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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
Interacting Two-Time Physics Field Theory With a BRST Gauge Invariant Action
We construct a field theoretic version of 2T-physics including interactions
in an action formalism. The approach is a BRST formulation based on the
underlying Sp(2,R)gauge symmetry, and shares some similarities with the
approach used to construct string field theory. In our first case of spinless
particles, the interaction is uniquely determined by the BRST gauge symmetry,
and it is different than the Chern-Simons type theory used in open string field
theory. After constructing a BRST gauge invariant action for 2T-physics field
theory with interactions in d+2 dimensions, we study its relation to standard
1T-physics field theory in (d-1)+1 dimensions by choosing gauges. In one gauge
we show that we obtain the Klein-Gordon field theory in (d-1)+1 dimensions with
unique SO(d,2) conformal invariant self interactions at the classical field
level. This SO(d,2) is the natural linear Lorentz symmetry of the 2T field
theory in d+2 dimensions. As indicated in Fig.1, in other gauges we expect to
derive a variety of SO(d,2)invariant 1T-physics field theories as gauge fixed
forms of the same 2T field theory, thus obtaining a unification of 1T-dynamics
in a field theoretic setting, including interactions. The BRST gauge
transformation should play the role of duality transformations among the
1T-physics holographic images of the same parent 2T field theory. The
availability of a field theory action opens the way for studying 2T-physics
with interactions at the quantum level through the path integral approach.Comment: 22 pages, 1 figure, v3 includes corrections of typos and some
comment
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
states) and open boundary conditions (two states and one each ). 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 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 is {\em -concise} if the finite entries of each column of
consist of or less intervals of identical numbers. We give an -time
algorithm to compute the row minima of any -concise matrix.
Our algorithm yields the first -time reductions from the
replacement-paths problem on an -node -edge undirected graph
(respectively, directed acyclic graph) to the single-source shortest-paths
problem on an -node -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
-time algorithms for the replacement-paths problem on the following
classes of -node -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
Dundee Discussion Papers in Economics 155:Lobbying for protection under uncertainty: a real option approach
Explicit construction of quasi-conserved local operator of translationally invariant non-integrable quantum spin chain in prethermalization
We numerically construct translationally invariant quasi-conserved operators
with maximum range M which best-commute with a non-integrable quantum spin
chain Hamiltonian, up to M = 12. In the large coupling limit, we find that the
residual norm of the commutator of the quasi-conserved operator decays
exponentially with its maximum range M at small M, and turns into a slower
decay at larger M. This quasi-conserved operator can be understood as a dressed
total "spin-z" operator, by comparing with the perturbative Schrieffer-Wolff
construction developed to high order reaching essentially the same maximum
range. We also examine the operator inverse participation ratio of the
operator, which suggests its localization in the operator Hilbert space. The
operator also shows almost exponentially decaying profile at short distance,
while the long-distance behavior is not clear due to limitations of our
numerical calculation. Further dynamical simulation confirms that the
prethermalization-equilibrated values are described by a generalized Gibbs
ensemble that includes such quasi-conserved operator.Comment: 22 pages with 13 pages of main text, 9 figures and 5 appendices
(published version
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