Ising Hamiltonians for Constrained Combinatorial Optimization Problems and the Metropolis-Hastings Warm-Starting Algorithm

Quantum approximate optimization algorithm (QAOA) is a promising variational quantum algorithm for combinatorial optimization problems. However, the implementation of QAOA is limited due to the requirement that the problems be mapped to Ising Hamiltonians and the nonconvex optimization landscapes. Although the Ising Hamiltonians for many NP hard problems have been obtained, a general method to obtain the Ising Hamiltonians for constrained combinatorial optimization problems (CCOPs) has not yet been investigated. In this paper, a general method is introduced to obtain the Ising Hamiltonians for CCOPs and the Metropolis-Hastings warm-starting algorithm for QAOA is presented which can provably converge to the global optimal solutions. The effectiveness of this method is demonstrated by tackling the minimum weight vertex cover (MWVC) problem, the minimum vertex cover (MVC) problem, and the maximal independent set problem as examples. The Ising Hamiltonian for the MWVC problem is obtained first time by using this method. The advantages of the Metropolis-Hastings warm-starting algorithm presented here is numerically analyzed through solving 30 randomly generated MVC cases with 1-depth QAOA

Poly[di-μ2-azido-μ3-pyrazine-2-carboxyl­ato-cadmium(II)]

The title compound, [Cd(C5H3N2O2)(N3)]n, has been pre­pared by the reaction of pyrazine-2-carboxylic acid, cadmium(II) nitrate and sodium azide. In the structure, the CdII atom is six-coordinated by two azide anions and three pyrazine-2-carboxyl­ate ligands. Each pyrazine-2-carboxyl­ate ligand bridges three CdII atoms, whereas the azide ligand bridges two CdII atoms, resulting in the formation of a two-dimensional metal–organic polymer developing parallel to the (100) plane

A role of corazonin receptor in larval-pupal transition and pupariation in the oriental fruit fly Bactrocera dorsalis (Hendel) (Diptera: Tephritidae)

Corazonin (Crz) is a neuropeptide hormone, but also a neuropeptide modulator that is internally released within the CNS, and it has a widespread distribution in insects with diverse physiological functions. Here, we identified and cloned the cDNAs of Bactrocera dorsalis that encode Crz and its receptor CrzR. Mature BdCrz has 11 residues with a unique Ser11 substitution (instead of the typical Asn) and a His in the evolutionary variable position 7. The BdCrzR cDNA encodes a putative protein of 608 amino acids with 7 putative transmembrane domains, typical for the structure of G-protein-coupled receptors. When expressed in Chinese hamster ovary (CHO) cells, the BdCrzR exhibited a high sensitivity and selectivity for Crz (EC50 approximate to 52.5 nM). With qPCR, the developmental stage and tissue-specific expression profiles in B. dorsalis demonstrated that both BdCrz and BdCrzR were highly expressed in the larval stage, and BdCrzR peaked in 2-day-old 3rd-instar larvae, suggesting that the BdCrzR may play an important role in the larval-pupal transition behavior. Immunochemical localization confirmed the production of Crz in the central nervous system (CNS), specifically by a group of three neurons in the dorso-lateral protocerebrum and eight pairs of lateral neurons in the ventral nerve cord. qPCR analysis located the BdCrzR in both the CNS and epitracheal gland, containing the Inka cells. Importantly, dsRNA-BdCrzR-mediated gene-silencing caused a delay in larval-pupal transition and pupariation, and this phenomenon agreed with a delayed expression of tyrosine hydroxylase and dopa-decarboxylase genes. We speculate that CrzR-silencing blocked dopamine synthesis, resulting in the inhibition of pupariation and cuticular melanization. Finally, injection of Crz in head-ligated larvae could rescue the effects. These findings provide a new insight into the roles of Crz signaling pathway components in B. dorsalis and support an important role of CrzR in larval-pupal transition and pupariation behavior

Bis[bis­(2-ethyl-5-methyl-1H-imidazol-4-yl-κN 3)methane](nitrato-κ2 O,O′)nickel(II) nitrate

In the title compound, [Ni(NO3)(C13H20N4)2]NO3, the NiII ion shows a distorted octa­hedral geometry formed by four N atoms from two bis­(2-ethyl-5-methyl-1H-imidazol-4-yl)methane ligands and two O atoms from a chelating nitrate anion. Three ethyl groups in the complex cation and the O atoms of the uncoordinated nitrate anion are disordered over two sets of positions [occupancy ratios of 0.52 (3):0.48 (3) and 0.63 (3):0.37 (3), respectively]. In the crystal, inter­molecular N—H⋯O hydrogen bonds connect the complex cations into a zigzag chain along [010] and further N—H⋯O hydrogen bonds between the chains and the uncoordinated nitrate anions lead to layers parallel to (100)

Aqua­[bis­(2-ethyl-5-methyl-1H-imidazol-4-yl-κN 3)methane]­oxalatocopper(II) dihydrate

In the title compound, [Cu(C2O4)(C13H20N4)(H2O)]·2H2O, the CuII atom exhibits a distorted square-pyramidal geometry with the two N atoms of the imidazole ligand and the two O atoms of the oxalate ligand forming the basal plane, while the O atom of the coordinated water mol­ecule is in an apical position. The CuII atom is shifted 0.232 (2) Å out of the basal plane toward the water mol­ecule. The asymmetric unit is completed by two solvent water mol­ecules. These water mol­ecules participate in the formation of an intricate three-dimensionnal network of hydrogen bonds involving the coordinated water mol­ecule and the NH groups

Joint Optimization of Offloading and Resources Allocation in Secure Mobile Edge Computing Systems

Mobile edge computing (MEC) has become a promising technology for real-time communications. Mobile devices can reduce the energy consumption and prolong the lifetime significantly via offloading the computing tasks to the MEC server. Moreover, physical layer security techniques can ensure the secure transmission of the offloading data. This paper investigates a MEC system that consists of an access point, multiple mobile devices and a malicious eavesdropper. The tasks allocation, local central processor's frequency, offloading power, and offloading timeslots are optimized jointly to minimize the total energy consumption of the system. A difference of convex algorithm based scheme is proposed to solve the joint optimization problem. Moreover, a Karush Kuhn Tucker conditions based algorithm is also proposed to reduce the computational complexity. Numerical results show that the proposed algorithms are very effective. Moreover, the power consumption for secure offloading decreases with the increase of the distance between the mobile devices and the eavesdropper