The Jacobian of a Sixth-Root-of-Unity Matroid

The Jacobian group (also called the sandpile group, Picard group, or critical group) of a graph or, more generally, of a regular matroid has been well studied. Sixth-root-of-unity matroids, also called complex unimodular matroids, are generalizations of regular matroids. This paper provides a definition, and establishes some basic properties, of the Jacobian group of a sixth-root-of-unity matroid

Tightness of exponential metrics for log-correlated Gaussian fields in arbitrary dimension

We prove the tightness of a natural approximation scheme for an analog of the Liouville quantum gravity metric on $\mathbb R^d$ for arbitrary $d\geq 2$. More precisely, let $\{h_n\}_{n\geq 1}$ be a suitable sequence of Gaussian random functions which approximates a log-correlated Gaussian field on $\mathbb R^d$. Consider the family of random metrics on $\mathbb R^d$ obtained by weighting the lengths of paths by $e^{\xi h_n}$, where $\xi > 0$ is a parameter. We prove that if $\xi$ belongs to the subcritical phase (which is defined by the condition that the distance exponent $Q(\xi)$ is greater than $\sqrt{2d}$), then after appropriate re-scaling, these metrics are tight and that every subsequential limit is a metric on $\mathbb R^d$ which induces the Euclidean topology. We include a substantial list of open problems.Comment: 68 pages, 8 figures; version 2 has updated reference

Anomalous tensile strength and thermal expansion, and low thermal conductivity in wide band gap boron monoxide monolayer

Most recently the formation of boron monoxide (BO) in the two-dimensional (2D) form has been confirmed experimentally (J. Am. Chem. Soc. 2023, 145, 14660). Motivated by the aforementioned finding, herein we theoretically explore the key physical properties of the single-layer and suspended BO. Density functional theory (DFT) results reveal that BO monolayer yields a large indirect band gap of 3.78 (2.18) eV on the basis of HSE06(PBE) functional. Ab-initio molecular dynamics results reveal the remarkable thermal stability of the BO monolayer at 1000 K. The thermal and mechanical properties at room temperature are furthermore investigated using a machine learning interatomic potential (MLIP). The developed MLIP-based model close to the ground state could very precisely reproduce the DFT predictions for the mechanical properties of the BO monolayer. The elastic modulus, tensile strength and lattice thermal conductivity of the BO monolayer at room temperature are predicted to be 107 GPa, 25 GPa and 5.6 W/mK, respectively. At the room temperature the BO monolayer is noticeably predicted to yield an ultrahigh negative thermal expansion coefficient, by almost 17 folds larger than that of the single-layer graphene. The presented results reveal the large indirect electronic band gap, decent thermal and dynamical stability, anomalously low elastic modulus to tensile strength ratio, ultrahigh negative thermal expansion coefficients and low lattice thermal conductivity of the BO monolayer

Influence of casting temperature on microstructures and mechanical properties of Cu50Zr45.5Ti2.5Y2 metallic glass prepared using copper mold casting [+ Erratum]

We investigated the influence of casting temperatures on microstructures and mechanical properties of rapidly solidified Cu50Zr45.5Ti2.5Y2 alloy. With casting temperatures increasing, the content of the crystalline phase decreases. At high casting temperature, i.e., 1723 K, glass forming ability (GFA) of the present alloy enhanced. It is implied that adjusting casting temperatures could be used for designing the microstructures of bulk metallic glass matrix composite (BMGC). Nano-indentation tests indicated that CuZr phases is a little softer and can accommodate more plastic deformation than the amorphous matrix. Compression tests confirmed that this kind of the second phase (CuZr) precipitated under lower casting temperatures helps to initiate multiple shear bands, resulting in great improvement of mechanical properties of the samples. Our work indicate that casting temperatures lead a great influence on GFA, microstructures and mechanical properties of rapidly solidified alloy and controlling casting temperatures is crucial to the application of BMGs

Dynamics and Impacts of Human-Algorithm Consensus in Logistics Scheduling: Evidence from A Field Experiment

Algorithms are being implemented to aid human decision-making and most studies on human-algorithm interactions focus on how to improve human-algorithm cooperation. However, excessive reliance on algorithms in decision-making may hinder the complementary value of humans and algorithms. There is a lack of empirical evidence on the impacts of human-algorithm consensus in collaborative decision-making. To address this gap, this paper reports a large-scale field experiment conducted by one of China\u27s largest logistics firms in the context of route scheduling. The experiment involved assigning routes to either a treatment group, where algorithms and human operators collaborated in decision-making, or a control group, where human operators made decisions independently. We plan to collect data to evaluate the effects of algorithm implementation and to analyze the patterns and effects of human-algorithm consensus in a long-term cooperation. Our study aims to contribute to the literature on human-algorithm interactions in operational decisions