local solution
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2021 ◽  
pp. 79-99
Author(s):  
Iwan J. Azis

AbstractHow do institutional arrangements and social capital work, and do cases on the ground corroborate what has been conceptualized? Some case-based evidence of MSMEs in different regions provide clues to that question. The role of trust and local solution to achieve a particular goal, including fostering environmental-friendly activities, is highlighted. The evidence also helps permeate the practical and moral thinking of the issues related to MSME operations influenced by local customs and customary laws.


Author(s):  
Junyu Zhang ◽  
Lin Xiao ◽  
Shuzhong Zhang

The cubic regularized Newton method of Nesterov and Polyak has become increasingly popular for nonconvex optimization because of its capability of finding an approximate local solution with a second order guarantee and its low iteration complexity. Several recent works extend this method to the setting of minimizing the average of N smooth functions by replacing the exact gradients and Hessians with subsampled approximations. It is shown that the total Hessian sample complexity can be reduced to be sublinear in N per iteration by leveraging stochastic variance reduction techniques. We present an adaptive variance reduction scheme for a subsampled Newton method with cubic regularization and show that the expected Hessian sample complexity is [Formula: see text] for finding an [Formula: see text]-approximate local solution (in terms of first and second order guarantees, respectively). Moreover, we show that the same Hessian sample complexity is retained with fixed sample sizes if exact gradients are used. The techniques of our analysis are different from previous works in that we do not rely on high probability bounds based on matrix concentration inequalities. Instead, we derive and utilize new bounds on the third and fourth order moments of the average of random matrices, which are of independent interest on their own.


Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Tomoko Sakiyama ◽  
Kotaro Uneme ◽  
Ikuo Arizono

ASrank has been proposed as an improved version of the ant colony optimisation (ACO) model. However, ASrank includes behaviours that do not exist in the actual biological system and fall into a local solution. To address this issue, we developed ASmulti, a new type of ASrank, in which each agent contributes to pheromone depositions by estimating its rank by interacting with the encountered agents. In this paper, we attempt further improvements in the performance of ASmulti by allowing agents to consider their position in a local hierarchy. Agents in the proposed model (AShierarchy) contribute to pheromone depositions by estimating the consistency between a local hierarchy and global (system) hierarchy. We show that, by using several TSP datasets, the proposed model can find a better solution than ASmulti.


2021 ◽  
Vol 24 (4) ◽  
pp. 1193-1219
Author(s):  
Ricardo Castillo ◽  
Miguel Loayza ◽  
Arlúcio Viana

Abstract We consider the following fractional reaction-diffusion equation u t ( t ) + ∂ t ∫ 0 t g α ( s ) A u ( t − s ) d s = t γ f ( u ) , $$ u_t(t) + \partial_t \int\nolimits_{0}^{t} g_{\alpha}(s) \mathcal{A} u(t-s) ds = t^{\gamma} f(u),$$ where g α (t) = t α−1/Γ(α) (0 < α < 1), f ∈ C([0, ∞)) is a non-decreasing function, γ > −1, and A $\mathcal{A}$ is an elliptic operator whose fundamental solution of its associated parabolic equation has Gaussian lower and upper bounds. We characterize the behavior of the functions f so that the above fractional reaction-diffusion equation has a bounded local solution in L r (Ω), for non-negative initial data u 0 ∈ L r (Ω), when r > 1 and Ω ⊂ ℝ N is either a smooth bounded domain or the whole space ℝ N . The case r = 1 is also studied.


2021 ◽  
Vol 5 (2) ◽  
pp. 57
Author(s):  
Mirko D’Ovidio ◽  
Anna Chiara Lai ◽  
Paola Loreti

We present a general series representation formula for the local solution of the Bernoulli equation with Caputo fractional derivatives. We then focus on a generalization of the fractional logistic equation and present some related numerical simulations.


2021 ◽  
Vol 13 (12) ◽  
pp. 2318
Author(s):  
Darío G. Lema ◽  
Oscar D. Pedrayes ◽  
Rubén Usamentiaga ◽  
Daniel F. García ◽  
Ángela Alonso

The recognition of livestock activity is essential to be eligible for subsides, to automatically supervise critical activities and to locate stray animals. In recent decades, research has been carried out into animal detection, but this paper also analyzes the detection of other key elements that can be used to verify the presence of livestock activity in a given terrain: manure piles, feeders, silage balls, silage storage areas, and slurry pits. In recent years, the trend is to apply Convolutional Neuronal Networks (CNN) as they offer significantly better results than those obtained by traditional techniques. To implement a livestock activity detection service, the following object detection algorithms have been evaluated: YOLOv2, YOLOv4, YOLOv5, SSD, and Azure Custom Vision. Since YOLOv5 offers the best results, producing a mean average precision (mAP) of 0.94, this detector is selected for the creation of a livestock activity recognition service. In order to deploy the service in the best infrastructure, the performance/cost ratio of various Azure cloud infrastructures are analyzed and compared with a local solution. The result is an efficient and accurate service that can help to identify the presence of livestock activity in a specified terrain.


Author(s):  
Sigmund Selberg ◽  
Achenef Tesfahun

AbstractThe Maxwell–Dirac system describes the interaction of an electron with its self-induced electromagnetic field. In space dimension $$d=3$$ d = 3 the system is charge-critical, that is, $$L^2$$ L 2 -critical for the spinor with respect to scaling, and local well-posedness is known almost down to the critical regularity. In the charge-subcritical dimensions $$d=1,2$$ d = 1 , 2 , global well-posedness is known in the charge class. Here we prove that these results are sharp (or almost sharp, if $$d=3$$ d = 3 ), by demonstrating ill-posedness below the charge regularity. In fact, for $$d \le 3$$ d ≤ 3 we exhibit a spinor datum belonging to $$H^s(\mathbb {R}^d)$$ H s ( R d ) for $$s<0$$ s < 0 , and to $$L^p(\mathbb {R}^d)$$ L p ( R d ) for $$1 \le p < 2$$ 1 ≤ p < 2 , but not to $$L^2(\mathbb {R}^d)$$ L 2 ( R d ) , which does not admit any local solution that can be approximated by smooth solutions in a reasonable sense.


2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Khaled Zennir ◽  
Aissa Boukarou ◽  
Rehab Nasser Alkhudhayr

The main result in this paper is to prove, in Bourgain type spaces, the existence of unique local solution to system of initial value problem described by integrable equations of modified Korteweg-de Vries (mKdV) by using linear and trilinear estimates, together with contraction mapping principle. Moreover, owing to the approximate conservation law, we prove the existence of global solution.


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