Stabilizer formalism for operator quantum error correction

Operator quantum error correction is a recently developed theory that provides a generalized and unified framework for active error correction and passive error avoiding schemes. In this Letter, we describe these codes using the stabilizer formalism. This is achieved by adding a gauge group to stabilizer codes that defines an equivalence class between encoded states. Gauge transformations leave the encoded information unchanged; their effect is absorbed by virtual gauge qubits that do not carry useful information. We illustrate the construction by identifying a gauge symmetry in Shor's 9-qubit code that allows us to remove 3 of its 8 stabilizer generators, leading to a simpler decoding procedure and a wider class of logical operations without affecting its essential properties. This opens the path to possible improvements of the error threshold of fault-tolerant quantum computing.

Error tolerance of topological codes with independent bit-flip and measurement errors

Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be calculated by mapping the underlying quantum problem to a related classical statistical-mechanical spin system with quenched disorder. Here, we present results for the general fault-tolerant regime, where we consider both qubit and measurement errors. However, unlike in previous studies, here we vary the strength of the different error sources independently. Our results highlight peculiar differences between toric and color codes. This study complements previous results published in New J. Phys. 13, 083006 (2011).

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

Bioinformàtica de ARNs: simulacions d'evolució de viroids i xarxes de molècules de ARN

L'objectiu pràctic principal d'aquest projecte va consistir en la construcció d'un codi informàtic destinat a efectuar simulacions de poblacions de molècules de ARN que es repliquen i evolucionen en el temps. Encara que el projecte es va dirigir cap a la investigació de la interacció entre els viroids i els mecanismes de defensa de la planta, els resultats finals del treball efectuat ens van conduir a conclusions aplicables a l'escala del genoma sencer i no només als viroids o ARNs. En aquest estudi es van analitzar, en l’àmbit de la genètica de poblacions, les conseqüències de la selecció natural endarrerida. Estudis clàssics de la evolució en aquest àmbit han considerat que un individu genera fills en proporció amb la seva superioritat reproductiva (o fitness), un procés en que es poden produir mutacions. L'adquisició de mutacions que produeixen en el individu una fitness molt baixa (mutacions deletèries) impliquen l'impossibilitat de reproducció. En la hipòtesi de selecció endarrerida, els individus que adquireixen mutacions deletèries encara es poden reproduir amb normalitat unes quantes generacions. Durant aquest retard o "compte enrere", els danys transmesos als fills podrien ser reparats mitjançant ulteriors mutacions compensatòries. En l'absència d'aquest tipus de mutacions compensatòries, el fill esdevé estèril i per tant no es podrà reproduir. En aquest treball s’ha estudiat les conseqüències genètiques al nivell poblacional d'aquest retard mitjançant simulacions numèriques i modelitzacions teòriques. Els resultats mostren que la selecció amb retard abaixa el llindar d'error (error threshold), posant en perill la supervivència de la població. De l'altra banda, sorprenentment, aquest retard no deixa cap traça al nivell de la diversitat de les seqüències genòmiques en la població. Aquestes conclusions suggereixen que la selecció endarrerida és difícilment detectada en les dades genètiques i per tant, podria ser un fenomen comú però rarament detectat.

Monitoring System Resources During Automated Testing in Symbian Operating System

Tässä diplomityössä esitellään ohjelmistotestauksen ja verifioinnin yleisiä periaatteita sekä käsitellään tarkemmin älypuhelinohjelmistojen verifiointia. Työssä esitellään myös älypuhelimissa käytettävä Symbian-käyttöjärjestelmä. Työn käytännön osuudessa suunniteltiin ja toteutettiin Symbian-käyttöjärjestelmässä toimiva palvelin, joka tarkkailee ja tallentaa järjestelmäresurssien käyttöä. Verifiointi on tärkeä ja kuluja aiheuttava tehtävä älypuhelinohjelmistojen kehityssyklissä. Kuluja voidaan vähentää automatisoimalla osa verifiointiprosessista. Toteutettu palvelin automatisoijärjestelmäresurssien tarkkailun tallentamalla tietoja niistä tiedostoon testien ajon aikana. Kun testit ajetaan uudestaan, uusia tuloksia vertaillaan lähdetallenteeseen. Jos tulokset eivät ole käyttäjän asettamien virherajojen sisällä, siitä ilmoitetaan käyttäjälle. Virherajojen ja lähdetallenteen määrittäminen saattaa osoittautua vaikeaksi. Kuitenkin, jos ne määritetään sopivasti, palvelin tuottaa hyödyllistä tietoa poikkeamista järjestelmäresurssien kulutuksessa testaajille.

The information capacity of hypercycles

Hypercycles are information integration systems which are thought to overcome the information crisis of prebiotic evolution by ensuring the coexistence of several short templates. For imperfect template replication, we derive a simple expression for the maximum number of distinct templates n(m). that can coexist in a hypercycle and show that it is a decreasing function of the length L of the templates. In the case of high replication accuracy we find that the product n(m)L tends to a constant value, limiting thus the information content of the hypercycle. Template coexistence is achieved either as a stationary equilibrium (stable fixed point) or a stable periodic orbit in which the total concentration of functional templates is nonzero. For the hypercycle system studied here we find numerical evidence that the existence of an unstable fixed point is a necessary condition for the presence of periodic orbits. (C) 2008 Elsevier Ltd. All rights reserved.

Package models and the information crisis of prebiotic evolution

The coexistence between different types of templates has been the choice solution to the information crisis of prebiotic evolution, triggered by the finding that a single RNA-like template cannot carry enough information to code for any useful replicase. In principle, confining d distinct templates of length L in a package or protocell, whose Survival depends on the coexistence of the templates it holds in, could resolve this crisis provided that d is made sufficiently large. Here we review the prototypical package model of Niesert et al. [1981. Origin of life between Scylla and Charybdis. J. Mol. Evol. 17, 348-353] which guarantees the greatest possible region of viability of the protocell population, and show that this model, and hence the entire package approach, does not resolve the information crisis. In particular, we show that the total information stored in a viable protocell (Ld) tends to a constant value that depends only on the spontaneous error rate per nucleotide of the template replication mechanism. As a result, an increase of d must be followed by a decrease of L, so that the net information gain is null. (C) 2008 Elsevier Ltd. All rights reserved.

A quasispecies approach to the evolution of sexual replication in unicellular organisms

This study develops a simplified model describing the evolutionary dynamics of a population composed of obligate sexually and asexually reproducing, unicellular organisms. The model assumes that the organisms have diploid genomes consisting of two chromosomes, and that the sexual organisms replicate by first dividing into haploid intermediates, which then combine with other haploids, followed by the normal mitotic division of the resulting diploid into two new daughter cells. We assume that the fitness landscape of the diploids is analogous to the single-fitness-peak approach often used in single-chromosome studies. That is, we assume a master chromosome that becomes defective with just one point mutation. The diploid fitness then depends on whether the genome has zero, one, or two copies of the master chromosome. We also assume that only pairs of haploids with a master chromosome are capable of combining so as to produce sexual diploid cells, and that this process is described by second-order kinetics. We find that, in a range of intermediate values of the replication fidelity, sexually reproducing cells can outcompete asexual ones, provided the initial abundance of sexual cells is above some threshold value. The range of values where sexual reproduction outcompetes asexual reproduction increases with decreasing replication rate and increasing population density. We critically evaluate a common approach, based on a group selection perspective, used to study the competition between populations and show its flaws in addressing the evolution of sex problem.

Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

Image Space Adaptive Rendering

In this thesis, we develop an adaptive framework for Monte Carlo rendering, and more specifically for Monte Carlo Path Tracing (MCPT) and its derivatives. MCPT is attractive because it can handle a wide variety of light transport effects, such as depth of field, motion blur, indirect illumination, participating media, and others, in an elegant and unified framework. However, MCPT is a sampling-based approach, and is only guaranteed to converge in the limit, as the sampling rate grows to infinity. At finite sampling rates, MCPT renderings are often plagued by noise artifacts that can be visually distracting. The adaptive framework developed in this thesis leverages two core strategies to address noise artifacts in renderings: adaptive sampling and adaptive reconstruction. Adaptive sampling consists in increasing the sampling rate on a per pixel basis, to ensure that each pixel value is below a predefined error threshold. Adaptive reconstruction leverages the available samples on a per pixel basis, in an attempt to have an optimal trade-off between minimizing the residual noise artifacts and preserving the edges in the image. In our framework, we greedily minimize the relative Mean Squared Error (rMSE) of the rendering by iterating over sampling and reconstruction steps. Given an initial set of samples, the reconstruction step aims at producing the rendering with the lowest rMSE on a per pixel basis, and the next sampling step then further reduces the rMSE by distributing additional samples according to the magnitude of the residual rMSE of the reconstruction. This iterative approach tightly couples the adaptive sampling and adaptive reconstruction strategies, by ensuring that we only sample densely regions of the image where adaptive reconstruction cannot properly resolve the noise. In a first implementation of our framework, we demonstrate the usefulness of our greedy error minimization using a simple reconstruction scheme leveraging a filterbank of isotropic Gaussian filters. In a second implementation, we integrate a powerful edge aware filter that can adapt to the anisotropy of the image. Finally, in a third implementation, we leverage auxiliary feature buffers that encode scene information (such as surface normals, position, or texture), to improve the robustness of the reconstruction in the presence of strong noise.

Gates for the kane quantum computer in the presence of dephasing

In this paper we investigate the effect of dephasing on proposed quantum gates for the solid-state Kane quantum computing architecture. Using a simple model of the decoherence, we find that the typical error in a controlled-NOT gate is 8.3x10(-5). We also compute the fidelities of Z, X, swap, and controlled Z operations under a variety of dephasing rates. We show that these numerical results are comparable with the error threshold required for fault tolerant quantum computation.

Above ground biomass estimation in Mediterranean multiple use systems with high spatial resolution satellite images

Forest biomass has been having an increasing importance in the world economy and in the evaluation of the forests development and monitoring. It was identified as a global strategic reserve, due to its applications in bioenergy, bioproduct development and issues related to reducing greenhouse gas emissions. The estimation of above ground biomass is frequently done with allometric functions per species with plot inventory data. An adequate sampling design and intensity for an error threshold is required. The estimation per unit area is done using an extrapolation method. This procedure is labour demanding and costly. The mail goal of this study is the development of allometric functions for the estimation of above ground biomass with ground cover as independent variable, for forest areas of holm aok (Quercus rotundifolia), cork oak (Quercus suber) and umbrella pine (Pinus pinea) in multiple use systems. Ground cover per species was derived from crown horizontal projection obtained by processing high resolution satellite images, orthorectified, geometrically and atmospheric corrected, with multi-resolution segmentation method and object oriented classification. Forest inventory data were used to estimate plot above ground biomass with published allometric functions at tree level. The developed functions were fitted for monospecies stands and for multispecies stands of Quercus rotundifolia and Quercus suber, and Quercus suber and Pinus pinea. The stand composition was considered adding dummy variables to distinguish monospecies from multispecies stands. The models showed a good performance. Noteworthy is that the dummy variables, reflecting the differences between species, originated improvements in the models. Significant differences were found for above ground biomass estimation with the functions with and without the dummy variables. An error threshold of 10% corresponds to stand areas of about 40 ha. This method enables the overall area evaluation, not requiring extrapolation procedures, for the three species, which occur frequently in multispecies stands.

Determination of Threshold Dose of Photodynamic Therapy to Measure Superficial Necrosis

Background Data: Photodynamic therapy (PDT) involves the photoinduction of cytotoxicity using a photosensitizer agent, a light source of the proper wavelength, and the presence of molecular oxygen. A model for tissue response to PDT based on the photodynamic threshold dose (Dth) has been widely used. In this model cells exposed to doses below Dth survive while at doses above the Dth necrosis takes place. Objective: This study evaluated the light Dth values by using two different methods of determination. One model concerns the depth of necrosis and the other the width of superficial necrosis. Materials and Methods: Using normal rat liver we investigated the depth and width of necrosis induced by PDT when a laser with a gaussian intensity profile is used. Different light doses, photosensitizers (Photogem, Photofrin, Photosan, Foscan, Photodithazine, and Radachlorin), and concentrations were employed. Each experiment was performed on five animals and the average and standard deviations were calculated. Results: A simple depth and width of necrosis model analysis allows us to determine the threshold dose by measuring both depth and surface data. Comparison shows that both measurements provide the same value within the degree of experimental error. Conclusion: This work demonstrates that by knowing the extent of the superficial necrotic area of a target tissue irradiated by a gaussian light beam, it is possible to estimate the threshold dose. This technique may find application where the determination of Dth must be done without cutting the tissue.

Tests for the hysteresis hypothesis in Brazilian industrialized exports: A threshold cointegration analysis

This paper examines the hysteresis hypothesis in the Brazilian industrialized exports using a time series analysis. This hypothesis finds an empirical representation into the nonlinear adjustments of the exported quantity to relative price changes. Thus, the threshold cointegration analysis proposed by Balke and Fomby [Balke, N.S. and Fomby, T.B. Threshold Cointegration. International Economic Review, 1997; 38; 627-645.] was used for estimating models with asymmetric adjustment of the error correction term. Amongst sixteen industrial sectors selected, there was evidence of nonlinearities in the residuals of long-run relationships of supply or demand for exports in nine of them. These nonlinearities represent asymmetric and/or discontinuous responses of exports to different representative measures of real exchange rates, in addition to other components of long-run demand or supply equations. (C) 2007 Elsevier B.V. All rights reserved.