The Variable Markov Oracle: Algorithms for Human Gesture Applications

This article introduces the Variable Markov Oracle (VMO) data structure for multivariate time series indexing. VMO can identify repetitive fragments and find sequential similarities between observations. VMO can also be viewed as a combination of online clustering algorithms with variable-order Markov constraints. The authors use VMO for gesture query-by-content and gesture following. A probabilistic interpretation of the VMO query-matching algorithm is proposed to find an analogy to the inference problem in a hidden Markov model (HMM). This probabilistic interpretation extends VMO to be not only a data structure but also a model for time series. Query-by-content experiments were conducted on a gesture database that was recorded using a Kinect 3D camera, showing state-of-the-art performance. The query-by-content experiments' results are compared to previous works using HMM and dynamic time warping. Gesture following is described in the context of an interactive dance environment that aims to integrate human movements with computer-generated graphics to create an augmented reality performance

Exact Quantum Many-Body Scar States in the Rydberg-Blockaded Atom Chain

A recent experiment in the Rydberg atom chain observed unusual oscillatory quench dynamics with a charge density wave initial state, and theoretical works identified a set of many-body "scar states" showing nonthermal behavior in the Hamiltonian as potentially responsible for the atypical dynamics. In the same nonintegrable Hamiltonian, we discover several eigenstates at \emph{infinite temperature} that can be represented exactly as matrix product states with finite bond dimension, for both periodic boundary conditions (two exact $E = 0$ states) and open boundary conditions (two $E = 0$ states and one each $E = \pm \sqrt{2}$). This discovery explicitly demonstrates violation of strong eigenstate thermalization hypothesis in this model and uncovers exact quantum many-body scar states. These states show signatures of translational symmetry breaking with period-2 bond-centered pattern, despite being in one dimension at infinite temperature. We show that the nearby many-body scar states can be well approximated as "quasiparticle excitations" on top of our exact $E = 0$ scar states, and propose a quasiparticle explanation of the strong oscillations observed in experiments.Comment: Published version. In addition to (v2): (1) Add additional proofs to the exact scar states and intuitions behind SMA and MMA to the appendices. (2) Add entanglement scaling of SMA and MMA to the appendice

Replacement Paths via Row Minima of Concise Matrices

Matrix $M$ is {\em $k$-concise} if the finite entries of each column of $M$ consist of $k$ or less intervals of identical numbers. We give an $O(n+m)$-time algorithm to compute the row minima of any $O(1)$-concise $n\times m$ matrix. Our algorithm yields the first $O(n+m)$-time reductions from the replacement-paths problem on an $n$-node $m$-edge undirected graph (respectively, directed acyclic graph) to the single-source shortest-paths problem on an $O(n)$-node $O(m)$-edge undirected graph (respectively, directed acyclic graph). That is, we prove that the replacement-paths problem is no harder than the single-source shortest-paths problem on undirected graphs and directed acyclic graphs. Moreover, our linear-time reductions lead to the first $O(n+m)$-time algorithms for the replacement-paths problem on the following classes of $n$-node $m$-edge graphs (1) undirected graphs in the word-RAM model of computation, (2) undirected planar graphs, (3) undirected minor-closed graphs, and (4) directed acyclic graphs.Comment: 23 pages, 1 table, 9 figures, accepted to SIAM Journal on Discrete Mathematic

Controlling for heterogeneity in gravity models of trade and integration

This paper compares various specifications of the gravity model of trade as nested versions of a general specification that uses bilateral country-pair fixed effects to control for heterogeneity. For each specification, we show that the atheoretical restrictions used to obtain them from the general model are not supported statistically. Because the gravity model has become the "workhorse" baseline model for estimating the effects of international integration, this has important empirical implications. In particular, we show that, unless heterogeneity is accounted for correctly, gravity models can greatly overestimate the effects of integration on the volume of trade.International trade

Experimental and analytical tools for evaluation of Stirling engine rod seal behavior

The first year of a two year experimental and analytical program is reported. The program is directed at the elastohydrodynamic behavior of sliding elastomeric rod seals for the Stirling engine. During the year, experimental and analytical tools were developed for evaluating seal leakage, seal friction, and the fluid film thickness at the seal/cylinder interface