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The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
We identify explicitly the fractional power spaces for the $L^2$ Dirichlet Laplacian and Dirichlet Stokes operators using the theory of real interpolation. The results are not new, but we hope that our arguments are relatively accessible.
All-optical image processing offers a high-speed, energy-efficient alternative to conventional electronic systems by leveraging the wave nature of light for parallel computation. However, traditional optical processors rely on bulky…
The aim of this dissertation is to clarify the structure of entanglement, a type of quantum correlations, in various quantum systems with a large number of degrees of freedom for holography between generic quantum systems and spacetimes…
Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…
The theory of asymptotic complexity provides an approach to characterizing the behavior of programs in terms of bounds on the number of computational steps executed or use of computational resources. We describe work using ACL2 to prove…
Articulated objects (e.g., doors and drawers) exist everywhere in our life. Different from rigid objects, articulated objects have higher degrees of freedom and are rich in geometries, semantics, and part functions. Modeling different kinds…
We present Encapsulated Substitution and Agentic Refinement on a Live Scaffold for Safe C-to-Rust Translation, a two-phase pipeline for translating real-world C projects to safe Rust. Existing approaches either produce unsafe output without…
Based on the previously developed Energy Conserving Semi Implicit Method (ECsim) code, we present its cylindrical implementation, called ECsim-CYL, to be used for axially symmetric problems. The main motivation for the development of the…
It was recently proved that in some special cases asymmetric truncated Toeplitz operators can be characterized in terms of compressed shifts and rank-two operators of special form. In this paper we show that such characterizations hold in…
This paper presents Haskell#, a coordination language targeted at the efficient implementation of parallel scientific applications on loosely coupled parallel architectures, using the functional language Haskell. Examples of applications,…
We describe a simple pre-training approach for point clouds. It works in three steps: 1. Mask all points occluded in a camera view; 2. Learn an encoder-decoder model to reconstruct the occluded points; 3. Use the encoder weights as…
The term GreenAI refers to a novel approach to Deep Learning, that is more aware of the ecological impact and the computational efficiency of its methods. The promoters of GreenAI suggested the use of Floating Point Operations (FLOPs) as a…
Topological defects play a pivotal role in the physics of liquid crystals and represent one of the most prominent and well studied aspects of mesophases. While in two-dimensional nematics, disclinations are traditionally treated as…
A Maple implementation of partitioned matrices is described. A recursive block data structure is used, with all operations preserving the block abstraction. These include constructor functions, ring operations such as addition and product,…
Increasingly FPGAs will be deployed at scale due to the need for increased need for power efficient computation and improved high level synthesis tool flows, creating a new category of device: data centre FPGAs. A method for using these…
In this paper we obtain a complete characterization of reducing, invariant, and hyperinvariant subspaces for the completely non-unitary component of a power partial isometry. In particular, precise characterization of reducing, invariant,…
In this paper we present some consequences of the description of matrix representations of asymmetric truncated Toeplitz operators acting between finite-dimensional model spaces. In particular, we prove that these operators can be…
We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce…
Applying ideas of fractional analogue of Monge-Amp\'ere operator by L. Caffarelli and F. Charro, we consider an analogue of fractional k-Hessian operators expressed as concave envelopes of fractional linear operators, and reproduce the same…