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

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

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

On the Concrete Security of LWE with Small Secret

Lattice-based cryptography is currently under consideration for standardization in the ongoing NIST PQC Post-Quantum Cryptography competition, and is used as the basis for Homomorphic Encryption schemes world-wide. Both applications rely specifically on the hardness of the Learning With Errors (LWE) problem. Most Homomorphic Encryption deployments use small secrets as an optimization, so it is important to understand the concrete security of LWE when sampling the secret from a non-uniform, small distribution. Although there are numerous heuristics used to estimate the running time and quality of lattice reduction algorithms such as BKZ2.0, more work is needed to validate and test these heuristics in practice to provide concrete security parameter recommendations, especially in the case of small secret. In this work, we introduce a new approach which uses concrete attacks on the LWE problem as a way to study the performance and quality of BKZ2.0 directly. We find that the security levels for certain values of the modulus q and dimension n are smaller than predicted by the online LWE Estimator, due to the fact that the attacks succeed on these uSVP lattices for blocksizes which are smaller than expected based on current estimates. We also find that many instances of the TU Darmstadt LWE challenges can be solved significantly faster when the secret is chosen from the binary or ternary distributions