A5010506226- Mathematical Analysis and Transform Methods
- Blockchain Technology Applications and Security
- Mathematical Dynamics and Fractals
- Distributed systems and fault tolerance
- Advanced Authentication Protocols Security
- Geometric Analysis and Curvature Flows
- Image and Signal Denoising Methods
- Cryptography and Data Security
- Advanced Differential Geometry Research
- Point processes and geometric inequalities
- Peer-to-Peer Network Technologies
- Access Control and Trust
- User Authentication and Security Systems
- Advanced Numerical Analysis Techniques
- Privacy, Security, and Data Protection
- Advanced Mathematical Modeling in Engineering
- Privacy-Preserving Technologies in Data
- Advanced Topology and Set Theory
Universitat Politècnica de Catalunya
2022-2024
University of Illinois Urbana-Champaign
2020-2021
Data is currently perceived as one of the most valuable resources by industry. In this context, data marketplaces have emerged for facilitating trading in a coordinated manner. To facilitate open, fair, and transparent trades, it necessary to ensure trust, both among different participants stakeholders, trust sense confidence ecosystem. Thanks emergent blockchain technologies, there are new decentralized that provide manner with disruptive services such automated conflict resolution, non...
Wallet applications play a crucial role in securely storing users' private keys needed to interact with the blockchain, while decentralized (DApps) take profit of blockchain technologies create transparent, tamper-proof environments without need for trust relationships. As DApps secure interconnection these is vital yet still challenging. This article introduces DA2Wa, protocol designed establish pairing between cryptocurrency wallet and DApp, both which run as isolated on same machine. The...
We study the family of vertical projections whose fibers are right cosets horizontal planes in Heisenberg group, \mathbb{H}^n . prove lower bounds for Hausdorff dimension distortion sets under these mappings with respect to natural quotient metric, which we show behaves like Euclidean metric this context. Our sharp a large part range, and give conjectural remaining range. approach also lets us improve known almost sure bound standard n \geq 2
Wallet applications play a crucial role in securely storing users' private keys needed to interact with the blockchain, while decentralised (DApps) take profit of blockchain technologies create transparent, tamper-proof environments without need for trust relationships.As DApps secure interconnection these is vital yet still challenging.This article introduces DA2Wa, protocol designed establish pairing between cryptocurrency wallet and DApp, both which run as isolated on same machine.The...
This paper establishes connections between the group-Fourier transform and geometry of measures in Heisenberg group. Firstly, it is shown that if Fourier a compactly supported, finite, Radon measure square integrable, then must have integrable density. If it's continuous In addition, an alternative formulation on group used to show energies can be computed via integrals appropriate frequency space. turns opens possibility using methods computation Hausdorff dimension sets.
This paper studies the Hausdorff dimension of intersection isotropic projections subsets $\mathbb{R}^{2n}$, as well intersections sets with planes. It is shown that if $A$ and $B$ are Borel $\mathbb{R}^{2n}$ greater than m, then for a positive measure set m-planes, images under orthogonal onto these planes have $m$-measure. In addition, measurable $m$, there $B\subset\mathbb{R}^{2n}$ $\dim B\leq m$ such all $x\in\mathbb{R}^{2n}\setminus B$ m-planes which translate by $x$ complement each...
Abstract This paper studies the Hausdorff dimension of intersection isotropic projections subsets ℝ 2 n , as well intersections sets with planes. It is shown that if A and B are Borel greater than m, then for a positive measure set m-planes, images under orthogonal onto these planes have m -measure. In addition, measurable there ⊂ dim ⩽ such all x ∈ \ m-planes which translate by complement each plane, intersects on – . These results applied to obtain analogous th Heisenberg group.