113 research outputs found
Multimodal Hierarchical Dirichlet Process-based Active Perception
In this paper, we propose an active perception method for recognizing object
categories based on the multimodal hierarchical Dirichlet process (MHDP). The
MHDP enables a robot to form object categories using multimodal information,
e.g., visual, auditory, and haptic information, which can be observed by
performing actions on an object. However, performing many actions on a target
object requires a long time. In a real-time scenario, i.e., when the time is
limited, the robot has to determine the set of actions that is most effective
for recognizing a target object. We propose an MHDP-based active perception
method that uses the information gain (IG) maximization criterion and lazy
greedy algorithm. We show that the IG maximization criterion is optimal in the
sense that the criterion is equivalent to a minimization of the expected
Kullback--Leibler divergence between a final recognition state and the
recognition state after the next set of actions. However, a straightforward
calculation of IG is practically impossible. Therefore, we derive an efficient
Monte Carlo approximation method for IG by making use of a property of the
MHDP. We also show that the IG has submodular and non-decreasing properties as
a set function because of the structure of the graphical model of the MHDP.
Therefore, the IG maximization problem is reduced to a submodular maximization
problem. This means that greedy and lazy greedy algorithms are effective and
have a theoretical justification for their performance. We conducted an
experiment using an upper-torso humanoid robot and a second one using synthetic
data. The experimental results show that the method enables the robot to select
a set of actions that allow it to recognize target objects quickly and
accurately. The results support our theoretical outcomes.Comment: submitte
Upper Cohen-Macaulay Dimension
In this paper, we define a homological invariant for finitely generated modules over a commutative noetherian local ring, which we call upper Cohen-Macaulay dimension. This invariant is quite similar to Cohen-Macaulay dimension that has been introduced by Gerko. Also we
define a homological invariant with respect to a local homomorphism of local rings. This invariant links upper Cohen-Macaulay dimension with Gorenstein dimension.</p
Homological invariants associated to semi-dualizing bimodules
Cohen-Macaulay dimension for modules over a commutative noetherian local ring
has been defined by A. A. Gerko. That is a homological invariant sharing many
properties with projective dimension and Gorenstein dimension. The main purpose
of this paper is to extend the notion of Cohen-Macaulay dimension for modules
over commutative noetherian local rings to that for bounded complexes over
non-commutative noetherian rings.Comment: 19 pages, to appear in J. Math. Kyoto Uni
Local cohomology based on a nonclosed support defined by a pair of ideals
We introduce an idea for generalization of a local cohomology module, which
we call a local cohomology module with respect to a pair of ideals (I,J), and
study their various properties. Some vanishing and nonvanishing theorems are
given for this generalized version of local cohomology. We also discuss its
connection with the ordinary local cohomology.Comment: 28 pages, minor corrections, to appear in J. Pure Appl. Algebr
The radius of a subcategory of modules
We introduce a new invariant for subcategories X of finitely generated
modules over a local ring R which we call the radius of X. We show that if R is
a complete intersection and X is resolving, then finiteness of the radius
forces X to contain only maximal Cohen-Macaulay modules. We also show that the
category of maximal Cohen-Macaulay modules has finite radius when R is a
Cohen-Macaulay complete local ring with perfect coefficient field. We link the
radius to many well-studied notions such as the dimension of the stable
category of maximal Cohen-Macaulay modules, finite/countable Cohen-Macaulay
representation type and the uniform Auslander condition.Comment: Final version, to appear in Algebra and Number Theor
Coexistence of Continuous Variable Quantum Key Distribution and 7 12.5 Gbit/s Classical Channels
We study coexistence of CV-QKD and 7 classical 12.5 Gbit/s on-off keying
channels in WDM transmission over the C-band. We demonstrate key generation
with a distilled secret key rate between 20 to 50 kbit/s in experiments running
continuously over 24 hours.Comment: 2018 IEEE Summer Topicals, paper MD4.
Noncommutative resolutions using syzygies
Given a noether algebra with a noncommutative resolution, a general construction of new noncommutative resolutions is given. As an application, it is proved that any finite length module over a regular local or polynomial ring gives rise, via suitable syzygies, to a noncommutative resolution
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