Thoughts on Barnette's Conjecture

We prove a new sufficient condition for a cubic 3-connected planar graph to be Hamiltonian. This condition is most easily described as a property of the dual graph. Let $G$ be a planar triangulation. Then the dual $G^*$ is a cubic 3-connected planar graph, and $G^*$ is bipartite if and only if $G$ is Eulerian. We prove that if the vertices of $G$ are (improperly) coloured blue and red, such that the blue vertices cover the faces of $G$, there is no blue cycle, and every red cycle contains a vertex of degree at most 4, then $G^*$ is Hamiltonian. This result implies the following special case of Barnette's Conjecture: if $G$ is an Eulerian planar triangulation, whose vertices are properly coloured blue, red and green, such that every red-green cycle contains a vertex of degree 4, then $G^*$ is Hamiltonian. Our final result highlights the limitations of using a proper colouring of $G$ as a starting point for proving Barnette's Conjecture. We also explain related results on Barnette's Conjecture that were obtained by Kelmans and for which detailed self-contained proofs have not been published.Comment: 12 pages, 7 figure

Tracing mobility patterns through the 6th-5th millennia BC in the Carpathian Basin with strontium and oxygen stable isotope analyses

The complexity of Neolithic population movements and their interpretation through material culture have been the subject of archaeological research for decades. One of the dominant narratives proposes that groups from the Starčevo-Ko¨ro¨ s-Criş complex spread from the central towards the northern Balkans in the Early Neolithic and eventually brought the Neolithic lifestyle into present-day Hungary. Broad geographical migrations were considered to shape the continuous expansion of Neolithic groups and individuals. However, recent archaeological research, aDNA, and isotope analyses challenged the synchronous appearance of specific material culture distributions and human movement dynamics through emphasizing communication networks and socio-cultural transformation processes. This paper seeks to retrace the complexity of Neolithic mobility patterns across Hungary by means of strontium and oxygen stable isotope analyses, which were performed on a total of 718 human dental enamel samples from 55 Neolithic sites spanning the period from the Starčevo to the Balaton-Lasinja culture in Transdanubia and from the Ko¨ro¨s to the Tiszapolga ´ r cultural groups on the Great Hungarian Plain (Alfo¨ ld). This study presents the largest strontium and oxygen isotope sample size for the Neolithic Carpathian Basin and discusses human mobility patterns on various geographical scales and throughout archaeological cultures, chronological periods, and sex and gender categories in a multiproxy analysis. Based on our results, we discuss the main stages of the Neolithisation processes and particularly trace individual movement behaviour such as exogamy patterns within extensive social networks. Furthermore, this paper presents an innovative differentiation between mobility patterns on small, micro-regional, and supra-regional scales, which provides new insights into the complex organisation of Neolithic communities.The complexity of Neolithic population movements and their interpretation through material culture have been the subject of archaeological research for decades. One of the dominant narratives proposes that groups from the Starčevo-Ko¨ro¨ s-Criş complex spread from the central towards the northern Balkans in the Early Neolithic and eventually brought the Neolithic lifestyle into present-day Hungary. Broad geographical migrations were considered to shape the continuous expansion of Neolithic groups and individuals. However, recent archaeological research, aDNA, and isotope analyses challenged the synchronous appearance of specific material culture distributions and human movement dynamics through emphasizing communication networks and socio-cultural transformation processes. This paper seeks to retrace the complexity of Neolithic mobility patterns across Hungary by means of strontium and oxygen stable isotope analyses, which were performed on a total of 718 human dental enamel samples from 55 Neolithic sites spanning the period from the Starčevo to the Balaton-Lasinja culture in Transdanubia and from the Ko¨ro¨s to the Tiszapolga ´ r cultural groups on the Great Hungarian Plain (Alfo¨ ld). This study presents the largest strontium and oxygen isotope sample size for the Neolithic Carpathian Basin and discusses human mobility patterns on various geographical scales and throughout archaeological cultures, chronological periods, and sex and gender categories in a multiproxy analysis. Based on our results, we discuss the main stages of the Neolithisation processes and particularly trace individual movement behaviour such as exogamy patterns within extensive social networks. Furthermore, this paper presents an innovative differentiation between mobility patterns on small, micro-regional, and supra-regional scales, which provides new insights into the complex organisation of Neolithic communities

CNN-based Euler's Elastica Inpainting with Deep Energy and Deep Image Prior

Euler's elastica constitute an appealing variational image inpainting model. It minimises an energy that involves the total variation as well as the level line curvature. These components are transparent and make it attractive for shape completion tasks. However, its gradient flow is a singular, anisotropic, and nonlinear PDE of fourth order, which is numerically challenging: It is difficult to find efficient algorithms that offer sharp edges and good rotation invariance. As a remedy, we design the first neural algorithm that simulates inpainting with Euler's Elastica. We use the deep energy concept which employs the variational energy as neural network loss. Furthermore, we pair it with a deep image prior where the network architecture itself acts as a prior. This yields better inpaintings by steering the optimisation trajectory closer to the desired solution. Our results are qualitatively on par with state-of-the-art algorithms on elastica-based shape completion. They combine good rotation invariance with sharp edges. Moreover, we benefit from the high efficiency and effortless parallelisation within a neural framework. Our neural elastica approach only requires 3x3 central difference stencils. It is thus much simpler than other well-performing algorithms for elastica inpainting. Last but not least, it is unsupervised as it requires no ground truth training data.Comment: In Proceedings of the 10th European Workshop on Visual Information Processing, Lisbon, 202

Heuristic-free Optimization of Force-Controlled Robot Search Strategies in Stochastic Environments

In both industrial and service domains, a central benefit of the use of robots is their ability to quickly and reliably execute repetitive tasks. However, even relatively simple peg-in-hole tasks are typically subject to stochastic variations, requiring search motions to find relevant features such as holes. While search improves robustness, it comes at the cost of increased runtime: More exhaustive search will maximize the probability of successfully executing a given task, but will significantly delay any downstream tasks. This trade-off is typically resolved by human experts according to simple heuristics, which are rarely optimal. This paper introduces an automatic, data-driven and heuristic-free approach to optimize robot search strategies. By training a neural model of the search strategy on a large set of simulated stochastic environments, conditioning it on few real-world examples and inverting the model, we can infer search strategies which adapt to the time-variant characteristics of the underlying probability distributions, while requiring very few real-world measurements. We evaluate our approach on two different industrial robots in the context of spiral and probe search for THT electronics assembly.Comment: 7 pages, 5 figures, accepted to the 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2022), Kyoto, Japan For code and data, see https://github.com/benjaminalt/dps

Frozen Stored Teeth : Autogenous Dentin as an Alternative Augmentation Material in Dentistry

Tooth Shell Technique (TST) with the use of autologous dentin has proven to be a suitable method of grafting in the context of lateral ridge augmentation. This present feasibility study aimed to retrospectively evaluate the preservation by lyophilization of processed dentin. Thus, the frozen stored processed dentin matrix (FST: 19 patients with 26 implants) was re-examined with that of processed teeth used immediately after extraction (IUT: 23 patients with 32 implants). Parameters of biological complications, horizontal hard tissue loss, osseointegration, and buccal lamella integrity were used for evaluation. For complications, the observation period was 5 months. Only one graft was lost (IUT group). In the area of minor complications, without the loss of an implant or augmentation, there were two cases of wound dehiscence and one case with inflammation and suppuration (IUT: n = 3, FST: n = 0). Osseointegration and integrity of the buccal lamella were present in all implants without exception. Statistically, there was no difference between the groups studied for the mean resorption of the crestal width and the buccal lamella. Results of this study show that prepared autologous dentin preserved with a conventional freezer had no disadvantage compared to immediately use autologous dentin in terms of complications and graft resorption in the context of TST

Energy dependence of transverse mass spectra of kaons produced in p+p and p+pbar interactions.A compilation

The data on m_T spectra of K0S K+ and K- mesons produced in all inelastic p+p and p+pbar interactions in the energy range sqrt(s)NN=4.7-1800GeV are compiled and analyzed. The spectra are parameterized by a single exponential function, dN/(m_T*dm_T)=C exp(-m_T/T), and the inverse slope parameter T is the main object of study. The T parameter is found to be similar for K0S, K+ and K- mesons. It increases monotonically with collision energy from T~30MeV at sqrt(s)NN=4.7GeV to T~220MeV at sqrt(s)NN=1800GeV. The T parameter measured in p+p and p+pbar interactions is significantly lower than the corresponding parameter obtained for central Pb+Pb collisions at all studied energies. Also the shape of the energy dependence of $T$ is different for central Pb+Pb collisions and p+p(pbar) interactions.Comment: more differential analysis adde