Recognizing Planar Laman Graphs

Laman graphs are the minimally rigid graphs in the plane. We present two algorithms for recognizing planar Laman graphs. A simple algorithm with running time O(n^(3/2)) and a more complicated algorithm with running time O(n log^3 n) based on involved planar network flow algorithms. Both improve upon the previously fastest algorithm for general graphs by Gabow and Westermann [Algorithmica, 7(5-6):465 - 497, 1992] with running time O(n sqrt{n log n}). To solve this problem we introduce two algorithms (with the running times stated above) that check whether for a directed planar graph G, disjoint sets S, T subseteq V(G), and a fixed k the following connectivity condition holds: for each vertex s in S there are k directed paths from s to T pairwise having only vertex s in common. This variant of connectivity seems interesting on its own

Maier-Saupe-type theory of ferroelectric nanoparticles in nematic liquid crystals

Several experiments have reported that ferroelectric nanoparticles have drastic effects on nematic liquid crystals--increasing the isotropic-nematic transition temperature by about 5 K, and greatly increasing the sensitivity to applied electric fields. In a recent paper [L. M. Lopatina and J. V. Selinger, Phys. Rev. Lett. 102, 197802 (2009)], we modeled these effects through a Landau theory, based on coupled orientational order parameters for the liquid crystal and the nanoparticles. This model has one important limitation: Like all Landau theories, it involves an expansion of the free energy in powers of the order parameters, and hence it overestimates the order parameters that occur in the low-temperature phase. For that reason, we now develop a new Maier-Saupe-type model, which explicitly shows the low-temperature saturation of the order parameters. This model reduces to the Landau theory in the limit of high temperature or weak coupling, but shows different behavior in the opposite limit. We compare these calculations with experimental results on ferroelectric nanoparticles in liquid crystals.Comment: 7 pages, including 2 postscript figures, uses REVTeX 4.

Image reconstruction from photon sparse data

We report an algorithm for reconstructing images when the average number of photons recorded per pixel is of order unity, i.e. photon-sparse data. The image optimisation algorithm minimises a cost function incorporating both a Poissonian log-likelihood term based on the deviation of the reconstructed image from the measured data and a regularization-term based upon the sum of the moduli of the second spatial derivatives of the reconstructed image pixel intensities. The balance between these two terms is set by a bootstrapping technique where the target value of the log-likelihood term is deduced from a smoothed version of the original data. When compared to the original data, the processed images exhibit lower residuals with respect to the true object. We use photon-sparse data from two different experimental systems, one system based on a single-photon, avalanche photo-diode array and the other system on a time-gated, intensified camera. However, this same processing technique could most likely be applied to any low photon-number image irrespective of how the data is collected

Functional implications of long non-coding RNAs in the pancreatic islets of Langerhans.

Type-2 diabetes (T2D) is a complex disease characterized by insulin resistance in target tissues and impaired insulin release from pancreatic beta cells. As central tissue of glucose homeostasis, the pancreatic islet continues to be an important focus of research to understand the pathophysiology of the disease. The increased access to human pancreatic islets has resulted in improved knowledge of islet function, and together with advances in RNA sequencing and related technologies, revealed the transcriptional and epigenetic landscape of human islet cells. The discovery of thousands of long non-coding RNA (lncRNA) transcripts highly enriched in the pancreatic islet and/or specifically expressed in the beta-cells, points to yet another layer of gene regulation of many hitherto unknown mechanistic principles governing islet cell functions. Here we review fundamental islet physiology and propose functional implications of the lncRNAs in islet development and endocrine cell functions. We also take into account important differences between rodent and human islets in terms of morphology and function, and suggest how species-specific lncRNAs may partly influence gene regulation to define the unique phenotypic identity of an organism and the functions of its constituent cells. The implication of primate-specific lncRNAs will be far-reaching in all aspects of diabetes research, but most importantly in the identification and development of novel targets to improve pancreatic islet cell functions as a therapeutic approach to treat T2D

Regulation of Pancreatic Beta Cell Stimulus-Secretion Coupling by microRNAs.

Increased blood glucose after a meal is countered by the subsequent increased release of the hypoglycemic hormone insulin from the pancreatic beta cells. The cascade of molecular events encompassing the initial sensing and transport of glucose into the beta cell, culminating with the exocytosis of the insulin large dense core granules (LDCVs) is termed "stimulus-secretion coupling." Impairment in any of the relevant processes leads to insufficient insulin release, which contributes to the development of type 2 diabetes (T2D). The fate of the beta cell, when exposed to environmental triggers of the disease, is determined by the possibility to adapt to the new situation by regulation of gene expression. As established factors of post-transcriptional regulation, microRNAs (miRNAs) are well-recognized mediators of beta cell plasticity and adaptation. Here, we put focus on the importance of comprehending the transcriptional regulation of miRNAs, and how miRNAs are implicated in stimulus-secretion coupling, specifically those influencing the late stages of insulin secretion. We suggest that efficient beta cell adaptation requires an optimal balance between transcriptional regulation of miRNAs themselves, and miRNA-dependent gene regulation. The increased knowledge of the beta cell transcriptional network inclusive of non-coding RNAs such as miRNAs is essential in identifying novel targets for the treatment of T2D

Wide-Area Geolocalization with a Limited Field of View Camera in Challenging Urban Environments

Cross-view geolocalization, a supplement or replacement for GPS, localizes an agent within a search area by matching ground-view images to overhead images. Significant progress has been made assuming a panoramic ground camera. Panoramic cameras' high complexity and cost make non-panoramic cameras more widely applicable, but also more challenging since they yield less scene overlap between ground and overhead images. This paper presents Restricted FOV Wide-Area Geolocalization (ReWAG), a cross-view geolocalization approach that combines a neural network and particle filter to globally localize a mobile agent with only odometry and a non-panoramic camera. ReWAG creates pose-aware embeddings and provides a strategy to incorporate particle pose into the Siamese network, improving localization accuracy by a factor of 100 compared to a vision transformer baseline. This extended work also presents ReWAG*, which improves upon ReWAG's generalization ability in previously unseen environments. ReWAG* repeatedly converges accurately on a dataset of images we have collected in Boston with a 72 degree field of view (FOV) camera, a location and FOV that ReWAG* was not trained on.Comment: 10 pages, 16 figures. Extension of ICRA 2023 paper arXiv:2209.1185