3,819 research outputs found
Unextendible Product Basis for Fermionic Systems
We discuss the concept of unextendible product basis (UPB) and generalized
UPB for fermionic systems, using Slater determinants as an analogue of product
states, in the antisymmetric subspace \wedge^ N \bC^M. We construct an
explicit example of generalized fermionic unextendible product basis (FUPB) of
minimum cardinality for any . We also show that any
bipartite antisymmetric space \wedge^ 2 \bC^M of codimension two is spanned
by Slater determinants, and the spaces of higher codimension may not be spanned
by Slater determinants. Furthermore, we construct an example of complex FUPB of
with minimum cardinality . In contrast, we show that a real FUPB
does not exist for . Finally we provide a systematic construction for
FUPBs of higher dimensions using FUPBs and UPBs of lower dimensions.Comment: 17 pages, no figure. Comments are welcom
Stochastic gravitational-wave background from spin loss of black holes
Although spinning black holes are shown to be stable in vacuum in general
relativity, there exists exotic mechanisms that can convert the spin energy of
black holes into gravitational waves. Such waves may be very weak in amplitude,
since the spin-down could take a long time, and a direct search may not be
feasible. We propose to search for the stochastic background associated with
the spin-down, and we relate the level of this background to the formation rate
of spinning black holes from the merger of binary black holes, as well as the
energy spectrum of waves emitted by the spin-down process. We argue that
current LIGO-Virgo observations are not inconsistent with the existence of a
spin-down process, as long as it is slow enough. On the other hand, the
background may still exist as long as a moderate fraction of spin energy is
emitted within Hubble time. This stochastic background could be one interesting
target of next generation GW detector network, such as LIGO Voyager, and could
be extracted from total stochastic background
Universal Entanglers for Bosonic and Fermionic Systems
A universal entangler (UE) is a unitary operation which maps all pure product
states to entangled states. It is known that for a bipartite system of
particles with a Hilbert space ,
a UE exists when and . It is also
known that whenever a UE exists, almost all unitaries are UEs; however to
verify whether a given unitary is a UE is very difficult since solving a
quadratic system of equations is NP-hard in general. This work examines the
existence and construction of UEs of bipartite bosonic/fermionic systems whose
wave functions sit in the symmetric/antisymmetric subspace of
. The development of a theory of UEs for
these types of systems needs considerably different approaches from that used
for UEs of distinguishable systems. This is because the general entanglement of
identical particle systems cannot be discussed in the usual way due to the
effect of (anti)-symmetrization which introduces "pseudo entanglement" that is
inaccessible in practice. We show that, unlike the distinguishable particle
case, UEs exist for bosonic/fermionic systems with Hilbert spaces which are
symmetric (resp. antisymmetric) subspaces of
if and only if (resp. ). To prove this we employ algebraic geometry to reason about the different
algebraic structures of the bosonic/fermionic systems. Additionally, due to the
relatively simple coherent state form of unentangled bosonic states, we are
able to give the explicit constructions of two bosonic UEs. Our investigation
provides insight into the entanglement properties of systems of
indisitinguishable particles, and in particular underscores the difference
between the entanglement structures of bosonic, fermionic and distinguishable
particle systems.Comment: 15 pages, comments welcome, TQC2013 Accepted Tal
Nasal Bacterial Microbiome: Probing a Healthy Porcine Family
Upper respiratory tract (URT) infection caused the leading and devastating diseases in pigs. It was believed that the normal microbiome of URT plays a vital role in health and disease development. As the entry point of the URT, little knowledge of bacterial microbiome in porcine nasal was known. A cultivation-independent approach directly to 16s ribosomal RNA genes enabled us to reveal the nasal bacterial community, structure and diversity. Here, we found that an unprecedented 207 phylotypes were characterized from 933 qualified clones, indicating the variable, species richness but particularly dominant bacterial microbiome. The dominant species were from genus Comamonas and Acinetobacter, which constitute core normal bacterial microbiome in porcine nasal. Moreover, a set of swine specific pathogens and zoonotic agents were detected in the swine nasal microbiome. Collectively, we provided a snapshot of our current knowledge of the community structure of porcine nasal bacterial ecosystem in a healthy family that will further enhance our view to understand URT infection and public health
Discriminative Nonparametric Latent Feature Relational Models with Data Augmentation
We present a discriminative nonparametric latent feature relational model
(LFRM) for link prediction to automatically infer the dimensionality of latent
features. Under the generic RegBayes (regularized Bayesian inference)
framework, we handily incorporate the prediction loss with probabilistic
inference of a Bayesian model; set distinct regularization parameters for
different types of links to handle the imbalance issue in real networks; and
unify the analysis of both the smooth logistic log-loss and the piecewise
linear hinge loss. For the nonconjugate posterior inference, we present a
simple Gibbs sampler via data augmentation, without making restricting
assumptions as done in variational methods. We further develop an approximate
sampler using stochastic gradient Langevin dynamics to handle large networks
with hundreds of thousands of entities and millions of links, orders of
magnitude larger than what existing LFRM models can process. Extensive studies
on various real networks show promising performance.Comment: Accepted by AAAI 201
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