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

Structural issues affecting mixed methods studies in health research: a qualitative study

<p>Abstract</p> <p>Background</p> <p>Health researchers undertake studies which combine qualitative and quantitative methods. Little attention has been paid to the structural issues affecting this mixed methods approach. We explored the facilitators and barriers to undertaking mixed methods studies in health research.</p> <p>Methods</p> <p>Face-to-face semi-structured interviews with 20 researchers experienced in mixed methods research in health in the United Kingdom.</p> <p>Results</p> <p>Structural facilitators for undertaking mixed methods studies included a perception that funding bodies promoted this approach, and the multidisciplinary constituency of some university departments. Structural barriers to exploiting the potential of these studies included a lack of education and training in mixed methods research, and a lack of templates for reporting mixed methods articles in peer-reviewed journals. The 'hierarchy of evidence' relating to effectiveness studies in health care research, with the randomised controlled trial as the gold standard, appeared to pervade the health research infrastructure. Thus integration of data and findings from qualitative and quantitative components of mixed methods studies, and dissemination of integrated outputs, tended to occur through serendipity and effort, further highlighting the presence of structural constraints. Researchers are agents who may also support current structures - journal reviewers and editors, and directors of postgraduate training courses - and thus have the ability to improve the structural support for exploiting the potential of mixed methods research.</p> <p>Conclusion</p> <p>The environment for health research in the UK appears to be conducive to mixed methods research but not to exploiting the potential of this approach. Structural change, as well as change in researcher behaviour, will be necessary if researchers are to fully exploit the potential of using mixed methods research.</p

Dissolution dominating calcification process in polar pteropods close to the point of aragonite undersaturation

Thecosome pteropods are abundant upper-ocean zooplankton that build aragonite shells. Ocean acidification results in the lowering of aragonite saturation levels in the surface layers, and several incubation studies have shown that rates of calcification in these organisms decrease as a result. This study provides a weight-specific net calcification rate function for thecosome pteropods that includes both rates of dissolution and calcification over a range of plausible future aragonite saturation states (Omega_Ar). We measured gross dissolution in the pteropod Limacina helicina antarctica in the Scotia Sea (Southern Ocean) by incubating living specimens across a range of aragonite saturation states for a maximum of 14 days. Specimens started dissolving almost immediately upon exposure to undersaturated conditions (Omega_Ar,0.8), losing 1.4% of shell mass per day. The observed rate of gross dissolution was different from that predicted by rate law kinetics of aragonite dissolution, in being higher at Var levels slightly above 1 and lower at Omega_Ar levels of between 1 and 0.8. This indicates that shell mass is affected by even transitional levels of saturation, but there is, nevertheless, some partial means of protection for shells when in undersaturated conditions. A function for gross dissolution against Var derived from the present observations was compared to a function for gross calcification derived by a different study, and showed that dissolution became the dominating process even at Omega_Ar levels close to 1, with net shell growth ceasing at an Omega_Ar of 1.03. Gross dissolution increasingly dominated net change in shell mass as saturation levels decreased below 1. As well as influencing their viability, such dissolution of pteropod shells in the surface layers will result in slower sinking velocities and decreased carbon and carbonate fluxes to the deep ocean

Challenges to the development of antigen-specific breast cancer vaccines

Continued progress in the development of antigen-specific breast cancer vaccines depends on the identification of appropriate target antigens, the establishment of effective immunization strategies, and the ability to circumvent immune escape mechanisms. Methods such as T cell epitope cloning and serological expression cloning (SEREX) have led to the identification of a number target antigens expressed in breast cancer. Improved immunization strategies, such as using dendritic cells to present tumor-associated antigens to T lymphocytes, have been shown to induce antigen-specific T cell responses in vivo and, in some cases, objective clinical responses. An outcome of successful tumor immunity is the evolution of antigen-loss tumor variants. The development of a polyvalent breast cancer vaccine, directed against a panel of tumor-associated antigens, may counteract this form of immune escape

The Effect of the CO32- to Ca2+ Ion activity ratio on calcite precipitation kinetics and Sr2+ partitioning

<p>Abstract</p> <p>Background</p> <p>A proposed strategy for immobilizing trace metals in the subsurface is to stimulate calcium carbonate precipitation and incorporate contaminants by co-precipitation. Such an approach will require injecting chemical amendments into the subsurface to generate supersaturated conditions that promote mineral precipitation. However, the formation of reactant mixing zones will create gradients in both the saturation state and ion activity ratios (i.e., <inline-formula><m:math name="1467-4866-13-1-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub><m:mrow><m:mi>a</m:mi></m:mrow><m:mrow><m:mi>C</m:mi><m:msup><m:mrow><m:msub><m:mrow><m:mi>O</m:mi></m:mrow><m:mrow><m:mn>3</m:mn></m:mrow></m:msub></m:mrow><m:mrow><m:mn>2</m:mn><m:mo class="MathClass-bin">-</m:mo></m:mrow></m:msup></m:mrow></m:msub><m:mo class="MathClass-bin">/</m:mo><m:msub><m:mrow><m:mi>a</m:mi></m:mrow><m:mrow><m:mi>C</m:mi><m:msup><m:mrow><m:mi>a</m:mi></m:mrow><m:mrow><m:mn>2</m:mn><m:mo class="MathClass-bin">+</m:mo></m:mrow></m:msup></m:mrow></m:msub></m:math></inline-formula>). To better understand the effect of ion activity ratios on CaCO₃precipitation kinetics and Sr²⁺co-precipitation, experiments were conducted under constant composition conditions where the supersaturation state (Ω) for calcite was held constant at 9.4, but the ion activity ratio <inline-formula><m:math name="1467-4866-13-1-i2" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mo class="MathClass-open">(</m:mo><m:mrow><m:mi>r</m:mi><m:mo class="MathClass-rel">=</m:mo><m:msub><m:mrow><m:mi>a</m:mi></m:mrow><m:mrow><m:mi>C</m:mi><m:msup><m:mrow><m:msub><m:mrow><m:mi>O</m:mi></m:mrow><m:mrow><m:mn>3</m:mn></m:mrow></m:msub></m:mrow><m:mrow><m:mn>2</m:mn><m:mo class="MathClass-bin">-</m:mo></m:mrow></m:msup></m:mrow></m:msub><m:mo class="MathClass-bin">/</m:mo><m:msub><m:mrow><m:mi>a</m:mi></m:mrow><m:mrow><m:mi>C</m:mi><m:msup><m:mrow><m:mi>a</m:mi></m:mrow><m:mrow><m:mn>2</m:mn><m:mo class="MathClass-bin">+</m:mo></m:mrow></m:msup></m:mrow></m:msub></m:mrow><m:mo class="MathClass-close">)</m:mo></m:mrow></m:math></inline-formula> was varied between 0.0032 and 4.15.</p> <p>Results</p> <p>Calcite was the only phase observed, by XRD, at the end of the experiments. Precipitation rates increased from 41.3 ± 3.4 μmol m^-2min^-1at <it>r = </it>0.0315 to a maximum rate of 74.5 ± 4.8 μmol m^-2min^-1at <it>r = </it>0.306 followed by a decrease to 46.3 ± 9.6 μmol m^-2min^-1at <it>r </it>= 1.822. The trend was simulated using a simple mass transfer model for solute uptake at the calcite surface. However, precipitation rates at fixed saturation states also evolved with time. Precipitation rates accelerated for low <it>r </it>values but slowed for high <it>r </it>values. These trends may be related to changes in effective reactive surface area. The <inline-formula><m:math xmlns:m="http://www.w3.org/1998/Math/MathML" name="1467-4866-13-1-i1"><m:msub><m:mrow><m:mi>a</m:mi></m:mrow><m:mrow><m:mi>C</m:mi><m:msup><m:mrow><m:msub><m:mrow><m:mi>O</m:mi></m:mrow><m:mrow><m:mn>3</m:mn></m:mrow></m:msub></m:mrow><m:mrow><m:mn>2</m:mn><m:mo class="MathClass-bin">-</m:mo></m:mrow></m:msup></m:mrow></m:msub><m:mo class="MathClass-bin">/</m:mo><m:msub><m:mrow><m:mi>a</m:mi></m:mrow><m:mrow><m:mi>C</m:mi><m:msup><m:mrow><m:mi>a</m:mi></m:mrow><m:mrow><m:mn>2</m:mn><m:mo class="MathClass-bin">+</m:mo></m:mrow></m:msup></m:mrow></m:msub></m:math></inline-formula> ratios did not affect the distribution coefficient for Sr in calcite (D^P_Sr²⁺), apart from the indirect effect associated with the established positive correlation between D^P_Sr²⁺and calcite precipitation rate.</p> <p>Conclusion</p> <p>At a constant supersaturation state (Ω = 9.4), varying the ion activity ratio affects the calcite precipitation rate. This behavior is not predicted by affinity-based rate models. Furthermore, at the highest ion ratio tested, no precipitation was observed, while at the lowest ion ratio precipitation occurred immediately and valid rate measurements could not be made. The maximum measured precipitation rate was 2-fold greater than the minima, and occurred at a carbonate to calcium ion activity ratio of 0.306. These findings have implications for predicting the progress and cost of remediation operations involving enhanced calcite precipitation where mineral precipitation rates, and the spatial/temporal distribution of those rates, can have significant impacts on the mobility of contaminants.</p

Semi-analytic results for quasi-normal frequencies

The last decade has seen considerable interest in the quasi-normal frequencies [QNFs] of black holes (and even wormholes), both asymptotically flat and with cosmological horizons. There is wide agreement that the QNFs are often of the form omega_n = (offset) + i n (gap), though some authors have encountered situations where this behaviour seems to fail. To get a better understanding of the general situation we consider a semi-analytic model based on a piecewise Eckart (Poeschl-Teller) potential, allowing for different heights and different rates of exponential falloff in the two asymptotic directions. This model is sufficiently general to capture and display key features of the black hole QNFs while simultaneously being analytically tractable, at least for asymptotically large imaginary parts of the QNFs. We shall derive an appropriate "quantization condition" for the asymptotic QNFs, and extract as much analytic information as possible. In particular, we shall explicitly verify that the (offset)+ i n (gap) behaviour is common but not universal, with this behaviour failing unless the ratio of rates of exponential falloff on the two sides of the potential is a rational number. (This is "common but not universal" in the sense that the rational numbers are dense in the reals.) We argue that this behaviour is likely to persist for black holes with cosmological horizons.Comment: V1: 28 pages, no figures. V2: 3 references added, no physics changes. V3: 29 pages, 9 references added, no physics changes; V4: reformatted, now 27 pages. Some clarifications, comparison with results obtained by monodromy techniques. This version accepted for publication in JHEP. V5: Minor typos fixed. Compatible with published versio

Recent advances on information transmission and storage assisted by noise

The interplay between nonlinear dynamic systems and noise has proved to be of great relevance in several application areas. In this presentation, we focus on the areas of information transmission and storage. We review some recent results on information transmission through nonlinear channels assisted by noise. We also present recent proposals of memory devices in which noise plays an essential role. Finally, we discuss new results on the influence of noise in memristors.Comment: To be published in "Theory and Applications of Nonlinear Dynamics: Model and Design of Complex Systems", Proceedings of ICAND 2012 (Springer, 2014

Use of mixed methods designs in substance research: a methodological necessity in Nigeria

The utility of mixed methods (qualitative and quantitative) is becoming increasingly accepted in health sciences, but substance studies are yet to substantially benefit from such utilities. While there is a growing number of mixed methods alcohol articles concerning developed countries, developing nations are yet to embrace this method. In the Nigerian context, the importance of mixed methods research is yet to be acknowledged. This article therefore, draws on alcohol studies to argue that mixed methods designs will better equip scholars to understand, explore, describe and explain why alcohol consumption and its related problems are increasing in Nigeria. It argues that as motives for consuming alcohol in contemporary Nigeria are multiple, complex and evolving, mixed method approaches that provide multiple pathways for proffering solutions to problems should be embraced

QTL analysis for resistance to foliar damage caused by Thrips tabaci and Frankliniella schultzei (Thysanoptera: Thripidae) feeding in cowpea [Vigna unguiculata (L.) Walp.]

Three quantitative trait loci (QTL) for resistance to Thrips tabaci and Frankliniella schultzei were identified using a cowpea recombinant inbred population of 127 F2:8 lines. An amplified fragment length polymorphism (AFLP) genetic linkage map and foliar feeding damage ratings were used to identify genomic regions contributing toward resistance to thrips damage. Based on Pearson correlation analysis, damage ratings were highly correlated (r ≥ 0.7463) across seven field experiments conducted in 2006, 2007, and 2008. Using the Kruskall–Wallis and Multiple-QTL model mapping packages of MapQTL 4.0 software, three QTL, Thr-1, Thr-2, and Thr-3, were identified on linkage groups 5 and 7 accounting for between 9.1 and 32.1% of the phenotypic variance. AFLP markers ACC-CAT7, ACG-CTC5, and AGG-CAT1 co-located with QTL peaks for Thr-1, Thr-2, and Thr-3, respectively. Results of this study will provide a resource for molecular marker development and the genetic characterization of foliar thrips resistance in cowpea