Schottky Algorithms: Classical meets Tropical

We present a new perspective on the Schottky problem that links numerical computing with tropical geometry. The task is to decide whether a symmetric matrix defines a Jacobian, and, if so, to compute the curve and its canonical embedding. We offer solutions and their implementations in genus four, both classically and tropically. The locus of cographic matroids arises from tropicalizing the Schottky-Igusa modular form.Comment: 17 page

Bounded gaps between primes in special sequences

We use Maynard's methods to show that there are bounded gaps between primes in the sequence $\{\lfloor n\alpha\rfloor\}$, where $\alpha$ is an irrational number of finite type. In addition, given a superlinear function $f$ satisfying some properties described by Leitmann, we show that for all $m$ there are infinitely many bounded intervals containing $m$ primes and at least one integer of the form $\lfloor f(q)\rfloor$ with $q$ a positive integer.Comment: 14 page

Equipopularity Classes of 132-Avoiding Permutations

The popularity of a pattern p in a set of permutations is the sum of the number of copies of p in each permutation of the set. We study pattern popularity in the set of 132-avoiding permutations. Two patterns are equipopular if, for all n, they have the same popularity in the set of length-n 132-avoiding permutations. There is a well-known bijection between 132-avoiding permutations and binary plane trees. The spines of a binary plane tree are defined as the connected components when all edges connecting left children to their parents are deleted, and the spine structure is the sorted sequence of lengths of the spines. Rudolph shows that patterns of the same length are equipopular if their associated binary plane trees have the same spine structure. We prove the converse of this result using the method of generating functions, which gives a complete classification of 132-avoiding permutations into equipopularity classes.Massachusetts Institute of Technology. Department of Mathematic

The role of physical environment in leisure service consumption: evidence from a ski resort setting

Despite the importance of physical environment in hedonic service consumption, little is known about the extent to which physical environment influences ski resort visitors’ cognition, emotion, and behaviors. This study investigated the relationships among physical environmental stimuli (i.e., layout accessibility, aesthetics, cleanliness, and other visitors), perceived quality of physical environment, excitement, and behavioral intentions in ski resort. This study also attempted to test the moderating role of enduring involvement in the formation of behavioral intentions. Results showed that cleanliness and other visitors significantly and positively influenced visitors’ perceived quality of physical environment and excitement. The results suggest that physical environment is of great importance for the ski resort business. Perceived quality was indeed a significant predictor of excitement, which, in turn, positively influenced behavioral intentions. Finally, the study found that the effect of excitement on behavioral intentions was significant across high and low enduring involvement groups

Micro-structural characterisation of non-easel painted artworks

University of Technology Sydney. Faculty of Science.Artist paint is one of the most heterogeneous materials encountered in museum conservation. While many scientific studies have been carried out on European easel paintings, less work has focused on other painted artworks, as well as works from other geographic regions. This thesis compiles results from four technical analysis projects on different types of non-easel painted artworks at the Indianapolis Museum of Art (IMA) and the Art Gallery of New South Wales (AGNSW), applying micro-analytical techniques, including FTIR microscopy, Raman microscopy, SEM-EDS, micro-XRF, XRD, Py-GC/MS, GC/MS and MFT. The painted artworks include 20th century ethnographic collections from the Highlands of Papua New Guinea, inked prints from the “Poem series” by Japanese artist Haku Maki, Robert Indiana’s painted aluminum outdoor sculptures, and Gustave Baumann’s home-made paint on paper. These works have not been previously investigated scientifically, and each presents specific museum curatorial and conservation concerns such as technical art history, lightfastness, paint degradation and treatment considerations. A range of natural and synthetic pigments, paint binders and deterioration products were characterized, contributing to the technical art history and understanding of paint degradation that informs conservation practices

How Private are DP-SGD Implementations?

We demonstrate a substantial gap between the privacy guarantees of the Adaptive Batch Linear Queries (ABLQ) mechanism under different types of batch sampling: (i) Shuffling, and (ii) Poisson subsampling; the typical analysis of Differentially Private Stochastic Gradient Descent (DP-SGD) follows by interpreting it as a post-processing of ABLQ. While shuffling-based DP-SGD is more commonly used in practical implementations, it has not been amenable to easy privacy analysis, either analytically or even numerically. On the other hand, Poisson subsampling-based DP-SGD is challenging to scalably implement, but has a well-understood privacy analysis, with multiple open-source numerically tight privacy accountants available. This has led to a common practice of using shuffling-based DP-SGD in practice, but using the privacy analysis for the corresponding Poisson subsampling version. Our result shows that there can be a substantial gap between the privacy analysis when using the two types of batch sampling, and thus advises caution in reporting privacy parameters for DP-SGD.Comment: Proceedings of ICML 202