An efficient algorithm to recognize local Clifford equivalence of graph states

In [Phys. Rev. A 69, 022316 (2004)] we presented a description of the action of local Clifford operations on graph states in terms of a graph transformation rule, known in graph theory as \emph{local complementation}. It was shown that two graph states are equivalent under the local Clifford group if and only if there exists a sequence of local complementations which relates their associated graphs. In this short note we report the existence of a polynomial time algorithm, published in [Combinatorica 11 (4), 315 (1991)], which decides whether two given graphs are related by a sequence of local complementations. Hence an efficient algorithm to detect local Clifford equivalence of graph states is obtained.Comment: 3 pages. Accepted in Phys. Rev.

Local invariants of stabilizer codes

In [Phys. Rev. A 58, 1833 (1998)] a family of polynomial invariants which separate the orbits of multi-qubit density operators $\rho$ under the action of the local unitary group was presented. We consider this family of invariants for the class of those $\rho$ which are the projection operators describing stabilizer codes and give a complete translation of these invariants into the binary framework in which stabilizer codes are usually described. Such an investigation of local invariants of quantum codes is of natural importance in quantum coding theory, since locally equivalent codes have the same error-correcting capabilities and local invariants are powerful tools to explore their structure. Moreover, the present result is relevant in the context of multipartite entanglement and the development of the measurement-based model of quantum computation known as the one-way quantum computer.Comment: 10 pages, 1 figure. Minor changes. Accepted in Phys. Rev.

A comes before B, like 1 comes before 2. Is the parietal cortex sensitive to ordinal relationships in both numbers and letters? An fMRI-adaptation study

How are number symbols (e.g., Arabic digits) represented in the brain? Functional resonance imaging adaptation (fMRI-A) research has indicated that the intraparietal sulcus (IPS) exhibits a decrease in activation with the repeated presentation of the same number, that is followed by a rebound effect with the presentation of a new number. This rebound effect is modulated by the numerical ratio or difference between presented numbers. It has been suggested that this ratio-dependent rebound effect is reflective of a link between the symbolic numerical representation system and an approximate magnitude system. Experiment 1 used fMRI-A to investigate an alternative hypothesis: that the rebound effect observed in the IPS is related to the ordinal relationships between symbols (e.g., 3 comes before 4; C after B). In Experiment 1, adult participants exhibited the predicted distance-dependent parametric rebound effect bilaterally in the IPS for number symbols during a number adaptation task, however, the same effect was not found anywhere in the brain in response to letters. When numbers were contrasted with letters (numbers \u3e letters), the left intraparietal lobule remained significant. Experiment 2 demonstrated that letter stimuli used in Experiment 1 generated a behavioral distance effect during an active ordinality task, despite the lack of a neural distance effect using fMRI-A. The current study does not support the hypothesis that general ordinal mechanisms underpin the neural parametric recovery effect in the IPS in response to number symbols. Additional research is needed to further our understanding of mechanisms underlying symbolic numerical representation in the brain

Local filtering operations on two qubits

We consider one single copy of a mixed state of two qubits and investigate how its entanglement changes under local quantum operations and classical communications (LQCC) of the type $\rho'\sim (A\otimes B)\rho(A\otimes B)^{\dagger}$. We consider a real matrix parameterization of the set of density matrices and show that these LQCC operations correspond to left and right multiplication by a Lorentz matrix, followed by normalization. A constructive way of bringing this matrix into a normal form is derived. This allows us to calculate explicitly the optimal local filterin operations for concentrating entanglement. Furthermore we give a complete characterization of the mixed states that can be purified arbitrary close to a Bell state. Finally we obtain a new way of calculating the entanglement of formation.Comment: 4 page

Timing the Brain: Mental Chronometry as a Tool in Neuroscience

Mental chronometry, which has origins dating back over a century, seeks to measure the time course of mental operations in the human nervous syste

Metacognition and Abstract Concepts

The problem of how concepts can refer to or be about the non‐mental world is particularly puzzling for abstract concepts. There is growing evidence that many characteristics beyond the perceptual are involved in grounding different kinds of abstract concept. A resource that has been suggested, but little explored, is introspection. This paper develops that suggestion by focusing specifically on metacognition—on the thoughts and feelings that thinkers have about a concept. One example of metacognition about concepts is the judgement that we should defer to others in how a given concept is used. Another example is our internal assessment of which concepts are dependable and useful, and which less so. Metacognition of this kind may be especially important for grounding abstract concepts

A Biologically Plausible SOM Representation of the Orthographic Form of 50,000 French Words

International audienceRecently, an important aspect of human visual word recognition has been characterized. The letter position is encoded in our brain using an explicit representation of order based on letter pairs: the open-bigram coding [15]. We hypothesize that spelling has evolved in order to minimize reading errors. Therefore, word recognition using bigrams — instead of letters — should be more efficient. First, we study the influence of the size of the neighborhood, which defines the number of bigrams per word, on the performance of the matching between bigrams and word. Our tests are conducted against one of the best recognition solutions used today by the industry, which matches letters to words. Secondly, we build a cortical map representation of the words in the bigram space — which implies numerous experiments in order to achieve a satisfactory projection. Third, we develop an ultra-fast version of the self-organizing map in order to achieve learning in minutes instead of months

Subitizing with Variational Autoencoders

Numerosity, the number of objects in a set, is a basic property of a given visual scene. Many animals develop the perceptual ability to subitize: the near-instantaneous identification of the numerosity in small sets of visual items. In computer vision, it has been shown that numerosity emerges as a statistical property in neural networks during unsupervised learning from simple synthetic images. In this work, we focus on more complex natural images using unsupervised hierarchical neural networks. Specifically, we show that variational autoencoders are able to spontaneously perform subitizing after training without supervision on a large amount images from the Salient Object Subitizing dataset. While our method is unable to outperform supervised convolutional networks for subitizing, we observe that the networks learn to encode numerosity as basic visual property. Moreover, we find that the learned representations are likely invariant to object area; an observation in alignment with studies on biological neural networks in cognitive neuroscience

Conteúdos linguísticos como subsídio à formação de professores alfabetizadores: a experiência do Brasil e de Portugal

Objetiva identificar em dois programas de formação de professores alfabetizadores – no Brasil, Pacto Nacional pela Alfabetização na Idade Certa (Pnaic) e, em Portugal, Programa Nacional do Ensino do Português (Pnep) – os conteúdos linguísticos relacionados ao ensino da leitura que fundamentaram a atualização dos professores com vistas a compreender como as descobertas científicas penetram o campo pedagógico. Por meio de análise documental, são apresentadas, de forma resumida, a estrutura e a organização dos dois programas e os respectivos conteúdos de formação. Há muita similaridade entre os dois programas com relação à organização e às estratégias metodológicas e há diferenças importantes quanto à atualidade dos conteúdos oferecidos aos professores alfabetizadores, assim como o tempo de formação aplicado a este conteúdo. A formação linguística do professor é essencial para desenvolver competência para o ensino da língua e, por conseguinte, melhorar as habilidades de ler e escrever dos alunos do ensino fundamental.This article aims to identify the linguistic contents related to the teaching of reading in two training programs for literacy teachers: Brazil’s National Pact for Literacy at the Right Age (Pacto Nacional pela Alfabetização na Idade Certa – Pnaic) and the National Program for Portuguese Teaching (Programa Nacional do Ensino do Português – Pnep) of Portugal. The focus is on the linguistic contents that served as foundation for the updating of teachers, in order to understand how scientific discoveries permeate the teaching field. Through documentary analysis, the structure and the organization of the two programs and their respective training contents are briefly presented. There are many similarities between the two programs, regarding the organization and the methodological strategies; but there are also differences in relation to the timeliness of the content offered to the literacy teachers, as well as to the duration of the training applied to the content. The linguistic training of teachers is essential to developing the competence for language teaching and, therefore; for the improvement of reading and writing skills of elementary school students.CIEC - Centro de Investigação em Estudos da Criança, IE, UMinho (UI 317 da FCT), PortugalFundos Nacionais através da FCT (Fundação para a Ciência e a Tecnologia) e cofinanciado pelo Fundo Europeu de Desenvolvimento Regional (FEDER) através do COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) com a referência POCI-01-0145-FEDER-007562info:eu-repo/semantics/publishedVersio

Brain activity during a visuospatial working memory task predicts arithmetical performance 2 years later

Visuospatial working memory (WM) capacity is highly correlated with mathematical reasoning abilities and can predict future development of arithmetical performance. Activity in the intraparietal sulcus (IPS) during visuospatial WM tasks correlates with interindividual differences in WM capacity. This region has also been implicated in numerical representation, and its structure and activity reflect arithmetical performance impairments (e.g., dyscalculia). We collected behavioral (N = 246) and neuroimaging data (N = 46) in a longitudinal sample to test whether IPS activity during a visuospatial WM task could provide more information than psychological testing alone and predict arithmetical performance 2 years later in healthy participants aged 6–16 years. Nonverbal reasoning and verbal and visuospatial WM measures were found to be independent predictors of arithmetical outcome. In addition, WM activation in the left IPS predicted arithmetical outcome independently of behavioral measures. A logistic model including both behavioral and imaging data showed improved sensitivity by correctly classifying more than twice as many children as poor arithmetical performers after 2 years than a model with behavioral measures only. These results demonstrate that neuroimaging data can provide useful information in addition to behavioral assessments and be used to improve the identification of individuals at risk of future low academic performance