347 research outputs found
Hypercontractivity of heat semigroups on free quantum groups
In this paper we study two semigroups of completely positive unital
self-adjoint maps on the von Neumann algebras of the free orthogonal quantum
group and the free permutation quantum group . We show that
these semigroups satisfy ultracontractivity and hypercontractivity estimates.
We also give results regarding spectral gap and logarithmic Sobolev
inequalities.Comment: 19 page
Existence results for some fourth-order nonlinear elliptic problems of local superlinearity and sublinearity
AbstractIn this paper we study the existence of positive solutions for the problem (0.1)Δ2u+cΔu=f(x,u)inΩ,u⩾0,u≢0inΩ,u=Δu=0on∂Ω, where c<λ1(Ω) and f(x,u) satisfies the local superlinearity and sublinearity condition
Is exponential gravity a viable description for the whole cosmological history?
Here we analysed a particular type of gravity, the so-called
exponential gravity which includes an exponential function of the Ricci scalar
in the action. Such term represents a correction to the usual Hilbert-Einstein
action. By using Supernovae Ia, Barionic Acoustic Oscillations, Cosmic
Microwave Background and data, the free parameters of the model are well
constrained. The results show that such corrections to General Relativity
become important at cosmological scales and at late-times, providing an
alternative to the dark energy problem. In addition, the fits do not determine
any significant difference statistically with respect to the CDM
model. Finally, such model is extended to include the inflationary epoch in the
same gravitational Lagrangian. As shown in the paper, the additional terms can
reproduce the inflationary epoch and satisfy the constraints from Planck data.Comment: 20 pages, 6 figures, analysis extended, version published in EPJ
Mass Loss and Chemical Structures of Wheat and Maize Straws in Response to Ultravoilet-B Radiation and Soil Contact
The role of photodegradation, an abiotic process, has been largely overlooked during straw decomposition in mesic ecosystems. We investigated the mass loss and chemical structures of straw decomposition in response to elevated UV-B radiation with or without soil contact over a 12-month litterbag experiment. Wheat and maize straw samples with and without soil contact were exposed to three radiation levels: a no-sunlight control, ambient solar UV-B, and artificially elevated UV-B radiation. A block control with soil contact was not included. Compared with the no-sunlight control, UV-B radiation increased the mass loss by 14-19% and the ambient radiation by 9-16% for wheat and maize straws without soil contact after 12 months. Elevated UV-B exposure decreased the decomposition rates of both wheat and maize straws when in contact with soil. Light exposure resulted in decreased O-alkyl carbons and increased alkyl carbons for both the wheat and maize straws compared with no-sunlight control. The difference in soil contact may influence the contribution of photodegradation to the overall straw decomposition process. These results indicate that we must take into account the effects of photodegradation when explaining the mechanisms of straw decomposition in mesic ecosystems
Robust Ranking Explanations
Robust explanations of machine learning models are critical to establish
human trust in the models. Due to limited cognition capability, most humans can
only interpret the top few salient features. It is critical to make top salient
features robust to adversarial attacks, especially those against the more
vulnerable gradient-based explanations. Existing defense measures robustness
using -norms, which have weaker protection power. We define explanation
thickness for measuring salient features ranking stability, and derive
tractable surrogate bounds of the thickness to design the \textit{R2ET}
algorithm to efficiently maximize the thickness and anchor top salient
features. Theoretically, we prove a connection between R2ET and adversarial
training. Experiments with a wide spectrum of network architectures and data
modalities, including brain networks, demonstrate that R2ET attains higher
explanation robustness under stealthy attacks while retaining accuracy.Comment: Accepted to IMLH (Interpretable ML in Healthcare) workshop at ICML
2023. arXiv admin note: substantial text overlap with arXiv:2212.1410
Contrastive Brain Network Learning via Hierarchical Signed Graph Pooling Model
Recently brain networks have been widely adopted to study brain dynamics,
brain development and brain diseases. Graph representation learning techniques
on brain functional networks can facilitate the discovery of novel biomarkers
for clinical phenotypes and neurodegenerative diseases. However, current graph
learning techniques have several issues on brain network mining. Firstly, most
current graph learning models are designed for unsigned graph, which hinders
the analysis of many signed network data (e.g., brain functional networks).
Meanwhile, the insufficiency of brain network data limits the model performance
on clinical phenotypes predictions. Moreover, few of current graph learning
model is interpretable, which may not be capable to provide biological insights
for model outcomes. Here, we propose an interpretable hierarchical signed graph
representation learning model to extract graph-level representations from brain
functional networks, which can be used for different prediction tasks. In order
to further improve the model performance, we also propose a new strategy to
augment functional brain network data for contrastive learning. We evaluate
this framework on different classification and regression tasks using the data
from HCP and OASIS. Our results from extensive experiments demonstrate the
superiority of the proposed model compared to several state-of-the-art
techniques. Additionally, we use graph saliency maps, derived from these
prediction tasks, to demonstrate detection and interpretation of phenotypic
biomarkers
Dendrimer-entrapped gold nanoparticles as potential CT contrast agents for blood pool imaging
The purpose of this study was to evaluate dendrimer-entrapped gold nanoparticles [Au DENPs] as a molecular imaging [MI] probe for computed tomography [CT]. Au DENPs were prepared by complexing AuCl4- ions with amine-terminated generation 5 poly(amidoamine) [G5.NH2] dendrimers. Resulting particles were sized using transmission electron microscopy. Serial dilutions (0.001 to 0.1 M) of either Au DENPs or iohexol were scanned by CT in vitro. Based on these results, Au DENPs were injected into mice, either subcutaneously (10 μL, 0.007 to 0.02 M) or intravenously (300 μL, 0.2 M), after which the mice were imaged by micro-CT or a standard mammography unit. Au DENPs prepared using G5.NH2 dendrimers as templates are quite uniform and have a size range of 2 to 4 nm. At Au concentrations above 0.01 M, the CT value of Au DENPs was higher than that of iohexol. A 10-μL subcutaneous dose of Au DENPs with [Au] ≥ 0.009 M could be detected by micro-CT. The vascular system could be imaged 5 and 20 min after injection of Au DENPs into the tail vein, and the urinary system could be imaged after 60 min. At comparable time points, the vascular system could not be imaged using iohexol, and the urinary system was imaged only indistinctly. Findings from this study suggested that Au DENPs prepared using G5.NH2 dendrimers as templates have good X-ray attenuation and a substantial circulation time. As their abundant surface amine groups have the ability to bind to a range of biological molecules, Au DENPs have the potential to be a useful MI probe for CT
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