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1. Exceptional Points of Degeneracy in Electromagnetic Periodic Waveguides and the Role of Symmetries

   https://doi.org/10.23919/EuCAP53622.2022.9769037  

   Mealy, Tarek; Nada, Mohamed Y.; Abdelshafy, Ahmed F.; Hafezi, Ehsan; Capolino, Filippo (March 2022, Published in: 2022 16th European Conference on Antennas and Propagation (EuCAP))

   We investigate the role of reflection and glide symmetry in periodic lossless waveguides on the dispersion diagram and on the existence of various orders of exceptional points of degeneracy (EPDs). We use an equivalent circuit network to model each unit-cell of the guiding structure. Assuming that a coupled-mode waveguide supports N modes in each direction, we derive the following conclusions. When N is even, we show that a periodic guiding structure with reflection symmetry may exhibit EPDs of maximum order N . To obtain a degenerate band edge (DBE) with only two coupled guiding structures, reflection symmetry must be broken. For odd N,N+1 is the maximum EPD order that may be obtained, and an EPD of order N is not allowed. We present an example of three coupled microstrip transmission lines and show that breaking the reflection symmetry by introducing glide symmetry enables the occurrence of a stationary inflection point (SIP), also called frozen mode, which is an EPD of order three. 

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2. A Local Algorithm for Structure-Preserving Graph Cut

   https://doi.org/10.1145/3097983.3098015  

   Zhou, Dawei; Zhang, Si; Yildirim, Mehmet Yigit; Alcorn, Scott; Tong, Hanghang; Davulcu, Hasan; He, Jingrui (August 2017, KDD)

   Nowadays, large-scale graph data is being generated in a variety of real-world applications, from social networks to co-authorship networks, from protein-protein interaction networks to road traffic networks. Many existing works on graph mining focus on the vertices and edges, with the first-order Markov chain as the underlying model. They fail to explore the high-order network structures, which are of key importance in many high impact domains. For example, in bank customer personally identifiable information (PII) networks, the star structures often correspond to a set of synthetic identities; in financial transaction networks, the loop structures may indicate the existence of money laundering. In this paper, we focus on mining user-specified high-order network structures and aim to find a structure-rich subgraph which does not break many such structures by separating the subgraph from the rest. A key challenge associated with finding a structure-rich subgraph is the prohibitive computational cost. To address this problem, inspired by the family of local graph clustering algorithms for efficiently identifying a low-conductance cut without exploring the entire graph, we propose to generalize the key idea to model high-order network structures. In particular, we start with a generic definition of high-order conductance, and define the high-order diffusion core, which is based on a high-order random walk induced by user-specified high-order network structure. Then we propose a novel High-Order Structure-Preserving LOcal Cut (HOSPLOC) algorithm, which runs in polylogarithmic time with respect to the number of edges in the graph. It starts with a seed vertex and iteratively explores its neighborhood until a subgraph with a small high-order conductance is found. Furthermore, we analyze its performance in terms of both effectiveness and efficiency. The experimental results on both synthetic graphs and real graphs demonstrate the effectiveness and efficiency of our proposed HOSPLOC algorithm. 

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3. Instantons in ${\varphi }^4$ theories: Transseries, virial theorems, and numerical aspects

   https://doi.org/10.1103/PhysRevD.110.036003  

   Giorgini, Ludovico T; Jentschura, Ulrich D; Malatesta, Enrico M; Rizzo, Tommaso; Zinn-Justin, Jean (August 2024, Physical Review D)

   We discuss numerical aspects of instantons in two- and three-dimensional ${\varphi }^4$theories with an internal $O\left(N\right)$symmetry group, the so-called $N$-vector model. By combining asymptotic transseries expansions for large arguments with convergence acceleration techniques, we obtain high-precision values for certain integrals of the instanton that naturally occur in loop corrections around instanton configurations. Knowledge of these numerical properties is necessary in order to evaluate corrections to the large-order factorial growth of perturbation theory in ${\varphi }^4$theories. The results contribute to the understanding of the mathematical structures underlying the instanton configurations. Published by the American Physical Society2024 

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4. Derivations of large classes of facet defining inequalities of the weak order polytope using ranking structures

   https://doi.org/10.1007/s10878-023-01075-w  

   Escobedo, Adolfo R.; Yasmin, Romena (September 2023, Journal of Combinatorial Optimization)

   Ordering polytopes have been instrumental to the study of combinatorial optimization problems arising in a variety of fields including comparative probability, computational social choice, and group decision-making. The weak order polytope is defined as the convex hull of the characteristic vectors of all binary orders on n alternatives that are reflexive, transitive, and total. By and large, facet defining inequalities (FDIs) of this polytope have been obtained through simple enumeration and through connections with other combinatorial polytopes. This paper derives five new large classes of FDIs by utilizing the equivalent representations of a weak order as a ranking of n alternatives that allows ties; this connection simplifies the construction of valid inequalities, and it enables groupings of characteristic vectors into useful structures. We demonstrate that a number of FDIs previously obtained through enumeration are actually special cases of the large classes. This work also introduces novel construction procedures for generating affinely independent members of the identified ranking structures. Additionally, it states two conjectures on how to derive many more large classes of FDIs using the featured techniques. 

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5. Below-Ground Net Primary Production (BNPP): Root Ingrowth Donuts in Chihuahuan Desert Grassland and Creosote Shrubland at the Sevilleta National Wildlife Refuge, New Mexico

   https://doi.org/10.6073/pasta/e38868ae3c3e11845128d2539c27520b  

   Collins, Scott (January 2021, Environmental Data Initiative)

   In 2005, annually harvested root ingrowth donut structures were co-located with previously established mini-rhizotron tubes established at four sites on McKenzie Flats located on the east side of Sevilleta NWR: 10 replicate structures in both burned and unburned blue and black grama dominated grassland plots at Deep Well, 10 replicates each on nitrogen fertilization plots and respective control plots on McKenzie Flats(20 total), 10 replicates in creosote dominated shrubland at the Five Points Creosote Core site and in 2011, 13 structures were put in the Monsoon site. Roots and soil are harvested annually in late fall after the growing season, and structures are reestablished in situ for consecutive harvests each year. Each structure allows roots to be harvested at two depths (0-15 and 15-30 cm) to estimate root production, or below ground net primary productivity. In order to compare estimates of root production from two methods, root ingrowth donuts were collocated with mini-rhizotron tubes at all localities except for the burned grassland plot at Deep Well. 

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