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In the paper, we consider the solvability of the two-dimensional Navier-Stokes equations in an exterior unit disk. On the boundary of the disk, the tangential velocity is subject to the perturbation of a rotation, and the normal velocity is subject to the perturbation of an interior sources or sinks. At infinity, the flow stays at rest. We will construct a solution to such problem, whose principal part admits a critical decay $O(|x|^{-1})$. The result is related to an open problem raised by V. I. Yudovich in [{\it Eleven great problems of mathematical hydrodynamics}, Mosc. Math. J. 3 (2003), no. 2, 711--737], where Problem 2b states that: {\em Prove or disprove the global existence of stationary and periodic flows of a viscous incompressible fluid in the presence of interior sources and sinks.} Our result partially gives a positive answer to this open in the exterior disk for the case when the interior source or sink is a perturbation of the constant state.

We investigate the acoustical characteristics of the Chinese transverse flute, the dizi, employing input impedance measurements, modeling and analysis. The input impedances for various fingerings of a bangdi in the key of F, a particular type of the dizi, are measured and compared to models using both the transfer matrix method and the Transfer Matrix Method with external Interaction (TMMI). In order to get more accurate modeling results, we provide specific transfer matrices for the unique components of the dizi, such as back end-holes, membrane hole and upstream branch. The matching volume length correction for holes drilled in a thick wall is also derived. Comparative analysis of modeling and measurement data validates the improved accuracy of TMMI, confirming the influence of radiated sound from closely spaced toneholes., Comment: 11 pages, 11 figures

AI systems for high quality music generation typically rely on extremely large musical datasets to train the AI models. This creates barriers to generating music beyond the genres represented in dominant datasets such as Western Classical music or pop music. We undertook a 4 month international research project summarised in this paper to explore the eXplainable AI (XAI) challenges and opportunities associated with reducing barriers to using marginalised genres of music with AI models. XAI opportunities identified included topics of improving transparency and control of AI models, explaining the ethics and bias of AI models, fine tuning large models with small datasets to reduce bias, and explaining style-transfer opportunities with AI models. Participants in the research emphasised that whilst it is hard to work with small datasets such as marginalised music and AI, such approaches strengthen cultural representation of underrepresented cultures and contribute to addressing issues of bias of deep learning models. We are now building on this project to bring together a global International Responsible AI Music community and invite people to join our network., Comment: In Proceedings of Explainable AI for the Arts Workshop 2024 (XAIxArts 2024) arXiv:2406.14485

We consider the generalized Leray's problem with the Navier-slip boundary condition in an infinite pipe $\mathcal{D}=\Sigma\times\mathbb{R}$. We show that if the flux $\Phi$ of the solution is no larger than a critical value that is \emph{independent with the friction ratio} of the Navier-slip boundary condition, the solution to the problem must be the parallel Poiseuille flow with the given flux. Compared with known related 3D results, this seems to be the first conclusion with the size of critical flux being uniform with the friction ratio $\alpha\in]0,\infty]$, and it is surprising since the prescribed uniqueness breaks down immediately when $\alpha=0$, even if $\Phi=0$. Our proof relies primarily on a refined gradient estimate of the Poiseuille flow with the Navier-slip boundary condition. Additionally, we prove the critical flux $\Phi_0\geq\frac{\pi}{16}$ provided that $\Sigma$ is a unit disk., Comment: 20 pages. All comments are welcome!

This second international workshop on explainable AI for the Arts (XAIxArts) brought together a community of researchers in HCI, Interaction Design, AI, explainable AI (XAI), and digital arts to explore the role of XAI for the Arts. Workshop held at the 16th ACM Conference on Creativity and Cognition (C&C 2024), Chicago, USA., Comment: Proceedings of The second international workshop on eXplainable AI for the Arts (XAIxArts)

In this paper, we study the local well-posedness of classical solutions to the ideal Hall-MHD equations whose magnetic field is supposed to be azimuthal in the $L^2$-based Sobolev spaces. By introducing a good unknown coupling with the original unknowns, we overcome difficulties arising from the lack of magnetic resistance, and establish a self-closed $H^m$ with $(3\leq m\in\mathbb{N})$ local energy estimate of the system. Here, a key cancellation related to $\theta$ derivatives is discovered. In order to apply this cancellation, part of the high-order energy estimates is performed in the cylindrical coordinate system, even though our solution is not assumed to be axially symmetric. During the proof, high-order derivative tensors of unknowns in the cylindrical coordinates system are carefully calculated, which would be useful in further researches on related topics., Comment: 23 pages. All comments are welcome!

This first international workshop on explainable AI for the Arts (XAIxArts) brought together a community of researchers in HCI, Interaction Design, AI, explainable AI (XAI), and digital arts to explore the role of XAI for the Arts. Workshop held at the 15th ACM Conference on Creativity and Cognition (C&C 2023).

This paper aims to develop a holistic evaluation method for piano sound quality to assist in purchasing decisions. Unlike previous studies that focused on the effect of piano performance techniques on sound quality, this study evaluates the inherent sound quality of different pianos. To derive quality evaluation systems, the study uses subjective questionnaires based on a piano sound quality dataset. The method selects the optimal piano classification models by comparing the fine-tuning results of different pre-training models of Convolutional Neural Networks (CNN). To improve the interpretability of the models, the study applies Equivalent Rectangular Bandwidth (ERB) analysis. The results reveal that musically trained individuals are better able to distinguish between the sound quality differences of different pianos. The best fine-tuned CNN pre-trained backbone achieves a high accuracy of 98.3\% as the piano classifier. However, the dataset is limited, and the audio is sliced to increase its quantity, resulting in a lack of diversity and balance, so we use focal loss to reduce the impact of data imbalance. To optimize the method, the dataset will be expanded, or few-shot learning techniques will be employed in future research.

In this paper, we obtain a refined temporal asymptotic upper bound of the global axially symmetric solution to the Boussinesq system with no thermal diffusivity. We show the spacial $W^{1,p}$-Sobolev ($2\leq p<\infty$) norm of the velocity can only grow at most algebraically as $t\to+\infty$. Under a signed potential condition imposed on the initial data, we further derive that the aforementioned norm is uniformly bounded at all times. Higher order estimates are also given: We find the $H^1$ norm of the temperature fluctuation grows sub-exponentially as $t\to+\infty$. Meanwhile, for any $m\geq 1$, we deduce that the $H^m$-temporal growth of the solution is slower than a double exponential function. As a result, these improve the results in \cite{HR:2010AIHP} where the authors only provided rough temporal asymptotic upper bounds while proving the global well-posedness., Comment: Minor revision

In this paper, we will solve the Leray's problem for the stationary Navier-Stokes system in a 2D infinite distorted strip with the Navier-slip boundary condition. The existence, uniqueness, regularity and asymptotic behavior of the solution will be investigated. Moreover, we discuss how the friction coefficient affects the well-posedness of the solution. Due to the validity of the Korn's inequality, all constants in each a priori estimate are independent of the friction coefficient. The main novelty is the total flux of the velocity can be relatively large (proportional to the {\it slip length}) when the friction coefficient of the Navier-slip boundary condition is small, which is essentially different from the 3D case., Comment: 45 pages. arXiv admin note: text overlap with arXiv:2204.10578. A remark is added to state the independent accomplishment of solving the 2D Leray's problem with the Navier-slip boundary condition by our group and Professor Chunjing Xie's group

Let $D$ be the exterior of a cone inside a ball, with its altitude angle at most $\pi/6$ in $\mathbb{R}^3$, which touches the $x_3$ axis at the origin. For any initial value $v_0 = v_{0,r}e_{r} + v_{0,\theta} e_{\theta} + v_{0,3} e_{3}$ in a $C^2(\overline{D})$ class, which has the usual even-odd-odd symmetry in the $x_3$ variable and has the partial smallness only in the swirl direction: $ | r v_{0, \theta} | \leq \frac{1}{100}$, the axially symmetric Navier-Stokes equations (ASNS) with Navier-Hodge-Lions slip boundary condition has a finite-energy solution that stays bounded for all time. In particular, no finite-time blowup of the fluid velocity occurs. Compared with standard smallness assumptions on the initial velocity, no size restriction is made on the components $v_{0,r}$ and $v_{0,3}$. In a broad sense, this result appears to solve $2/3$ of the regularity problem of ASNS in such domains in the class of solutions with the above symmetry. Equivalently, this result is connected to the general open question which asks that if an absolute smallness of one component of the initial velocity implies the global smoothness, see e.g. page 873 in \cite{CZZ17}. Our result seems to give a positive answer in a special setting. As a byproduct, we also construct an unbounded solution of the forced Navier Stokes equation in a special cusp domain that has finite energy. The forcing term, with the scaling factor of $-1$, is in the standard regularity class. This result confirms the intuition that if the channel of a fluid is very thin, arbitrarily high speed in the classical sense can be attained under a mildly singular force which is physically reasonable in view that Newtonian gravity and Coulomb force have scaling factor $-2$., Comment: 85 pages. A blow up solution in a special cusp domain, two references and a few sentences added

The original Leray's problem concerns the well-posedness of weak solutions to the steady incompressible Navier-Stokes equations in a distorted pipe, which approach to the Poiseuille flow subject to the no-slip boundary condition at spacial infinity. In this paper, the same problem with the Navier-slip boundary condition instead of the no-slip boundary condition, is addressed. Due to the complexity of the boundary condition, some new ideas, presented as follows, are introduced to handle the extra difficulties caused by boundary terms. First, the Poiseuille flow in the semi-infinite straight pipe with the Navier-slip boundary condition will be introduced, which will be served as the asymptotic profile of the solution to the generalized Leray's problem at spacial infinity. Second, a solenoidal vector function defined in the whole pipe, satisfying the Navier-slip boundary condition, having the designated flux and equalling to the Poiseuille flow at large distance, will be carefully constructed. This plays an important role in reformulating our problem. Third, the energy estimates depend on a combined $L^2$ estimate of the gradient and the stress tensor of the velocity.

Smooth solutions of the stationary Navier-Stokes equations in an infinitely long pipe, equipped with the Navier-slip or Navier-Hodge-Lions boundary condition, are considered in this paper. Three main results are presented. First, when equipped with the Navier-slip boundary condition, it is shown that, $W^{1,\infty}$ axially symmetric solutions with zero flux at one cross section, must be swirling solutions: $u=(- C x_2, C x_1,0)$, and $x_3-$periodic solutions must be helical solutions: $u=(-C_1x_2,C_1x_1,C_2)$. Second, also equipped with the Navier-slip boundary condition, if the swirl or vertical component of the axially symmetric solution is independent of the vertical variable $x_3$, solutions are also proven to be helical solutions. In the case of the vertical component being independent of $x_3$, the $W^{1,\infty}$ assumption is not needed. In the case of the swirl component being independent of $x_3$, the $W^{1,\infty}$ assumption can be relaxed extensively such that the horizontal radial component of the velocity, $u_r$, can grow exponentially with respect to the distance to the origin. Also, by constructing a counterexample, we show that the growing assumption on $u_r$ is optimal. Third, when equipped with the Navier-Hodge-Lions boundary condition, we can show that if the gradient of the velocity grows sublinearly, then the solution, enjoying the Liouville-type theorem, is a trivial shear flow: $(0,0,C)$., Comment: Compared to the previous version, title is chagned. Two new resutls is added and one result is improved. Also one new contributed author is added

In this paper, we consider regularity criteria of a class of 3D axially symmetric MHD-Boussinesq systems without magnetic resistivity or thermal diffusivity. Under some Prodi-Serrin type critical assumptions on the horizontal angular component of the velocity, we will prove that strong solutions of the axially symmetric MHD-Boussinesq system can be smoothly extended beyond the possible blow-up time $T_\ast$ if the magnetic field contains only the horizontal swirl component. No a priori assumption on the magnetic field and the temperature fluctuation is imposed., Comment: 20 pages, all comments are welcome

Singing voice conversion is converting the timbre in the source singing to the target speaker's voice while keeping singing content the same. However, singing data for target speaker is much more difficult to collect compared with normal speech data.In this paper, we introduce a singing voice conversion algorithm that is capable of generating high quality target speaker's singing using only his/her normal speech data. First, we manage to integrate the training and conversion process of speech and singing into one framework by unifying the features used in standard speech synthesis system and singing synthesis system. In this way, normal speech data can also contribute to singing voice conversion training, making the singing voice conversion system more robust especially when the singing database is small.Moreover, in order to achieve one-shot singing voice conversion, a speaker embedding module is developed using both speech and singing data, which provides target speaker identify information during conversion. Experiments indicate proposed sing conversion system can convert source singing to target speaker's high-quality singing with only 20 seconds of target speaker's enrollment speech data., Comment: Accepted by Interspeech 2020

In this paper, we derive asymptotic properties of both the velocity and the vorticity fields to the 3-dimensional axially symmetric Navier-Stokes equations at infinity under the generalized D-solution assumption $\int_{\mathbb{R}^3}|\nabla u|^qdx<\infty$ for $2

We propose an algorithm that is capable of synthesizing high quality target speaker's singing voice given only their normal speech samples. The proposed algorithm first integrate speech and singing synthesis into a unified framework, and learns universal speaker embeddings that are shareable between speech and singing synthesis tasks. Specifically, the speaker embeddings learned from normal speech via the speech synthesis objective are shared with those learned from singing samples via the singing synthesis objective in the unified training framework. This makes the learned speaker embedding a transferable representation for both speaking and singing. We evaluate the proposed algorithm on singing voice conversion task where the content of original singing is covered with the timbre of another speaker's voice learned purely from their normal speech samples. Our experiments indicate that the proposed algorithm generates high-quality singing voices that sound highly similar to target speaker's voice given only his or her normal speech samples. We believe that proposed algorithm will open up new opportunities for singing synthesis and conversion for broader users and applications., Comment: Submitted to ICASSP-2020

Unlike melody extraction and other aspects of music transcription, research on playing technique detection is still in its early stages. Compared to existing work mostly focused on playing technique detection for individual single notes, we propose a general end-to-end method based on Sound Event Detection by FCN for musical instrument playing technique detection. In our case, we choose Erhu, a well-known Chinese bowed-stringed instrument, to experiment with our method. Because of the limitation of FCN, we present an algorithm to detect on variable length audio. The effectiveness of the proposed framework is tested on a new dataset, its categorization of techniques is similar to our training dataset. The highest accuracy of our 3 experiments on the new test set is 87.31%. Furthermore, we also evaluate the performance of the proposed framework on 10 real-world studio music (produced by midi) and 7 real-world recording samples to address the ability of generalization on our model., Comment: Submitted to ICASSP 2020

In the paper \cite{KNSS:1}, the authors make the following conjecture: {\it any bounded ancient mild solution of the 3D axially symmetric Navier-Stokes equations is constant.} And it is proved in the case that the solution is swirl free. Our purpose of this paper is to improve their result by allowing that the solution can grow with a power smaller than 1 with respect to the distance to the origin. Also, we will show that such a power is optimal to prove the Liouville type theorem since we can find counterexamples for the Navier-Stokes equations such that the Liouville theorem fails if the solution can grow linearly., Comment: 10 pages

In this paper, we study the stationary magnetohydrodynamics system in $\mathbb{R}^2\times\mathbb{T}$. We prove trivialness of D-solutions (the velocity field $u$ and the magnetic field $h$) when they are swirl-free. Meanwhile, this Liouville type theorem also holds provided $u$ is swirl-free and $h$ is axially symmetric, or both $u$ and $h$ are axially symmetric. Our method is also valid for certain related boundary value problems in the slab $\mathbb{R}^2\times[-\pi,\,\pi]$., Comment: 16 pages

Two main results will be presented in our paper. First, we will prove the regularity of solutions to axially symmetric Navier-Stokes equations under a $log$ supercritical assumption on the horizontally radial component $u^r$ and vertical component $u^z$, accompanied by a $log$ subcritical assumption on the horizontally angular component $u^\theta$ of the velocity. Second, the precise Green function for the operator $-(\Delta-\frac{1}{r^2})$ under the axially symmetric situation, where $r$ is the distance to the symmetric axis, and some weighted $L^p$ estimates of it will be given. This will serve as a tool for the study of axially symmetric Navier-Stokes equations. As an application, we will prove the regularity of solutions to axially symmetric Navier-Stokes equations under a critical (or a subcritical) assumption on the angular component $w^\theta$ of the vorticity., Comment: Final version, to appear in Comm. Pure Appl. Anal

In this paper, we study the finite-time blow up of solutions to the following semilinear wave equation with time-dependent damping \[ \partial_t^2u-\Delta u+\frac{\mu}{1+t}\partial_tu=|u|^p \] in $\mathbb{R}_{+}\times\mathbb{R}^n$. More precisely, for $0\leq\mu\leq 2,\mu \neq1$ and $n\geq 2$, there is no global solution for $1

We prove H\"older continuity of weak solutions of the uniformly elliptic and parabolic equations %$\Delta u-\frac{A}{|x|^{2+\beta}}u=0,\,\,(\beta\geq 0)$, and variable second order term coefficients case $%% \begin{equation}\label{01} \partial_{i} (a_{ij}(x) \partial_{j}u(x)) - \frac{A}{|x|^{2+\beta}} u(x) =0\quad (A>0,\quad\beta\geq 0), \end{equation} \begin{equation}\label{02} \partial_{i} (a_{ij}(x,t) \partial_{j}u(x,t)) - \frac{A}{|x|^{2+\beta}} u(x,t)-\partial_{t}u(x,t) =0\quad (A>0,\quad\beta\geq 0), \end{equation} with critical or supercritical 0-order term coefficients which are beyond De Giorgi-Nash-Moser's Theory. We also prove, in some special cases, weak solutions are even differentiable. Previously P. Baras and J. A. Goldstein \cite{Baras1984} treated the case when $A<0$, $(a_{ij})=I$ and $\beta=0$ for which they show that there does not exist any regular positive solution or singular positive solutions, depending on the size of $|A|$. When $A>0$, $\beta=0$ and $(a_{ij})=I$, P. D. Milman and Y. A. Semenov \cite{Milman2003}\cite{Milman2004} obtain bounds for the heat kernel., Comment: 32 pages