affine model
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2022 ◽  
Vol 82 (1) ◽  
Author(s):  
Oscar Castillo-Felisola ◽  
Oscar Orellana ◽  
José Perdiguero ◽  
Francisca Ramírez ◽  
Aureliano Skirzewski ◽  
...  

AbstractThe polynomial affine gravity is a model that is built up without the explicit use of a metric tensor field. In this article we reformulate the three-dimensional model and, given the decomposition of the affine connection, we analyse the consistently truncated sectors. Using the cosmological ansatz for the connection, we scan the cosmological solutions on the truncated sectors. We discuss the emergence of different kinds of metrics.


2021 ◽  
Vol 83 (6-7) ◽  
Author(s):  
Mirko Pasquini ◽  
David Angeli

AbstractHybrid models of genetic regulatory networks allow for a simpler analysis with respect to fully detailed quantitative models, still maintaining the main dynamical features of interest. In this paper we consider a piecewise affine model of a genetic regulatory network, in which the parameters describing the production function are affected by polytopic uncertainties. In the first part of the paper, after recalling how the problem of finding a Lyapunov function is solved in the nominal case, we present the considered polytopic uncertain system and then, after describing how to deal with sliding mode solutions, we prove a result of existence of a parameter dependent Lyapunov function subject to the solution of a feasibility linear matrix inequalities problem. In the second part of the paper, based on the previously described Lyapunov function, we are able to determine a set of domains where the system is guaranteed to converge, with the exception of a zero measure set of times, independently from the uncertainty realization. Finally a three nodes network example shows the validity of the results.


2021 ◽  
Vol 8 (3) ◽  
pp. 1-20
Author(s):  
Michael A. Bender ◽  
Alex Conway ◽  
Martín Farach-Colton ◽  
William Jannen ◽  
Yizheng Jiao ◽  
...  

Storage devices have complex performance profiles, including costs to initiate IOs (e.g., seek times in hard drives), parallelism and bank conflicts (in SSDs), costs to transfer data, and firmware-internal operations. The Disk-access Machine (DAM) model simplifies reality by assuming that storage devices transfer data in blocks of size B and that all transfers have unit cost. Despite its simplifications, the DAM model is reasonably accurate. In fact, if B is set to the half-bandwidth point, where the latency and bandwidth of the hardware are equal, then the DAM approximates the IO cost on any hardware to within a factor of 2. Furthermore, the DAM model explains the popularity of B-trees in the 1970s and the current popularity of B ɛ -trees and log-structured merge trees. But it fails to explain why some B-trees use small nodes, whereas all B ɛ -trees use large nodes. In a DAM, all IOs, and hence all nodes, are the same size. In this article, we show that the affine and PDAM models, which are small refinements of the DAM model, yield a surprisingly large improvement in predictability without sacrificing ease of use. We present benchmarks on a large collection of storage devices showing that the affine and PDAM models give good approximations of the performance characteristics of hard drives and SSDs, respectively. We show that the affine model explains node-size choices in B-trees and B ɛ -trees. Furthermore, the models predict that B-trees are highly sensitive to variations in the node size, whereas B ɛ -trees are much less sensitive. These predictions are born out empirically. Finally, we show that in both the affine and PDAM models, it pays to organize data structures to exploit varying IO size. In the affine model, B ɛ -trees can be optimized so that all operations are simultaneously optimal, even up to lower-order terms. In the PDAM model, B ɛ -trees (or B-trees) can be organized so that both sequential and concurrent workloads are handled efficiently. We conclude that the DAM model is useful as a first cut when designing or analyzing an algorithm or data structure but the affine and PDAM models enable the algorithm designer to optimize parameter choices and fill in design details.


2021 ◽  
Vol 01 (03) ◽  
Author(s):  
Abid Raza ◽  
Fahad Mumtaz Malik ◽  
Rameez Khan ◽  
Naveed Mazhar ◽  
Hameed Ullah ◽  
...  

A nonlinear control technique for autonomous control of a tri-rotor unmanned aerial vehicle is presented in this paper. First, a comprehensive mathematical model is developed using the Newton–Euler approach for a tri-rotor, which is found to be highly nonlinear and coupled. Then, the equivalent input affine model is extracted by applying a suitable transformation. Finally, the sliding mode control for trajectory tracking is chosen which is immune to matched external disturbances, parametric uncertainties, and modeling errors. The proposed controller performance has been verified for appropriate inputs under wind disturbances using MATLAB, and the simulation results are presented.


2021 ◽  
Vol 5 (3) ◽  
pp. 65
Author(s):  
Vincent Tartaglione ◽  
Jocelyn Sabatier ◽  
Christophe Farges

This article deals with the random sequential adsorption (RSA) of 2D disks of the same size on fractal surfaces with a Hausdorff dimension 1<d<2. According to the literature and confirmed by numerical simulations in the paper, the high coverage regime exhibits fractional dynamics, i.e., dynamics in t−1/d where d is the fractal dimension of the surface. The main contribution this paper is that it proposes to capture this behavior with a particular class of nonlinear model: a driftless control affine model.


2021 ◽  
Vol 11 (11) ◽  
pp. 5055
Author(s):  
Hong Liang ◽  
Ankang Yu ◽  
Mingwen Shao ◽  
Yuru Tian

Due to the characteristics of low signal-to-noise ratio and low contrast, low-light images will have problems such as color distortion, low visibility, and accompanying noise, which will cause the accuracy of the target detection problem to drop or even miss the detection target. However, recalibrating the dataset for this type of image will face problems such as increased cost or reduced model robustness. To solve this kind of problem, we propose a low-light image enhancement model based on deep learning. In this paper, the feature extraction is guided by the illumination map and noise map, and then the neural network is trained to predict the local affine model coefficients in the bilateral space. Through these methods, our network can effectively denoise and enhance images. We have conducted extensive experiments on the LOL datasets, and the results show that, compared with traditional image enhancement algorithms, the model is superior to traditional methods in image quality and speed.


2021 ◽  
Vol 40 (2) ◽  
pp. 285-302
Author(s):  
Ernesto Mordecki ◽  
Andrés Sosa Rodríguez

We introduce a dynamical country risk index for emerging economies. The proposal is based on the intensity approach of credit risk, i.e. the default is the first jump of a point process with stochastic intensity. Two different models are used to estimate the yield spread. They differ in the relationship between the default-free instantaneous interest rate process and the intensity process. The dynamics of the interest rates is modeled through a multidimensional affine model, and the Kalman filter with an Expectation-Maximization algorithm is used to calibrate it. The USD interest rates constitute part of the input of the model, while prices of relevant domestic bonds in the emerging market complete the input. For an application, we select the Uruguayan bond market as the emerging economy.


Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 49
Author(s):  
Richard Cushman

In this paper, we construct an affine model of a Riemann surface with a flat Riemannian metric associated to a Schwarz–Christoffel mapping of the upper half plane onto a rational triangle. We explain the relation between the geodesics on this Riemann surface and billiard motions in a regular stellated n-gon in the complex plane.


Author(s):  
N Aaron Pancost

Abstract I estimate a dynamic term structure model on an unbalanced panel of Treasury coupon bonds, without relying on an interpolated zero-coupon yield curve. A linearity-generating model, which separates the parameters that govern the cross-sectional and time-series moments of the model, takes about 8 min to estimate on a sample of over 1 million bond prices. The traditional exponential affine model takes about 2 hr, because of a convexity term in coupon-bond prices that cannot be concentrated out of the cross-sectional likelihood. I quantify the on-the-run premium and a “notes versus bonds” premium from 1990 to 2017 in a single, easy-to-estimate no-arbitrage model.


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