33 research outputs found
A SURVEY OF LIMITED NONDETERMINISM IN COMPUTATIONAL COMPLEXITY THEORY
Nondeterminism is typically used as an inherent part of the computational models used incomputational complexity. However, much work has been done looking at nondeterminism asa separate resource added to deterministic machines. This survey examines several differentapproaches to limiting the amount of nondeterminism, including Kintala and Fischer\u27s βhierarchy, and Cai and Chen\u27s guess-and-check model
Alternating Hierarchies for Time-Space Tradeoffs
Nepomnjascii's Theorem states that for all 0 0 the
class of languages recognized in nondeterministic time n^k and space
n^\epsilon, NTISP[n^k, n^\epsilon ], is contained in the linear time hierarchy.
By considering restrictions on the size of the universal quantifiers in the
linear time hierarchy, this paper refines Nepomnjascii's result to give a sub-
hierarchy, Eu-LinH, of the linear time hierarchy that is contained in NP and
which contains NTISP[n^k, n^\epsilon ]. Hence, Eu-LinH contains NL and SC. This
paper investigates basic structural properties of Eu-LinH. Then the
relationships between Eu-LinH and the classes NL, SC, and NP are considered to
see if they can shed light on the NL = NP or SC = NP questions. Finally, a new
hierarchy, zeta -LinH, is defined to reduce the space requirements needed for
the upper bound on Eu-LinH.Comment: 14 page
Quantum decision making by social agents
The influence of additional information on the decision making of agents, who
are interacting members of a society, is analyzed within the mathematical
framework based on the use of quantum probabilities. The introduction of social
interactions, which influence the decisions of individual agents, leads to a
generalization of the quantum decision theory developed earlier by the authors
for separate individuals. The generalized approach is free of the standard
paradoxes of classical decision theory. This approach also explains the
error-attenuation effects observed for the paradoxes occurring when decision
makers, who are members of a society, consult with each other, increasing in
this way the available mutual information. A precise correspondence between
quantum decision theory and classical utility theory is formulated via the
introduction of an intermediate probabilistic version of utility theory of a
novel form, which obeys the requirement that zero-utility prospects should have
zero probability weights.Comment: This paper has been withdrawn by the authors because a much extended
and improved version has been submitted as arXiv:1510.02686 under the new
title "Role of information in decision making of social agents
Stochasticity,complexity and synchronization in semiconductor lasers
The purpose of this Thesis is study the dynamical behavior of semiconductor
lasers with optical feedback, as well as analyze the synchronization of this kind of
systems under different coupling arquitectures. This study has been done from an
experimental point of view, but in some cases we have used numerical models in
order to verify and/or extend the experimental results.
A semiconductor laser in absence of any optical feedback emits light at constant
power. If one wants to induce dynamics in the laser, a good strategy is to introduce
an external cavity able to reflect the emitted light back into the laser. Due to this
feedback, the laser can show a large variety of dynamical behaviors. In this Thesis
we will focus mainly in a dynamical regime known as low frequency fluctuations
regime (LFF). The LFF regime takes place when the pump current of the laser is
close to its threshold current and the feedback strength is sufficiently large, and it
consists in sudden intensity dropouts arising at irregular times, followed by a gradual
and stepwise recovery.
During this Thesis, we have characterized in detail the dynamical behavior of
the time between intensity dropouts for a semiconductor laser with feedback, by
using different statistical techniques based on information theory concepts. We
have quantified the probability of appearance of certain patterns within the temporal
series, as well as its degree of complexity. As a result of these studies, we can conclude
that the dynamics of a semiconductor laser with optical feedback is stochastic for
pump current values close to the laser threshold. On the other hand, for larger pump
currents the dynamics is basically deterministic (chaotic). Numerical simulations
have shown a good qualitative and quantitive agreement with the experimental
results.
During this Thesis we have also studied the ability of semiconductor lasers to
synchronize under different coupling architectures. First, we have characterized the
leader-laggard dynamics showed by two semiconductor lasers bidirectionally coupled
operating at the LFF regime, with a method that takes into account the number
of forbidden patterns that appears in the temporal series. We have quantified the
degree of stochasticity of the system as a function of the pump current of both lasers.
A second coupling architecture studied here, consists in two lasers unidirectionally
coupled via two paths. In this case, we have analyzed how the synchronization is
affected under different values of the coupling strength of both paths, as well as
the potential of this system (or rather, the lack thereof) to be used in chaotic
communications.
Finally we have characterized the synchronization at zero lag for two lasers coupled
bidirectionally via a passive relay. In particular, we have studied the desynchronization
events and their statistics for different pump currents.
The experimental results obtained in this Thesis give a global perspective of the
dynamical statistical properties of semiconductor laser dynamics, both isolated or
coupled to other lasers, which contributes to a better understanding of this kind of
dynamical systems.L’objectiu d’aquesta Tesi ´es l’estudi de la din`amica de l`asers de semiconductor
amb retroalimentaci´o `optica, aix´ý com l’an`alisis de la sincronitzaci´o d’aquest tipus
de sistemes sota diferents arquitectures d’acoblament. Aquest estudi s’ha fet sempre
des d’un punt de vista b`asicament experimental, tot i que en alguns casos hem
utilitzat models num`erics per tal de verificar i/o ampliar els resultats experimentals.
Un l`aser de semiconductor en abs`encia de retroalimentaci´o `optica o altres perturbacions
externes, emet llum a una intensitat pr`acticament constant. Aix´ý doncs, si el
que es vol ´es indu¨ýr din`amica en el l`aser, una bona estrat`egia ´es introdu¨ýr una cavitat
externa capa¸c de reflexar la llum cap al l`aser. Un cop la llum ´es reinjectada, els l`asers
de semiconductor poden mostrar una gran varietat de comportaments din`amics. En
aquesta tesis ens centrarem principalment en un r`egim din`amic anomenat r`egim de
fluctuacions de baixa frequ`encia (LFF en les seves sigles en angl`es). El r`egim d’LFF
es d´ona quan el corrent d’injecci´o del l`aser es troba a prop del seu corrent llindar
i la intensitat de la retroalimentaci´o ´es suficientment gran, i est`a caracteritzat per
sobtades caigudes de la intensitat a temps irregulars, seguides per una recuperaci´o
gradual i escalonada.
Durant aquesta Tesi, hem caracteritzat de forma detallada el comportament din`amic
de la distribuci´o dels temps entre les caigudes d’intensitat d’un l`aser de semiconductor
amb retroalimentaci´o `optica, utilitzant diferents m`etodes estad´ýstics basats
en conceptes de teoria de la informaci´o. En particular, hem quantificat la probabilitat
d’aparici´o de certs patrons dins les s`eries temporals, aix´ý com el grau de
complexitat d’aquestes. Durant aquest estudi hem observat que la din`amica d’un
l`aser de semiconductor amb retroalimentaci´o es estoc`astica per valors del corrent
d’injecci´o propers al corrent llindar del l`aser. D’altra banda, per a valors m´es grans
del corrent d’injecci´o la din`amica ´es m´es determinista (ca`otica). Les simulacions
num`eriques realitzades han mostrat un acord qualitatiu i quantitatiu amb els resultats
experimentals.
Durant aquesta Tesi tamb´e hem estudiat la sincronitzaci´o entre l`asers de semiconductor.
Hem analitzat diferents arquitectures d’acoblament. Primer hem caracteritzat
la din`amica leader-laggard que presenten dos l`asers de semiconductor acoblats
bidireccionalment operant en r`egim de LFFs, amb un m`etode que t´e en compte el
nombre de patrons prohibits que apareixen en la s`erie temporal. Hem quantificat
el grau d’estocasticitat del sistema en funci´o del nivell de bombeig al qual est`an
sotmesos els dos l`asers.
La seg¨uent arquitectura d’acoblament que hem estudiat consisteix en dos l`asers
acoblats unidireccionalment a trav´es de dos camins. En aquest cas hem analitzat
com es veu afectada la sincronitzaci´o sota diferents valors de l’acoblament dels dos
camins, aix´ý com el potencial d’aquest esquema experimental per realitzar comunicacions
ca`otiques.
Per ´ultim hem caracteritzat la sincronitzaci´o a retard zero per dos l`asers acoblats
bidireccionalment, a on els dos l`asers tenen la seva pr`opia realimentaci´o `optica. En
particular, hem estudiat els events de desincronitzaci´o i la seva estad´ýstica per a
diferents corrents d’injecci´o.
Els resultats experimentals obtinguts en aquesta Tesi, ofereixen una prespectiva
global de les propietats estad´ýstiques de la din`amica de l`asers de semiconductor,
tant a¨ýllats com acoblats a altres l`asers, que contribueixen a entendre millor aquests
sistemes din`amics
Recommended from our members
New Algorithms in Computational Microscopy
Microscopy plays an important role in providing tools to microscopically observe objects and their surrounding areas with much higher resolution ranging from the scale between molecular machineries (angstrom) and individual cells (micrometer). Under microscopes, illumination, such as visible light and electron-magnetic radiation/electron beam, interacts with samples, then they are scattered to a plane and are recorded. Computational microscopy corresponds to image reconstruction from these measurements as well as improving quality of the images. Along with the evolution of microscopy, new studies are discovered and algorithms need development not only to provide high-resolution imaging but also to decipher new and advanced research. In this dissertation, we focus on algorithm development for inverse problems in microscopy, specifically phase retrieval and tomography, and the application of these techniques to machine learning. The four studies in this dissertation demonstrates the use of optimization and calculus of variation in imaging science and other different disciplines.Study 1 focuses on coherent diffractive imaging (CDI) or phase retrieval, a non-linear inverse problem that aims to recover 2D image from it Fourier transforms in modulus taking into account that extra information provided by oversampling as a second constraint. To solve this two-constraint minimization, we proceed from Hamilton-Jacobi partial differential equation (HJ-PDE) and its Hopf-Lax formula. Introducing generalized Bregman distance to the HJ-PDE and applying Legendre transform, we derive our generalized proximal smoothing (GPS) algorithm under the form of primal-dual hybrid gradient (PDHG). While the reflection operator, known as extrapolating momentum, helps overcome local minima, the smoothing by the generalized Bregman distance is adjusted to improve convergence and consistency of phase retrieval.Study 2 focuses on electron tomography, 3D image reconstruction from a set of 2D projections obtained from a transmission electron microscope (TEM) or X-ray microscope. Notice that current tomography algorithms limit to a single tilt axis and fail to work with fully or partially missing data. In the light of calculus of variations and Fourier slice theorem (FST), we develop a highly accurate tomography iterative algorithm that can provide higher resolution imaging and work with missing data as well as has capability to perform multiple-tilt-axis tomography. The algorithm is further developed to work with non-isolated objects and partially-blocked projections which have become more popular in experiment. The success of real space iterative reconstruction engine (RESIRE) opens a new era to the study of tomography in material science and magnetic structures (vector Tomography).Study 3 and 4 are applications of our algorithms to machine learning. Study 3 develops a backward Euler method in a stochastic manner to solve K-mean clustering, a well-known non-convex optimization problem. The algorithm has been shown to improve minimums and consistency, providing a new powerful tool to the class of classification techniques. Study 4 is a direct application of GPS to deep learning gradient descent algorithms. Linearizing the Hopf-Lax formula derived in GPS, we derive our method Laplacian smoothing gradient descent (LSGD), simply known as gradient smoothing. Our experiment shows that LSGD has the ability to search for better and flatter minimums, reduce variation, and obtain higher accuracy and consistency
Ergatic dynamic control systems
Synthesis and analysis of systems containing a man in their control circuits are considered. The concepts of ergonomics and ergatic systems are defined, and tasks and problems of ergonomics are outlined. The synthesis of the structure of an astronautic ergatic organism is presented, as well as the synthesis of nonstationary ergatic systems. Problems of selecting the criteria for complex systems are considered, and the results are presented from a study of ergatic control systems with any degree of human participation