted in the reaction centers, and the phonon population in these modes obeys the Bose-Einstein distribution at a given temperature. It is found that the energy transport is not only robust against the static disorder and the thermal noise, but it can also be enhanced by increasing the randomness and temperature in most parameter regimes. Relevance of our work to the highly efficient energy transport in photosynthetic systems is discussed.Comment: 21 pages, 6 figure

Entanglement fidelity and measurement of entanglement preserving in quantum processes

The entanglement fidelity provides a measure of how well the entanglement between two subsystems is preserved in a quantum process. By using a simple model we show that in some cases this quantity in its original definition fails in the measurement of the entanglement preserving. On the contrary, the modified entanglement fidelity, obtained by using a proper local unitary transformation on a subsystem, is shown to exhibit the behavior similar to that of the concurrence in the quantum evolution.Comment: 4 pages, 2 figures. v2: repaired a severe oversight, removed an incorrect claim, added references; v3: version accepted for publication in Phys. Rev.

THE TAXONOMIC TREAMENT OF CAMELLIA LUUANA (SECT. DALATIA) IN THE CENTRAL HIGHLANDS, VIETNAM

Camellia luuana Orel & Curry is known only from its type locality, Ta Dung Nature Reserve, now Ta Dung National Park, Dak Nong Province, the Central Highlands of Vietnam. No characteristics of fruit and seeds, which are the most important to divide genera in Theaceae (Chang & Ren, 1998; Ming & Bartholomew, 2007; Sealy, 1958), were presented in its protologue. After carefully reviewing the protologue, specimens, and images of Camellia luuana, relevant species and genera, and conducting a field investigation around its type locality, we concluded that this species is not a member of Camellia, but a member of  Pyrenaria

Local vertical measurements and violation of Bell inequality

For two qubits belonging to Alice and Bob, we derive an approach to setup the bound of Bell operator in the condition that Alice and Bob continue to perform local vertical measurements. For pure states we find that if the entanglement of the two qubits is less than 0.2644 (measured with von Neumann entropy) the violation of the Bell inequality will never be realized, and only when the entanglement is equal to 1 the maximal violation ($2\sqrt{2}$) can occur. For specific form of mixed states, we prove that the bound of the Bell inequality depends on the concurrence. Only when the concurrence is greater than 0.6 the violation of the Bell inequality can occur, and the maximal violation can never be achieved. We suggest that the bound of the Bell operator in the condition of local vertical measurements may be used as a measure of the entanglement.Comment: 4 pages, 3 figure

Reward Teaching for Federated Multi-armed Bandits

Most of the existing federated multi-armed bandits (FMAB) designs are based on the presumption that clients will implement the specified design to collaborate with the server. In reality, however, it may not be possible to modify the clients' existing protocols. To address this challenge, this work focuses on clients who always maximize their individual cumulative rewards, and introduces a novel idea of ``reward teaching'', where the server guides the clients towards global optimality through implicit local reward adjustments. Under this framework, the server faces two tightly coupled tasks of bandit learning and target teaching, whose combination is non-trivial and challenging. A phased approach, called Teaching-After-Learning (TAL), is first designed to encourage and discourage clients' explorations separately. General performance analyses of TAL are established when the clients' strategies satisfy certain mild requirements. With novel technical approaches developed to analyze the warm-start behaviors of bandit algorithms, particularized guarantees of TAL with clients running UCB or epsilon-greedy strategies are then obtained. These results demonstrate that TAL achieves logarithmic regrets while only incurring logarithmic adjustment costs, which is order-optimal w.r.t. a natural lower bound. As a further extension, the Teaching-While-Learning (TWL) algorithm is developed with the idea of successive arm elimination to break the non-adaptive phase separation in TAL. Rigorous analyses demonstrate that when facing clients with UCB1, TWL outperforms TAL in terms of the dependencies on sub-optimality gaps thanks to its adaptive design. Experimental results demonstrate the effectiveness and generality of the proposed algorithms.Comment: Accepted to IEEE Transactions on Signal Processin