Related papers: Topological metrology and its application to optic…
Light has shown up an incredibe capability in precision measurement based on opto-mechanic interaction in high vacuum by isolating environment noises. However, there are still obstructions, such as displacement and mass estimation error,…
Dimensional metrology and positioning operations are used in many fields of particle accelerator projects. This lecture gives the basic tools to designers in the field of measure by analysing the spatial layout of measurement systems since…
Addressing subwavelength object and displacement is crucial in optical nanometrology. We show in this Letter that nano antennas with subwavelength structures can be addressed precisely by incident beams with singularity. This accurate…
The thesis presents the subject of synthetic topology, especially with relation to metric spaces. A model of synthetic topology is a categorical model in which objects possess an intrinsic topology in a suitable sense, and all morphisms are…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…
As one of the main pillars of quantum technologies, quantum metrology aims to improve measurement precision using techniques from quantum information. The two main strategies to achieve this are the preparation of nonclassical states and…
We develop a weak measurement scheme for measuring orbital angular momentum (OAM) of light based on the global topology in wave function. We introduce the spin-orbit coupling to transform the measurement of OAM to the pre- and postselected…
We consider the problem where a network of sensors has to detect the presence of targets at any of $n$ possible locations in a finite region. All such locations may not be occupied by a target. The data from sensors is fused to determine…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. This is applied by Du (2010) [A note on cone…
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
In this paper, we study some topological characteristics of the n-normed spaces. We observe convergence sequences, closed sets, and bounded sets in the n-normed spaces using norms of quotient spaces that will be constructed. These norms…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
Place recognition is a key module in robotic navigation. The existing line of studies mostly focuses on visual place recognition to recognize previously visited places solely based on their appearance. In this paper, we address structural…
Topological data analysis is a powerful tool for describing topological signatures in real world data. An important challenge in topological data analysis is matching significant topological signals across distinct systems. In geometry and…
We use the first Betti number of a complex to characterize the morphological structure of granular samples in mechanical equilibrium. We analyze two-dimensional granular packings after a tapping process by means of both simulations and…
We introduce a new class of filtrations indexed by attracting levels in dynamical systems, providing novel inputs for persistent homology and related methods in topological data analysis. These filtrations quantify, in a forward direction,…
Aberrations limit optical systems in many situations, for example when imaging in biological tissue. Machine learning offers novel ways to improve imaging under such conditions by learning inverse models of aberrations. Learning requires…
We propose a functorial framework for persistent homology based on finite topological spaces and their associated posets. Starting from a finite metric space, we associate a filtration of finite topologies whose structure maps are…
Increasing the light scattering efficiency of nanostructured materials is becoming an active field of research both in fundamental science and commercial applications. In this context, the challenge is to use inexpensive organic materials…