scholarly journals Computing from projections of random points

2019 ◽  
Vol 20 (01) ◽  
pp. 1950014
Author(s):  
Noam Greenberg ◽  
Joseph S. Miller ◽  
André Nies
Keyword(s):  
Cost Function ◽  
Random Sequence ◽  
Turing Degrees ◽  
Orthogonal Projections ◽  
Open Set ◽  
Proper Subclass ◽  
The Family ◽  
Function Characterization ◽  
The Cost ◽  
The Ideal

We study the sets that are computable from both halves of some (Martin–Löf) random sequence, which we call [Formula: see text]-bases. We show that the collection of such sets forms an ideal in the Turing degrees that is generated by its c.e. elements. It is a proper subideal of the [Formula: see text]-trivial sets. We characterize [Formula: see text]-bases as the sets computable from both halves of Chaitin’s [Formula: see text], and as the sets that obey the cost function [Formula: see text]. Generalizing these results yields a dense hierarchy of subideals in the [Formula: see text]-trivial degrees: For [Formula: see text], let [Formula: see text] be the collection of sets that are below any [Formula: see text] out of [Formula: see text] columns of some random sequence. As before, this is an ideal generated by its c.e. elements and the random sequence in the definition can always be taken to be [Formula: see text]. Furthermore, the corresponding cost function characterization reveals that [Formula: see text] is independent of the particular representation of the rational [Formula: see text], and that [Formula: see text] is properly contained in [Formula: see text] for rational numbers [Formula: see text]. These results are proved using a generalization of the Loomis–Whitney inequality, which bounds the measure of an open set in terms of the measures of its projections. The generality allows us to analyze arbitrary families of orthogonal projections. As it turns out, these do not give us new subideals of the [Formula: see text]-trivial sets; we can calculate from the family which [Formula: see text] it characterizes. We finish by studying the union of [Formula: see text] for [Formula: see text]; we prove that this ideal consists of the sets that are robustly computable from some random sequence. This class was previously studied by Hirschfeldt [D. R. Hirschfeldt, C. G. Jockusch, R. Kuyper and P. E. Schupp, Coarse reducibility and algorithmic randomness, J. Symbolic Logic 81(3) (2016) 1028–1046], who showed that it is a proper subclass of the [Formula: see text]-trivial sets. We prove that all such sets are robustly computable from [Formula: see text], and that they form a proper subideal of the sets computable from every (weakly) LR-hard random sequence. We also show that the ideal cannot be characterized by a cost function, giving the first such example of a [Formula: see text] subideal of the [Formula: see text]-trivial sets.

Implementation by Vote-Buying Mechanisms

2021 ◽  
Vol 111 (9) ◽  
pp. 2811-2828
Author(s):  
Jon X. Eguia ◽  
Dimitrios Xefteris
Keyword(s):  
Willingness To Pay ◽  
Cost Function ◽  
Social Choice ◽  
Wealth Inequality ◽  
Single Parameter ◽  
Vote Buying ◽  
The Family ◽  
The Cost ◽  
Social Choice Rules

Vote-buying mechanisms allow agents to express any level of support for their preferred alternative at an increasing cost. Focusing on large societies with wealth inequality, we prove that the family of binary social choice rules implemented by well-behaved vote-buying mechanisms is indexed by a single parameter, which determines the importance assigned to the agents’ willingness to pay to affect outcomes and to the number of supporters for each alternative. This parameter depends solely on the elasticity of the cost function near its origin: as this elasticity decreases, the intensities of support matter relatively more for outcomes than the supporters’ count. (JEL D63, D71, D72)

Mereka yang Tidak Dibayar Tinggi: Ibuisme, Taman Kanak-kanak, dan Kampung di Indramayu

2018 ◽  
Vol 3 (2) ◽  
pp. 121
Author(s):  
Mochammad Arief Wicaksono
Keyword(s):  
Kindergarten Teachers ◽  
New Order ◽  
The Family ◽  
Role Of Women ◽  
Community Pressure ◽  
The Village ◽  
Depth Interviews ◽  
The Ideal

The ideology of state-ibuism has always been interwoven with how the New Order regime until nowadays government constructing the “ideal” role of women in the family and community through the PKK (Pembinaan Kesejahteraan Keluarga) organization. However, in Cangkring Village, Indramayu, the ideology of ibuism works not because of the massive government regulating the role of women through the PKK organization, but it is possible because of the structure of the kampung community itself. Through involved observations and in-depth interviews about a kindergarten in the village, a group of housewives who dedicated themselves to teaching in kindergarten were met without getting paid high. From these socio-cultural phenomenons, this paper will describe descriptively and analytically that housewives in the Cangkring village are willing to become kindergarten teachers because of their moral burden as part of the warga kampung and also from community pressure from people who want their children to be able to read and write.

scholarly journals Further steps on the reconstruction of convex polyominoes from orthogonal projections

2021 ◽  
Author(s):  
Paolo Dulio ◽  
Andrea Frosini ◽  
Simone Rinaldi ◽  
Lama Tarsissi ◽  
Laurent Vuillon
Keyword(s):  
Discrete Geometry ◽  
Convex Subset ◽  
Convex Sets ◽  
A Priori ◽  
Orthogonal Projections ◽  
Reconstruction Process ◽  
Combinatorial Properties ◽  
The Family ◽  
Discrete Counterpart ◽  
Interior Part

AbstractA remarkable family of discrete sets which has recently attracted the attention of the discrete geometry community is the family of convex polyominoes, that are the discrete counterpart of Euclidean convex sets, and combine the constraints of convexity and connectedness. In this paper we study the problem of their reconstruction from orthogonal projections, relying on the approach defined by Barcucci et al. (Theor Comput Sci 155(2):321–347, 1996). In particular, during the reconstruction process it may be necessary to expand a convex subset of the interior part of the polyomino, say the polyomino kernel, by adding points at specific positions of its contour, without losing its convexity. To reach this goal we consider convexity in terms of certain combinatorial properties of the boundary word encoding the polyomino. So, we first show some conditions that allow us to extend the kernel maintaining the convexity. Then, we provide examples where the addition of one or two points causes a loss of convexity, which can be restored by adding other points, whose number and positions cannot be determined a priori.

scholarly journals An Adaptive Optimization Method Based on Learning Rate Schedule for Neural Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 850
Author(s):  
Dokkyun Yi ◽  
Sangmin Ji ◽  
Jieun Park
Keyword(s):  
Artificial Intelligence ◽  
Cost Function ◽  
Numerical Experiments ◽  
Global Minimum ◽  
Optimization Method ◽  
Learning Method ◽  
Adaptive Optimization ◽  
The Cost ◽  
Proof Of Convergence ◽  
Learning Data

Artificial intelligence (AI) is achieved by optimizing the cost function constructed from learning data. Changing the parameters in the cost function is an AI learning process (or AI learning for convenience). If AI learning is well performed, then the value of the cost function is the global minimum. In order to obtain the well-learned AI learning, the parameter should be no change in the value of the cost function at the global minimum. One useful optimization method is the momentum method; however, the momentum method has difficulty stopping the parameter when the value of the cost function satisfies the global minimum (non-stop problem). The proposed method is based on the momentum method. In order to solve the non-stop problem of the momentum method, we use the value of the cost function to our method. Therefore, as the learning method processes, the mechanism in our method reduces the amount of change in the parameter by the effect of the value of the cost function. We verified the method through proof of convergence and numerical experiments with existing methods to ensure that the learning works well.

scholarly journals Analysis of Non-Idealities on CMOS Passive Mixers

Electronics ◽  
2021 ◽  
Vol 10 (9) ◽  
pp. 1105
Author(s):  
Antonio D. Martinez-Perez ◽  
Francisco Aznar ◽  
Guillermo Royo ◽  
Santiago Celma
Keyword(s):  
Final Section ◽  
Cmos Technology ◽  
Monte Carlo Analysis ◽  
Image Rejection ◽  
Structure Approach ◽  
Quadrature Scheme ◽  
Current State ◽  
The Cost ◽  
Image Rejection Ratio ◽  
The Ideal

In the current state of the art, WiFi-alike standards require achieving a high Image Rejection Ratio (IRR) while having low power consumption. Thus, quadrature structures based on passive ring mixers offer an attractive and widely used solution, as they can achieve a high IRR while being a passive block. However, it is not easy for the designer to know when a simple quadrature scheme is enough and when they should aim for a double quadrature structure approach, as the latter can improve the performance at the cost of requiring more area and complexity. This study focuses on the IRR, which crucially depends on the symmetry between the I and Q branches. Non-idealities (component mismatches, parasitics, etc.) will degrade the ideal balance by affecting the mixer and/or following/previous stages. This paper analyses the effect of imbalances, providing the constraints for obtaining a 40 dB IRR in the case of a conversion from a one-hundred-megahertz signal to the five-gigahertz range (upconversion) and vice versa (downconversion) for simple and double quadrature schemes. All simulations were carried out with complete device models from 65 nm standard CMOS technology and also a post-layout Monte Carlo analysis was included for mismatch analysis. The final section includes guidelines to help designers choose the most adequate scheme for each case.

Sorting permutations by fragmentation-weighted operations

2020 ◽  
Vol 18 (02) ◽  
pp. 2050006 ◽  
Author(s):  
Alexsandro Oliveira Alexandrino ◽  
Carla Negri Lintzmayer ◽  
Zanoni Dias
Keyword(s):  
Approximation Algorithms ◽  
Computational Biology ◽  
Cost Function ◽  
Traditional Approach ◽  
Upper Bounds ◽  
Evolutionary Distance ◽  
Lower And Upper Bounds ◽  
Approximation Factor ◽  
New Type ◽  
The Cost

One of the main problems in Computational Biology is to find the evolutionary distance among species. In most approaches, such distance only involves rearrangements, which are mutations that alter large pieces of the species’ genome. When we represent genomes as permutations, the problem of transforming one genome into another is equivalent to the problem of Sorting Permutations by Rearrangement Operations. The traditional approach is to consider that any rearrangement has the same probability to happen, and so, the goal is to find a minimum sequence of operations which sorts the permutation. However, studies have shown that some rearrangements are more likely to happen than others, and so a weighted approach is more realistic. In a weighted approach, the goal is to find a sequence which sorts the permutations, such that the cost of that sequence is minimum. This work introduces a new type of cost function, which is related to the amount of fragmentation caused by a rearrangement. We present some results about the lower and upper bounds for the fragmentation-weighted problems and the relation between the unweighted and the fragmentation-weighted approach. Our main results are 2-approximation algorithms for five versions of this problem involving reversals and transpositions. We also give bounds for the diameters concerning these problems and provide an improved approximation factor for simple permutations considering transpositions.

Maximum Likelihood Ensemble Filter: Theoretical Aspects

2005 ◽  
Vol 133 (6) ◽  
pp. 1710-1726 ◽  
Author(s):  
Milija Zupanski
Keyword(s):  
Maximum Likelihood ◽  
Data Assimilation ◽  
Cost Function ◽  
Ensemble Data Assimilation ◽  
Error Covariance ◽  
Ensemble Data ◽  
Analysis Error ◽  
Nonlinear Observation ◽  
The Cost ◽  
Maximum Likelihood Ensemble Filter

Abstract A new ensemble-based data assimilation method, named the maximum likelihood ensemble filter (MLEF), is presented. The analysis solution maximizes the likelihood of the posterior probability distribution, obtained by minimization of a cost function that depends on a general nonlinear observation operator. The MLEF belongs to the class of deterministic ensemble filters, since no perturbed observations are employed. As in variational and ensemble data assimilation methods, the cost function is derived using a Gaussian probability density function framework. Like other ensemble data assimilation algorithms, the MLEF produces an estimate of the analysis uncertainty (e.g., analysis error covariance). In addition to the common use of ensembles in calculation of the forecast error covariance, the ensembles in MLEF are exploited to efficiently calculate the Hessian preconditioning and the gradient of the cost function. A sufficient number of iterative minimization steps is 2–3, because of superior Hessian preconditioning. The MLEF method is well suited for use with highly nonlinear observation operators, for a small additional computational cost of minimization. The consistent treatment of nonlinear observation operators through optimization is an advantage of the MLEF over other ensemble data assimilation algorithms. The cost of MLEF is comparable to the cost of existing ensemble Kalman filter algorithms. The method is directly applicable to most complex forecast models and observation operators. In this paper, the MLEF method is applied to data assimilation with the one-dimensional Korteweg–de Vries–Burgers equation. The tested observation operator is quadratic, in order to make the assimilation problem more challenging. The results illustrate the stability of the MLEF performance, as well as the benefit of the cost function minimization. The improvement is noted in terms of the rms error, as well as the analysis error covariance. The statistics of innovation vectors (observation minus forecast) also indicate a stable performance of the MLEF algorithm. Additional experiments suggest the amplified benefit of targeted observations in ensemble data assimilation.

Using the cost function to generate Marshallian demand systems

2000 ◽  
Vol 25 (2) ◽  
pp. 209-227 ◽  
Author(s):  
Keith R. McLaren ◽  
Peter D. Rossitter ◽  
Alan A. Powell
Keyword(s):  
Cost Function ◽  
Demand Systems ◽  
The Cost
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