The present article discusses how the combination of structural (qualitative) and algorithmic (quantitative) perspectives provides valuable insights into geolinguistic patterning and variability, and hence testifies t...
详细信息
The present article discusses how the combination of structural (qualitative) and algorithmic (quantitative) perspectives provides valuable insights into geolinguistic patterning and variability, and hence testifies to the importance of the integrating approach in addressing geolinguistic complexity. In doing so, it shows how language is constantly modulated in the form of innovations that emerge in structurally layered and causal formations, dictated by a subtle interplay between system-based and system- external properties. A case that accounts for this kind of geolinguistic complexity is provided by this data-driven study on Berber (Afro-asiatic), which shows how certain phonological and morphological innovation processes triggered by the vocalisation of the liquids /r/, /(sic)/, /rr/ and /(rr) double under dot/ in Rif Berber (North, Northeast, and Northwest Morocco) create language variation and change. Furthermore, the Berber data examined demonstrate the significant role of certain system-internal factors, such as economy and code conformity, in the diffusion of new phonetic, phonological, and morphological items. In order to better understand the intricacy of the various vocalisation phenomena addressed in the study, the results of the qualitative analysis (synchrony and diachrony) are also contrasted with the algorithmic results ensuing from computing geolinguistic distances by means of the Levenshtein distance calculating method with phone strings tokenised in pair-wise alignments (pondered variables).
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors ha...
详细信息
We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors have bounded depth. For such applications, the complexity of the algorithm improves traditional lattice reduction by replacing some dependence on the bit-length of the input vectors by some dependence on the bound for the output vectors. If the bit-length of the target vectors is unrelated to the bit-length of the input, then our algorithm is only linear in the bit-length of the input entries, which is an improvement over the quadratic complexity floating-point LLL algorithms. To illustrate the usefulness of this algorithm we show that a direct application to factoring univariate polynomials over the integers leads to the first complexity bound improvement since 1984. A second application is algebraic number reconstruction, where a new complexity bound is obtained as well.
We propose several constructions for the original multiplication algorithm of D.V. and G.V. Chudnovsky in order to improve its scalar complexity. We highlight the set of generic strategies who underlay the optimizatio...
详细信息
We propose several constructions for the original multiplication algorithm of D.V. and G.V. Chudnovsky in order to improve its scalar complexity. We highlight the set of generic strategies who underlay the optimization of the scalar complexity, according to parameterizable criteria. As an example, we apply this analysis to the construction of type elliptic Chudnovsky(2) multiplication algorithms for small extensions. As a case study, we significantly improve the Baum-Shokrollahi construction for multiplication in F-256/F-4.
We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypotheses testing in a framework of classical mathematical statistics. The methods for id...
详细信息
We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypotheses testing in a framework of classical mathematical statistics. The methods for identity testing and nonparametric testing of serial independence for time series are suggested. (C) 2006 Elsevier B.V. All rights reserved.
A model of learning from positive and negative examples in concept lattices is considered. Lattice- and graph-theoretic interpretations of learning concept-based classification rules (called hypotheses) and classifica...
详细信息
A model of learning from positive and negative examples in concept lattices is considered. Lattice- and graph-theoretic interpretations of learning concept-based classification rules (called hypotheses) and classification in this model are given. The problems of counting all formal concepts, all hypotheses, and all minimal hypotheses are shown to be #P-complete. NP-completeness of some decision problems related to learning and classification in this setting is demonstrated and several conditions of tractability of these problems are considered. Some useful particular cases where these problems can be solved in polynomial time are indicated. (C) 2004 Elsevier B.V. All rights reserved.
We investigate a population of binary mistake sequences that result from learning with parametric models of different order. We obtain estimates of their error, algorithmic complexity and divergence from a purely rand...
详细信息
We investigate a population of binary mistake sequences that result from learning with parametric models of different order. We obtain estimates of their error, algorithmic complexity and divergence from a purely random Bernoulli sequence. We study the relationship of these variables to the learner's information density parameter which is defined as the ratio between the lengths of the compressed to uncompressed files that contain the learner's decision rule. The results indicate that good learners have a low information density rho while bad learners have a high rho. Bad learners generate mistake sequences that are atypically complex or diverge stochastically from a purely random Bernoulli sequence. Good learners generate typically complex sequences with low divergence from Bernoulli sequences and they include mistake sequences generated by the Bayes optimal predictor. Based on the static algorithmic interference model of [18] the learner here acts as a static structure which "scatters" the bits of an input sequence (to be predicted) in proportion to its information density rho thereby deforming its randomness characteristics. (C) 2010 Elsevier B.V. All rights reserved.
Projecting fields between different meshes commonly arises in computational physics. This operation may require a supermesh construction and in this case its computational cost is proportional to the number of cells o...
详细信息
Projecting fields between different meshes commonly arises in computational physics. This operation may require a supermesh construction and in this case its computational cost is proportional to the number of cells of the supermesh n. Given any two quasi-uniform meshes of n(A) and n(B) cells respectively, we show under standard assumptions that nis proportional to n(A)+ n(B). This result substantially improves on the best currently available upper bound on nand is fundamental for the analysis of algorithms that use supermeshes. (c) 2020 Elsevier Inc. All rights reserved.
Promising approaches for efficient detection in multiple-input multiple-output (MIMO) wireless systems are based on sphere-decoding (SD). The conventional (and optimum) norm that is used to conduct the tree traversal ...
详细信息
Promising approaches for efficient detection in multiple-input multiple-output (MIMO) wireless systems are based on sphere-decoding (SD). The conventional (and optimum) norm that is used to conduct the tree traversal step in SD is the l(2)-norm. It was, however, recently observed that using the l(infinity)-norm instead reduces the hardware complexity of SD considerably at only a marginal performance loss. These savings result from a reduction in the length of the critical path in the circuit and the silicon area required for metric computation, but are also, as observed previously through simulation results, a consequence of a reduction in the computational (i.e., algorithmic) complexity. The aim of this paper is an analytical performance and computational complexity analysis of l(infinity)-norm SD. For independent and identically distributed (i.i.d.) Rayleigh fading MIMO channels, we show that l(infinity)-norm SD achieves full diversity order with an asymptotic SNR gap, compared to l(2)-norm SD, that increases at most linearly in the number of receive antennas. Moreover, we provide a closed l(infinity)-form expression for the computational complexity of-norm SD based on which we establish that its complexity scales exponentially in the system size. Finally, we characterize the tree pruning behavior of l(infinity)-norm SD and show that it behaves fundamentally different from that of l(2)-norm SD.
Some basic issues in the statistical mechanics of learning from examples are reviewed. The approach of statistical physics is contrasted with the analysis of learning within the framework of mathematical statistics an...
详细信息
Some basic issues in the statistical mechanics of learning from examples are reviewed. The approach of statistical physics is contrasted with the analysis of learning within the framework of mathematical statistics and the question of the algorithmic complexity of explicit learning prescriptions is addressed. Even in very simple learning scenarios, the typical properties of which can be analyzed in great quantitative detail by methods from statistical mechanics, the determination of a suitable hypothesis approximating the target rule may be an NP-complete problem. Some special learning setups are suggested as model systems for the comparison between the approaches of statistical mechanics and computer science to the theory of computationally hard problems. (C) 2001 Elsevier Science B.V. All rights reserved.
We consider several variations of the problems of covering a set of barriers (modeled as line segments) using sensors that can detect any intruder crossing any of the barriers. Sensors are initially located in the pla...
详细信息
We consider several variations of the problems of covering a set of barriers (modeled as line segments) using sensors that can detect any intruder crossing any of the barriers. Sensors are initially located in the plane and they can relocate to the barriers. We assume that each sensor can detect any intruder in a circular area of fixed range centered at the sensor. Given a set of barriers and a set of sensors located in the plane, we study three problems: (i) the feasibility of barrier coverage, (ii) the problem of minimizing the largest relocation distance of a sensor (MinMax), and (iii) the problem of minimizing the sum of relocation distances of sensors (MinSum). When sensors are permitted to move to arbitrary positions on the barrier, the MinMax problem is shown to be strongly NP-complete for sensors with arbitrary ranges. We also study the case when sensors are restricted to use perpendicular movement to one of the barriers. We show that when the barriers are parallel, both the MinMax and MinSum problems can be solved in polynomial time. In contrast, we show that even the feasibility problem is strongly NP-complete if two perpendicular barriers are to be covered, even if the sensors are located at integer positions, and have only two possible sensing ranges. On the other hand, we give an O(n(3/2)) algorithm for a natural special case of this last problem. (C) 2015 Elsevier B.V. All rights reserved.
暂无评论