Infinitesimal Limit Research Articles

Nucleotide detection mechanism and comparison based on low-dimensional materials: A review.

The recent pandemic has led to the fabrication of new nucleic acid sensors that can detect infinitesimal limits immediately and effectively. Therefore, various techniques have been demonstrated using low-dimensional materials that exhibit ultrahigh detection and accuracy. Numerous detection approaches have been reported, and new methods for impulse sensing are being explored. All ongoing research converges at one unique point, that is, an impetus: the enhanced limit of detection of sensors. There are several reviews on the detection of viruses and other proteins related to disease control point of care; however, to the best of our knowledge, none summarizes the various nucleotide sensors and describes their limits of detection and mechanisms. To understand the far-reaching impact of this discipline, we briefly discussed conventional and nanomaterial-based sensors, and then proposed the feature prospects of these devices. Two types of sensing mechanisms were further divided into their sub-branches: polymerase chain reaction and photospectrometric-based sensors. The nanomaterial-based sensor was further subdivided into optical and electrical sensors. The optical sensors included fluorescence (FL), surface plasmon resonance (SPR), colorimetric, and surface-enhanced Raman scattering (SERS), while electrical sensors included electrochemical luminescence (ECL), microfluidic chip, and field-effect transistor (FET). A synopsis of sensing materials, mechanisms, detection limits, and ranges has been provided. The sensing mechanism and materials used were discussed for each category in terms of length, collectively forming a fusing platform to highlight the ultrahigh detection technique of nucleotide sensors. We discussed potential trends in improving the fabrication of nucleotide nanosensors based on low-dimensional materials. In this area, particular aspects, including sensitivity, detection mechanism, stability, and challenges, were addressed. The optimization of the sensing performance and selection of the best sensor were concluded. Recent trends in the atomic-scale simulation of the development of Deoxyribonucleic acid (DNA) sensors using 2D materials were highlighted. A critical overview of the challenges and opportunities of deoxyribonucleic acid sensors was explored, and progress made in deoxyribonucleic acid detection over the past decade with a family of deoxyribonucleic acid sensors was described. Areas in which further research is needed were included in the future scope.

Celestial recursion

We examine the BCFW recursion relations for celestial amplitudes and how they inform the celestial bootstrap program. We start by recasting the celestial incarnation of the BCFW shift as a generalization of the action of familiar asymptotic symmetries on hard particles, before focusing on two limits: z → ∞ and z → 0. We then discuss how the celestial CFT data encodes the large-z behavior determining which shifts are allowed, while the infinitesimal limit is tied to the celestial bootstrap program via the BG equations that constrain the MHV sector. The extension to super-BCFW is also presented. We close by remarking on several open questions for future study.

Optimization of the DRESOR method for application in a medium with large scattering albedo

The Distribution of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface (DRESOR) method, one of the most effective methods to solve the radiation intensity problem with high directional resolution in radiation transfer analysis, suffers performance degradation as the medium scattering albedo becomes large. A scheme is put forward to subdivide the discrete energy beam step length, and take its infinitesimal limit to calculate the scattering/reflection fraction (DRESOR value) with high efficiency and precision. The preliminary simulation results show that when the scattering albedo is greater than 0.5, the optimized DRESOR method can greatly reduce the calculation time and improve the calculation accuracy.

First-principles calculations of steady-state voltage-controlled magnetism: Application to x-ray absorption spectroscopy experiments

Recent x-ray absorption experiments have demonstrated the possibility to accurately monitor the magnetism of metallic hetero-structures controlled via a time-independent perturbation caused for example by a static electric field. Using a first-principles, non-equilibrium Green function scheme, we show how the measured dichroic signal for the corresponding steady-state situation can be related to the underlying electronic structure and its response to the external stimulus. The suggested approach works from the infinitesimal limit of linear response to the regime of strong electric field effects, which is realized in present experimental high sensitivity investigations.

P6582Control and stability theory, modelling ventricular dynamics in superficial 12-lead ECG as a novel contribution to non-invasive risk stratification of Brugada ECG patterns(?)

Abstract Background Brugada syndrome (BrS) risk stratification in asymptomatic subjects is still currently the most important yet unresolved clinical problem to determine the subset of patients with BrS requiring ICD implantation. The underlying pathophysiological mechanisms responsible for BrS ECG patterns remain unknown, as well as the mechanisms of the sudden onset of polymorphic ventricular tachycardia which leads to ventricular fibrillation and sudden cardiac death (SCD). Purpose This study aims to analyze from a totally alternative perspective, superficial 12-lead ECG signals. It departs from the numerous and various attempts to characterize and measure single morphology of specific and individual ECG segments, intervals and waves, rather focusing on and studying the dynamics and stability of the superficial 12-lead ECG signal as a whole to determine stability parameters able to contribute to BrS ECG pattern risk stratification and differential diagnosis of BrS. Methods A quantitative stability control closed loop system has been designed to model the electrophysiology dynamics of the cardiac conduction system with a 12-lead superficial ECG signal being the input and output of the system (Fig. 1). A normal ECG signal and a type-1 coved Brugada pattern ECG-V2 portion have been scanned, digitized and quantitatively processed to obtain stability parameters (poles and zeros in the S-plane). Scanning was performed by Digitizeit – Digital River GmbH. Processing in the S-plane was performed by ©2019 Wolfram Demonstrations Project & Contributors, http://demonstrations.wolfram.com/, poles and zeros and Microsoft Excel software was also used. Results Poles and zeros of the system for type-1 coved Brugada pattern ECG-V2 and for the normal ECG-V2 are shown in Fig. 2, together with stability. Conclusions Based on our data, 1. It appears that portions of the ECG patterns, approximated by mathematical continuous time models representing, at the infinitesimal limit, every possible pattern and behaviors of an ECG signal, such as repolarization patterns, may exhibit interesting dynamics characteristics of stability and can be stratified as stable, marginally stable or unstable. 2. Such a classification may then be implemented to risk stratify repolarization patterns. When tending to instability, such patterns seem to be associated to high risk repolarization patterns such as BrS coved type-1 pattern, hence indicating higher risk of developing polymorphic VT or SCD. In conclusion, more work will be needed to further this methodology to improve the understanding of the effects of the various physiological and pathological substrates involved with malignant arrhythmias and to improve risk stratification strategies to determine the subset of patients with Brugada syndrome requiring ICD insertion. Control systems and stability theory may indeed indicate an interesting and effective procedure for future work.

The Effects of Demography and Genetics on the Neutral Distribution of Quantitative Traits.

Neutral models for quantitative trait evolution are useful for identifying phenotypes under selection. These models often assume normally distributed phenotypes. This assumption may be violated when a trait is affected by relatively few variants or when the effects of those variants arise from skewed or heavy tailed distributions. Molecular phenotypes such as gene expression levels may have these properties. To accommodate deviations from normality, models making fewer assumptions about the underlying genetics and patterns of variation are needed. Here, we develop a general neutral model for quantitative trait variation using a coalescent approach. This model allows interpretation of trait distributions in terms of familiar population genetic parameters because it is based on the coalescent. We show how the normal distribution resulting from the infinitesimal limit, where the number of loci grows large as the effect size per mutation becomes small, depends only on expected pairwise coalescent times. We then demonstrate how deviations from normality depend on demography through the distribution of coalescence times as well as through genetic parameters. In particular, population growth events exacerbate deviations while bottlenecks reduce them. We demonstrate the practical applications of this model by showing how to sample from the neutral distribution of [Formula: see text], the ratio of the variance between subpopulations to that in the overall population. We further show it is likely impossible to distinguish sparsity from skewed or heavy tailed mutational effects using only sampled trait values. The model analyzed here greatly expands the parameter space for neutral trait models.

A derivative-free upscaled theory for analysis of defects

Notwithstanding its recent focus on microstructure-driven non-classical aspects, a breakthrough model in continuum mechanics that can evolve the macroscopic deformation of a solid body undergoing fracture whilst systematically incorporating the microstructural information remains elusive. In addressing this issue, we presently obtain, based on the molecular level information, a derivative-free balance law pertaining to a higher scale of interest and useful in a continuum or discrete setting. Derived using a probabilistic projection technique, the law exploits certain microstructural information in a weakly unique manner. The projection generalizes the notion of directional derivative and, depending on the application, may be interpreted as a discrete Cauchy–Born map with the structure of the classical deformation gradient emerging in the infinitesimal limit. As an illustration, we use the Tersoff–Brenner potential and obtain a discrete macroscopic model for studying the deformation of a single-walled carbon nanotube (SWCNT). The macroscopic (or continuum) model shows the effect of chirality – a molecular phenomenon – in its deformation profile. We also demonstrate the deformation of a fractured SWCNT, which is a first-of-its-kind simulation, and predict crack branching phenomena in agreement with molecular dynamics simulations. As another example, we have included simulation results for fractured SWCNT bundle with a view to establishing our claim regarding the efficacy of the proposed method.

Entropy and geometry of quantum states

We compare the roles of the Bures–Helstrom (BH) and Bogoliubov–Kubo–Mori (BKM) metrics in the subject of quantum information geometry. We note that there are two limits involved in state discrimination, which we call the “thermodynamic” limit (of [Formula: see text], the number of realizations going to infinity) and the infinitesimal limit (of the separation of states tending to zero). We show that these two limits do not commute in the quantum case. Taking the infinitesimal limit first leads to the BH metric and the corresponding Cramér–Rao bound, which is widely accepted in this subject. Taking limits in the opposite order leads to the BKM metric, which results in a weaker Cramér–Rao bound. This lack of commutation of limits is a purely quantum phenomenon arising from quantum entanglement. We can exploit this phenomenon to gain a quantum advantage in state discrimination and get around the limitation imposed by the Bures–Helstrom Cramér–Rao (BHCR) bound. We propose a technologically feasible experiment with cold atoms to demonstrate the quantum advantage in the simple case of two qubits.

Irreversible Local Markov Chains with Rapid Convergence towards Equilibrium.

We study the continuous one-dimensional hard-sphere model and present irreversible local Markov chains that mix on faster time scales than the reversible heat bath or Metropolis algorithms. The mixing time scales appear to fall into two distinct universality classes, both faster than for reversible local Markov chains. The event-chain algorithm, the infinitesimal limit of one of these Markov chains, belongs to the class presenting the fastest decay. For the lattice-gas limit of the hard-sphere model, reversible local Markov chains correspond to the symmetric simple exclusion process (SEP) with periodic boundary conditions. The two universality classes for irreversible Markov chains are realized by the totally asymmetric SEP (TASEP), and by a faster variant (lifted TASEP) that we propose here. We discuss how our irreversible hard-sphere Markov chains generalize to arbitrary repulsive pair interactions and carry over to higher dimensions through the concept of lifted Markov chains and the recently introduced factorized Metropolis acceptance rule.

Generalized Lyapunov-Razumikhin method for retarded differential inclusions: Applications to discontinuous neural networks

In this paper, a general class of nonlinear dynamical systems described by retarded differential equations with discontinuous right-hand sides is considered. Under the extended Filippov-framework, we investigate some basic stability problems for retarded differential inclusions (RDI) with given initial conditions by using the generalized Lyapunov-Razumikhin method. Comparing with the previous work, the main results given in this paper show that the Lyapunov-Razumikhin function is allowed to have a indefinite or positive definite derivative for almost everywhere along the solution trajectories of RDI. However, in most of the existing literature, the derivative (if it exists) of Lyapunov-Razumikhin function is required to be negative or semi-negative definite for almost everywhere. In addition, the Lyapunov-Razumikhin function in this paper is allowed to be non-smooth. To deal with the stability, we also drop the specific condition that the Lyapunov-Razumikhin function should have an infinitesimal upper limit. Finally, we apply the proposed Razumikhin techniques to handle the stability or stabilization control of discontinuous time-delayed neural networks. Meanwhile, we present two examples to demonstrate the effectiveness of the developed method.

Existence, Stability, and Symmetry of Relative Equilibria with a Dominant Vortex

We analyze existence, stability, and symmetry of point vortex relative equilibria with one dominant vortex and $N$ vortices with infinitesimal circulation. The dimension of the problem can be reduced by taking an infinitesimal circulation limit, resulting in the so-called $(1+N)$-vortex problem. In this work, we first generalize the reduction to allow for circulations of varying signs and weights. We then prove that symmetric configurations require equality of two circulation parameters in the $(1+3)$-vortex problem and show that there are stable asymmetric relative equilibria. In a number of examples, we use rigorous methods from algebraic geometry to count all relative equilibria.

Fractional Variation of Hölderian Functions

Abstract The paper demonstrates the basic properties of the local fractional variation operators (termed fractal variation operators). The action of the operators is demonstrated for local characterization of Hölderian functions. In particular, it is established that a class of such functions exhibits singular behavior under the action of fractal variation operators in infinitesimal limit. The link between the limit of the fractal variation of a function and its derivative is demonstrated. The paper presents a number of examples, including the calculation of the fractional variation of Cauchy sequences leading to the Dirac’s delta-function.

TEV—A Program for the Determination of the Thermal Expansion Tensor from Diffraction Data

TEV (Thermal Expansion Visualizing) is a user-friendly program for the calculation of the thermal expansion tensor αij from diffraction data. Unit cell parameters determined from temperature dependent data collections can be provided as input. An intuitive graphical user interface enables fitting of the evolution of individual lattice parameters to polynomials up to fifth order. Alternatively, polynomial representations obtained from other fitting programs or from the literature can be entered. The polynomials and their derivatives are employed for the calculation of the tensor components of αij in the infinitesimal limit. The tensor components, eigenvalues, eigenvectors and their angles with the crystallographic axes can be evaluated for individual temperatures or for temperature ranges. Values of the tensor in directions parallel to either [uvw]’s of the crystal lattice or vectors (hkl) of reciprocal space can be calculated. Finally, the 3-D representation surface for the second rank tensor and pre- or user-defined 2-D sections can be plotted and saved in a bitmap format. TEV is written in JAVA. The distribution contains an EXE-file for Windows users and a system independent JAR-file for running the software under Linux and Mac OS X. The program can be downloaded from the following link: http://www.uibk.ac.at/mineralogie/downloads/TEV.html (Institute of Mineralogy and Petrography, University of Innsbruck, Innsbruck, Austria)

Optimal Design of Stochastic Distributed Order Linear SISO Systems Using Hybrid Spectral Method

The distributed order concept, which is a parallel connection of fractional order integrals and derivatives taken to the infinitesimal limit in delta order, has been the main focus in many engineering areas recently. On the other hand, there are few numerical methods available for analyzing distributed order systems, particularly under stochastic forcing. This paper proposes a novel numerical scheme for analyzing the behavior of a distributed order linear single input single output control system under random forcing. The method is based on the operational matrix technique to handle stochastic distributed order systems. The existing Monte Carlo, polynomial chaos, and frequency methods were first adapted to the stochastic distributed order system for comparison. Numerical examples were used to illustrate the accuracy and computational efficiency of the proposed method for the analysis of stochastic distributed order systems. The stability of the systems under stochastic perturbations can also be inferred easily from the moment of random output obtained using the proposed method. Based on the hybrid spectral framework, the optimal design was elaborated on by minimizing the suitably defined constrained-optimization problem.

Geometrical Applications of Split Octonions

It is shown that physical signals and space-time intervals modeled on split-octonion geometry naturally exhibit properties from conventional (3 + 1)-theory (e.g., number of dimensions, existence of maximal velocities, Heisenberg uncertainty, and particle generations). This paper demonstrates these properties using an explicit representation of the automorphisms on split-octonions, the noncompact form of the exceptional Lie groupG2. This group generates specific rotations of (3 + 4)-vector parts of split octonions with three extra time-like coordinates and in infinitesimal limit imitates standard Poincare transformations. In this picture translations are represented by noncompact Lorentz-type rotations towards the extra time-like coordinates. It is shown how theG2algebra’s chirality yields an intrinsic left-right asymmetry of a certain 3-vector (spin), as well as a parity violating effect on light emitted by a moving quantum system. Elementary particles are connected with the special elements of the algebra which nullify octonionic intervals. Then the zero-norm conditions lead to free particle Lagrangians, which allow virtual trajectories also and exhibit the appearance of spatial horizons governing by mass parameters.

A predator-prey system involving five limit cycles

In this paper we consider the multiparameter system introduced in \cite{sch}, which corresponds to an extension of the classic minimal Daphnia-algae model. It is shown that there is a neighborhood in the parameter space where the system in the realistic quadrant has a unique equilibrium point which is a repelling weak focus of order four enclosed by a global attractor hyperbolic limit cycle. For a small enough change of the parameters in this neighborhood, bifurcation occurs from the weak focus four infinitesimal Hopf limit cycles (alternating the type of stability) such that the last bifurcated limit cycle is an attractor. Moreover, for certain values of parameters, we concluded that this applied model has five concentric limit cycles, three of them being stable hyperbolic limit cycles. This gives a positive answer to a question raised in \cite{col, Llo}.

Modeling fracture in the context of a strain-limiting theory of elasticity: A single plane-strain crack

Implicit constitutive relations afford a logically consistent framework for formulating strain-limiting, nonlinear elastic constitutive models utilizing the classical linearized strain tensor. This is in marked contrast to traditional Cauchy or Green elastic formulations which give rise to customary linear elasticity in the infinitesimal strain limit. Within this strain-limiting elastic constitutive setting, the present paper investigates the asymptotic behavior of the stress field at the tip of a straight plane-strain fracture. It is shown that within the general class of crack-tip asymptotic expansions considered, the only cases satisfying the required boundary conditions correspond to bounded stresses. This is in agreement with previous results for the corresponding anti-plane shear fracture problem.

Stability Analysis of Retarded Differential Inclusions

Retarded differential inclusions have drawn more and more attention, due to the development of feedback control systems with delays and dynamical systems determined by retarded differential equations with a discontinuous right-hand side. The purpose of this paper is to establish a result on the stability and asymptotical stability for retarded differential inclusions. Comparing with the previous results, the main result obtained in this paper allows Lyapunov functions to be nonsmooth. Moreover, to deal with the asymptotical stability, it is not required that Lyapunov functions should have an infinitesimal upper limit, but this condition is needed in most of the previous results. To demonstrate applicability, we use the main result in the analysis of asymptotical stability of a class of neural networks with discontinuous activations and delays.

Infinitesimal etendue and Simultaneous Multiple Surface (SMS) concentrators for fixed receiver troughs

In order to increase the cost-effectiveness of conventional parabolic trough (PT) fields it is essential to reduce Capital Expenditure (Capex) as well as Operations and Maintenance (O&M) costs, in particular the need for flexible hosing or rotating joints, which are used because the tubular receiver also tracks in a solidary way with the trough. One possible alternative is to design a different type of optic with the center of mass on the center of the tubular receiver, generating the possibility of it being fixed, thereby dispensing with flexible hosing or rotating joints, without penalizing its overall efficiency or even concentration. In this work, two possible optical solutions, combining parabolic-type primaries with second-stage non-imaging optics concentrators for fixed receivers, are presented. These concentrators are designed using the Simultaneous Multiple Surface (SMS) design method and the infinitesimal etendue limit. A performance comparison with a conventional PT in terms of optical efficiency, CAP (Concentration-Acceptance Product) and other performance data are also presented, including an estimate of the total amount of yearly collected energy (kWh/m2 of entrance aperture) for one particular location – Faro (Portugal).

The Exact Complex-Valued Solution for Steady Surface Waves

The two exact complex-valued solutions for the 2D problem of surface waves propagation along a free surface of infinitely deep ideal incompressible liquid are presented. These solutions aren’t subjected to superposition principle but their linear combination leads to the theory of linear waves in infinitesimal limit and to nonlinear Stokes’ solution for the waves of small but finite amplitude.