COVID-19 and immersion: physical, virtual, and home spaces

This article considers the dramatic adaptations that have occurred in themed immersive spaces as they have dealt with the challenging dynamics of COVID-19. As COVID-19 has been a respiratory disease, it has impacted the operations of theme parks, casinos, cruise ships, and other immersive spaces, especially as such spaces have relied, traditionally, on physical forms of entertainment and immersion. The writing begins with a consideration of the COVID-19 challenges noted in the theme park and cruise ship industries. OceanMedallionTM and MyMagic+ technologies are considered for their possible positive role in addressing the operational dynamics during the pandemic. Issues of guest accessibility, environmental design, and psychological and existential conditions of guests are also discussed. The second section of the article focuses on how virtual forms of immersive design may assist in the safe operation of immersive spaces. Included is an emphasis on virtual and augmented reality technologies of rides, including those at Toy Story Mania, Fear the Walking Dead Survival, and Swamp Motel. The article concludes with a discussion of home-based immersion, including interactive media, exercise technology, and virtual tourism. Case studies that are analyzed include Faroe Islands virtual tourism, NordicTrack/iFit exercise bikes, and the Void virtual reality space

Osteoblastoma in the occipital bone: A case report of a rare tumor in the calvarium

Osteoblastomas infrequently occur in the calvarium, displaying a preference for temporal and frontal bones when it does. We present an unusual case of a large, expansile osteoblastoma in the occipital bone of a 23-year-old man who presented with a nontender lump at the back of his head. Initial computed tomography scan showed a large occipital bone mass, and after additional imaging, a gross total resection was performed. Histopathological examination revealed an osteoblastoma. Although these tumors are benign, overlapping imaging characteristics of lesions affecting the calvarium often present a diagnostic dilemma. This case emphasizes the importance of imaging in the management and work-up of these patients to decrease the risk of complications and assists surgeons in their preoperative planning

A User's Guide to the AI Lab: Getting Started at Tech Square

MIT Artificial Intelligence Laborator

Superpolynomial smoothed complexity of 3-FLIP in Local Max-Cut

We construct a graph with $n$ vertices where the smoothed runtime of the 3-FLIP algorithm for the 3-Opt Local Max-Cut problem can be as large as $2^{\Omega(\sqrt{n})}$. This provides the first example where a local search algorithm for the Max-Cut problem can fail to be efficient in the framework of smoothed analysis. We also give a new construction of graphs where the runtime of the FLIP algorithm for the Local Max-Cut problem is $2^{\Omega(n)}$ for any pivot rule. This graph is much smaller and has a simpler structure than previous constructions.Comment: 18 pages, 3 figure

The 2014 International Planning Competition: Progress and Trends

We review the 2014 International Planning Competition (IPC-2014), the eighth in a series of competitions starting in 1998. IPC-2014 was held in three separate parts to assess state-of-the-art in three prominent areas of planning research: the deterministic (classical) part (IPCD), the learning part (IPCL), and the probabilistic part (IPPC). Each part evaluated planning systems in ways that pushed the edge of existing planner performance by introducing new challenges, novel tasks, or both. The competition surpassed again the number of competitors than its predecessor, highlighting the competition’s central role in shaping the landscape of ongoing developments in evaluating planning systems

The structure and density of kk-product-free sets in the free semigroup

The free semigroup $\mathcal{F}$ over a finite alphabet $\mathcal{A}$ is the set of all finite words with letters from $\mathcal{A}$ equipped with the operation of concatenation. A subset $S$ of $\mathcal{F}$ is $k$-product-free if no element of $S$ can be obtained by concatenating $k$ words from $S$, and strongly $k$-product-free if no element of $S$ is a (non-trivial) concatenation of at most $k$ words from $S$. We prove that a $k$-product-free subset of $\mathcal{F}$ has upper Banach density at most $1/\rho(k)$, where $\rho(k) = \min\{\ell \colon \ell \nmid k - 1\}$. We also determine the structure of the extremal $k$-product-free subsets for all $k \notin \{3, 5, 7, 13\}$; a special case of this proves a conjecture of Leader, Letzter, Narayanan, and Walters. We further determine the structure of all strongly $k$-product-free sets with maximum density. Finally, we prove that $k$-product-free subsets of the free group have upper Banach density at most $1/\rho(k)$, which confirms a conjecture of Ortega, Ru\'{e}, and Serra.Comment: 31 pages, added density results for the free grou

Flashes and Rainbows in Tournaments

Colour the edges of the complete graph with vertex set $\{1, 2, \dotsc, n\}$ with an arbitrary number of colours. What is the smallest integer $f(l,k)$ such that if $n > f(l,k)$ then there must exist a monotone monochromatic path of length $l$ or a monotone rainbow path of length $k$? Lefmann, R\"{o}dl, and Thomas conjectured in 1992 that $f(l, k) = l^{k - 1}$ and proved this for $l \ge (3 k)^{2 k}$. We prove the conjecture for $l \geq k^4 (\log k)^{1 + o(1)}$ and establish the general upper bound $f(l, k) \leq k (\log k)^{1 + o(1)} \cdot l^{k - 1}$. This reduces the gap between the best lower and upper bounds from exponential to polynomial in $k$. We also generalise some of these results to the tournament setting.Comment: 14 page

Reconstructing a point set from a random subset of its pairwise distances

Let $V$ be a set of $n$ points on the real line. Suppose that each pairwise distance is known independently with probability $p$. How much of $V$ can be reconstructed up to isometry? We prove that $p = (\log n)/n$ is a sharp threshold for reconstructing all of $V$ which improves a result of Benjamini and Tzalik. This follows from a hitting time result for the random process where the pairwise distances are revealed one-by-one uniformly at random. We also show that $1/n$ is a weak threshold for reconstructing a linear proportion of $V$.Comment: 13 page