623509 research outputs found
Sort by
On a cross-diffusion system arising in image denosing
Full text linkWe study a generalization of a cross-diffusion problem deduced from a
nonlinear complex-variable diffusion model for signal and image denoising.
We prove the existence of weak solutions of the time-independent problem with
fidelity terms under mild conditions on the data problem. Then, we show that
this translates on the well-posedness of a quasi-steady state approximation of
the evolution problem, and also prove the existence of weak solutions of the
latter under more restrictive hypothesis.
We finally perform some numerical simulations for image denoising, comparing
the performance of the cross-diffusion model and its corresponding scalar
Perona-Malik equation.Comment: To appear in Computers & Mathematics with Application
Variational characterization of the regularity of Monge-Brenier maps
Full text linkOn an abstract Wiener space, assume that T is the solution of the quadratic Monge problem associated to the Wiener measure and a second one with a Radon-Nikodym derivative of exponential type. Under the finite information hypothesis, using a variational method, we prove that T minimizes a certain functional originating from the large deviations theory. Applying a variational method a la Euler, we obtain the Sobolev regularity of the backward Monge-Brenier map. A similar result also holds for the forward Monge-Brenier map.arXiv admin note: text overlap with arXiv:math/0403497, arXiv:math/040710
A differentiable monoid of smooth maps on Lie groupoids
Full text linkIn this article we investigate a monoid of smooth mappings on the space of
arrows of a Lie groupoid and its group of units. The group of units turns out
to be an infinite-dimensional Lie group which is regular in the sense of
Milnor. Furthermore, this group is closely connected to the group of bisections
of the Lie groupoid. Under suitable conditions, i.e. the source map of the Lie
groupoid is proper, one also obtains a differentiable structure on the monoid
and can identify the bisection group as a Lie subgroup of its group of units.
Finally, relations between groupoids associated to the underlying Lie groupoid
and subgroups of the monoid are obtained. The key tool driving the
investigation is a generalisation of a result by A. Stacey which we establish
in the present article. This result, called the Stacey-Roberts Lemma, asserts
that pushforwards of submersions yield submersions between the
infinite-dimensional manifolds of mappings.Comment: 35 pages, v3: Step 4 in the proof of Lemma C.4 was critically flawed,
added explanation and reference to P. Steffens work arXiv:2404.07931 where a
correct argument is contained in Lemma 3.2.18. All results thus remain vali
The coarse index class with support
Full text linkWe construct the coarse index class with support condition (as an element of
coarse -homology) of an equivariant Dirac operator on a complete Riemannian
manifold endowed with a proper, isometric action of a group. We further show a
coarse relative index theorem and discuss the compatibility of the index with
the suspension isomorphism.Comment: 42 pages: revised version, Section on graded -categories and
algebras adde
An algorithm to find maximum area polygons circumscribed about a convex polygon
Full text linkA convex polygon Q is circumscribed about a convex polygon P if every vertex
of P lies on at least one side of Q. We present an algorithm for finding a
maximum area convex polygon circumscribed about any given convex n-gon in
O(n^3) time. As an application, we disprove a conjecture of Farris. Moreover,
for the special case of regular n-gons we find an explicit solution.Comment: In this version we correct an error in Theorem 4 of the published
versio
A Comprehensive Survey on Visual Question Answering Datasets and Algorithms
No full textVisual question answering (VQA) refers to the problem where, given an image and a natural language question about the image, a correct natural language answer has to be generated. A VQA model has to demonstrate both the visual understanding of the image and the semantic understanding of the question, demonstrating reasoning capability. Since the inception of this field, a plethora of VQA datasets and models have been published. In this article, we meticulously analyze the current state of VQA datasets and models, while cleanly dividing them into distinct categories and then summarizing the methodologies and characteristics of each category. We divide VQA datasets into four categories: (1) available datasets that contain a rich collection of authentic images, (2) synthetic datasets that contain only synthetic images produced through artificial means, (3) diagnostic datasets that are specially designed to test model performance in a particular area, e.g., understanding the scene text, and (4) KB (Knowledge-Based) datasets that are designed to measure a model\u27s ability to utilize outside knowledge. Concurrently, we explore six main paradigms of VQA models: fusion, where we discuss different methods of fusing information between visual and textual modalities; attention, the technique of using information from one modality to filter information from another; external knowledge base, where we discuss different models utilizing outside information; composition or reasoning, where we analyze techniques to answer advanced questions that require complex reasoning steps; explanation, which is the process of generating visual and textual descriptions to verify sound reasoning; and graph models, which encode and manipulate relationships through nodes in a graph. We also discuss some miscellaneous topics, such as scene text understanding, counting, and bias reduction
Continuously tunable coherent pulse generation in semiconductor lasers
No full textIn a laser, the control of its spectral emission depends on the physical dimensions of the optical resonator, limiting it to a set of discrete cavity modes at specific frequencies. Here, we overcome this fundamental limit by demonstrating a monolithic semiconductor laser with a continuously tunable repetition rate from 4 up to 16 GHz, by employing a microwave driving signal that induces a spatiotemporal gain modulation along the entire laser cavity, generating intracavity mode-locked pulses with a continuously tunable group velocity. At the output, frequency combs with continuously tunable mode spacings are generated in the frequency domain, and coherent pulse trains with continuously tunable repetition rates are generated in the time domain. Our results pave the way for fully tunable chip-scale lasers and frequency combs, advantageous for use in a diverse variety of fields, from fundamental studies to applications such as high-resolution and dual-comb spectroscopy.9 pages, 5 figure
A new view of the Spiral Structure of the Northern Outer Milky Way in Carbon Monoxide
No full textBased on 32162 molecular clouds from the Milky Way Imaging Scroll Painting project, we obtain new face-on molecular gas maps of the northern outer Galaxy. The total molecular gas surface density map reveals three segments of spirals, extending 16-43 kiloparsecs in length. The Perseus and Outer arms stand out prominently, appearing as quasi-continuous structures along most of their length. At the Galactic outskirts, about 1306 clouds connect the two segments of the new spiral arm discovered by Dame & Thaddeus (2011) in the first quadrant and Sun et al. (2015) in the second quadrant, possibly extending the arm into the outer third quadrant. Logarithmic spirals can be fitted to the CO arm segments with pitch angles ranging from 4 to 12 degree. These CO arms extend beyond previous CO studies and the optical radius, reaching a galactic radius of about 22 kiloparsecs, comparable to the HI radial range.10 pages, 4 figures, 1 table, ApJL accepte
Numerical Methods for Optimal Control Problems with SPDEs
No full textThis paper investigates numerical methods for solving stochastic linear quadratic (SLQ) optimal control problems governed by stochastic partial differential equations (SPDEs). Two distinct approaches, the open-loop and closed-loop ones, are developed to ensure convergence rates in the fully discrete setting. The open-loop approach, utilizing the finite element method for spatial discretization and the Euler method for temporal discretization, addresses the complexities of coupled forward-backward SPDEs and employs a gradient descent framework suited for high-dimensional spaces. Separately, the closed-loop approach applies a feedback strategy, focusing on Riccati equation for spatio-temporal discretization. Both approaches are rigorously designed to handle the challenges of fully discrete SLQ problems, providing rigorous convergence rates and computational frameworks
ESTVocoder: An Excitation-Spectral-Transformed Neural Vocoder Conditioned on Mel Spectrogram
No full textThis paper proposes ESTVocoder, a novel excitation-spectral-transformed neural vocoder within the framework of source-filter theory. The ESTVocoder transforms the amplitude and phase spectra of the excitation into the corresponding speech amplitude and phase spectra using a neural filter whose backbone is ConvNeXt v2 blocks. Finally, the speech waveform is reconstructed through the inverse short-time Fourier transform (ISTFT). The excitation is constructed based on the F0: for voiced segments, it contains full harmonic information, while for unvoiced segments, it is represented by noise. The excitation provides the filter with prior knowledge of the amplitude and phase patterns, expecting to reduce the modeling difficulty compared to conventional neural vocoders. To ensure the fidelity of the synthesized speech, an adversarial training strategy is applied to ESTVocoder with multi-scale and multi-resolution discriminators. Analysis-synthesis and text-to-speech experiments both confirm that our proposed ESTVocoder outperforms or is comparable to other baseline neural vocoders, e.g., HiFi-GAN, SiFi-GAN, and Vocos, in terms of synthesized speech quality, with a reasonable model complexity and generation speed. Additional analysis experiments also demonstrate that the introduced excitation effectively accelerates the model\u27s convergence process, thanks to the speech spectral prior information contained in the excitation.Accepted by NCMMSC202