13,988 research outputs found
Split degenerate states and stable p+ip phases from holography
In this paper, we investigate the p+p superfluid phases in the complex
vector field holographic p-wave model. We find that in the probe limit, the
p+p phase and the p-wave phase are equally stable, hence the p and p
orders can be mixed with an arbitrary ratio to form more general p+p
phases, which are also equally stable with the p-wave and p+p phases. As a
result, the system possesses a degenerate thermal state in the superfluid
region. We further study the case with considering the back reaction on the
metric, and find that the degenerate ground states will be separated into
p-wave and p+p phases, and the p-wave phase is more stable. Finally, due to
the different critical temperature of the zeroth order phase transitions from
p-wave and p+p phases to the normal phase, there is a temperature region
where the p+p phase exists but the p-wave phase doesn't. In this region we
find the stable p+p phase for the first time.Comment: 16 pages, 5 figures; typos correcte
On singular value distribution of large dimensional auto-covariance matrices
Let be a sequence of independent dimensional
random vectors and a given integer. From a sample
of the
sequence, the so-called lag auto-covariance matrix is
. When the
dimension is large compared to the sample size , this paper establishes
the limit of the singular value distribution of assuming that and
grow to infinity proportionally and the sequence satisfies a Lindeberg
condition on fourth order moments. Compared to existing asymptotic results on
sample covariance matrices developed in random matrix theory, the case of an
auto-covariance matrix is much more involved due to the fact that the summands
are dependent and the matrix is not symmetric. Several new techniques
are introduced for the derivation of the main theorem
On the Performance of Spectrum Sensing Algorithms using Multiple Antennas
In recent years, some spectrum sensing algorithms using multiple antennas,
such as the eigenvalue based detection (EBD), have attracted a lot of
attention. In this paper, we are interested in deriving the asymptotic
distributions of the test statistics of the EBD algorithms. Two EBD algorithms
using sample covariance matrices are considered: maximum eigenvalue detection
(MED) and condition number detection (CND). The earlier studies usually assume
that the number of antennas (K) and the number of samples (N) are both large,
thus random matrix theory (RMT) can be used to derive the asymptotic
distributions of the maximum and minimum eigenvalues of the sample covariance
matrices. While assuming the number of antennas being large simplifies the
derivations, in practice, the number of antennas equipped at a single secondary
user is usually small, say 2 or 3, and once designed, this antenna number is
fixed. Thus in this paper, our objective is to derive the asymptotic
distributions of the eigenvalues and condition numbers of the sample covariance
matrices for any fixed K but large N, from which the probability of detection
and probability of false alarm can be obtained. The proposed methodology can
also be used to analyze the performance of other EBD algorithms. Finally,
computer simulations are presented to validate the accuracy of the derived
results.Comment: IEEE GlobeCom 201
A Broad Learning Approach for Context-Aware Mobile Application Recommendation
With the rapid development of mobile apps, the availability of a large number
of mobile apps in application stores brings challenge to locate appropriate
apps for users. Providing accurate mobile app recommendation for users becomes
an imperative task. Conventional approaches mainly focus on learning users'
preferences and app features to predict the user-app ratings. However, most of
them did not consider the interactions among the context information of apps.
To address this issue, we propose a broad learning approach for
\textbf{C}ontext-\textbf{A}ware app recommendation with \textbf{T}ensor
\textbf{A}nalysis (CATA). Specifically, we utilize a tensor-based framework to
effectively integrate user's preference, app category information and
multi-view features to facilitate the performance of app rating prediction. The
multidimensional structure is employed to capture the hidden relationships
between multiple app categories with multi-view features. We develop an
efficient factorization method which applies Tucker decomposition to learn the
full-order interactions within multiple categories and features. Furthermore,
we employ a group norm regularization to learn the group-wise
feature importance of each view with respect to each app category. Experiments
on two real-world mobile app datasets demonstrate the effectiveness of the
proposed method
Enumeration of permutations by the parity of descent position
Noticing that some recent variations of descent polynomials are special cases
of Carlitz and Scoville's four-variable polynomials, which enumerate
permutations by the parity of descent and ascent position, we prove a
q-analogue of Carlitz-Scoville's generating function by counting the inversion
number and a type B analogue by enumerating the signed permutations with
respect to the parity of desecnt and ascent position. As a by-product of our
formulas, we obtain a q-analogue of Chebikin's formula for alternating descent
polynomials, an alternative proof of Sun's gamma-positivity of her bivariate
Eulerian polynomials and a type B analogue, the latter refines Petersen's
gamma-positivity of the type B Eulerian polynomials.Comment: 26 page
- …