66,593 research outputs found
A Vanishing Result for the Universal Bundle on a Toric Quiver Variety
Let Q be a finite quiver without oriented cycles. Denote by U --> M the fine
moduli space of stable thin sincere representations of Q with respect to the
canonical stability notion. We prove Ext^i(U,U) = 0 for all i >0 and compute
the endomorphism algebra of the universal bundle U. Moreover, we obtain a
necessary and sufficient condition for when this algebra is isomorphic to the
path algebra kQ of the quiver Q. If so, then the bounded derived category of
finitely generated right kQ-modules is embedded into that of coherent sheaves
on M.Comment: 13 pages with a couple of small figures LaTeX 2.0
Colour appearance is affected not only by perceptual but also by linguistic context
Terminology is a crucial problem in science, since quite often the terms used to denote theoretical concepts are directly taken from the vocabulary of common words, which usually have multiple meanings. To solve this problem, scientists must operationalize the theoretical concepts they use but, in psychology, sometimes, this can be a difficult task, since the meaning of the terms used to give the instructions to observers can interfere with the spontaneous meaning that observers give to those terms. Starting from some empirical observations, we show that colour appearance is affected not only by the perceptual but also by the linguistic context
Lemmings is PSPACE-complete
Lemmings is a computer puzzle game developed by DMA Design and published by
Psygnosis in 1991, in which the player has to guide a tribe of lemming
creatures to safety through a hazardous landscape, by assigning them specific
skills that modify their behavior in different ways. In this paper we study the
optimization problem of saving the highest number of lemmings in a given
landscape with a given number of available skills.
We prove that the game is PSPACE-complete, even if there is only one lemming
to save, and only Builder and Basher skills are available. We thereby settle an
open problem posed by Cormode in 2004, and again by Forisek in 2010. However we
also prove that, if we restrict the game to levels in which the available
Builder skills are only polynomially many (and there is any number of other
skills), then the game is solvable in NP. Similarly, if the available Basher,
Miner, and Digger skills are polynomially many, the game is solvable in NP.
Furthermore, we show that saving the maximum number of lemmings is APX-hard,
even when only one type of skill is available, whatever this skill is. This
contrasts with the membership in P of the decision problem restricted to levels
with no "deadly areas" (such as water or traps) and only Climber and Floater
skills, as previously established by Cormode.Comment: 26 pages, 11 figure
A survey about framing the bases of Impulsive Mechanics of constrained systems into a jet-bundle geometric context
We illustrate how the different kinds of constraints acting on an impulsive
mechanical system can be clearly described in the geometric setup given by the
configuration space--time bundle and its
first jet extension in a way that ensures total
compliance with axioms and invariance requirements of Classical Mechanics. We
specify the differences between geometric and constitutive characterizations of
a constraint. We point out the relevance of the role played by the concept of
frame of reference, underlining when the frame independence is mandatorily
required and when a choice of a frame is an inescapable need. The thorough
rationalization allows the introduction of unusual but meaningful kinds of
constraints, such as unilateral kinetic constraints or breakable constraints,
and of new theoretical aspects, such as the possible dependence of the
impulsive reaction by the active forces acting on the system
ImageSpirit: Verbal Guided Image Parsing
Humans describe images in terms of nouns and adjectives while algorithms
operate on images represented as sets of pixels. Bridging this gap between how
humans would like to access images versus their typical representation is the
goal of image parsing, which involves assigning object and attribute labels to
pixel. In this paper we propose treating nouns as object labels and adjectives
as visual attribute labels. This allows us to formulate the image parsing
problem as one of jointly estimating per-pixel object and attribute labels from
a set of training images. We propose an efficient (interactive time) solution.
Using the extracted labels as handles, our system empowers a user to verbally
refine the results. This enables hands-free parsing of an image into pixel-wise
object/attribute labels that correspond to human semantics. Verbally selecting
objects of interests enables a novel and natural interaction modality that can
possibly be used to interact with new generation devices (e.g. smart phones,
Google Glass, living room devices). We demonstrate our system on a large number
of real-world images with varying complexity. To help understand the tradeoffs
compared to traditional mouse based interactions, results are reported for both
a large scale quantitative evaluation and a user study.Comment: http://mmcheng.net/imagespirit
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