Higher melonic theories

We classify a large set of melonic theories with arbitrary $q$-fold interactions, demonstrating that the interaction vertices exhibit a range of symmetries, always of the form $\mathbb{Z}_2^n$ for some $n$, which may be $0$. The number of different theories proliferates quickly as $q$ increases above $8$ and is related to the problem of counting one-factorizations of complete graphs. The symmetries of the interaction vertex lead to an effective interaction strength that enters into the Schwinger-Dyson equation for the two-point function as well as the kernel used for constructing higher-point functions.Comment: 43 pages, 12 figure

Investigation of hearing loss in elderly vertigo and dizziness patients in the past 10 years

BackgroundVertigo and hearing loss are both prevalent in the elderly. This study retrospectively analyzed hearing test results from elderly patients experiencing vertigo and dizziness at ENT outpatient over a 10-year period, in order to study the patterns of hearing loss in this patient population.MethodsNine thousand three hundred eighty four patients over 50 years old underwent retrospective collection and screening of outpatient diagnosis, pure tone audiometry, acoustic immittance measurement (tympanogram) and auditory brainstem response (ABR) test. The patient's audiograms are divided into 7 subtypes according to a set of fixed criteria. Meanwhile, K-Means clustering analysis method was used to classify the audiogram.ResultsThe Jerger classification of tympanogram in elderly patients with vertigo and dizziness showed the majority falling under type A. The leading audiogram shapes were flat (27.81% in right ear and 26.89% in left ear), high-frequency gently sloping (25.97% in right ear and 27.34% in left ear), and high-frequency steeply sloping (21.60% in right ear and 22.53% in left ear). Meniere's disease (MD; 30.87%), benign recurrent vertigo (BRV; 19.07%), and benign paroxysmal positional vertigo (BPPV; 15.66%) were the most common etiologies in elderly vestibular diseases. We observed statistically significant differences in hearing thresholds among these vestibular diseases (P < 0.001). K-Means clustering analysis suggested that the optimal number of clusters was three, with sample sizes for the three clusters being 2,747, 2,413, and 4,139, respectively. The ANOVA statistical results of each characteristic value showed P < 0.001.ConclusionThe elderly patients often have mild to moderate hearing loss as a concomitant symptom with vertigo. Female patients have better hearing thresholds than males. The dominant audiometric shapes in this patient population were flat, high-frequency gently sloping, and high-frequency steeply sloping according to a set of fixed criteria. This study highlights the need for tailored strategies in managing hearing loss in elderly patients with vertigo and dizziness

Study on risk control of water inrush in tunnel construction period considering uncertainty

Water inrush risk is a bottleneck problem affecting the safety and smooth construction of tunnel engineering works, so the risk control of water inrush is important, however, geological uncertainty and artificial uncertainty always accompany tunnel construction. Uncertainty will not only affect the accuracy of water inrush risk assessment results, but also affect the reliability of water inrush risk decision-making results. How to control the influence of uncertainty on water inrush risk is key to solving the problem of water inrush risk control. Based on the definition of improved risk, a risk analysis model of water inrush based on a fuzzy Bayesian network is constructed. The main factors affecting the risk of water inrush are determined by sensitivity analysis, and possible schemes in risk control of water inrush are proposed. Based on the characteristics of risk control of water inrush in a tunnel, a multi-attribute group decision-making model is constructed to determine the optimal water inrush risk control scheme, so that the optimal scheme for reducing uncertainty in risk control of water inrush is determined. Finally, this system is applied to Shiziyuan Tunnel. The results show that the proposed risk control system for reducing uncertainty of water inrush is efficacious. First published online 21 August 201

Non-Archimedean and Non-Local Physics

\noindent Physics defined on real manifolds and equipped with locality has achieved many successes theoretically as well as in describing our universe. Nevertheless, from a mathematical point of view, it is not as privileged. This thesis explores the possibility of non-Archimedean and non-local physics by studying a range of discrete and continuous models. We begin by discussing how continuous dimensions with different topologies emerge from a sparse coupling lattice model inspired by a recent cold atom experiment proposal. A field theory with both non-Archimedean and Archimedean dimensions is then studied. The propagator of the theory possesses oscillatory behavior. We work out the renormalization and compare the theory with the quantum Dyson's hierarchical model at the criticality. We then proceed to study two non-local field theories: the non-local non-linear sigma model and the non-local quantum electrodynamics. Non-locality altered the behavior of NLSM profoundly by eliminating the Ricci flow and demanding higher-order covariant corrections in the target space. At the same time, the interplay between non-locality and gauge symmetry generates unique RG flows in the non-local QED and makes the theory more controllable. We conclude by introducing a monodromy defect defined in $O(N)$ symmetric conformal theories, which by definition, supports a non-local CFT on the defect. Throughout the journey, we want to convey the idea that non-Archimedean physics and non-local physics exhibits rich and unique phenomena yet are not disconnected from the more ordinary physics. \hfill \noindent The following authors contributed to Chapter 1: Steve Gubser, Christian Jepsen, and Brian Trundy\cite{gubser2018continuum}. \noindent The following authors contributed to Chapter 2: Steve Gubser, Christian Jepsen, and Brian Trundy\cite{gubser2019mixed}. \noindent The following authors contributed to Chapter 3: Steve Gubser, Christian Jepsen, Brian Trundy, and Amos Yarom\cite{Gubser:2019uyf}. \noindent The following authors contributed to Chapter 4: Matthew Heydeman, Christian Jepsen, and Amos Yarom\cite{Heydeman:2020ijz}. \noindent The following authors contributed to Chapter 5: Simone Giombi, Elizabeth Helfenberger, and Himanshu Khanchandani\cite{Giombi:2021uae}

Polyakov’s confinement mechanism for generalized Maxwell theory

Abstract We study fractional-derivative Maxwell theory, as appears in effective descriptions of, for example, large N f QED3, graphene, and some types of surface defects. We argue that when the theory is realized on a lattice, monopole condensation leads to a confining phase via the Polyakov confinement mechanism