Microscopic models for Kitaev's sixteenfold way of anyon theories

In two dimensions, the topological order described by $\mathbb{Z}_2$ gauge theory coupled to free or weakly interacting fermions with a nonzero spectral Chern number $\nu$ is classified by $\nu \; \mathrm{mod}\; 16$ as predicted by Kitaev [Ann. Phys. 321, 2 (2006)]. Here we provide a systematic and complete construction of microscopic models realizing this so-called sixteenfold way of anyon theories. These models are defined by $\Gamma$ matrices satisfying the Clifford algebra, enjoy a global $\mathrm{SO}(\nu)$ symmetry, and live on either square or honeycomb lattices depending on the parity of $\nu$. We show that all these models are exactly solvable by using a Majorana representation and characterize the topological order by calculating the topological spin of an anyonic quasiparticle and the ground-state degeneracy. The possible relevance of the $\nu=2$ and $\nu=3$ models to materials with Kugel-Khomskii-type spin-orbital interactions is discussed.Comment: 6+9 pages, 2+1 figures, published versio

Universal minimal cost of coherent biochemical oscillations

Biochemical clocks are essential for virtually all living systems. A biochemical clock that is isolated from an external periodic signal and subjected to fluctuations can oscillate coherently only for a finite number of oscillations. Furthermore, such an autonomous clock can oscillate only if it consumes free energy. What is the minimum amount of free energy consumption required for a certain number of coherent oscillations? We conjecture a universal bound that answers this question. A system that oscillates coherently for $\mathcal{N}$ oscillations has a minimal free energy cost per oscillation of $4\pi^2\mathcal{N} k_B T$. Our bound is valid for general finite Markov processes, is conjectured based on extensive numerical evidence, is illustrated with numerical simulations of a known model for a biochemical oscillator, and applies to existing experimental data.Comment: 4 pages, 3 figure

Opening the random forest black box by the analysis of the mutual impact of features

Random forest is a popular machine learning approach for the analysis of high-dimensional data because it is flexible and provides variable importance measures for the selection of relevant features. However, the complex relationships between the features are usually not considered for the selection and thus also neglected for the characterization of the analysed samples. Here we propose two novel approaches that focus on the mutual impact of features in random forests. Mutual forest impact (MFI) is a relation parameter that evaluates the mutual association of the featurs to the outcome and, hence, goes beyond the analysis of correlation coefficients. Mutual impurity reduction (MIR) is an importance measure that combines this relation parameter with the importance of the individual features. MIR and MFI are implemented together with testing procedures that generate p-values for the selection of related and important features. Applications to various simulated data sets and the comparison to other methods for feature selection and relation analysis show that MFI and MIR are very promising to shed light on the complex relationships between features and outcome. In addition, they are not affected by common biases, e.g. that features with many possible splits or high minor allele frequencies are prefered

Urinary incontinence-85: an expanded prostate cancer composite (EPIC) score cutoff value for urinary incontinence determined using long-term functional data by repeated prospective EPIC-score self-assessment after radical prostatectomy

PURPOSE: To determine an objective cutoff value (COV) for urinary incontinence (UI) using the Expanded Prostate Cancer Composite (EPIC) score after radical prostatectomy (RP). METHODS: From 2004-2013, all RP patients at our institution completed the EPIC urinary domain (EPIC-UD) questionnaire preoperatively and 6 weeks; 3, 6, 9, 12, and 18 months postoperatively; and yearly thereafter. The EPIC-UD is composed of several questions, 4 of which address UI qualitatively (EPIC-UI). Furthermore, patients were asked to complete a global quality of life (QoL) questionnaire regarding continence. The EPIC COV was calculated using receiver operating characteristic (ROC) analysis. Correlations between the EPIC-UI and quantitative QoL were evaluated using the Kendall-Tau test. RESULTS: We analyzed 239 patients with a median age of 63 years (interquartile range [IQR], 59-66 years), a median follow-up of 48 months (IQR, 30-78 months) and a median preoperative EPIC-UI score of 100 (IQR, 91.75-100). The ROC analysis for the distinction between EPIC-UI and the use of ≤1 pad/day yielded an EPIC-UI COV of >85, which we termed the UI-85, with an area under the curve of 0.857 (P<0.0001). A stronger correlation was seen between QoL scores and the UI-85 (1 year postoperatively: correlation coefficient [CC], 0.592; P<0.0001) than between QoL and not using a pad (CC, 0.512; P<0.0001). CONCLUSIONS: The calculated COV of the EPIC-UI for continence was 85. UI is a multidimensional condition that cannot be adequately characterized by a single piece of information, such as pad usage only. Hence, the UI-85 represents a nuanced and straightforward tool for monitoring and comparing continence between different time points and cohorts in a multidimensional and objective manner

CoSimPy: An open-source python library for MRI radiofrequency Coil EM/Circuit Cosimulation

Background and objectives: The Electromagnetic/Circuit cosimulation method represents a valuable and effective strategy to address those problems where a radiative structure has to interact with external supporting circuitries. This is of particular concern for Magnetic Resonance Imaging (MRI), radiofrequency (RF) coils design, where the supporting circuitry optimisation represents, generally, a crucial aspect. This article presents CoSimPy, an open-source Python circuit simulation library for Electromagnetic/Circuit cosimulations and specifically optimised for MRI, RF coils design.Methods: CoSimPy is designed following an Object-orientated programming. In addition to the essential methods aimed to performed the Electromagnetic/Circuit cosimulations, many others are implemented both to simplify the standard workflow and to evaluate the RF coils performance. In this article, the theory which underlies the fundamental methods of CoSimPy is shown together with the basic framework of the library.Results: In the paper, the reliability of CoSimPy is successfully tested against a full-wave electromagnetic simulations involving a reference setup. The library is made available httys://github.com/umbertozanovello/CoSimpy under together with a detailed documentation providing guidelines and examples. CoSimPy is distributed under the Massachusetts Institute of Technology (MIT) license.Conclusions: CoSimPy demonstrated to be an agile tool employable for Electromagnetic/Circuit cosimulations. Its distribution is meant to fulfil the needs of several researchers also avoiding duplication of effort in writing custom implementations. CoSimPy is under constant development and aims to represent a coworking environment where scientists can implement additional methods whose sharing can represent an advantage for the community. Finally, even if CoSimPy is designed with special focus on MRI, it represents an efficient and practical tool potentially employable wherever electronic devices made of radiative and circuitry components are involved. (C) 2022 Published by Elsevier B.V

Fractionalized fermionic quantum criticality in spin-orbital Mott insulators

We study transitions between topological phases featuring emergent fractionalized excitations in two-dimensional models for Mott insulators with spin and orbital degrees of freedom. The models realize fermionic quantum critical points in fractionalized Gross-Neveu$^\ast$ universality classes in (2+1) dimensions. They are characterized by the same set of critical exponents as their ordinary Gross-Neveu counterparts, but feature a different energy spectrum, reflecting the nontrivial topology of the adjacent phases. We exemplify this in a square-lattice model, for which an exact mapping to a $t$-$V$ model of spinless fermions allows us to make use of large-scale numerical results, as well as in a honeycomb-lattice model, for which we employ $\epsilon$-expansion and large-$N$ methods to estimate the critical behavior. Our results are potentially relevant for Mott insulators with $d^1$ electronic configurations and strong spin-orbit coupling, or for twisted bilayer structures of Kitaev materials.Comment: 6+6 pages, 2+3 figures; v3 (minor changes, discussion on strong-coupling limit