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The conditions present in both in vitro and in vivo ecosystems determine the microbial population harbouring it. One commonly accepted theory is that a species with a high substrate affinity and low growth rate (k-strategist) will win the competition against a second species with a lower substrate affinity and higher growth rate (r-strategist) if both species are subjected to low substrate concentrations. In this study two nitrite oxidizing bacteria (NOB), Nitrospira defluvii (k-strategist) and Nitrobacter vulgaris (r-strategist), were cultivated in a continuous reactor systems. The minimal hydraulic retention time (HRT) required for maintaining the slower growing Nitrospira was first determined. A reactor containing Nitrobacter was set to the same HRT and Nitrospira was injected to evaluate the effect of the dilution rate on the competition between both species. By following the microbial population dynamics with qPCR analysis, it was shown that not only the substrate affinity drives the competition between k- and r-strategists but also the dilution rate. Experimental data and numerical simulations both revealed that the washout of Nitrobacter was significantly delayed at dilution rates close to the mu max of Nitrospira. The competition could be even reverted towards Nitrobacter (r-strategist) despite of low nitrite concentrations and dilution rates lower than the ae max of Nitrospira.

When Siegrist (1989) derived an expression for the probability that player A wins a game that consists of a sequence of Bernoulli trials, the winner being the first player to win n trials and have a lead of at least k, he noted the desirability of giving a direct probabilistic argument. Here we present such an argument, and extend the domain of applicability of the results beyond Bernoulli trials, including cases (such as the tie-break in lawn tennis) where the probability of winning each trial cannot reasonably be taken as constant, and to where there is Markov dependence between successive trials.

Additional file 1: Table S1. Table displaying optimal cut-offs for the six tumor features determined previously (Walker et al. 2023) in the additive feature combination approach. Table S2. SLS tumors (n=13) that showed discordant MMR IHC findings between clinical diagnostic testing before study entry and testing completed internally during this study and the change in their MMR status and/or pattern of MMR protein loss. Table S3. The concordance between the final MMR IHC result and the predicted dMMR status from the additive feature combination approach overall and by tumor type. Table S4. The tumor MLH1 methylation testing completed for SLS tumors prior to entering the study showing either negative, inconclusive, or not tested results and the subsequent MLH1 methylation testing results from internal testing using MethyLight and MS-HRM assays highlighting the positive MLH1 methylation results found by this study. Table S5. Presentation of germline pathogenic variants and variants of uncertain clinical significance (VUS) identified in the MMR, MUTYH and POLE genes. Table S6. Summary of the clinicopathological features for the double somatic MMR mutation (dMMR-DS) tumors overall and by tumor type. Figure S1. Bar plots presenting the results from the additive tumor feature combination approach to assess the MMR status in the double somatic mutation cohort for A) all tumors combined and separated by B) CRC, C) EC and D) SST tissue types. Figure S2. Bar plot presenting the prevalence of pathogenic/likely pathogenic somatic mutations (including loss of heterozygosity, LOH) by subtype for the study cohort. Figure S3. Pie graphs displaying the frequency of the mutation combination type (two single somatic mutations versus a single somatic mutation with loss of heterozygosity (LOH)) as well as the type of mutation A) overall and B) separated by tissue type. Figure S4. Bar graphs presenting the site distribution in the double somatic mutation cohort across all CRCs and SSTs. Figure S5. Boxplots presenting the site distribution in the double somatic mutation cohort across all A) CRCs and B) SSTs. Significant (< 0.05) p-values are indicated for pairwise (t-test) and multigroup comparisons (Anova). Figure S6. Scatter plots presenting the PREMM5 score distribution in the test cohort for A) all tumors combined and separated by B) CRC, C) EC and D) SST tissue types. Figure S7. The distribution of tumor values for each of the six features that are included in the additive feature combination approach for determining tumor dMMR status grouped by molecular subtype and by combining sporadic dMMR groups dMMR-DS and dMMR-MLH1me into a “sporadic combined” group.

Consider a sequence of Bernoulli trials between players A and B in which player A wins each trial with probability p∈ [0, 1]. For positive integers n and k with k ≦ n, an (n, k) contest is one in which the first player to win at least n trials and to be ahead of his opponent by at least k trials wins the contest. The (n, 1) contest is the Banach match problem and the (n, n) contest is the gambler's ruin problem. Many real contests (such as the World Series in baseball and the tennis game) have an (n, 1) or an (n, 2) format. The (n, k) contest is formulated in terms of the first-exit time of the graph of a random walk from a certain region of the state-time space. Explicit results are obtained for the probability that player A wins an (n, k) contest and the expected number of trials in an (n, k) contest. Comparisons of (n, k) contests are made in terms of the probability that the stronger player wins and the expected number of trials.

Additional file 1: Supplementary Table 1. Female Sub-analysis investigating the association between SPS and characteristics/ lifestyle factors. Supplementary Table 2. Female Sub-analysis investigating the association between WHO criteria I and characteristics/ lifestyle factors. Supplementary Table 3. Female Sub-analysis investigating the association between WHO criteria III and characteristics/ lifestyle factors. Supplementary Table 4. Female Sub-analysis investigating the association between both WHO criteria I and III and characteristics/ lifestyle factors. Supplementary Table 5. Female Sub-analysis investigating the association between CRC and characteristics/ lifestyle factors. Supplementary Table 6. Female Sub-analysis investigating the association between SPS patients with no CRC and characteristics/ lifestyle factors

Introduction: Although Singapore national guidelines recommend influenza vaccination for individuals with comorbidities, the vaccine uptake remains relatively low. This study examines the rates of influenza vaccine prescriptions in a clinic population, and patient, doctor and clinic factors that could affect the vaccine prescribing rates. Materials and Methods: This retrospective review utilised electronic medical records from HIV-infected patients seen in an infectious disease (ID) specialist clinic. Data from 40 randomly selected patients per physician were analysed for the outcome of influenza vaccine prescriptions from 1 January to 31 December 2007. All 7 consultants and the 6 ID registrars who had spent at least 4 months in the Department during 2007 were included. Data analysed included patient, physician, and clinic characteristics, and clinically relevant outcomes of admission within a year, and the length of hospital stay. Results: Of the 461 HIV-infected patients analysed for this study, only 107 (23%) were prescribed influenza vaccine in 2007. Vaccine prescribing rates by individual physicians ranged from 0% to 77%. The outcome of vaccine prescribing was analysed by patient demographics (age >40 years, gender, race), physician characteristics (doctor grade, gender and training), and clinic volumes (number of patients per clinic session). Multivariate analysis demonstrated that patients with female doctors (OR 1.8, 95% CI, 1.1 to 3.0, P = 0.017), and doctors with overseas medical training (OR 11.6, 95% CI, 6.0 to 22.2, P

BACKGROUND: Substantial evidence supports an association between use of menopausal hormone therapy and decreased colorectal cancer (CRC) risk, indicating a role of exogenous sex hormones in CRC development. However, findings on endogenous oestrogen exposure and CRC are inconsistent. METHODS: We used a Mendelian randomisation approach to test for a causal effect of age at menarche and age at menopause as surrogates for endogenous oestrogen exposure on CRC risk. Weighted genetic risk scores based on 358 single-nucleotide polymorphisms associated with age at menarche and 51 single-nucleotide polymorphisms associated with age at menopause were used to estimate the association with CRC risk using logistic regression in 12,944 women diagnosed with CRC and 10,741 women without CRC from three consortia. Sensitivity analyses were conducted to address pleiotropy and possible confounding by body mass index. RESULTS: Genetic risk scores for age at menarche (odds ratio per year 0.98, 95% confidence interval: 0.95-1.02) and age at menopause (odds ratio 0.98, 95% confidence interval: 0.94-1.01) were not significantly associated with CRC risk. The sensitivity analyses yielded similar results. CONCLUSIONS: Our study does not support a causal relationship between genetic risk scores for age at menarche and age at menopause and CRC risk.

We initiate the study of the algorithmic complexity of Maker-Breaker games played on edge sets of graphs for general graphs. We mainly consider three of the big four such games: the connectivity game, perfect matching game, and $H$-game. Maker wins if she claims the edges of a spanning tree in the first, a perfect matching in the second, and a copy of a fixed graph $H$ in the third. We prove that deciding who wins the perfect matching game and the $H$-game is PSPACE-complete, even for the latter in graphs of small diameter if $H$ is a tree. Seeking to find the smallest graph $H$ such that the $H$-game is PSPACE-complete, we also prove that there exists such an $H$ of order 51 and size 57. On the positive side, we show that the connectivity game and arboricity-$k$ game are polynomial-time solvable. We then give several positive results for the $H$-game, first giving a structural characterization for Breaker to win the $P_4$-game, which gives a linear-time algorithm for the $P_4$-game. We provide a structural characterization for Maker to win the $K_{1,\ell}$-game in trees, which implies a linear-time algorithm for the $K_{1,\ell}$-game in trees. Lastly, we prove that the $K_{1,\ell}$-game in any graph, and the $H$-game in trees are both FPT parameterized by the length of the game. We leave the complexity of the last of the big four games, the Hamiltonicity game, as an open question.

We give a general construction of sequential games among multiple players, as well as a construction of the composition of sequential games. We obtain new properties of the optimal class of win-by-k games, including closure under composition and independence between the winner of the game and the number of points played. We obtain new results on the asymptotic efficiency of the n-point, win-by-k games.

We analyze the following general version of the deterministic Hats game. Several sages wearing colored hats occupy the vertices of a graph. Each sage can have a hat of one of k colors. Each sage tries to guess the color of his own hat merely on the basis of observing the hats of his neighbors without exchanging any information. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colors. We present an example of a planar graph for which the sages win for k = 14. We also give an easy proof of the theorem about the Hats game on “windmill” graphs.

Objective To compare colorectal cancer (CRC) incidences in carriers of pathogenic variants of the MMR genes in the PLSD and IMRC cohorts, of which only the former included mandatory colonoscopy surveillance for all participants. Methods CRC incidences were calculated in an intervention group comprising a cohort of confirmed carriers of pathogenic or likely pathogenic variants in mismatch repair genes (path_MMR) followed prospectively by the Prospective Lynch Syndrome Database (PLSD). All had colonoscopy surveillance, with polypectomy when polyps were identified. Comparison was made with a retrospective cohort reported by the International Mismatch Repair Consortium (IMRC). This comprised confirmed and inferred path_MMR carriers who were first- or second-degree relatives of Lynch syndrome probands. Results In the PLSD, 8,153 subjects had follow-up colonoscopy surveillance for a total of 67,604 years and 578 carriers had CRC diagnosed. Average cumulative incidences of CRC in path_MLH1 carriers at 70 years of age were 52% in males and 41% in females; for path_MSH2 50% and 39%; for path_MSH6 13% and 17% and for path_PMS2 11% and 8%. In contrast, in the IMRC cohort, corresponding cumulative incidences were 40% and 27%; 34% and 23%; 16% and 8% and 7% and 6%. Comparing just the European carriers in the two series gave similar findings. Numbers in the PLSD series did not allow comparisons of carriers from other continents separately. Cumulative incidences at 25 years were < 1% in all retrospective groups. Conclusions Prospectively observed CRC incidences (PLSD) in path_MLH1 and path_MSH2 carriers undergoing colonoscopy surveillance and polypectomy were higher than in the retrospective (IMRC) series, and were not reduced in path_MSH6 carriers. These findings were the opposite to those expected. CRC point incidence before 50 years of age was reduced in path_PMS2 carriers subjected to colonoscopy, but not significantly so.

We analyze the following general version of the deterministic Hats game. Several sages wearing colored hats occupy the vertices of a graph. Each sage can have a hat of one of $k$ colors. Each sage tries to guess the color of his own hat merely on the basis of observing the hats of his neighbors without exchanging any information. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colors. We present an example of a planar graph for which the sages win for $k = 14$. We also give an easy proof of the theorem about the Hats game on "windmill" graphs., Comment: 8 pages

Purpose: Reducing colorectal cancer incidence and mortality through early detection would improve efficacy if targeted. We developed a colorectal cancer risk prediction model incorporating personal, family, genetic, and environmental risk factors to enhance prevention. Methods: A familial risk profile (FRP) was calculated to summarize individuals' risk based on detailed cancer family history (FH), family structure, probabilities of mutation in major colorectal cancer susceptibility genes, and a polygenic component. We developed risk models, including individuals' FRP or binary colorectal cancer FH, and colorectal cancer risk factors collected at enrollment using population-based colorectal cancer cases (N = 4,445) and controls (N = 3,967) recruited by the Colon Cancer Family Registry Cohort (CCFRC). Model validation used CCFRC follow-up data for population-based (N = 12,052) and clinic-based (N = 5,584) relatives with no cancer history at recruitment to assess model calibration [expected/observed rate ratio (E/O)] and discrimination [area under the receiver-operating-characteristic curve (AUC)]. Results: The E/O [95% confidence interval (CI)] for FRP models for population-based relatives were 1.04 (0.74–1.45) for men and 0.86 (0.64–1.20) for women, and for clinic-based relatives were 1.15 (0.87–1.58) for men and 1.04 (0.76–1.45) for women. The age-adjusted AUCs (95% CI) for FRP models for population-based relatives were 0.69 (0.60–0.78) for men and 0.70 (0.62–0.77) for women, and for clinic-based relatives were 0.77 (0.69–0.84) for men and 0.68 (0.60–0.76) for women. The incremental values of AUC for FRP over FH models for population-based relatives were 0.08 (0.01–0.15) for men and 0.10 (0.04–0.16) for women, and for clinic-based relatives were 0.11 (0.05–0.17) for men and 0.11 (0.06–0.17) for women. Conclusions: Both models calibrated well. The FRP-based model provided better risk stratification and risk discrimination than the FH-based model. Impact: Our findings suggest detailed FH may be useful for targeted risk-based screening and clinical management.

International audience; We define and study the following two-player game on a graph G. Let k ∈ N *. A set of k guards is occupying some vertices of G while one spy is standing at some node. At each turn, first the spy may move along at most s edges, where s ∈ N * is his speed. Then, each guard may move along one edge. The spy and the guards may occupy the same vertices. The spy has to escape the surveillance of the guards, i.e., must reach a vertex at distance more than d ∈ N (a predefined distance) from every guard. Can the spy win against k guards? Similarly, what is the minimum distance d such that k guards may ensure that at least one of them remains at distance at most d from the spy? This game generalizes two well-studied games: Cops and robber games (when s = 1) and Eternal Dominating Set (when s is unbounded). We consider the computational complexity of the problem, showing that it is NP-hard (for every speed s and distance d) and that some variant of it is PSPACE-hard in DAGs. Then, we establish tight tradeoffs between the number of guards, the speed s of the spy and the required distance d when G is a path or a cycle.

Genome-wide association studies have been successful in elucidating the genetic basis of colorectal cancer, but there remains unexplained variability in genetic risk. To identify new risk variants and to confirm reported associations, we conducted a genome-wide association study in 1,701 colorectal cancer cases and 14,082 cancer-free controls from the Finnish population. A total of 9,068,015 genetic variants were imputed and tested, and 30 promising variants were studied in additional 11,647 cases and 12,356 controls of European ancestry. The previously reported association between the single-nucleotide polymorphism rs992157 (2q35) and colorectal cancer was independently replicated (p=2.08x10-4; OR, 1.14; 95% CI, 1.06-1.23), and it was genome-wide significant in combined analysis (p=1.50x10-9; OR, 1.12; 95% CI, 1.08-1.16). Variants at 2q35, 6p21.2, 8q23.3, 8q24.21, 10q22.3, 10q24.2, 11q13.4, 11q23.1, 14q22.2, 15q13.3, 18q21.1, 20p12.3, and 20q13.33 were associated with colorectal cancer in the Finnish population (false discovery rate

The previous mean-field calculation [Myaing Thi Win and K. Hagino, Phys. Rev. C{\bf 78}, 054311 (2008)] has shown that the oblate deformation in $^{28,30,32}$Si disappears when a $\Lambda$ particle is added to these nuclei. We here investigate this phenomenon by taking into account the effects beyond the mean-field approximation. To this end, we employ the microscopic particle-rotor model based on the covariant density functional theory. We show that the deformation of $^{30}$Si does not completely disappear, even though it is somewhat reduced, after a $\Lambda$ particle is added if the beyond-mean-field effect is taken into account. We also discuss the impurity effect of $\Lambda$ particle on the electric quadrupole transition, and show that an addition of a $\Lambda$ particle leads to a reduction in the $B(E2)$ value, as a consequence of the reduction in the deformation parameter., Comment: 6 pages, 5 figures. The version to appear in Phys. Rev. C

While elevated blood cholesterol has been associated with an increased risk of colorectal cancer (CRC) in observational studies, causality is uncertain. Here we apply a Mendelian randomisation (MR) analysis to examine the potential causal relationship between lipid traits and CRC risk. We used single nucleotide polymorphisms (SNPs) associated with blood levels of total cholesterol (TC), triglyceride (TG), low-density lipoprotein (LDL), and high-density lipoprotein (HDL) as instrumental variables (IV). We calculated MR estimates for each risk factor with CRC using SNP-CRC associations from 9,254 cases and 18,386 controls. Genetically predicted higher TC was associated with an elevated risk of CRC (odds ratios (OR) per unit SD increase = 1.46, 95% confidence interval [CI]: 1.20-1.79, P=1.68x10−4). The pooled ORs for LDL, HDL, and TG were 1.05 (95% CI: 0.92-1.18, P=0.49), 0.94 (95% CI: 0.84-1.05, P= 0.27), and 0.98 (95% CI: 0.85-1.12, P=0.75) respectively. A genetic risk score for 3-hydoxy-3-methylglutaryl-coenzyme A reductase (HMGCR) to mimic the effects of statin therapy was associated with a reduced CRC risk (OR=0.69, 95% CI: 0.49-0.99, P=0.046). This study supports a causal relationship between higher levels of TC with CRC risk, and a further rationale for implementing public health strategies to reduce the prevalence of hyperlipidaemia. This article is protected by copyright. All rights reserved.

BACKGROUND:Genome-wide association studies have identified at least 15 independent common genetic variants associated with colorectal cancer (CRC) risk. The aim of this study was to investigate whether 11 of these variants are associated with CRC risk for carriers of germline mutations in DNA mismatch repair (MMR) genes.METHODS:A total of 927 MMR gene mutation carriers (360 MLH1, 442 MSH2, 85 MSH6 and 40 PMS2) from 315 families enrolled in the Colon Cancer Family Registry, were genotyped for the single nucleotide polymorphisms (SNPs): rs16892766 (8q23.3), rs6983267 (8q24.21), rs719725 (9p24), rs10795668 (10p14), rs3802842 (11q23.1), rs4444235 (14q22.2), rs4779584 (15q13.3), rs9929218 (16q22.1), rs4939827 (18q21.1), rs10411210 (19q13.1) and rs961253 (20p12.3). We used a weighted Cox regression to estimate CRC risk for homozygous and heterozygous carriers of the risk allele compared with homozygous non-carriers as well as for an additive per allele model (on the log scale).RESULTS:Over a total of 40,978 person-years observation, 426 (46%) carriers were diagnosed with CRC at a mean age of 44.3 years. For all carriers combined, we found no evidence of an association between CRC risk and the total number of risk alleles (hazard ratio [HR] per risk allele=0.97, 95% confidence interval [CI]=0.88-1.07, p=0.52).CONCLUSIONS:We found no evidence that the SNPs associated with CRC in the general population are modifiers of the risk for MMR gene mutation carriers overall, and therefore any evidence of proven clinical utility in Lynch syndrome.

Judy Bland: School Nutrition Program Employees Impact the Lives of Children. Roxie Rodgers Dinstel: Extension/Food Bank Partnership Unites to Fill Funding Gap in Alaska. Karen Ensle: Should I Eat the Fish I Catch - An Outreach Project to Pregnant Women. Susan Hansen: Child Care Providers – An Untapped Audience. Vicki Hayman: State and County Based Educators Team Up to Participate in Adolescent Calcium Research Project. Susan Holladay: Healthy Eating, Healthy Living. Luanne J. Hughes: Designing an Agriculture and Nutrition Education Program for Youth. Jo Anne Kock: SIDS Awareness in Southern Nevada. Marilyn A. Sachs: LifeWorks Make Life Work. Jo Shuford-Law: Cooperative Extension & Dietetic Interns = “Win-Win”. Linda K. Walter: A Team Approach to Community Health.

We derive an upper bound and investigate some approximations on the symbol error probability (SEP) for coherent detection of M-ary phase-shift keying, using an array of antennas with optimum combining in wireless systems in the presence of multiple uncorrelated equal-power cochannel interferers and thermal noise in a Rayleigh fading environment. Our results are general and valid for an arbitrary number of antenna elements as well as an arbitrary number of interferers. In particular, the exact SEP is derived for an arbitrary number of antennas and interferers; the computational complexity of the exact solution depends on the minimum number of antennas and interferers. Moreover, closed-form approximations are provided for the cases of dual optimum combining with an arbitrary number of interferers, and of two interferers with an arbitrary number of antenna elements. We show that our bounds and approximations are close to Monte Carlo simulation results for all cases considered in this paper.

Two subtypes of the human cannabinoid receptor have been identified. The CB1 receptor is primarily distributed in the central nervous system, whereas the CB2 receptor is associated with peripheral tissue, including the spleen. These two subtypes are also distinguished by their ligand-binding profiles. The goal of this study was to identify critical residues in transmembrane region III (TM3) of the receptors that contribute to subtype specificity in ligand binding. For this purpose, a chimeric cannabinoid receptor [CB1/2(TM3)] was generated in which the TM3 of CB1 was replaced with the corresponding region of CB2. These receptors were stably expressed in Chinese hamster ovary cells for evaluation. The binding affinities of CB1/2(TM3) and the wild-type CB1 receptor to several prototype ligands were similar with one notable exception: the chimeric receptor exhibited a 4-fold enhancement in binding affinity to WIN 55,212-2 (K(d) = 4.8 nM) relative to that observed with CB1 (K(d) = 21.7 nM). Two additional aminoalkylindoles, JWH 015 and JWH 018, also bound the chimeric receptor (K(i) = 1.0 microM and 1.4 nM, respectively) with higher affinity compared with the wild-type CB1 (K(i) = 5.2 microM and 9.8 nM, respectively). Furthermore, the increase in binding affinities of the aminoalkylindoles were reflected in the EC(50) values for the ligand-induced inhibition of intracellular cAMP levels mediated by the chimeric receptor. This pattern mirrors the selectivity of WIN 55,212-2 binding to CB2 compared with CB1. Site-specific mutagenesis of the most notable amino acid changes in the chimeric receptor, Gly195 to Ser and Ala198 to Met, revealed that the enhancement in WIN 55,212-2 binding is contributed to by the Ser but not by the Met residue. The data indicate that the amino acid differences in TM3 between CB1 and CB2 play a critical role in subtype selectivity for this class of compounds.

Last month (February 2014) we posted three games in which you were asked to pick a positive integer. The question in each was: What is the highest number you should think about picking? Here, we offer solutions to all three. How did you do?1. Found dollar.Alice and Bob are vying for a found dollar, with lowest number the winner and a tie winning it for neither. Sadly, the only "Nash equilibrium" solution is for both players to choose "1" and the dollar to go unclaimed---a mini "prisoner's dilemma." Collaboration could have won each of them 50 cents.2. Zero sum.Here, the writer of the lower number wins $1 from the other player, unless it is lower by only 1, in which case the player with the higher number would win $2 from the other player. A tie would result in no money changing hands. This problem was published by Martin Gardner, appearing as Problem 11.13 in his The Collossal Book of Short Puzzles and Problems (W.W. Norton & Co., New York, 2006). The Nash equilibrium solution would be to write "1," "2," "3," "4," or "5" with probabilities 1/16, 5/16, 1/4, 5/16, and 1/16, respectively. (Gardner did not provide a proof, but it is not difficult to show this is a Nash equilibrium strategy and, with a little more work, the only one.) The highest number either player should consider writing is thus "5." 3. Swedish lottery.This game, which I included in my book Mathematical Puzzles: A Conoisseur's Collection (A K Peters Ltd., Natick, MA, 2001) as "Swedish Lottery," has the surprising property that the equilibrium strategy calls for playing every positive integer with positive probability. There is no largest integer you should consider playing. To see this, imagine for the sake of reaching a contradiction that there is a highest number you (and the other players) should ever play; call it number k. When would you win playing k? Only when the other players choose the same lower number. But if you played k+1, you would win all those times plus the times the other two players both play k. k+1 is thus a better choice than k, contradicting the assumption that the strategy is a Nash equilibrium. There is, in fact, a common Nash equilibrium strategy for Alice, Bob, and Charlie---calling for the number j to be selected with probability (1--r)rj−1 where r is the root of a certain cubic equation and approximately 0.543689. The probabilities for choosing 1, 2, 3, and 4 are about 0.456311, 0.248091, 0.134884, and 0.073335, respectively; the probability of choosing a number greater than 100 is teeny. As an experiment in 2010, I ran a Swedish Lottery among 40 graduate students in Dartmouth's Computer Science Department. The winning number was 6. A much larger version---actually a game a day for 47 straight days---was run in Sweden in 2007 under the name "Limbo." The number of players each day averaged 53,785; the lowest winning number was 162, the highest 4,465. For more, see http://swopec.hhs.se/hastef/papers/hastef0671.pdf.

incorporation of [%]methionine into protein has recovered to control levels. We therefore shifted the exposure to anisomycin putting it either before 5-HT application (by 12 h) or after the last 5-HT application (0.5 h or 4 h). In each case, anisomycin had no statistically significant effect on the 5-HT-induced long-term facilitation (65 k lo%, n = 4; 51 f 19%,n = 4;90 k 32%,n = 4,respectively). &-Amanitin applied 0.5 h after 5-HT application also had no significant effect on the 5-HT-induced long-term facilitation Thus, long-term facilitation of an identified synaptic connection, important for the storage of long-term behavioural sensitization in Aplysia, shows a narrow critical time win(47 k 5%. n = 4).