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For most problems pertaining to perfect matchings, one may restrict attention to matching covered graphs -- that is, connected nontrivial graphs with the property that each edge belongs to some perfect matching. There is extensive literature on these graphs that are also known as $1$-extendable graphs (since each edge extends to a perfect matching) including an ear decomposition theorem due to Lovasz and Plummer. A cycle $C$ of a graph $G$ is conformal if $G-V(C)$ has a perfect matching; such cycles play an important role in the study of perfect matchings, especially when investigating the Pfaffian orientation problem. A matching covered graph $G$ is cycle-extendable if -- for each even cycle $C$ -- the cycle $C$ is conformal, or equivalently, each perfect matching of $C$ extends to a perfect matching of $G$, or equivalently, $C$ is the symmetric difference of two perfect matchings of $G$, or equivalently, $C$ extends to an ear decomposition of $G$. In the literature, these are also known as cycle-nice or as $1$-cycle resonant graphs. Zhang, Wang, Yuan, Ng and Cheng [Discrete Mathematics, 345:7 (2022), 112876] provided a characterization of claw-free cycle-extendable graphs. Guo and Zhang [Discrete Mathematics, 275:1-3 (2004), 151-164] and independently Zhang and Li [Discrete Applied Mathematics, 160:13-14 (2012), 2069-2074], provided characterizations of bipartite planar cycle-extendable graphs. In this paper, we establish a characterization of all planar cycle-extendable graphs -- in terms of $K_2$ and four infinite families., Comment: Submitted to a journal

We report on the realization of a large-scale quantum-processing architecture surpassing the tier of 1000 atomic qubits. By tiling multiple microlens-generated tweezer arrays, each operated by an independent laser source, we can eliminate laser-power limitations in the number of allocatable qubits. Already with two separate arrays, we implement combined 2D configurations of 3000 qubit sites with a mean number of 1167(46) single-atom quantum systems. The transfer of atoms between the two arrays is achieved with high efficiency. Thus, supercharging one array designated as quantum processing unit with atoms from the secondary array significantly increases the number of qubits and the initial filling fraction. This drastically enlarges attainable qubit cluster sizes and success probabilities allowing us to demonstrate the defect-free assembly of clusters of up to 441 qubits with persistent stabilization at near-unity filling fraction over tens of detection cycles. The presented method substantiates neutral atom quantum information science by facilitating configurable geometries of highly scalable quantum registers with immediate application in Rydberg-state mediated quantum simulation, fault-tolerant universal quantum computation, quantum sensing, and quantum metrology.

State-of-the-art individual-atom tweezer platforms have relied on loading schemes based on spatially superimposing the tweezer array with a cloud of cold atoms created beforehand. Together with immanent atom loss, this dramatically limits the data rate, as the application sequence must be alternated with the time-consuming phases of magneto-optical trapping and laser cooling. We introduce a modular scheme built on an additional cold-atom reservoir and an array of buffer traps effectively decoupling cold-atom accumulation and single-atom supply from the quantum-register operation. For this purpose, we connect a microlens-based tweezer array to a cloud of laser-cooled atoms held in an auxiliary large-focus dipole trap by utilizing atom transport and buffer traps for dedicated single-atom supply. We demonstrate deterministic loading of a hexagonal target structure with atoms solely originating from the reservoir trap. The results facilitate increased data rates and unlock a path to continuous operation of individual-atom tweezer arrays in quantum science, making use of discrete functional modules, operated in parallel and spatially separated.

Polymer coatings on cellulosic fibres are widely used to enhance the natural fibre properties by improving, for example, the hydrophobicity and wet strength. Here, we investigate the effects of a terpolymer P(S-co-MABP-co-PyMA) coating on cotton linters and eucalyptus fibres to improve the resistance of cellulose fibres against wetness. Coated and uncoated fibres were characterised by using scanning electron microscopy, contact angle measurements, Raman spectroscopy and atomic force microscopy with the objective of correlating macroscopic properties such as the hydrophobicity of the fleece with microscopic properties such as the coating distribution and local nanomechanics. The scanning electron and fluorescence microscopy results revealed the distribution of the coating on the paper fleeces and fibres. Contact angle measurements proved the hydrophobic character of the coated fleece, which was also confirmed by Raman spectroscopy measurements that investigated the water uptake in single fibres. The water uptake also induced a change in the local mechanical properties, as measured by atomic force microscopy. These results verify the basic functionality of the hydrophobic coating on fibres and paper fleeces but call into question the homogeneity of the coating., Comment: 24 pages, 5 figures, submitted

We discuss the construction of the physical configuration space for Yang-Mills quantum mechanics and Yang-Mills theory on a cylinder. We explicitly eliminate the redundant degrees of freedom by either fixing a gauge or introducing gauge invariant variables. Both methods are shown to be equivalent if the Gribov problem is treated properly and the necessary boundary identifications on the Gribov horizon are performed. In addition, we analyze the significance of non-generic configurations and clarify the relation between the Gribov problem and coordinate singularities., Comment: 52 pages LaTeX2e, 8 postscript figures, uses epsfig, amsmath, amssymb

This paper explores various aspects of training preschool teachers in the Federal Republic of Germany to cooperate with parents in the education of their children. An initial discussion of teacher training programs in Germany focuses on the lack of a theoretical concept of socialization and social work as a basis for working with parents, and the resulting lack of daily application of such theoretical concepts. An analysis of the reasons for these difficulties, accompanied by specific arguments in favor of training teachers to work with parents, comprises the largest section of the paper. Laws, government guidelines, and literary and educational works supportive of this aspect of teacher training are analyzed, and expected forms of parent participation as well as those which have been practiced and tested are briefly described. Facets of active parent-teacher cooperation include joint responsibility towards the child, cooperative supervision, improvement of the educational competence of both parent and teacher, and a positive side-effect on social contacts and activities in the neighborhood and the community. An additional form of parent-teacher communication, written communication (providing information, reinforcement, and support) is briefly commented upon. Finally, a review of research on parent-teacher cooperative strategies in various schools in the Federal Republic of Germany is presented. (CM)