Bulking II: Classifications of Cellular Automata

This paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three notions of simulation between cellular automata and study the quasi-order structures induced by these simulation relations on the whole set of cellular automata. Various aspects of these quasi-orders are considered (induced equivalence relations, maximum elements, induced orders, etc) providing several formal tools allowing to classify cellular automata

Undecidability of the global fixed point attractor problem on circular cellular automata.

A great amount of work has been devoted to the understanding of the long-time behavior of cellular automata (CA). As for any other kind of dynamical system, the long-time behavior of a CA is described by its attractors. In this context, it has been proved that it is undecidable to know whether every circular configuration of a given CA evolves to some fixed point (not unique). In this paper we prove that it remains undecidable to know whether every circular configuration of a given CA evolves to the {\em same} fixed point. Our proof is based on properties concerning NW-deterministic periodic tilings of the plane. As a corollary it is concluded the (already proved) undecidability of the periodic tiling problem (nevertheless, our approach could also be used to prove this result in a direct and very simple way).De nombreux travaux ont été consacrés à la compréhension de l'évolution à long terme des automates cellulaires (AC). Comme pour les autres types de systèmes dynamiques, cette évolution à long terme est décrite par ses attracteurs. Dans ce contexte, il a été démontré indécidable de savoir si toute configuration périodique d'un AC donné évolue vers un point fixe (peut-{\^e}tre non unique). Dans cet article, nous prouvons l'indécidabilité de savoir si toute configuration périodique evolue vers le {\em m{\^e}me} point fixe. Notre preuve s'appuie sur les propietés des pavages NW-déterministe et périodiques du plan. Comme corollaire, nous obtenons l'indécidabilité (déjà connue) de la pavabilité périodique (cependant notre approche permet d'arriver à ce résultat de fa{\c{c}}on simple et directe)

Cross-point architecture for spin transfer torque magnetic random access memory

Spin transfer torque magnetic random access memory (STT-MRAM) is considered as one of the most promising candidates to build up a true universal memory thanks to its fast write/read speed, infinite endurance and non-volatility. However the conventional access architecture based on 1 transistor + 1 memory cell limits its storage density as the selection transistor should be large enough to ensure the write current higher than the critical current for the STT operation. This paper describes a design of cross-point architecture for STT-MRAM. The mean area per word corresponds to only two transistors, which are shared by a number of bits (e.g. 64). This leads to significant improvement of data density (e.g. 1.75 F2/bit). Special techniques are also presented to address the sneak currents and low speed issues of conventional cross-point architecture, which are difficult to surmount and few efficient design solutions have been reported in the literature. By using a STT-MRAM SPICE model including precise experimental parameters and STMicroelectronics 65 nm technology, some chip characteristic results such as cell area, data access speed and power have been calculated or simulated to demonstrate the expected performances of this new memory architecture

New Solutions to the Firing Squad Synchronization Problems for Neural and Hyperdag P Systems

We propose two uniform solutions to an open question: the Firing Squad Synchronization Problem (FSSP), for hyperdag and symmetric neural P systems, with anonymous cells. Our solutions take e_c+5 and 6e_c+7 steps, respectively, where e_c is the eccentricity of the commander cell of the dag or digraph underlying these P systems. The first and fast solution is based on a novel proposal, which dynamically extends P systems with mobile channels. The second solution is substantially longer, but is solely based on classical rules and static channels. In contrast to the previous solutions, which work for tree-based P systems, our solutions synchronize to any subset of the underlying digraph; and do not require membrane polarizations or conditional rules, but require states, as typically used in hyperdag and neural P systems

Cerebral activations during number multiplication and comparison: a PET study

Positron emission tomography was used to examine the cerebral networks underlying number comparison and multiplication in eight normal volunteers. Cerebral blood flow was measured within anatomical regions of interest defined in each subject using magnetic resonance imaging. Three conditions were used: rest with eyes closed, mental multiplication of pairs of arabic digits and larger-smaller comparison of the same pairs. Both multiplication and comparison activated the left and right lateral occipital cortices, the left precentral gyrus, and the supplementary motor area. Beyond these common activations, multiplication activated also the left and right inferior parietal gyri, the left fusiform and lingual gyri, and the right cuneus. Relative to comparison, multiplication also yielded superior activity in the left lenticular nucleus and in Brodmann's area 8, and induced a hemispheric asymmetry in the activation of the precentral and inferior frontal gyri. Conversely, relative to multiplication, comparison yielded superior activity in the right superior temporal gyrus, the left and right middle temporal gyri, the right superior frontal gyrus, and the right inferior frontal gyrus. These results underline the role of bilateral inferior parietal regions in number processing and suggest that multiplication and comparison may rest on partially distinct networks

Evaluation of polygenic risk scores for breast and ovarian cancer risk prediction in BRCA1 and BRCA2 mutation carriers

Background: Genome-wide association studies (GWAS) have identified 94 common single-nucleotide polymorphisms (SNPs) associated with breast cancer (BC) risk and 18 associated with ovarian cancer (OC) risk. Several of these are also associated with risk of BC or OC for women who carry a pathogenic mutation in the high-risk BC and OC genes BRCA1 or BRCA2. The combined effects of these variants on BC or OC risk for BRCA1 and BRCA2 mutation carriers have not yet been assessed while their clinical management could benefit from improved personalized risk estimates. Methods: We constructed polygenic risk scores (PRS) using BC and OC susceptibility SNPs identified through population-based GWAS: for BC (overall, estrogen receptor [ER]-positive, and ER-negative) and for OC. Using data from 15 252 female BRCA1 and 8211 BRCA2 carriers, the association of each PRS with BC or OC risk was evaluated using a weighted cohort approach, with time to diagnosis as the outcome and estimation of the hazard ratios (HRs) per standard deviation increase in the PRS. Results: The PRS for ER-negative BC displayed the strongest association with BC risk in BRCA1 carriers (HR = 1.27, 95% confidence interval [CI] = 1.23 to 1.31, P = 8.2 x 10(53)). In BRCA2 carriers, the strongest association with BC risk was seen for the overall BC PRS (HR = 1.22, 95% CI = 1.17 to 1.28, P = 7.2 x 10(-20)). The OC PRS was strongly associated with OC risk for both BRCA1 and BRCA2 carriers. These translate to differences in absolute risks (more than 10% in each case) between the top and bottom deciles of the PRS distribution; for example, the OC risk was 6% by age 80 years for BRCA2 carriers at the 10th percentile of the OC PRS compared with 19% risk for those at the 90th percentile of PRS. Conclusions: BC and OC PRS are predictive of cancer risk in BRCA1 and BRCA2 carriers. Incorporation of the PRS into risk prediction models has promise to better inform decisions on cancer risk management

BRCA2 polymorphic stop codon K3326X and the risk of breast, prostate, and ovarian cancers

Background: The K3326X variant in BRCA2 (BRCA2*c.9976A>T; p.Lys3326*; rs11571833) has been found to be associated with small increased risks of breast cancer. However, it is not clear to what extent linkage disequilibrium with fully pathogenic mutations might account for this association. There is scant information about the effect of K3326X in other hormone-related cancers. Methods: Using weighted logistic regression, we analyzed data from the large iCOGS study including 76 637 cancer case patients and 83 796 control patients to estimate odds ratios (ORw) and 95% confidence intervals (CIs) for K3326X variant carriers in relation to breast, ovarian, and prostate cancer risks, with weights defined as probability of not having a pathogenic BRCA2 variant. Using Cox proportional hazards modeling, we also examined the associations of K3326X with breast and ovarian cancer risks among 7183 BRCA1 variant carriers. All statistical tests were two-sided. Results: The K3326X variant was associated with breast (ORw = 1.28, 95% CI = 1.17 to 1.40, P = 5.9x10- 6) and invasive ovarian cancer (ORw = 1.26, 95% CI = 1.10 to 1.43, P = 3.8x10-3). These associations were stronger for serous ovarian cancer and for estrogen receptor–negative breast cancer (ORw = 1.46, 95% CI = 1.2 to 1.70, P = 3.4x10-5 and ORw = 1.50, 95% CI = 1.28 to 1.76, P = 4.1x10-5, respectively). For BRCA1 mutation carriers, there was a statistically significant inverse association of the K3326X variant with risk of ovarian cancer (HR = 0.43, 95% CI = 0.22 to 0.84, P = .013) but no association with breast cancer. No association with prostate cancer was observed. Conclusions: Our study provides evidence that the K3326X variant is associated with risk of developing breast and ovarian cancers independent of other pathogenic variants in BRCA2. Further studies are needed to determine the biological mechanism of action responsible for these associations

Identification of a BRCA2-Specific modifier locus at 6p24 related to breast cancer risk

Common genetic variants contribute to the observed variation in breast cancer risk for BRCA2 mutation carriers; those known to date have all been found through population-based genome-wide association studies (GWAS). To comprehensively identify breast cancer risk modifying loci for BRCA2 mutation carriers, we conducted a deep replication of an ongoing GWAS discovery study. Using the ranked P-values of the breast cancer associations with the imputed genotype of 1.4 M SNPs, 19,029 SNPs were selected and designed for inclusion on a custom Illumina array that included a total of 211,155 SNPs as part of a multi-consortial project. DNA samples from 3,881 breast cancer affected and 4,330 unaffected BRCA2 mutation carriers from 47 studies belonging to the Consortium of Investigators of Modifiers of BRCA1/2 were genotyped and available for analysis. We replicated previously reported breast cancer susceptibility alleles in these BRCA2 mutation carriers and for several regions (including FGFR2, MAP3K1, CDKN2A/B, and PTHLH) identified SNPs that have stronger evidence of association than those previously published. We also identified a novel susceptibility allele at 6p24 that was inversely associated with risk in BRCA2 mutation carriers (rs9348512; per allele HR = 0.85, 95% CI 0.80-0.90, P = 3.9×10−8). This SNP was not associated with breast cancer risk either in the general population or in BRCA1 mutation carriers. The locus lies within a region containing TFAP2A, which encodes a transcriptional activation protein that interacts with several tumor suppressor genes. This report identifies the first breast cancer risk locus specific to a BRCA2 mutation background. This comprehensive update of novel and previously reported breast cancer susceptibility loci contributes to the establishment of a panel of SNPs that modify breast cancer risk in BRCA2 mutation carriers. This panel may have clinical utility for women with BRCA2 mutations weighing options for medical prevention of breast cancer