Results 261 to 270 of about 165,815 (307)
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A Priori Estimates of the Generalization Error for Autoencoders
ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020Autoencoder is a machine learning model which aims for dimensionality reduction, by reconstructing its input through a bottleneck with lower dimension than the input. It is among the most popular models used in unsupervised learning and semi-supervised learning. In this paper, we build theoretical understanding about autoencoders.
Zehao Don, Weinan E, Chao Ma 0012
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2012
In this chapter we determine a priori estimates on the behavior at infinity of positive solutions of the equation $$ \Delta u + a(x)u-b(x)u^{\sigma} \geq 0, \,\,\,\, \sigma > 1 $$ (4.1) on M under assumptions on \( a(x) \) and \( b(x) \) related to the geometrical requirement $$ \mathrm{Ric} \geq-(m-1)H^{2}(1+r(x)^{2})^{\frac{\delta}{2}} $
Paolo Mastrolia +2 more
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In this chapter we determine a priori estimates on the behavior at infinity of positive solutions of the equation $$ \Delta u + a(x)u-b(x)u^{\sigma} \geq 0, \,\,\,\, \sigma > 1 $$ (4.1) on M under assumptions on \( a(x) \) and \( b(x) \) related to the geometrical requirement $$ \mathrm{Ric} \geq-(m-1)H^{2}(1+r(x)^{2})^{\frac{\delta}{2}} $
Paolo Mastrolia +2 more
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Optimal conditions forL∞-regularity and a priori estimates for semilinear elliptic systems
Journal of Mathematical Analysis and Applications, 2009 In this paper, we present a bootstrap procedure for semilinear elliptic systems with n (⩾3) components. Combining with the Lp–Lq-estimates, it yields the optimal L∞-regularity conditions for the three well known types of weak solutions: H01-solutions, L1-
Yuxiang Li
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A priori estimates for nonlinear differential inequalities and applications
Journal of Mathematical Analysis and Applications, 2011 The aim of the paper is to derive a priori estimates and obtain the Harnack-type inequalities of positive weak solutions for the nonlinear differential inequalities in an exterior domain or interior domain.
Fengquan Li
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Estimation of functionals in an a priori density
Journal of Soviet Mathematics, 1988We are concerned with the estimation of linear and quadratic functionals of the form \[ (1)\quad \Phi (g)=\int_{\Theta}\phi (\theta)g(\theta)\mu (d\theta),\quad and\quad (2)\quad \Omega (g)=\int_{\Theta}\omega (\theta)g^ 2(\theta)\mu (d\theta) \] in an unknown a priori density. One of the methods for obtaining the desired estimates is to estimate first
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A Priori Estimation of Organic Reaction Yields
Angewandte Chemie, 2015AbstractA thermodynamically guided calculation of free energies of substrate and product molecules allows for the estimation of the yields of organic reactions. The non‐ideality of the system and the solvent effects are taken into account through the activity coefficients calculated at the molecular level by perturbed‐chain statistical associating ...
Emami, Fateme S. +6 more
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Estimating semantic content: An A priori approach
International Journal of Intelligent Systems, 1988We present our research into the use of the logical structure of natural language discourse to generate estimates of the quantity of semantic content contained within a passage. These estimates of the degree of meaningfulness are recovered from the logical form of the passage, without actually recovering its meaning or necessitating real understanding.
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Existence of EMS Solutions and a Priori Estimates
SIAM Journal on Matrix Analysis and Applications, 1995The author establishes the solvability of the nonlinear EMS (estimate, maximize, smooth) equations in the nonnegative quadrant by use of the Brouwer fixed point theorem and a priori estimates from the Perron- Frobenius theory. Existence of solutions and an a priori estimate are also proven for a generalization of the EMS equations.
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1991
This Chapter 6 and the next Chapter 7 are devoted to the proof of Theorem 1.2. In this chapter we study the operator Ap, and prove a priori estimates for the operator Ap − λI (Theorem 6.3) which will play a fundamental role in the next chapter. In the proof we make good use of Agmon’s method (Proposition 6.4). This is a technique of treating a spectral
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This Chapter 6 and the next Chapter 7 are devoted to the proof of Theorem 1.2. In this chapter we study the operator Ap, and prove a priori estimates for the operator Ap − λI (Theorem 6.3) which will play a fundamental role in the next chapter. In the proof we make good use of Agmon’s method (Proposition 6.4). This is a technique of treating a spectral
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1982
As we have shown in § 3, if A is an arbitrary operator with a dense domain and if equation (A) is correctly solvable on R(A), i.e., if one has the estimate $$ \parallel x{\parallel _E} \leqslant k\parallel Ax{\parallel _F}\;\;(x \in D(A)) $$ (7.1) then the adjoint equation (A*) is everywhere solvable.
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As we have shown in § 3, if A is an arbitrary operator with a dense domain and if equation (A) is correctly solvable on R(A), i.e., if one has the estimate $$ \parallel x{\parallel _E} \leqslant k\parallel Ax{\parallel _F}\;\;(x \in D(A)) $$ (7.1) then the adjoint equation (A*) is everywhere solvable.
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