Nivat's conjecture holds for sums of two periodic configurations

Nivat's conjecture is a long-standing open combinatorial problem. It concerns two-dimensional configurations, that is, maps $\mathbb Z^2 \rightarrow \mathcal A$ where $\mathcal A$ is a finite set of symbols. Such configurations are often understood as colorings of a two-dimensional square grid. Let $P_c(m,n)$ denote the number of distinct $m \times n$ block patterns occurring in a configuration $c$. Configurations satisfying $P_c(m,n) \leq mn$ for some $m,n \in \mathbb N$ are said to have low rectangular complexity. Nivat conjectured that such configurations are necessarily periodic. Recently, Kari and the author showed that low complexity configurations can be decomposed into a sum of periodic configurations. In this paper we show that if there are at most two components, Nivat's conjecture holds. As a corollary we obtain an alternative proof of a result of Cyr and Kra: If there exist $m,n \in \mathbb N$ such that $P_c(m,n) \leq mn/2$, then $c$ is periodic. The technique used in this paper combines the algebraic approach of Kari and the author with balanced sets of Cyr and Kra.Comment: Accepted for SOFSEM 2018. This version includes an appendix with proofs. 12 pages + references + appendi

Turbulent nitrate fluxes in the Lower St. Lawrence Estuary, Canada

Turbulent vertical nitrate fluxes were calculated using new turbulent microstructure observations in the Lower St. Lawrence Estuary (LSLE), Canada. Two stations were compared: the head of the Laurentian Channel (HLC), where intense mixing occurs on the shallow sill that marks the upstream limit of the LSLE, and another station located about 100 km downstream (St. 23), more representative of the LSLE mean mixing conditions. Mean turbulent diffusivities and nitrate fluxes at the base of the surface layer for both stations were, respectively (with 95% confidence intervals): inline image and inline image. Observations suggest that the interplay between large isopleth heaving near the sill and strong turbulence is the key mechanism to sustain such high turbulent nitrate fluxes at the HLC (two to three orders of magnitude higher than those at Station 23). Calculations also suggest that nitrate fluxes at the HLC alone can sustain primary production rates of inline image over the whole LSLE, approximately enough to account for a large part of the phytoplankton bloom and for most of the postbloom production. Surfacing nitrates are also believed to be consumed within the LSLE, not leaving much to be exported to the rest of the Gulf of St. Lawrence

Hsp70 in mitochondrial biogenesis

The family of hsp70 (70 kilodalton heat shock protein) molecular chaperones plays an essential and diverse role in cellular physiology, Hsp70 proteins appear to elicit their effects by interacting with polypeptides that present domains which exhibit non-native conformations at distinct stages during their life in the cell. In this paper we review work pertaining to the functions of hsp70 proteins in chaperoning mitochondrial protein biogenesis. Hsp70 proteins function in protein synthesis, protein translocation across mitochondrial membranes, protein folding and finally the delivery of misfolded proteins to proteolytic enzymes in the mitochondrial matrix

Differential regulation of Hsp70 subfamilies by the eukaryotic DnaJ homologue YDJ1

In Saccharomyces cerevisiae Ydj1p, a DnaJ homolog, is localized to the cytosol with the Ssa and Ssb Hsp70 proteins. Ydj1p helps facilitate polypeptide translocation across mitochondrial and endoplasmic reticulum membranes (Caplan, A. J., Cyr, D. M., and Douglas, M. G. (1992) CeLL 71, 1143-1155) and can directly interact with Ssa1p to regulate chaperone activity (Cyr, D. M., Lu, X., and Douglas, M. G. (1992) J. Biol. Chem. 287, 20927-20931). In this study, the role of Ydj1p in modulating ATP-dependent reactions catalyzed by Ssa and Ssb Hsp70 proteins has been examined using purified components and compared with that of other Hsp70 homologs BiP and DnaK. Ssalp, Ssa2p, and Ssb1/2p all formed stable complexes with the mitochondrial presequence peptide, F1β(1-51)

Early events in the transport of proteins into mitochondria : import competition by a mitochondrial presequence

Studies with a synthetic presequence peptide, F1 beta 1-20, corresponding to the NH2-terminal 20 amino acids of the F1-ATPase beta-subunit precursor (pF1 beta) show that although this peptide binds avidly to phospholipid bi-layers it does not efficiently compete for import of full-length precursor into mitochondria, Ki approximately 100 microM (Hoyt, D.W., Cyr, D.M., Gierasch, L.M., and Douglas, M.G. (1991) J. Biol. Chem. 266, 21693-21699). Herein we report that longer F1 beta presequence peptides F1 beta 1-32 + 2, F1 beta 1-32SQ + 2, and F1 beta 21-51 + 3 compete for mitochondrial import at 1000-, 250-, and 25-fold lower concentrations, respectively, than F1 beta 1-20. A longer peptide, F1 beta 1-51 + 3, was no more effective as an import competitor than F1 beta 1-32 + 2. Both minimal length and amphiphilic character appear required in order for F1 beta peptides to block mitochondrial import. Import competition by longer F1 beta peptides seems to occur at a step common to all precursors since they blocked import of precursors to F1-ATPase alpha- and beta-subunits and the ADP/ATP carrier protein. Dissipation of membrane potential (delta psi) across the inner mitochondrial membrane is observed in the presence of F1 beta-peptides, but this mechanism alone does not account for the observed import inhibition. F1 beta 1-32 + 2 and 21-51 + 3 block import of pF1 beta 100% at peptide concentrations which dissipate delta psi less than 25%. In contrast, experiments with valinomycin demonstrate that when mitochondrial delta psi is reduced 25% import of pF1 beta is inhibited only 25%. Therefore, at least 75% of maximal import inhibition observed in the presence of F1 beta 1-32 + 2 and F1 beta 21-51 + 3 does not result from dissipation of delta psi. Import inhibition by F1 beta-peptides is reversible and can be overcome by increasing the amount of full-length precursor in import reactions. F1 beta presequence peptides and full-length precursor are therefore likely to compete for a common import step. Presequence dependent binding of pF1 beta to trypsin-sensitive elements on the outer mitochondrial membrane is insensitive to inhibitory concentrations of F1 beta presequence peptide. We conclude that import inhibition by F1 beta presequence peptides is competitive and occurs at a site beyond initial interaction of precursor proteins with mitochondria

Mind-Body Skills Groups for Adolescents with Depression in Primary Care: A Pilot Study

Objective: To determine acceptability and preliminary effectiveness of Mind-Body Skills Groups (MBSGs) as a treatment for depressed adolescents in primary care. Methods: A single arm clinical trial was conducted. A 10-week MBSG program was implemented in primary care. Participants completed self-report measures at baseline, post-intervention, and 3-months following the MBSGs. Measures included the Children’s Depression Inventory-2, Suicidal Ideation Questionnaire, Mindful Attention Awareness Scale, Self-Efficacy for Depressed Adolescents, rumination subscale of the Children’s Response Style Questionnaire, and a short acceptability questionnaire. Results: Participants included 43 adolescents. The total depression scores significantly improved following the MBSG intervention and continued to improve significantly from post-treatment to follow-up. Mindfulness, self-efficacy, rumination, and suicidal ideation all had significant improvement following the intervention. Acceptability of the program was strong, and attendance was excellent. Discussion: Preliminary evidence suggests that MBSGs are an acceptable treatment for primary care settings and lead to improved depression symptoms in adolescents.Sandra Eskenazi Mental Health Center and the Herbert Simon Family Foundation (070241-00002B

Occupational exposure to solvents and risk of head and neck cancer in women: a population-based case–control study in France

Objective Our objective was to investigate the association between head and neck cancer and occupational exposure to chlorinated, oxygenated and petroleum solvents in women. Methods Investigation of occupational and environmental CAuses of REspiratory cancers (ICARE), a French population-based case–control study, included 296 squamous cell carcinomas of the head and neck (HNSCC) in women and 775 female controls. Lifelong occupational history was collected. Job-exposure matrices allowed to assess exposure to 5 chlorinated solvents (carbon tetrachloride; chloroform; methylene chloride; perchloroethylene; trichloroethylene), 5 petroleum solvents (benzene; special petroleum product; gasoline; white spirits and other light aromatic mixtures; diesel, fuels and kerosene) and 5 oxygenated solvents (alcohols; ketones and esters; ethylene glycol; diethyl ether; tetrahydrofuran). OR and 95% CIs, adjusted for smoking, alcohol drinking, age and geographical area, were estimated with logistic models. Results Elevated ORs were observed among women ever exposed to perchloroethylene (OR=2.97, 95% CI 1.05 to 8.45) and trichloroethylene (OR=2.15, 95% CI 1.21 to 3.81). These ORs increased with exposure duration (OR=3.75, 95% CI 0.64 to 21.9 and OR=4.44, 95% CI 1.56 to 12.6 for 10 years or more, respectively). No significantly increased risk of HNSCC was found for occupational exposure to the other chlorinated, petroleum or oxygenated solvents. Conclusions These findings suggest that exposure to perchloroethylene or trichloroethylene may increase the risk of HNSCC in women. In our study, there is no clear evidence that the other studied solvents are risk factors for HNSCC

Benchmarking quantum control methods on a 12-qubit system

In this letter, we present an experimental benchmark of operational control methods in quantum information processors extended up to 12 qubits. We implement universal control of this large Hilbert space using two complementary approaches and discuss their accuracy and scalability. Despite decoherence, we were able to reach a 12-coherence state (or 12-qubits pseudo-pure cat state), and decode it into an 11 qubit plus one qutrit labeled observable pseudo-pure state using liquid state nuclear magnetic resonance quantum information processors.Comment: 11 pages, 4 figures, to be published in PR

Difference schemes with point symmetries and their numerical tests

Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new difference schemes are tested as numerical methods. The obtained numerical solutions are shown to be much more accurate than those obtained by standard methods without an increase in cost. For an example involving a solution with a singularity in the integration region the symmetry preserving scheme, contrary to standard ones, provides solutions valid beyond the singular point.Comment: 26 pages 7 figure