70,347 research outputs found

### A generalization of d'Alembert formula

In this paper we find a closed form of the solution for the factored
inhomogeneous linear equation \begin{equation*}
\prod_{j=1}^{n}(\frac{\hbox{d}}{\hbox{d}t}-A_{j}) u(t) =f(t). \end{equation*}
Under the hypothesis $A_{1},A_{2}, ..., A_{n}$ are infinitesimal generators of
mutually commuting strongly continuous semigroups of bounded linear operators
on a Banach space $X$. Here we do not assume that $A_{j}$s are distinct and we
offer the computational method to get explicit solutions of certain partial
differential equations.Comment: 17 page

### The origin of quantum nonlocality

Quantum entanglement is the quintessential characteristic of quantum
mechanics and the basis for quantum information processing. When one of two
maximally entangled particles is measured, without measurement the state of
another one is determined simultaneously no matter how far the two particles is
from each other. How can these phenomena take place since no object can move
faster than light speed in a vacuum? The key problem is due to the ignorance of
the interaction between a particle and a quantum vacuum. Just like the case
where a gun suffers recoil from its firing of a bullet, when a particle is
created from the quantum vacuum, the vacuum will be somewhat "broken"
correspondingly, which can be described by a shadow state in the vacuum.
Through their shadows in the vacuum two quantum entangled particles can have a
distance-independent instantaneous interaction with each other. Quantum
teleportation, quantum swap, and wave function collapse are explained in a
similar way. Quantum object can be interpreted as a composite made up of a
particle and the shadowed quantum vacuum which is responsible for the wave
characteristic of the particle wave duality. The quantum vacuum is not only the
origin of all possible kinds of particles, but also the origin and the core of
Eastern mystics.Comment: 6 pages, 2 figure

### New Physics Searches with Higgs-photon associated production at the Higgs Factory

The Higgs factory is designed for precise measurement of Higgs characters and
search for new physics. In this paper we propose that $e^+e^- \to \gamma h$
process could be a useful channel for new physics, which is normally expressed
model independently by effective field theory. We calculate the cross section
in both the Standard Model and effective field theory approach, and find that
the new physics effects of $\gamma h$ have only two degrees of freedom, much
fewer than the Higgsstrahlung process. This point could be used to reduce the
degeneracies of Wilson coefficients. We also calculated for the first time the
2$\sigma$ bounds of $\gamma h$ at the Higgs factory, and prove that $\gamma h$
is more sensitive to some dimension-6 operators than the current experimental
data. In the optimistic scenario new physics effects may be observed at the
CEPC or FCC-ee after the first couple of years of their run.Comment: 5 pages, 3 figures, submitted to Chinese Physics

### Mass minimizers and concentration for nonlinear Choquard equations in $\R^N$

In this paper, we study the existence of minimizers to the following
functional related to the nonlinear Choquard equation:
E(u)=\frac{1}{2}\ds\int_{\R^N}|\nabla
u|^2+\frac{1}{2}\ds\int_{\R^N}V(x)|u|^2-\frac{1}{2p}\ds\int_{\R^N}(I_\al*|u|^p)|u|^p
on $\widetilde{S}(c)=\{u\in H^1(\R^N)|\ \int_{\R^N}V(x)|u|^2<+\infty,\
|u|_2=c,c>0\},$where$N\geq1\al\in(0,N)$,$\frac{N+\alpha}{N}\leq
p<\frac{N+\alpha}{(N-2)_+}$and$I_\al:\R^N\rightarrow\R$is the Riesz
potential. We present sharp existence results for$E(u)$constrained on$\widetilde{S}(c)$when$V(x)\equiv0$for all$\frac{N+\alpha}{N}\leq
p<\frac{N+\alpha}{(N-2)_+}$. For the mass critical case$p=\frac{N+\alpha+2}{N}$, we show that if$0\leq V(x)\in
L_{loc}^{\infty}(\R^N)$and$\lim\limits_{|x|\rightarrow+\infty}V(x)=+\infty$,
then mass minimizers exist only if$0<c<c_*=|Q|_2$and concentrate at the
flattest minimum of$V$as$c$approaches$c_*$from below, where$Q$is a
groundstate solution of$-\Delta
u+u=(I_\alpha*|u|^{\frac{N+\alpha+2}{N}})|u|^{\frac{N+\alpha+2}{N}-2}u$in$\R^N$

### Bidirectional Recurrent Neural Networks for Medical Event Detection in Electronic Health Records

Sequence labeling for extraction of medical events and their attributes from
unstructured text in Electronic Health Record (EHR) notes is a key step towards
semantic understanding of EHRs. It has important applications in health
informatics including pharmacovigilance and drug surveillance. The state of the
art supervised machine learning models in this domain are based on Conditional
Random Fields (CRFs) with features calculated from fixed context windows. In
this application, we explored various recurrent neural network frameworks and
show that they significantly outperformed the CRF models.Comment: In proceedings of NAACL HLT 201

### Maximal hypersurfaces over exterior domains

In this paper, we study the exterior problem for the maximal surface
equation. We obtain the precise asymptotic behavior of the exterior solution at
infinity. And we prove that the exterior Dirichlet problem is uniquely solvable
given admissible boundary data and prescribed asymptotic behavior at infinity.Comment: 24 pages, 1 figur

### Calibrating Structured Output Predictors for Natural Language Processing

We address the problem of calibrating prediction confidence for output
entities of interest in natural language processing (NLP) applications. It is
important that NLP applications such as named entity recognition and question
answering produce calibrated confidence scores for their predictions,
especially if the system is to be deployed in a safety-critical domain such as
healthcare. However, the output space of such structured prediction models is
often too large to adapt binary or multi-class calibration methods directly. In
this study, we propose a general calibration scheme for output entities of
interest in neural-network based structured prediction models. Our proposed
method can be used with any binary class calibration scheme and a neural
network model. Additionally, we show that our calibration method can also be
used as an uncertainty-aware, entity-specific decoding step to improve the
performance of the underlying model at no additional training cost or data
requirements. We show that our method outperforms current calibration
techniques for named-entity-recognition, part-of-speech and question answering.
We also improve our model's performance from our decoding step across several
tasks and benchmark datasets. Our method improves the calibration and model
performance on out-of-domain test scenarios as well.Comment: ACL 2020; 9 pages + 4 page appendi

### Multi-modal Face Pose Estimation with Multi-task Manifold Deep Learning

Human face pose estimation aims at estimating the gazing direction or head
postures with 2D images. It gives some very important information such as
communicative gestures, saliency detection and so on, which attracts plenty of
attention recently. However, it is challenging because of complex background,
various orientations and face appearance visibility. Therefore, a descriptive
representation of face images and mapping it to poses are critical. In this
paper, we make use of multi-modal data and propose a novel face pose estimation
method that uses a novel deep learning framework named Multi-task Manifold Deep
Learning $M^2DL$. It is based on feature extraction with improved deep neural
networks and multi-modal mapping relationship with multi-task learning. In the
proposed deep learning based framework, Manifold Regularized Convolutional
Layers (MRCL) improve traditional convolutional layers by learning the
relationship among outputs of neurons. Besides, in the proposed mapping
relationship learning method, different modals of face representations are
naturally combined to learn the mapping function from face images to poses. In
this way, the computed mapping model with multiple tasks is improved.
Experimental results on three challenging benchmark datasets DPOSE, HPID and
BKHPD demonstrate the outstanding performance of $M^2DL$

### Histogram Transform-based Speaker Identification

A novel text-independent speaker identification (SI) method is proposed. This
method uses the Mel-frequency Cepstral coefficients (MFCCs) and the dynamic
information among adjacent frames as feature sets to capture speaker's
characteristics. In order to utilize dynamic information, we design super-MFCCs
features by cascading three neighboring MFCCs frames together. The probability
density function (PDF) of these super-MFCCs features is estimated by the
recently proposed histogram transform~(HT) method, which generates more
training data by random transforms to realize the histogram PDF estimation and
recedes the commonly occurred discontinuity problem in multivariate histograms
computing. Compared to the conventional PDF estimation methods, such as
Gaussian mixture models, the HT model shows promising improvement in the SI
performance.Comment: Technical Repor

### Neural Semantic Encoders

We present a memory augmented neural network for natural language
understanding: Neural Semantic Encoders. NSE is equipped with a novel memory
update rule and has a variable sized encoding memory that evolves over time and
maintains the understanding of input sequences through read}, compose and write
operations. NSE can also access multiple and shared memories. In this paper, we
demonstrated the effectiveness and the flexibility of NSE on five different
natural language tasks: natural language inference, question answering,
sentence classification, document sentiment analysis and machine translation
where NSE achieved state-of-the-art performance when evaluated on publically
available benchmarks. For example, our shared-memory model showed an
encouraging result on neural machine translation, improving an attention-based
baseline by approximately 1.0 BLEU.Comment: Accepted in EACL 2017, added: comparison with NTM, qualitative
analysis and memory visualizatio

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