Search results for "Linear"
showing 10 items of 7165 documents
PageRank model of opinion formation on Ulam networks
2013
We consider a PageRank model of opinion formation on Ulam networks, generated by the intermittency map and the typical Chirikov map. The Ulam networks generated by these maps have certain similarities with such scale-free networks as the World Wide Web (WWW), showing an algebraic decay of the PageRank probability. We find that the opinion formation process on Ulam networks have certain similarities but also distinct features comparing to the WWW. We attribute these distinctions to internal differences in network structure of the Ulam and WWW networks. We also analyze the process of opinion formation in the frame of generalized Sznajd model which protects opinion of small communities.
A comparative analysis of the statistical properties of large mobile phone calling networks.
2014
Mobile phone calling is one of the most widely used communication methods in modern society. The records of calls among mobile phone users provide us a valuable proxy for the understanding of human communication patterns embedded in social networks. Mobile phone users call each other forming a directed calling network. If only reciprocal calls are considered, we obtain an undirected mutual calling network. The preferential communication behavior between two connected users can be statistically tested and it results in two Bonferroni networks with statistically validated edges. We perform a comparative analysis of the statistical properties of these four networks, which are constructed from …
PRINCIPAL POLYNOMIAL ANALYSIS
2014
© 2014 World Scientific Publishing Company. This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of maximal variance by means of curves instead of straight lines. Contrarily to previous approaches PPA reduces to performing simple univariate regressions which makes it computationally feasible and robust. Moreover PPA shows a number of interesting analytical properties. First PPA is a volume preserving map which in turn guarantees the existence of the inverse. Second such an inverse can be obtained…
Probabilistic Memristive Networks: Application of a Master Equation to Networks of Binary ReRAM cells
2020
Abstract The possibility of using non-deterministic circuit components has been gaining significant attention in recent years. The modeling and simulation of their circuits require novel approaches, as now the state of a circuit at an arbitrary moment in time cannot be predicted deterministically. Generally, these circuits should be described in terms of probabilities, the circuit variables should be calculated on average, and correlation functions should be used to explore interrelations among the variables. In this paper, we use, for the first time, a master equation to analyze the networks composed of probabilistic binary memristors. Analytical solutions of the master equation for the ca…
Quantum finite multitape automata
1999
Quantum finite automata were introduced by C.Moore, J.P. Crutchfield, and by A.Kondacs and J.Watrous. This notion is not a generalization of the deterministic finite automata. Moreover, it was proved that not all regular languages can be recognized by quantum finite automata. A.Ambainis and R.Freivalds proved that for some languages quantum finite automata may be exponentially more concise rather than both deterministic and probabilistic finite automata. In this paper we introduce the notion of quantum finite multitape automata and prove that there is a language recognized by a quantum finite automaton but not by a deterministic or probabilistic finite automata. This is the first result on …
The minimal probabilistic and quantum finite automata recognizing uncountably many languages with fixed cutpoints
2019
Discrete Mathematics & Theoretical Computer Science ; vol. 22 no. 1 ; Automata, Logic and Semantics ; 1365-8050
A Quantum Lovasz Local Lemma
2012
The Lovasz Local Lemma (LLL) is a powerful tool in probability theory to show the existence of combinatorial objects meeting a prescribed collection of "weakly dependent" criteria. We show that the LLL extends to a much more general geometric setting, where events are replaced with subspaces and probability is replaced with relative dimension, which allows to lower bound the dimension of the intersection of vector spaces under certain independence conditions. Our result immediately applies to the k-QSAT problem: For instance we show that any collection of rank 1 projectors with the property that each qubit appears in at most $2^k/(e \cdot k)$ of them, has a joint satisfiable state. We then …
A quantum vocal theory of sound
2020
Concepts and formalism from acoustics are often used to exemplify quantum mechanics. Conversely, quantum mechanics could be used to achieve a new perspective on acoustics, as shown by Gabor studies. Here, we focus in particular on the study of human voice, considered as a probe to investigate the world of sounds. We present a theoretical framework that is based on observables of vocal production, and on some measurement apparati that can be used both for analysis and synthesis. In analogy to the description of spin states of a particle, the quantum-mechanical formalism is used to describe the relations between the fundamental states associated with phonetic labels such as phonation, turbule…
A novel exact representation of stationary colored Gaussian processes (fractional differential approach)
2010
A novel representation of functions, called generalized Taylor form, is applied to the filtering of white noise processes. It is shown that every Gaussian colored noise can be expressed as the output of a set of linear fractional stochastic differential equations whose solution is a weighted sum of fractional Brownian motions. The exact form of the weighting coefficients is given and it is shown that it is related to the fractional moments of the target spectral density of the colored noise.
Thresholding projection estimators in functional linear models
2008
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule allows to get consistency under broad assumptions as well as minimax rates of convergence under additional regularity hypotheses. We also consider the particular case of Sobolev spaces generated by the trigonometric basis which permits to get easily mean squared error of prediction as well as estimators of the derivatives of the regression function. We prove these estimators are minimax and rates of convergence are given for some particular cases.