This paper is concerned with the properties of L2-normalized minimizers of the Gross–Pitaevskii (GP) functional for a two-dimensional Bose–Einstein condensate with attractive interaction and ...ring-shaped potential. By establishing some delicate estimates on the least energy of the GP functional, we prove that symmetry breaking occurs for the minimizers of the GP functional as the interaction strength a>0 approaches a critical value a⁎, each minimizer of the GP functional concentrates to a point on the circular bottom of the potential well and then is non-radially symmetric as a↗a⁎. However, when a>0 is suitably small we prove that the minimizers of the GP functional are unique, and this unique minimizer is radially symmetric.
With the increasing demands for sharing confidential information among massive Internet of Things (IoT) devices in 5G and beyond wireless networks, many applications require the common secret key ...generation for a group of IoT devices. However, most of the existing works on physical layer secret key generation (PLKG) only focus on the pairwise key generation between two users, which is a low efficient and high cost to be extended to the scenarios of group key generation. In this work, we propose a new efficient multiple-input-multiple-output (MIMO) physical layer group secret key generation scheme to reduce the consumption of channel probing and improve the efficiency for group key generation. Different from current schemes, in the proposed scheme, the transmitter randomly generates the group secret key and directly broadcasts the downlink data symbols to the group users. At the receiver end, each group user can efficiently "observe" the common group key through the downlink broadcasting data symbols, while keeping perfect secrecy of the shared group key against eavesdroppers. The performance of reliability, security, and the group key generation rate is fully investigated, which shows the advantages of high efficiency, low consumption, and strong robustness of the proposed scheme. Extensive simulations are conducted to validate the effectiveness of the proposed scheme.
In this paper, we consider the following Schrödinger–Poisson system
(
P
λ
)
{
−
Δ
u
+
(
1
+
μ
g
(
x
)
)
u
+
λ
ϕ
(
x
)
u
=
|
u
|
p
−
1
u
,
x
∈
R
3
,
−
Δ
ϕ
=
u
2
,
lim
|
x
|
→
+
∞
ϕ
(
x
)
=
0
,
where
...λ,
μ are positive parameters,
p
∈
(
1
,
5
)
,
g
(
x
)
∈
L
∞
(
R
3
)
is nonnegative and
g
(
x
)
≡
0
on a bounded domain in
R
3
. In this case,
μ
g
(
x
)
represents a potential well that steepens as
μ getting large. If
μ
=
0
,
(
P
λ
)
was well studied in Ruiz (2006)
18. If
μ
≠
0
and
g
(
x
)
is not radially symmetric, it is unknown whether
(
P
λ
)
has a nontrivial solution for
p
∈
(
1
,
2
)
. By priori estimates and approximation methods we prove that
(
P
λ
)
with
p
∈
(
1
,
2
)
has a ground state if
μ large and
λ small. In the meantime, we prove also that
(
P
λ
)
with
p
∈
3
,
5
)
has a nontrivial solution for any
λ
>
0
and
μ large. Moreover, some behaviors of the solutions of
(
P
λ
)
as
λ
→
0
,
μ
→
+
∞
and
|
x
|
→
+
∞
are discussed.
Optimizing Kernel Machines Using Deep Learning Huan Song; Thiagarajan, Jayaraman J.; Sattigeri, Prasanna ...
IEEE transaction on neural networks and learning systems,
11/2018, Volume:
29, Issue:
11
Journal Article
Open access
Building highly nonlinear and nonparametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing ...kernel Hilbert space (RKHS) for inferring non-linear models through the construction of similarity functions from data. These methods are particularly preferred in cases where the training data sizes are limited and when prior knowledge of the data similarities is available. Despite their usefulness, they are limited by the computational complexity and their inability to support end-to-end learning with a task-specific objective. On the other hand, deep neural networks have become the de facto solution for end-to-end inference in several learning paradigms. In this paper, we explore the idea of using deep architectures to perform kernel machine optimization, for both computational efficiency and end-to-end inferencing. To this end, we develop the deep kernel machine optimization framework, that creates an ensemble of dense embeddings using Nyström kernel approximations and utilizes deep learning to generate task-specific representations through the fusion of the embeddings. Intuitively, the filters of the network are trained to fuse information from an ensemble of linear subspaces in the RKHS. Furthermore, we introduce the kernel dropout regularization to enable improved training convergence. Finally, we extend this framework to the multiple kernel case, by coupling a global fusion layer with pretrained deep kernel machines for each of the constituent kernels. Using case studies with limited training data, and lack of explicit feature sources, we demonstrate the effectiveness of our framework over conventional model inferencing techniques.
We investigate the existence and number of limit cycles in a class of general planar piecewise linear systems constituted by two linear subsystems with node–node dynamics. Using the Liénard-like ...canonical form with seven parameters, some sufficient and necessary conditions for the existence of limit cycles are given by studying the fixed points of proper Poincaré maps. In particular, we prove the existence of at least two nested limit cycles and describe some parameter regions where two limit cycles exist. The main results are applied to the PWL Morris–Lecar neural model to determine the existence and stability of the limit cycles.
We are concerned with the following constrained minimization problem:e(a1,a2,β):=inf{Ea1,a2,β(u1,u2):‖u1‖L2(R3)=‖u2‖L2(R3)=1}, where Ea1,a2,β is the energy functional associated to two coupled ...pseudo-relativistic Hartree equations involving three parameters a1,a2,β and two trapping potentials V1(x) and V2(x). In this paper, we obtain the existence of minimizers of e(a1,a2,β) for possible a1,a2 and β under suitable conditions on the potentials, which generalizes the results of the papers 17–19 in different senses.
Understanding how and why species evolve requires knowledge on intraspecific divergence. In this study, we examined intraspecific divergence in the endangered hot‐spring snake (Thermophis baileyi), ...an endemic species on the Qinghai‐Tibet Plateau (QTP). Whole‐genome resequencing of 58 sampled individuals from 15 populations was performed to identify the drivers of intraspecific divergence and explore the potential roles of genes under selection. Our analyses resolved three groups, with major intergroup admixture occurring in regions of group contact. Divergence probably occurred during the Pleistocene as a result of glacial climatic oscillations, Yadong‐Gulu rift, and geothermal fields differentiation, while complex gene flow between group pairs reflected a unique intraspecific divergence pattern on the QTP. Intergroup fixed loci involved selected genes functionally related to divergence and local adaptation, especially adaptation to hot spring microenvironments in different geothermal fields. Analysis of structural variants, genetic diversity, inbreeding, and genetic load indicated that the hot‐spring snake population has declined to a low level with decreased diversity, which is important for the conservation management of this endangered species. Our study demonstrated that the integration of demographic history, gene flow, genomic divergence genes, and other information is necessary to distinguish the evolutionary processes involved in speciation.
Psychiatric reactions to life stressors are common in the general population and may result in immune dysfunction. Whether such reactions contribute to the risk of autoimmune disease remains unclear.
...To determine whether there is an association between stress-related disorders and subsequent autoimmune disease.
Population- and sibling-matched retrospective cohort study conducted in Sweden from January 1, 1981, to December 31, 2013. The cohort included 106 464 exposed patients with stress-related disorders, with 1 064 640 matched unexposed persons and 126 652 full siblings of these patients.
Diagnosis of stress-related disorders, ie, posttraumatic stress disorder, acute stress reaction, adjustment disorder, and other stress reactions.
Stress-related disorder and autoimmune diseases were identified through the National Patient Register. The Cox model was used to estimate hazard ratios (HRs) with 95% CIs of 41 autoimmune diseases beyond 1 year after the diagnosis of stress-related disorders, controlling for multiple risk factors.
The median age at diagnosis of stress-related disorders was 41 years (interquartile range, 33-50 years) and 40% of the exposed patients were male. During a mean follow-up of 10 years, the incidence rate of autoimmune diseases was 9.1, 6.0, and 6.5 per 1000 person-years among the exposed, matched unexposed, and sibling cohorts, respectively (absolute rate difference, 3.12 95% CI, 2.99-3.25 and 2.49 95% CI, 2.23-2.76 per 1000 person-years compared with the population- and sibling-based reference groups, respectively). Compared with the unexposed population, patients with stress-related disorders were at increased risk of autoimmune disease (HR, 1.36 95% CI, 1.33-1.40). The HRs for patients with posttraumatic stress disorder were 1.46 (95% CI, 1.32-1.61) for any and 2.29 (95% CI, 1.72-3.04) for multiple (≥3) autoimmune diseases. These associations were consistent in the sibling-based comparison. Relative risk elevations were more pronounced among younger patients (HR, 1.48 95% CI, 1.42-1.55; 1.41 95% CI, 1.33-1.48; 1.31 95% CI, 1.24-1.37; and 1.23 95% CI, 1.17-1.30 for age at ≤33, 34-41, 42-50, and ≥51 years, respectively; P for interaction < .001). Persistent use of selective serotonin reuptake inhibitors during the first year of posttraumatic stress disorder diagnosis was associated with attenuated relative risk of autoimmune disease (HR, 3.64 95% CI, 2.00-6.62; 2.65 95% CI, 1.57-4.45; and 1.82 95% CI, 1.09-3.02 for duration ≤179, 180-319, and ≥320 days, respectively; P for trend = .03).
In this Swedish cohort, exposure to a stress-related disorder was significantly associated with increased risk of subsequent autoimmune disease, compared with matched unexposed individuals and with full siblings. Further studies are needed to better understand the underlying mechanisms.
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