3,460 research outputs found
Analyticity for the (generalized) Navier-Stokes equations with rough initial data
We study the Cauchy problem for the (generalized) incompressible
Navier-Stokes equations \begin{align} u_t+(-\Delta)^{\alpha}u+u\cdot \nabla u
+\nabla p=0, \ \ {\rm div} u=0, \ \ u(0,x)= u_0. \nonumber \end{align} We show
the analyticity of the local solutions of the Navier-Stokes equation
() with any initial data in critical Besov spaces
with
and the solution is global if is sufficiently small in
. In the case , the analyticity
for the local solutions of the Navier-Stokes equation () with any
initial data in modulation space is obtained.
We prove the global well-posedness for a fractional Navier-stokes equation
() with small data in critical Besov spaces
and show the
analyticity of solutions with small initial data either in
or in
.
Similar results also hold for all .Comment: 31 page
Long Trend Dynamics in Social Media
A main characteristic of social media is that its diverse content, copiously
generated by both standard outlets and general users, constantly competes for
the scarce attention of large audiences. Out of this flood of information some
topics manage to get enough attention to become the most popular ones and thus
to be prominently displayed as trends. Equally important, some of these trends
persist long enough so as to shape part of the social agenda. How this happens
is the focus of this paper. By introducing a stochastic dynamical model that
takes into account the user's repeated involvement with given topics, we can
predict the distribution of trend durations as well as the thresholds in
popularity that lead to their emergence within social media. Detailed
measurements of datasets from Twitter confirm the validity of the model and its
predictions
Purification of an elicitor from Magnaporthe oryzae inducing defense resistance in rice
Inducible defenses that contribute to overall resistance in plant can be triggered by elicitors. A novel elicitor, derived from the mycelia of the blast fungus Magnaporthe oryzae, was purified to homogeneity by HiPrep 16/20 DEAE-Sepharose FF, Concanavalin A-Sepharose 4B and HiPrep 16/60 Sephacryl S-100 column chromatography. The purified elicitor appeared as single band corresponding to a molecular weight of 48.53 kDa on sodium dodecyl sulfate-polyacrylamide gel electrophresis (SDS-PAGE) and a pI of 6.01 on isoeletric focusing (IEF) gel. Treatment with the purified elicitor increased the activities of phenylalanine ammonium-lyase (PAL) and peroxidase (POD) in rice susceptible cultivar CO39. Timecourse analysis showed peak accumulation of PAL appeared at 24 h after treatment, and it was higher in challenge-inoculated plants than non-challenge plants. POD accumulation showed similar kinetics with PAL, but the largest peak appeared at 36 h after treatment. Compared to the untreated control plants, pretreatment of rice leaves with the purified elicitor provided an enhanced level of protection against M. oryzae. N-terminal blocked elicitor was identified as hypothetical protein MG 05155.4 with 26.28% mass fingerprint coverage by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). The results suggest that the purified elicitor is involved in inducing resistance against blast fungus.Keywords: Magnaporthe oryzae, elicitor, purification, induced resistanc
EEG-Based Emotion Recognition Using Regularized Graph Neural Networks
Electroencephalography (EEG) measures the neuronal activities in different
brain regions via electrodes. Many existing studies on EEG-based emotion
recognition do not fully exploit the topology of EEG channels. In this paper,
we propose a regularized graph neural network (RGNN) for EEG-based emotion
recognition. RGNN considers the biological topology among different brain
regions to capture both local and global relations among different EEG
channels. Specifically, we model the inter-channel relations in EEG signals via
an adjacency matrix in a graph neural network where the connection and
sparseness of the adjacency matrix are inspired by neuroscience theories of
human brain organization. In addition, we propose two regularizers, namely
node-wise domain adversarial training (NodeDAT) and emotion-aware distribution
learning (EmotionDL), to better handle cross-subject EEG variations and noisy
labels, respectively. Extensive experiments on two public datasets, SEED and
SEED-IV, demonstrate the superior performance of our model than
state-of-the-art models in most experimental settings. Moreover, ablation
studies show that the proposed adjacency matrix and two regularizers contribute
consistent and significant gain to the performance of our RGNN model. Finally,
investigations on the neuronal activities reveal important brain regions and
inter-channel relations for EEG-based emotion recognition
An Affect-Rich Neural Conversational Model with Biased Attention and Weighted Cross-Entropy Loss
Affect conveys important implicit information in human communication. Having
the capability to correctly express affect during human-machine conversations
is one of the major milestones in artificial intelligence. In recent years,
extensive research on open-domain neural conversational models has been
conducted. However, embedding affect into such models is still under explored.
In this paper, we propose an end-to-end affect-rich open-domain neural
conversational model that produces responses not only appropriate in syntax and
semantics, but also with rich affect. Our model extends the Seq2Seq model and
adopts VAD (Valence, Arousal and Dominance) affective notations to embed each
word with affects. In addition, our model considers the effect of negators and
intensifiers via a novel affective attention mechanism, which biases attention
towards affect-rich words in input sentences. Lastly, we train our model with
an affect-incorporated objective function to encourage the generation of
affect-rich words in the output responses. Evaluations based on both perplexity
and human evaluations show that our model outperforms the state-of-the-art
baseline model of comparable size in producing natural and affect-rich
responses.Comment: AAAI-1
Trends in Social Media : Persistence and Decay
Social media generates a prodigious wealth of real-time content at an
incessant rate. From all the content that people create and share, only a few
topics manage to attract enough attention to rise to the top and become
temporal trends which are displayed to users. The question of what factors
cause the formation and persistence of trends is an important one that has not
been answered yet. In this paper, we conduct an intensive study of trending
topics on Twitter and provide a theoretical basis for the formation,
persistence and decay of trends. We also demonstrate empirically how factors
such as user activity and number of followers do not contribute strongly to
trend creation and its propagation. In fact, we find that the resonance of the
content with the users of the social network plays a major role in causing
trends
Analytical study of the holographic superconductor from higher derivative theory
In this paper, we analytically study the holographic superconductor models
with the high derivative (HD) coupling terms. Using the Sturm-Liouville (SL)
eigenvalue method, we perturbatively calculate the critical temperature. The
analytical results are in good agreement with the numerical results. It
confirms that the perturbative method in terms of the HD coupling parameters is
available. Along the same line, we analytically calculate the value of the
condensation near the critical temperature. We find that the phase transition
is second order with mean field behavior, which is independent of the HD
coupling parameters. Then in the low temperature limit, we also calculate the
conductivity, which is qualitatively consistent with the numerical one. We find
that the superconducting energy gap is proportional to the value of the
condensation. But we note that since the condensation changes with the HD
coupling parameters, as the function of the HD coupling parameters, the
superconducting energy gap follows the same change trend as that of the
condensation.Comment: 10 pages, 5 figure
Textual and Quantitative Research on China’s Action Plan for Promoting the Development of Big Data From the Perspective of Policy Tools
The research on the development of big data from the perspective of policy tools, to help policy makers look for policy tools that can provide guidance and support for the development of big data. The research is of significant theoretical and practical value for promoting development of big data and realizing the strategy of data power country. Using content analysis method and quantitative analysis methods, this paper evaluates and discusses China’s action plan for the development of big data from the perspective of policy tools. Government uses more supply-side and demand-side policy tools to stimulate and support the development of big data. Nevertheless, the stage of technology research and development stage has not been given enough attention. To improve and update China’s action plan for promoting the development of big data, policy tools system needs to be integrated or coordinated with data powerful country’s value-chain
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