Quantum Annealing versus Digital Computing

Quantum annealing is getting increasing attention in combinatorial optimization. The quantum processing unit by D-Wave is constructed to approximately solve Ising models on so-called Chimera graphs. Ising models are equivalent to quadratic unconstrained binary optimization (QUBO) problems and maximum cut problems on the associated graphs. We have tailored branch-and-cut as well as semidefinite programming algorithms for solving Ising models for Chimera graphs to provable optimality and use the strength of these approaches for comparing our solution values to those obtained on the current quantum annealing machine, D-Wave 2000Q. This allows for the assessment of the quality of solutions produced by the D-Wave hardware. In addition, we also evaluate the performance of a heuristic by Selby. It has been a matter of discussion in the literature how well the D-Wave hardware performs at its native task, and our experiments shed some more light on this issue. In particular, we examine how reliably the D-Wave computer can deliver true optimum solutions and present some surprising results.

Effect of spectral manipulation and seasonal variations on cut foliage production and quality of Philodendron (Philodendron ‘Xanadu’)

Influence of spectral manipulation of light using coloured nets and seasonal variation on cut foliage yield and quality of Philodendron ‘Xanadu’ was evaluated under red, green, white and black coloured shade nets permitting light intensities ranging from 240.50 to 370μ mol m-2 s-1 (75% shade net), for two consecutive years from 2014-16, at ICARIIHR, Bengaluru. The plants grown under white shade net (75% shade) resulted in higher foliage production plant-1month-1 (14.53) and were on par with those grown under green shade net. The quality of the cut foliage in plants grown under white shade net with respect to stalk length (24.91 cm) and width of the lamina (5.19 cm) was on par with those under green and black shade nets. Coloured shade nets did not influence the vase life of the cut foliage. Developmental stages of the foliage under the different coloured nets have indicated that leaves attained the harvestable maturity stage at 29.92 days post-emergence under white shade. Cultivation of Philodendron ‘Xanadu’ under white shade resulted in maximum cut foliage yield and quality.

Local classical MAX-CUT algorithm outperforms p=2 QAOA on high-girth regular graphs

The p-stage Quantum Approximate Optimization Algorithm (QAOAp) is a promising approach for combinatorial optimization on noisy intermediate-scale quantum (NISQ) devices, but its theoretical behavior is not well understood beyond p=1. We analyze QAOA2 for the maximum cut problem (MAX-CUT), deriving a graph-size-independent expression for the expected cut fraction on any D-regular graph of girth >5 (i.e. without triangles, squares, or pentagons).We show that for all degrees D≥2 and every D-regular graph G of girth >5, QAOA2 has a larger expected cut fraction than QAOA1 on G. However, we also show that there exists a 2-local randomized classical algorithm A such that A has a larger expected cut fraction than QAOA2 on all G. This supports our conjecture that for every constant p, there exists a local classical MAX-CUT algorithm that performs as well as QAOAp on all graphs.

Graph Neural Networks for Maximum Constraint Satisfaction

Many combinatorial optimization problems can be phrased in the language of constraint satisfaction problems. We introduce a graph neural network architecture for solving such optimization problems. The architecture is generic; it works for all binary constraint satisfaction problems. Training is unsupervised, and it is sufficient to train on relatively small instances; the resulting networks perform well on much larger instances (at least 10-times larger). We experimentally evaluate our approach for a variety of problems, including Maximum Cut and Maximum Independent Set. Despite being generic, we show that our approach matches or surpasses most greedy and semi-definite programming based algorithms and sometimes even outperforms state-of-the-art heuristics for the specific problems.

Exact Facetial Odd-Cycle Separation for Maximum Cut and Binary Quadratic Optimization

The exact solution of the NP-hard (nondeterministic polynomial-time hard) maximum cut problem is important in many applications across, for example, physics, chemistry, neuroscience, and circuit layout—which is also due to its equivalence to the unconstrained binary quadratic optimization problem. Leading solution methods are based on linear or semidefinite programming and require the separation of the so-called odd-cycle inequalities. In their groundbreaking research, F. Barahona and A. R. Mahjoub have given an informal description of a polynomial-time algorithm for this problem. As pointed out recently, however, additional effort is necessary to guarantee that the inequalities obtained correspond to facets of the cut polytope. In this paper, we shed more light on a so enhanced separation procedure and investigate experimentally how it performs in comparison with an ideal setting where one could even employ the sparsest, most violated, or geometrically most promising facet-defining odd-cycle inequalities. Summary of Contribution: This paper aims at a better capability to solve binary quadratic optimization or maximum cut problems and their various applications using integer programming techniques. To this end, the paper describes enhancements to a well-known algorithm for the central separation problem arising in this context; it is demonstrated experimentally that these enhancements are worthwhile from a computational point of view. The linear relaxations of the aforementioned problems are typically solved using fewer iterations and cutting planes than with a nonenhanced approach. It is also shown that the enhanced procedure is only slightly inferior to an ideal, enumerative, and, in practice, intractable global cutting-plane selection.

Quantitative determination of cut efficiency during soft tissue surgery using diode lasers in the wavelength range between 400 and 1500 nm

Within the scope of this ex vivo study, the cut efficiency was investigated with eight diode laser wavelengths in the range from 400 to 1500 nm. Incisions on porcine gingiva samples were generated in CW-mode at a power range of 0.5–4 W using a bare fiber (∅ = 320 μm) in contact and non-contact mode at a cut speed of 2 mm/s. Cut depths, cut widths, and thermal damages were recorded based on histological sections and were evaluated via measurement masks. Moreover, with respect to the controllability of a therapeutic measure, an efficiency factor was defined. At powers above 2 W, for 445 nm, the maximum cut depth was 820 μm and 344 μm for 810 nm, respectively. At all wavelength and power ranges, the cut width averaged 125 μm. At minimum output power (0.5 W), the spatial expansion of the thermal damage in the tissue surface layer corresponds in the blue/green wavelength range from the very beginning of the laser impact to the fiber core diameter. It could be shown that increases in the diode laser power output do not correlate to the same extent with the incision depth nor with thermal damage to tissue.

MODULAR MACHINE FOR OIL-BEARING ROSE PRODUCTION

The cultivation of oil-bearing roses requires signifi cant labor and energy resources. The research aims to develop a multifunctional farm implement to mechanize technological operations in rose-growing on small and medium-sized farms. The modular farm implement includes a platform-type base module. Depending on the technological operation performed, it incorporates a spraying system, pneumatic pruning system, side panels, or two workplaces for rose pickers. Using computer simulation with a simulation model created using the “Solid Works” software package, the author determined the profi les and the type of materials for the base module production. Graphoanalytical models help establish the parameters of the other modules of the modular machine. The conducted experimental tests proved the constructive strength of the technical solutions and the functional suitability of the modular machine. It was found that in oil-bearing rose plantations, the farm implement performs spraying at the consumption rates of 300…400 l/ha for treatment of the soil surface area under the rose bushes and 1000 l/ha and more for disease and pest control, foliar feeding, and other activities. The variant of the modular machine for selective pruning is ergonomic and effi cient at a maximum cut diameter of up to 25 mm and pressure in the tractor pneumatic system between 0.3…0.73 MPa. The highest eff ect of mechanized oil-bearing rose harvesting with the modular machine could be achieved in well-maintained plantations. The optimal height of the bushes should be 1.5…1.6 m, and the operation should be performed in the period of active fl owering (after 4-5 years of planting or rejuvenation). It is also possible to use the modular machine for transportation purposes. Experimental tests of the developed modular machine for oil-bearing rose production proved the constructive strength of the technical solutions and its functional

Investigation of Failure Criteria and Experimental Process of the Composite Specimen with Mechanical Joints under Tensile Loading

Generally, composite materials are used to obtain better engineering properties, including higher hardness, greater strength, lower weight, heat resistance, moisture and corrosion, which are not present in homogeneous materials such as metals, which are more commonly used in composite design. In this article, experimental study of the composite specimen with mechanical joints under tensile loading, joints of composite material structures, failure criteria in composite materials, tensile impact test is investigated. The results of research work it shows that maximum strength, the hand lay-up can be designed with [0º, 45º, 90º, -45º] s and layers with 45º fibers is very important, because these fibers in these layers have a significant role in increasing the resistance of the piecework under shear stresses due to the passage of stress lines along the hole; In other words, the maximum cut occurs at a 45º angle, and these layers resist this shear stress.