Quantum Phase Transitions around the Staggered Valence Bond Solid

Motivated by recent numerical results, we study the quantum phase transitions between Z_2 spin liquid, Neel ordered, and various valence bond solid (VBS) states on the honeycomb and square lattices, with emphasis on the staggered VBS. In contrast to the well-understood columnar VBS order, the staggered VBS is not described by an XY order parameter with Z_N anisotropy close to these quantum phase transitions. Instead, we demonstrate that on the honeycomb lattice, the staggered VBS is more appropriately described as an O(3) or CP(2) order parameter with cubic anisotropy, while on the square lattice it is described by an O(4) or CP(3) order parameter.Comment: 9 pages, 4 figure

SFF-Oriented Modeling and Process Planning of Functionally Graded Materials Using a Novel Equal Distance Offset Approach

This paper deals with the modeling and process planning of solid freeform fabrication (SFF) of 3D functionally graded materials (FGMs). A novel approach of representation and process planning of FGMs, termed as equal distance offset (EDO), is developed. In EDO, a neutral arbitrary 3D CAD model is adaptively sliced into a series of 2D layers. Within each layer, 2D material gradients are designed and represented via dividing the 2D shape into several sub-regions enclosed by iso-composition contours. If needed, the material composition gradient within each of sub-regions can be further determined by applying the equal distance offset algorithm to each sub-region. Using this approach, an arbitrary-shaped 3D FGM object with linear or non-linear composition gradients can be represented and fabricated via suitable SFF machines.Mechanical Engineerin

Tropical Principal Component Analysis and its Application to Phylogenetics

Principal component analysis is a widely-used method for the dimensionality reduction of a given data set in a high-dimensional Euclidean space. Here we define and analyze two analogues of principal component analysis in the setting of tropical geometry. In one approach, we study the Stiefel tropical linear space of fixed dimension closest to the data points in the tropical projective torus; in the other approach, we consider the tropical polytope with a fixed number of vertices closest to the data points. We then give approximative algorithms for both approaches and apply them to phylogenetics, testing the methods on simulated phylogenetic data and on an empirical dataset of Apicomplexa genomes.Comment: 28 page

Solid Freeform Fabrication of Artificial Human Teeth

In this paper, we describe a solid freeform fabrication procedure for human dental restoration via porcelain slurry micro-extrusion. Based on submicron-sized dental porcelain powder obtained via ball milling process, a porcelain slurry formulation has been developed. The formulation developed allows the porcelain slurry to show a pseudoplastic behavior and moderate viscosity, which permits the slurry to re-shape to form a near rectangular cross section. A well-controlled cross-section geometry of the extrudate is important for micro-extrusion to obtain uniform 2-D planes and for the addition of the sequential layers to form a 3-D object. Human teeth are restored by this method directly from CAD digital models. After sintering, shrinkage of the artificial teeth is uniform in all directions. Microstructure of the sintered teeth is identical to that made via traditional dental restoration processes.Mechanical Engineerin

Implementing Controlled Digital Lending with Google Drive and Apps Script: A Case Study at the NYU Shanghai Library

The unexpected outbreak of COVID-19 near the beginning of 2020 has significantly interrupted the daily operation of a wide range of academic institutions worldwide. As a result, libraries faced a challenge of providing their patrons access to physical collections while the campuses may remain closed. Discussions on the implementation of Controlled Digital Lending (CDL) among libraries have been trending ever since. In theory, CDL enables libraries to digitize a physical item from their collections and loan the access-restricted file to one user at a time based on the “owned to loaned” ratio in the library’s collections, for a limited time. Despite all the discussions and enthusiasm about CDL, there is, however, still a lack of technical infrastructure to support individual libraries to manage their self-hosted collections. With COVID-19 still very much a presence in our lives, many libraries are more than eager to figure out the best approach to circulating materials that only exist in print form to their users in a secure and legitimate way. This article describes the author's temporary but creative implementation of CDL amid the COVID-19 pandemic. We managed to work out a technical solution in a very short time, to lend out digital versions of library materials to users when the library is physically inaccessible to them. By collaborating with our campus IT, a Google Spreadsheet with Google Apps Scripts was developed to allow a team of Access Services Staff to do hourly loans, which is a desired function for our reserve collection. Further, when the access to a file expires, staff will be notified via email. We hope our experience can be useful for those libraries that are interested in lending their physical materials using CDL and are in urgent need for an applicable solution without a cost

Sharp Information-Theoretic Thresholds for Shuffled Linear Regression

This paper studies the problem of shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we consider the model $y = \Pi_* X \beta_* + w$, where $X$ is an $n \times d$ standard Gaussian design matrix, $w$ is Gaussian noise with entrywise variance $\sigma^2$, $\Pi_*$ is an unknown $n \times n$ permutation matrix, and $\beta_*$ is the regression coefficient, also unknown. Previous work has shown that, in the large $n$-limit, the minimal signal-to-noise ratio ($\mathsf{SNR}$), $\lVert \beta_* \rVert^2/\sigma^2$, for recovering the unknown permutation exactly with high probability is between $n^2$ and $n^C$ for some absolute constant $C$ and the sharp threshold is unknown even for $d=1$. We show that this threshold is precisely $\mathsf{SNR} = n^4$ for exact recovery throughout the sublinear regime $d=o(n)$. As a by-product of our analysis, we also determine the sharp threshold of almost exact recovery to be $\mathsf{SNR} = n^2$, where all but a vanishing fraction of the permutation is reconstructed.Comment: 18 pages (9 main, 1 references, 8 appendix