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Takeshi Sasaki

Publications and source records attributed to Takeshi Sasaki.

12 recordsLinked to original sources

A Human-Inspired Decoupled Architecture for Efficient Audio Representation Learning

While self-supervised learning (SSL) has revolutionized audio representation, the excessive parameterization and quadratic computational cost of standard Transformers limit their deployment on resource-constrained devices. To address this bottleneck, we propose HEAR (Human-inspired Efficient Audio Representation), a novel decoupled architecture. Inspired by the human cognitive ability to isolate local acoustic features from global context, HEAR splits the processing pipeline into two dedicated modules: an Acoustic Model for local feature extraction and a Task Model for global semantic integration. Coupled with an Acoustic Tokenizer trained via knowledge distillation, our approach enables robust Masked Audio Modeling (MAM). Extensive experiments demonstrate that HEAR requires only 15M parameters and 9.47 GFLOPs for inference, operating at a fraction of the computational cost of conventional foundation models (which typically require 85M-94M parameters). Despite this high efficiency, HEAR achieves highly competitive performance across diverse audio classification benchmarks. The code and pre-trained models are available at https://github.com/HarunoriKawano/HEAR

cs.SD

Shift operators of the Dotsenko-Fateev equation and its higher order versions

We find shift operators for the Dotsenko-Fateev equation, which is a differential equation of order 3, and for the three Fuchsian differential equations of order 4, 5 and 6, respectively, which are connected with the Dotsenko-Fateev equation via addition and middle convolution. These shift operators are used to study reducible cases.

math.CA

Fuchsian differential equations of order 3,...,6 with three singular points and an accessory parameter II, Equations of order 3

Fuchsian differential equations of order 3 with three singular points and with an accessory parameter are studied. When local exponents are generic, no shift operator is found, for codimension-1 subfamilies, neither. We found shift operators for several codimension-2 subfamilies of which accessory parameter is assigned as a cubic polynomial in the local exponents. The Dotsenko-Fateev equation is one of them.

math.CA

A study of a Fuchsian system of rank 8 in 3 variables and the ordinary differential equations as its restrictions

A Fuchsian system of rank 8 in 3 variables with 4 parameters is presented. The singular locus consists of six planes and a cubic surface. The restriction of the system onto the intersection of two singular planes is an ordinary differential equation of order four with three singular points. A middle convolution of this equation turns out to be the tensor product of two Gauss hypergeometric equation, and another middle convolution sends this equation to the Dotsenko-Fateev equation. Local solutions to these ordinary differential equations are found. Their coefficients are sums of products of the Gamma functions. These sums can be expressed as special values of the generalized hypergeometric series $_4F_3$ at 1. Keywords: Fuchsian differential equation, hypergeometric differential equation, middle convolution, Dotsenko-Fateev equation, recurrence formula, series solution

math.CA

General-affine invariants of plane curves and space curves

We present a fundamental theory of curves in the affine plane and the affine space, equipped with the general-affine groups ${\rm GA}(2)={\rm GL}(2,{\bf R})\ltimes {\bf R}^2$ and ${\rm GA}(3)={\rm GL}(3,{\bf R})\ltimes {\bf R}^3$, respectively. We define general-affine length parameter and curvatures and show how such invariants determine the curve up to general-affine motions. We then study the extremal problem of the general-affine length functional and derive a variational formula. We give several examples of curves and also discuss some relations with equiaffine treatment and projective treatment of curves.

math.DG

Discrete flat surfaces and linear Weingarten surfaces in hyperbolic 3-space

We define discrete flat surfaces in hyperbolic 3-space from the perspective of discrete integrable systems and prove properties that justify the definition. We show how these surfaces correspond to previously defined discrete constant mean curvature 1 surfaces in hyperbolic 3-space, and we also describe discrete focal surfaces (discrete caustics) that can be used to define singularities on discrete flat surfaces. We also examine discrete linear Weingarten surfaces of Bryant type in hyperbolic 3-space, and consider an example of a discrete flat surface related to the Airy equation that exhibits swallowtail singularities and a Stokes phenomenon.

math.DG

Tests of Non-Equivalence among Absolutely Nonsingular Tensors through Geometric Invariants

4x4x3 absolutely nonsingular tensors are characterized by their determinant polynomial. Non-quivalence among absolutely nonsingular tensors with respect to a class of linear transformations, which do not chage the tensor rank,is studied. It is shown theoretically that affine geometric invariants of the constant surface of a determinant polynomial is useful to discriminate non-equivalence among absolutely nonsingular tensors. Also numerical caluculations are presented and these invariants are shown to be useful indeed. For the caluculation of invarinats by 20-spherical design is also commented. We showed that an algebraic problem in tensor data analysis can be attacked by an affine geometric method.

stat.OT

Method to determine argon metastable number density and plasma electron temperature from spectral emission originating from four 4p argon levels

A simple model and method is proposed here to determine argon metastable number densities and electron temperature with the assumption of a Maxwell-Boltzmann electron energy distribution. This method is based on the availability of experimental relative emission intensities of only four argon lines that originate from any of the 4p argon levels. The proposed model has a relatively wide range of validity for laboratory plasmas that contain argon gas and can be a valuable tool for the emerging field of atmospheric microplasmas, for which diagnostics is still limited.

physics.plasm-ph

Hyperbolic Schwarz map for the hypergeometric differential equation

The Schwarz map of the hypergeometric differential equation is studied since the beginning of the last century. Its target is the complex projective line, the 2-sphere. This paper introduces the hyperbolic Schwarz map, whose target is the hyperbolic 3-space. This map can be considered to be a lifting to the 3-space of the Schwarz map. This paper studies the singularities of this map, and visualize its image when the monodromy group is a finite group or a typical Fuchsian group. General cases will be treated in a forthcoming paper.

math.CA

Derived Schwarz map of the hypergeometric differential equation and a parallel family of flat fronts

In the previous paper (math.CA/0609196) we defined a map, called the hyperbolic Schwarz map, from the one-dimensional projective space to the three-dimensional hyperbolic space by use of solutions of the hypergeometric differential equation, and thus obtained closed flat surfaces belonging to the class of flat fronts. We continue the study of such flat fronts in this paper. First, we introduce the notion of derived Schwarz maps of the hypergeometric differential equation and, second, we construct a parallel family of flat fronts connecting the classical Schwarz map and the derived Schwarz map.

math.CA