Algorithmic enhancements to a backpropagation interior point learning rule

2002 ◽  
Author(s):  
Jun Ji ◽  
G.V. Meghabghab
Keyword(s):  
Interior Point ◽  
Learning Rule

ARFIS: Adaptive-Receiver-Based Fuzzy Inference System for Diffusion- Based Molecular Communications

2020 ◽  
Vol 16 (2) ◽  
pp. 280-289
Author(s):  
Ghalib H. Alshammri ◽  
Walid K. M. Ahmed ◽  
Victor B. Lawrence
Keyword(s):  
Fuzzy Inference System ◽  
Fuzzy Inference ◽  
Detection Threshold ◽  
Learning Rule ◽  
Optimal Number ◽  
Molecular Communication ◽  
Inference System ◽  
Detection Scheme ◽  
Adaptive Receiver ◽  
Detection Schemes

Background: The architecture and sequential learning rule-based underlying ARFIS (adaptive-receiver-based fuzzy inference system) are proposed to estimate and predict the adaptive threshold-based detection scheme for diffusion-based molecular communication (DMC). Method: The proposed system forwards an estimate of the received bits based on the current molecular cumulative concentration, which is derived using sequential training-based principle with weight and bias and an input-output mapping based on both human knowledge in the form of fuzzy IFTHEN rules. The ARFIS architecture is employed to model nonlinear molecular communication to predict the received bits over time series. Result: This procedure is suitable for binary On-OFF-Keying (Book signaling), where the receiver bio-nanomachine (Rx Bio-NM) adapts the 1/0-bit detection threshold based on all previous received molecular cumulative concentrations to alleviate the inter-symbol interference (ISI) problem and reception noise. Conclusion: Theoretical and simulation results show the improvement in diffusion-based molecular throughput and the optimal number of molecules in transmission. Furthermore, the performance evaluation in various noisy channel sources shows promising improvement in the un-coded bit error rate (BER) compared with other threshold-based detection schemes in the literature.

scholarly journals On the Boundary Dieudonné–Pick Lemma

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1108
Author(s):  
Olga Kudryavtseva ◽  
Aleksei Solodov
Keyword(s):  
Fixed Point ◽  
Interior Point ◽  
Sharp Estimate ◽  
General Boundary ◽  
Extremal Functions ◽  
Angular Derivative ◽  
Additional Information ◽  
Carathéodory Theorem ◽  
Class Of Functions ◽  
Boundary Fixed Point

The class of holomorphic self-maps of a disk with a boundary fixed point is studied. For this class of functions, the famous Julia–Carathéodory theorem gives a sharp estimate of the angular derivative at the boundary fixed point in terms of the image of the interior point. In the case when additional information about the value of the derivative at the interior point is known, a sharp estimate of the angular derivative at the boundary fixed point is obtained. As a consequence, the sharpness of the boundary Dieudonné–Pick lemma is established and the class of the extremal functions is identified. An unimprovable strengthening of the Osserman general boundary lemma is also obtained.

A New Predictor-corrector Infeasible Interior-point Algorithm for Linear Optimization in aWide Neighborhood

2020 ◽  
Vol 177 (2) ◽  
pp. 141-156
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Linear Optimization ◽  
Point Method ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Positive Direction ◽  
Complexity Result ◽  
Infeasible Interior Point Method ◽  
Predictor Corrector

In this paper, we propose a Mizuno-Todd-Ye type predictor-corrector infeasible interior-point method for linear optimization based on a wide neighborhood of the central path. According to Ai-Zhang’s original idea, we use two directions of distinct and orthogonal corresponding to the negative and positive parts of the right side vector of the centering equation of the central path. In the predictor stage, the step size along the corresponded infeasible directions to the negative part is chosen. In the corrector stage by modifying the positive directions system a full-Newton step is removed. We show that, in addition to the predictor step, our method reduces the duality gap in the corrector step and this can be a prominent feature of our method. We prove that the iteration complexity of the new algorithm is 𝒪(n log ɛ−1), which coincides with the best known complexity result for infeasible interior-point methods, where ɛ > 0 is the required precision. Due to the positive direction new system, we improve the theoretical complexity bound for this kind of infeasible interior-point method [1] by a factor of n . Numerical results are also provided to demonstrate the performance of the proposed algorithm.

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