Related papers: Internal split opfibrations and cofunctors
Sharply o-minimal structures (denoted \so-minimal) are a strict subclass of the o-minimal structures, aimed at capturing some finer features of structures arising from algebraic geometry and Hodge theory. Sharp o-minimality associates to…
We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and…
Practical and useful quantum information processing (QIP) requires significant improvements with respect to current systems, both in error rates of basic operations and in scale. Individual trapped-ion qubits' fundamental qualities are…
Optical coherence tomography (OCT) is a non-invasive 3D modality widely used in ophthalmology for imaging the retina. Achieving automated, anatomically coherent retinal layer segmentation on OCT is important for the detection and monitoring…
Various problems of mathematical physics consider octonions and split-octonions as a mathematical structure, which underpins the eight-dimensional nature of these problems. Therefore, it is not surprising that octonionic analysis has become…
In this work we theoretically investigate a hybrid system of two optomechanically coupled resonators, which exhibits induced transparency. This is realized by coupling an optical ring resonator to a toroid. In the semiclassical analyses,…
The subject under study is an open subsystem of a larger linear and conservative system and the way in which it is coupled to the rest of system. Examples are a model of crystalline solid as a lattice of coupled oscillators with a finite…
Multi-step assembly of individual protein building blocks is key to the formation of essential higher-order structures inside and outside of cells. Optical tweezers is a technique well suited to investigate the mechanics and dynamics of…
We make explicit a larger structural phenomenon hidden behind the existence of normalizers in terms of existence of certain cartesian maps related to the kernel functor.
This work makes a substantial step in the field of split computing, i.e., how to split a deep neural network to host its early part on an embedded device and the rest on a server. So far, potential split locations have been identified…
Photonic nonreciprocal components, such as isolators and circulators, provide highly desirable functionalities for optical circuitry. This motivates the active investigation of mechanisms that break reciprocity, and pose alternatives to…
We present a novel design of optical micro-cavity where the optical energy resides primarily in free space, therefore is readily accessible to foreign objects such as atoms, molecules, mechanical resonators, etc. We describe the physics of…
A pseudoscopic (inverted depth) image made with spiral diffracting elements intermediated by a pinhole is explained by its symmetry properties. The whole process is made under common white light illumination and allows the projection of…
In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented…
Complex colloidal cluster morphologies are desirable for the fabrication of advanced materials, such as photonic crystals and meta-materials, and can be formed through evaporation-driven packing. By coupling lattice Boltzmann and discrete…
Glasses are traditionally characterized by their rugged landscape of disordered low-energy states and their slow relaxation towards thermodynamic equilibrium. Far from equilibrium, dynamical forms of glassy behavior with anomalous algebraic…
We present a macroscopic theory of capillary condensation in slits formed by parallel walls of unequal length. Using the concept of an edge contact angle, we identify four distinct condensation states and derive Kelvin-like relations for…
In the context of the Floquet theory, using a variation of parameter argument, we show that the logarithm of the monodromy of a real periodic Lie system with appropriate properties admits a splitting into two parts, called dynamic and…
In this article we study different aspects of Hermitian operators applying the concept of positive decompositions. On the one hand, we characterize the positivity of an Hermitian operator by means of a norm condition where the factors of…
Optomechanical crystals provide coupling between phonons and photons by confining them to commensurate wavelength-scale dimensions. We present a new concept for designing optomechanical crystals capable of achieving unprecedented coupling…