arXiv subjects

Akash Anand

Publications and source records attributed to Akash Anand.

22 records · Page 2Linked to original sources

arXiv2018

Wearable Audio and IMU Based Shot Detection in Racquet Sports

Wearables like smartwatches which are embedded with sensors and powerful processors, provide a strong platform for development of analytics solutions in sports domain. To analyze players' games, while motion sensor based shot detection has been extensively studied in sports like Tennis, Golf, Baseball; Table Tennis and Badminton are relatively less explored due to possible less intense hand motion during shots. In our paper, we propose a novel, computationally inexpensive and real-time system for shot detection in table tennis, based on fusion of Inertial Measurement Unit (IMU) and audio sensor data embedded in a wrist-worn wearable. The system builds upon our presented methodology for synchronizing IMU and audio sensor input in time using detected shots and achieves 95.6% accuracy. To our knowledge, it is the first fusion-based solution for sports analysis in wearables. Shot detectors for other racquet sports as well as further analytics to provide features like shot classification, rally analysis and recommendations, can easily be built over our proposed solution.

cs.LG↗

arXiv2017

A Nyström-based finite element method on polygonal elements

We consider families of finite elements on polygonal meshes, that are defined implicitly on each mesh cell as solutions of local Poisson problems with polynomial data. Functions in the local space on each mesh cell are evaluated via Nyström discretizations of associated integral equations, allowing for curvilinear polygons and non-polynomial boundary data. Several experiments demonstrate the approximation quality of interpolated functions in these spaces.

math.NA↗

arXiv2016

Module tensor product of subnormal modules need not be subnormal

Let $κ: \mathbb D \times \mathbb D \to \mathbb C$ be a diagonal positive definite kernel and let $\mathscr H_κ$ denote the associated reproducing kernel Hilbert space of holomorphic functions on the open unit disc $\mathbb D$. Assume that $zf \in \mathscr H$ whenever $f \in \mathscr H.$ Then $\mathscr H$ is a Hilbert module over the polynomial ring $\mathbb C[z]$ with module action $p \cdot f \mapsto pf$. We say that $\mathscr H_κ$ is a subnormal Hilbert module if the operator $\mathscr M_{z}$ of multiplication by the coordinate function $z$ on $\mathscr H_κ$ is subnormal. %If $κ_1$ and $κ_2$ are two diagonal positive definite kernels then so is their pointwise (tensor) product $κ:=κ_1κ_2$. In [Oper. Theory Adv. Appl, 32: 219-241, 1988], N. Salinas asked whether the module tensor product $\mathscr H_{κ_1} \otimes_{\mathbb C[z]} \mathscr H_{κ_2}$ of subnormal Hilbert modules $\mathscr H_{κ_1}$ and $\mathscr H_{κ_2}$ is again subnormal. In this regard, we describe all subnormal module tensor products $L^2_a(\mathbb D, w_{s_1}) \otimes_{\mathbb C[z]} L^2_a(\mathbb D, w_{s_2})$, where $L^2_a(\mathbb D, w_s)$ denotes the weighted Bergman Hilbert module with radial weight $$w_s(z)=\frac{1}{s π}|z|^{\frac{2(1-s)}{s}}~(z \in \mathbb D, ~s > 0).$$ In particular, the module tensor product $L^2_a(\mathbb D, w_{s}) \otimes_{\mathbb C[z]} L^2_a(\mathbb D, w_{s})$ is never subnormal for any $s \geq 6$. Thus the answer to this question is no.

math.FA↗

arXiv2015

An efficient high-order Nyström scheme for acoustic scattering by inhomogeneous penetrable media with discontinuous material interface

This text proposes a fast, rapidly convergent Nyström method for the solution of the Lippmann-Schwinger integral equation that mathematically models the scattering of time-harmonic acoustic waves by inhomogeneous obstacles, while allowing the material properties to jump across the interface. The method works with overlapping coordinate charts as a description of the given scatterer. In particular, it employs "partitions of unity" to simplify the implementation of high-order quadratures along with suitable changes of parametric variables to analytically resolve the singularities present in the integral operator to achieve desired accuracies in approximations. To deal with the discontinuous material interface in a high-order manner, a specialized quadrature is used in the boundary region. The approach further utilizes an FFT based strategy that uses equivalent source approximations to accelerate the evaluation of large number of interactions that arise in the approximation of the volumetric integral operator and thus achieves a reduced computational complexity of $O(N \log N)$ for an $N$-point discretization. A detailed discussion on the solution methodology along with a variety of numerical experiments to exemplify its performance in terms of both speed and accuracy are presented in this paper.

math.NA↗