Spectral Network Principle for Frequency Synchronization in Repulsive Laser Networks

Network synchronization of lasers is critical for reaching high-power levels and for effective optical computing. Yet, the role of network topology for the frequency synchronization of lasers is not well understood. Here, we report our significant progress toward solving this critical problem for networks of heterogeneous laser model oscillators with repulsive coupling. We discover a general approximate principle for predicting the onset of frequency synchronization from the spectral knowledge of a complex matrix representing a combination of the signless Laplacian induced by repulsive coupling and a matrix associated with intrinsic frequency detuning. We show that the gap between the two smallest eigenvalues of the complex matrix generally controls the coupling threshold for frequency synchronization. In stark contrast with Laplacian networks, we demonstrate that local rings and all-to-all networks prevent frequency synchronization, whereas full bipartite networks have optimal synchronization properties. Beyond laser models, we show that, with a few exceptions, the spectral principle can be applied to repulsive Kuramoto networks. Our results may provide guidelines for optimal designs of scalable laser networks capable of achieving reliable synchronization

Optical Potts Machine through Networks of Three-Photon Down-Conversion Oscillators

In recent years there has been a growing interest in optical simulation of lattice spin models for applications in classical computing. Here, we propose optical implementation of a three-state Potts spin model by using networks of coupled parametric oscillators with phase tristability. We first show that the cubic nonlinear process of spontaneous three-photon down-conversion is accompanied by a tristability in the phase of the subharmonic signal between three states with 2��/3 phase contrast. The phase of such a parametric oscillator behaves like a three-state spin system. Next, we show that a network of dissipatively coupled three-photon down-conversion oscillators emulates the three-state planar Potts model. We discuss potential applications of the proposed system for all-optical optimization of combinatorial problems such as graph 3-COL and MAX-3-CUT

Combinatorial Optimization with Photonics-Inspired Clock Models

NP-hard combinatorial optimization problems are in general hard problems that their computational complexity grows faster than polynomial scaling with the size of the problem. Thus, over the years there has been a great interest in developing unconventional methods and algorithms for solving such problems. Here, inspired by the nonlinear optical process of q-photon down-conversion, in which a photon is converted into q degenerate lower energy photons, we introduce a nonlinear dynamical model that builds on coupled single-variable phase oscillators and allows for efficiently approximating the ground state of the classical q-state planar Potts Hamiltonian. This reduces the exhaustive search in the large discrete solution space of a large class of combinatorial problems that are represented by the Potts Hamiltonian to solving a system of coupled dynamical equations. To reduce the problem of trapping into local minima, we introduce two different mechanisms by utilizing controlled chaotic dynamics and by dynamical formation of the cost function through adiabatic parameter tuning. The proposed algorithm is applied to graph-q-partitioning problems on several complex graphs

Arrayed Waveguide Lens for Beam Steering

Integrated planar lenses are critical components for analog optical information processing that enable a wide range of applications including beam steering. Conventional planar lenses require gradient index control which makes their on-chip realization challenging. Here, we introduce a new approach for beam steering by designing an array of coupled waveguides with segmented tails that allow for simultaneously achieving planar lensing and off-chip radiation. The proposed arrayed waveguide lens is built on engineering the evanescent coupling between adjacent channels to realize a photonic lattice with an equi-distant ladder of propagation constants that emulates the continuous parabolic index profile. Through coupled-mode analysis and full-wave numerical simulations, we show that selective excitation of waveguide channels enables beam steering with large field-of-views of ∼60°. The proposed arrayed waveguide lens can serve as a compact component in integrated photonic circuits for applications in imaging, sensing, and metrology

Improvement in Cardiac Function following Transplantation of Human Umbilical Cord Matrix-Derived Mesenchymal Cells

Objectives: Human umbilical cord mesenchymal cells (hUCM) can be easily obtained and processed in a laboratory. These cells may be considered as a suitable source in the repair of heart failure diseases. We, therefore, examined whether these cells may contribute to heart regeneration following an acute experimental myocardial infarction (MI). Methods: MI-induced animals received 5 ! 10 6 hUCM cells, 5 ! 10 6 5-azacytidine-treated cells (dhUCM), or PBS alone, subepicardially. A group of animals with MI and no other former intervention served as controls. dhUCM cells were assessed for F-actin, myogenin and troponin-I expression. Re-sults: dhUCM cells appeared as binucleated cells with extensive cytoplasmic processes. These differentiated cells were F-actin and myogenin positive. Thirty days after LAD ligation, left ventricular ejection fraction and the percentage of fractional shortening improved significantly in cell-receiving animals. In addition, the amount of scar tissue was significantly reduced in hUCM and dhUCM groups compared to MI group (p ! 0.05). These parameters were comparable between hUCM and dhUCM groups. Histopathological evaluations revealed that some engrafted cells adjacent to and remote from the MI area expressed troponin-I, F-actin and connexin43. Conclusion: These findings demonstrated the potential therapeutic use of either differentiated or undifferentiated hUCM cells in treatment of heart failure conditions

Optical Potts machine through networks of three-photon down-conversion oscillators

In recent years, there has been a growing interest in optical simulation of lattice spin models for applications in unconventional computing. Here, we propose optical implementation of a three-state Potts spin model by using networks of coupled parametric oscillators with phase tristability. We first show that the cubic nonlinear process of spontaneous three-photon down-conversion is accompanied by a tristability in the phase of the subharmonic signal between three states with 2π/3 phase contrast. The phase of such a parametric oscillator behaves like a three-state spin system. Next, we show that a network of dissipatively coupled three-photon down-conversion oscillators emulates the three-state planar Potts model. We discuss potential applications of the proposed system for all-optical optimization of combinatorial problems such as graph 3-COL and MAX 3-CUT

An Efficient Protocol for Embryonic Carcinoma Cells P19 Differentiation to Cardiomyocytes Using Oxytocin as Inducer

Background: The capability of embryonic carcinoma cells P19 in differentiation to Cardiomyocyte was examined through inducing effects of Oxytocin (OT) and 5-Azacytidin (5Az) individually and compared with each other in laboratory condition. Materials and Methods: P19 Embryoid Bodies (EBs) was formed through hanging drops method. Then, EBs were treated with (5Az) or (OT) and the EB medium (Ctrl) until 12 days. Morphology and beating number per minute were recorded every two days. Viability was carried out every three days. The expression of several cardiomyocyte-associated genes was assessed by RT-PCR. Results: The beating area percentage of EBs in OT treatment groups was more than that of the 5Az group in all days of experiment. However, only in final stage, a significant increase was observed in beating area of OT group. There was no significant difference in viability and morphological changes. OT induction expressed three more specific proteins in cell culture than 5Az. Conclusion: Statistical analysis revealed that response to OT inducer was more excessive than 5Az in all treatment groups. The Oxytocin was found to be effective inducer of cardiomyocytes differentiation from embryonic carcinoma cells P19 than 5-azacytidine