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It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…
We propose symmetric power transformation to enhance the capacity of Implicit Neural Representation~(INR) from the perspective of data transformation. Unlike prior work utilizing random permutation or index rearrangement, our method…
Nonlinear processes in the quantum regime are essential for many applications, such as quantum-limited amplification, measurement and control of quantum systems. In particular, the field of quantum error correction relies heavily on…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
We consider the representation of operators in terms of tensor networks and their application to ground-state approximation and time evolution of systems with long-range interactions. We provide an explicit construction to represent an…
High-order bases provide major advantages over linear ones in terms of efficiency, as they provide (for the same physical model) higher accuracy for the same running time, and reliability, as they are less affected by locking artifacts and…
In the control of classical mechanical systems, the feedback has been successfully applied to the production of the desired nonlinear dynamics. However, how much this can be done is still an open problem in quantum mechanical systems. This…
We report a class of symmetry-intergable third-order evolution equations in 1+1 dimensions under the condition that the equations admit a second-order recursion operator that contains an adjoint symmetry (integrating factor) of order six.…
We study the two-dimensional Dirac operator with an arbitrary combination of electrostatic and Lorentz scalar $\delta$-interactions of constant strengths supported on a smooth closed curve. For any combination of the coupling constants a…
Human beings process stereoscopic correspondence across multiple scales. However, this bio-inspiration is ignored by state-of-the-art cost aggregation methods for dense stereo correspondence. In this paper, a generic cross-scale cost…
This paper introduces IRIS, an Immersive Robot Interaction System leveraging Extended Reality (XR). Existing XR-based systems enable efficient data collection but are often challenging to reproduce and reuse due to their specificity to…
Given a bounded linear operator $T$ on separable Hilbert space, we develop an approach allowing one to construct a matrix representation for $T$ having certain specified algebraic or asymptotic structure. We obtain matrix representations…
We analyze the parabolic Dirac operator $D \pm i\partial_t$ in a biquaternionic setting, characterizing its kernel via generalized div-curl systems and Cauchy-Riemann-type relations between the real and imaginary parts. Using the machinery…
Integral equation methods for the solution of partial differential equations, when coupled with suitable fast algorithms, yield geometrically flexible, asymptotically optimal and well-conditioned schemes in either interior or exterior…
We give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries. We in particular discuss decomposition methods, which reduce the problem to a number of…
Planning contact interactions is one of the core challenges of many robotic tasks. Optimizing contact locations while taking dynamics into account is computationally costly and, in environments that are only partially observable, executing…
Solving systems of polynomial equations, particularly those with finitely many solutions, is a crucial challenge across many scientific fields. Traditional methods like Gr\"obner and Border bases are fundamental but suffer from high…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…
Global discrete optimization is notoriously difficult due to the lack of gradient information and the curse of dimensionality, making exhaustive search infeasible. Tensor cross approximation is an efficient technique to approximate…
Even for simple arithmetic tasks like integer addition, it is challenging for Transformers to generalize to longer sequences than those encountered during training. To tackle this problem, we propose position coupling, a simple yet…