421,151 research outputs found
Concurrence of quasi pure quantum states
We derive an analytic approximation for the concurrence of weakly mixed
bipartite quantum states - typical objects in state of the art experiments.
This approximation is shown to be a lower bound of the concurrence of arbitrary
states
Improved Revenue Bounds for Posted-Price and Second-Price Mechanisms
We study revenue maximization through sequential posted-price (SPP)
mechanisms in single-dimensional settings with buyers and independent but
not necessarily identical value distributions. We construct the SPP mechanisms
by considering the best of two simple pricing rules: one that imitates the
revenue optimal mchanism, namely the Myersonian mechanism, via the taxation
principle and the other that posts a uniform price. Our pricing rules are
rather generalizable and yield the first improvement over long-established
approximation factors in several settings. We design factor-revealing
mathematical programs that crisply capture the approximation factor of our SPP
mechanism. In the single-unit setting, our SPP mechanism yields a better
approximation factor than the state of the art prior to our work (Azar,
Chiplunkar & Kaplan, 2018). In the multi-unit setting, our SPP mechanism yields
the first improved approximation factor over the state of the art after over
nine years (Yan, 2011 and Chakraborty et al., 2010). Our results on SPP
mechanisms immediately imply improved performance guarantees for the equivalent
free-order prophet inequality problem. In the position auction setting, our SPP
mechanism yields the first higher-than approximation factor. In eager
second-price (ESP) auctions, our two simple pricing rules lead to the first
improved approximation factor that is strictly greater than what is obtained by
the SPP mechanism in the single-unit setting.Comment: Accepted to Operations Researc
On a Problem of Weighted Low-Rank Approximation of Matrices
We study a weighted low rank approximation that is inspired by a problem of
constrained low rank approximation of matrices as initiated by the work of
Golub, Hoffman, and Stewart (Linear Algebra and Its Applications, 88-89(1987),
317-327). Our results reduce to that of Golub, Hoffman, and Stewart in the
limiting cases. We also propose an algorithm based on the alternating direction
method to solve our weighted low rank approximation problem and compare it with
the state-of-art general algorithms such as the weighted total alternating
least squares and the EM algorithm
Faces of the Teouma Lapita People: Art, Accuracy and Facial Approximation
In 2008 we completed facial approximations of four individuals from the early Lapita Culture, a seafaring people who were the first to settle the islands of the Western Pacific circa 3000 years ago. Typically an approximation is performed as a 3D sculpture or using computer graphics. We chose to sketch what we have been able to determine from the remains because the artistic conventions of drawing work with visual perception in ways that are more complementary to the knowledge, theories and methods that make up the facial approximation of human remains
Embedding based on function approximation for large scale image search
The objective of this paper is to design an embedding method that maps local
features describing an image (e.g. SIFT) to a higher dimensional representation
useful for the image retrieval problem. First, motivated by the relationship
between the linear approximation of a nonlinear function in high dimensional
space and the stateof-the-art feature representation used in image retrieval,
i.e., VLAD, we propose a new approach for the approximation. The embedded
vectors resulted by the function approximation process are then aggregated to
form a single representation for image retrieval. Second, in order to make the
proposed embedding method applicable to large scale problem, we further derive
its fast version in which the embedded vectors can be efficiently computed,
i.e., in the closed-form. We compare the proposed embedding methods with the
state of the art in the context of image search under various settings: when
the images are represented by medium length vectors, short vectors, or binary
vectors. The experimental results show that the proposed embedding methods
outperform existing the state of the art on the standard public image retrieval
benchmarks.Comment: Accepted to TPAMI 2017. The implementation and precomputed features
of the proposed F-FAemb are released at the following link:
http://tinyurl.com/F-FAem
- …