Proportion Of Tails Research Articles

A microstructural hydration model for cemented paste backfill considering internal sulfate attacks

Abstract Cemented paste backfill (CPB) is a type of cementitious material produced with tailings, cement, and water. Typically, CPB has a high proportion of tailings (75–80 wt%), which may contain a large amount of sulfide minerals that can cause serious attacks in the CPB system. In this study, we proposed a microstructural hydration model to investigate the influence of internal sulfate attacks (ISA) on CPB. The ISA model was verified using experimental observations and was used to investigate the microstructure and strength evolution of CPB. Finally, the proposed ISA model was implemented in PFC2D to analyze the failure mode of CPB during uniaxial compressive loading. The results of the proposed ISA model agreed well with the experimental observations. Based on this model, the microstructure evolution of CPB can be classified into solid–liquid two-phase stage and solid-phase stage. Under the influence of ISA, the short-term CPB strength (≤28 days) increased at an accelerated rate whereas the long-term CPB strength (≥56 days) decreased, which could be well explained by the proposed ISA model. The PFC2D simulation results had a good agreement with those of the experiment, and the failure mode of the CPB specimen under the influence of ISA was mainly tensile.

SM22 is required for the maintenance of actin-rich structures generated during bacterial infections

The host actin cytoskeleton is utilized by an assortment of pathogenic bacteria to colonize and cause disease in their hosts. Two prominently studied actin-hijacking bacteria are enteropathogenic Escherichia coli (EPEC) and Listeria monocytogenes. EPEC form actin-rich pedestals atop its host cells to move across the intestinal epithelia, while Listeria monocytogenes generate branched actin networks arranged as actin clouds around the bacteria and as comet tails for propulsion within and amongst their host cells. Previous mass spectrometry analysis revealed that a member of the calponin family of actin-bundling proteins, transgelin/SM22 was enriched in EPEC pedestals. To validate that finding and examine the role of SM22 during infections, we initially immunolocalized SM22 in EPEC and L. monocytogenes infected cells, used siRNA to deplete SM22 and EGFP-SM22 to overexpress SM22, then quantified the alterations to the bacterially generated actin structures. SM22 concentrated at all bacterially-generated actin structures. Depletion of SM22 resulted in fewer pedestals and comet tails and caused comet tails to shorten. The decrease in comet tail abundance caused a proportional increase in actin clouds whereas overexpression of SM22 reversed the actin cloud to comet tail proportions and increased comet tail length, while not influencing EPEC pedestal abundance. Thus, we demonstrate that SM22 plays a role in regulating the transitions and morphological appearance of bacterially generated actin-rich structures during infections.

Automatic early warning of tail biting in pigs: 3D cameras can detect lowered tail posture before an outbreak.

Tail biting is a major welfare and economic problem for indoor pig producers worldwide. Low tail posture is an early warning sign which could reduce tail biting unpredictability. Taking a precision livestock farming approach, we used Time-of-flight 3D cameras, processing data with machine vision algorithms, to automate the measurement of pig tail posture. Validation of the 3D algorithm found an accuracy of 73.9% at detecting low vs. not low tails (Sensitivity 88.4%, Specificity 66.8%). Twenty-three groups of 29 pigs per group were reared with intact (not docked) tails under typical commercial conditions over 8 batches. 15 groups had tail biting outbreaks, following which enrichment was added to pens and biters and/or victims were removed and treated. 3D data from outbreak groups showed the proportion of low tail detections increased pre-outbreak and declined post-outbreak. Pre-outbreak, the increase in low tails occurred at an increasing rate over time, and the proportion of low tails was higher one week pre-outbreak (-1) than 2 weeks pre-outbreak (-2). Within each batch, an outbreak and a non-outbreak control group were identified. Outbreak groups had more 3D low tail detections in weeks -1, +1 and +2 than their matched controls. Comparing 3D tail posture and tail injury scoring data, a greater proportion of low tails was associated with more injured pigs. Low tails might indicate more than just tail biting as tail posture varied between groups and over time and the proportion of low tails increased when pigs were moved to a new pen. Our findings demonstrate the potential for a 3D machine vision system to automate tail posture detection and provide early warning of tail biting on farm.

Perceptions of randomness in binary sequences: Normative, heuristic, or both?

When people consider a series of random binary events, such as tossing an unbiased coin and recording the sequence of heads (H) and tails (T), they tend to erroneously rate sequences with less internal structure or order (such as HTTHT) as more probable than sequences containing more structure or order (such as HHHHH). This is traditionally explained as a local representativeness effect: Participants assume that the properties of long sequences of random outcomes—such as an equal proportion of heads and tails, and little internal structure—should also apply to short sequences. However, recent theoretical work has noted that the probability of a particular sequence of say, heads and tails of length n, occurring within a larger (>n) sequence of coin flips actually differs by sequence, so P(HHHHH) <P(HTTHT). In this alternative account, people apply rational norms based on limited experience. We test these accounts. Participants in Experiment 1 rated the likelihood of occurrence for all possible strings of 4, 5, and 6 observations in a sequence of coin flips. Judgments were better explained by representativeness in alternation rate, relative proportion of heads and tails, and sequence complexity, than by objective probabilities. Experiments 2 and 3 gave similar results using incentivized binary choice procedures. Overall the evidence suggests that participants are not sensitive to variation in objective probabilities of a sub-sequence occurring; they appear to use heuristics based on several distinct forms of representativeness.

How Useful Are Aggregate Measures of Systemic Risk?

Following the financial crisis of 2008–2009, a large body of literature has emerged that attempts to quantify and measure systemic risk. In this article, the author focuses on some of the more popular systemic risk indicators from this literature and asks how well they work in the following sense: At the aggregate level, what information do we learn from these systemic risk indicators that is above that which is readily observable in the market? Several popular measures provide very little incremental information beyond that contained in implied volatilities and credit spreads—information that is commonly known to market participants. For some indicators, where neither the cross-sectional mean nor standard deviation contains meaningful incremental information, the author finds that the tail proportion (the cross-sectional proportion of indicators experiencing a tail realization) does contain information that is not already observable in the market.

Physiological responses and accumulation of heavy metals and arsenic of Medicago sativa L. growing on acidic copper mine tailings in arid lands

Acidic copper mine tailings with high levels of heavy metals and arsenic pose a great risk to ecosystems and human beings. Physiological responses and phytoaccumulation of heavy metals and arsenic in Medicago sativa L. growing in soils with various proportions of acidic copper mine tailings were assessed in this study. Seed germination of M. sativa was enhanced by 5–10% tailings but inhibited at higher proportions (30% and 50%) of tailings. Seedling growth, cell membrane and photosynthesis were adversely affected when the plants were grown in soils with high proportions of tailings. The activities of antioxidant enzymes (catalase, superoxide dismutase and guaiocol peroxidase) increased with increasing proportions of tailings, indicating that the antioxidant system was not impaired and can tolerate the toxicity of mine tailings. The plants grew well in soil containing up to 50% of acidic copper mine tailings. Heavy metals and arsenic except Hg were overwhelmingly immobilized in roots. Medicago sativa is a promising plant species for revegetation and phytostabilization of acidic copper mine tailings in arid lands. However, the high mobility of Hg from root to shoot may pose risk to animals.

Biological effects of long term fine limestone tailings discharge in a fjord ecosystem

Benthic infaunal data collected from 1993 to 2010 were analysed to examine the effect of long term discharge of fine limestone tailings on macrofaunal species assemblages in a fjord. Relative distance from the outfall and proportion of fine tailings in the sediment were correlated with benthic community structure. Diversity decreased with increasing proportion of fine tailings. Biological Traits Analysis (BTA) was used to explore the temporal and spatial effects of the tailings gradient on macrofaunal functional attributes. BTA revealed that all stations along a pressure gradient of fine limestone tailings were dominated by free-living species. As the proportion of fine tailings in the sediment increased, there was an increase in fauna that were smaller, highly mobile, living on or nearer the surface sediment, with shorter lifespans. There was a decrease in permanent tube dwellers, those fauna with low or no mobility, that live deeper in the sediment and have longer lifespans (>5yrs).

Exploring architecture of xyloglucan cellulose nanocrystal complexes through enzyme susceptibility at different adsorption regimes.

Xyloglucan (XG) is believed to act as a cementing material that contributes to the cross-linking and mechanical properties of the cellulose framework in plant cell walls. XG can adsorb to the cellulose nanocrystal (CNC) surface in vitro in order to simulate this in vivo relationship. The target of our work was to investigate the sorption behavior of tamarind seed XG on CNC extracted from cotton linters at different XG/CNC concentration ratios, that is, different adsorption regimes regarding the XG-CNC complex organization and the enzymatic susceptibility of XG. First, we determined the adsorption isotherm. Second, XG-CNC complexes were enzymatically hydrolyzed using a xyloglucan-specific endoglucanase in order to quantify the different XG fractions involved in binding to CNC and to determine adsorption regimes, that is, presence of loops, tails, and trains. Finally, the architecture of the XG-CNC complex was investigated by transmission electron microscopy imaging of negatively stained XG-CNC suspensions and XG immunolabeled suspensions at different XG/CNC concentration ratios, both before and after xyloglucanase hydrolysis process. This study revealed that an increasing XG/CNC concentration ratio led to a change in the XG binding organization to CNC. At low XG/CNC concentration ratios, almost all XG chains were bound as trains to the CNC surface. In contrast, at increasing XG/CNC concentration ratios, the proportion of loops and tails increases. The organization change induces CNC aggregation to form a cellulose/XG network at low XG/CNC regimes, whereas CNC remains in the form of individual particles at higher XG/CNC regimes. Results are discussed both regarding the biological role of XG in plant cell walls and in the perspective of designing new biobased materials.

Effects of tail docking and docking length on neuroanatomical changes in healed tail tips of pigs

In pig production, piglets are tail docked at birth in order to prevent tail biting later in life. In order to examine the effects of tail docking and docking length on the formation of neuromas, we used 65 pigs and the following four treatments: intact tails (n=18); leaving 75% (n=17); leaving 50% (n=19); or leaving 25% (n=11) of the tail length on the pigs. The piglets were docked between day 2 and 4 after birth using a gas-heated apparatus, and were kept under conventional conditions until slaughter at 22 weeks of age, where tails were removed and examined macroscopically and histologically. The tail lengths and diameters differed at slaughter (lengths: 30.6±0.6; 24.9±0.4; 19.8±0.6; 8.7±0.6 cm; P<0.001; tail diameter: 0.5±0.03; 0.8±0.02; 1.0±0.03; 1.4±0.04 cm; P<0.001, respectively). Docking resulted in a higher proportion of tails with neuromas (64 v. 0%; P<0.001), number of neuromas per tail (1.0±0.2 v. 0; P<0.001) and size of neuromas (1023±592 v. 0 μm; P<0.001). The results show that tail docking piglets using hot-iron cautery causes formation of neuromas in the outermost part of the tail tip. The presence of neuromas might lead to altered nociceptive thresholds, which need to be confirmed in future studies.

Characteristics Variation of Tailings Using Cemented Paste Backfill Technique

Cemented paste backfill has been proposed in the mining industry for managing metal mill tailings. Low sulfide tailing (0.49 wt%) samples were prepared into different cemented pastes that were mixed with flocculants (polymerized aluminum chloride). The best mixing proportions of tailings, binder, flocculant, and filling structure (containing 0.5 wt% of ordinary Portland cement in one paste layer, 100 g/L polymerization aluminum chloride) were determined through leaching experiment. The addition of polymerization aluminum chloride improved the mechanical property of the paste. The strength of the cemented pastes by adding 100 g/L flocculant met the requirement of mine backfill. The cemented paste could also fix heavy metals, as shown in the paste leachate analysis of copper (Cu, about 0.01–0.08 mg/L of concentration) and chromium (Cr, about 0.03 mg/L of concentration). In summary, results from this study demonstrate that tailings can be managed by cemented paste backfill technique, preventing its contamination of the environment.

Delayed tail loss during the invasion of mouse skin by cercariae of Schistosoma japonicum

A traditional assumption is that schistosome cercariae lose their tails at the onset of penetration. It has, however, recently been demonstrated that, for Schistosoma mansoni, cercarial tails were not invariably being shed as penetration took place and a high proportion of tails entered human skin under experimental conditions. This phenomenon was termed delayed tail loss (DTL). In this paper, we report that DTL also happens with S. japonicum cercariae during penetration of mouse skin. It occurred at all cercarial densities tested, from as few as 10 cercariae/2·25 cm(2) of mouse skin up to 200 cercariae. Furthermore, it was demonstrated that there was a density-dependent increase in DTL as cercarial densities increased. No such density-dependent enhancement was shown for percentage attachment over the same cercarial density range.

Study on the Sprayed Concrete with Iron Tailings

This essay is the subject of national eleventh five support schemes: The analysis of key technology on emission reduction and comprehension utilization of solid waste from large iron ore mine (Number:2008BAB32B14). The purpose of this test is to replace natural sand with the same amount of iron tailings and find a new technology method to utilize iron tailings. Based on theory of the preparation of sprayed concrete, this experiment made ratio test with 20%, 40%, 60%, 80% and 100% iron tailings content, and finally achieved the result which met the engineering required, after multiple batches of laboratory tests. By studying mechanical properties of sprayed concrete mixing different proportions of iron tailings, the optimal ratio of iron tailings to replace nature sand have been gotten. The result indicates that with 20% iron tailings to replace nature sand, the performance of sprayed concrete is the best.

Experimental study on the mechanism effect of seepage on microstructure of tailings

The deformation of microstructure of tailings caused by seepage is the main factor that leads the tailings dam to be damaged and lose stability. The effect of seepage on microstructure of tailings has been studied by a self-made observation testing apparatus of micro-mechanics and deformation of tailings, and its mechanism also has been explained in mechanics of particulate matter. The results show that the deformation response to microstructure of tailings is fast under load. The settlement of sample increases stepwise. Firstly, the fine particles crumble, then skeleton particles move, so as to noticeable settlement. Because the loose particles migrate taken by seepage water, the upper pores become bigger and lower pores become smaller. The relation of seepage water and settlement changing with time could be divided into two stages. In each stage, the rates of seepage and settlement reduce with time, and between the two stages, the rate of settlement increases significantly and the rate of seepage reduces with time. The seepage has significant effect on the particle size distribution of tailings in different depths, which has a little effect on the coarse tailings; the proportion of fine tailings increases significantly with the depth increasing; the minimum particle size decreases gradually and median diameter reduces stepwise with the depth increasing.

Analysis of the Dry Mortar Produced with Iron Tailings

This essay is the subject of national eleventh five support schemes: The analysis of key technology on emission reduction and comprehension utilization of solid waste from large iron ore mine (Number:2008BAB32B14). The purpose of this test is to replace natural sand with the same amount of iron tailings and find a new technology method to utilize solid waste, iron tailings, efficiently and valuably. Pre-determined cement, fly ash and cellulose ether are reasonable, which guaranteed the expected results of iron tailings instead of natural sand test .The proportion of iron tailings to replace natural sand is 0, 30%, 50%, 80%, 100%. Proportion design of M5, M7.5, M10, M15, M20 iron tailings dry mortar is determined by preliminary test. Respectively test water consumption, consistency and folding strength and compressive strength in 3d, 7d and 28d. Experiment results showed that the cementing material, PO42.5 cement made in Heng-sheng-ran Building Material Technology Co., Ltd. Beijing, has a good effect on smaller solid particles of iron tailings. After analyzing test data result, according to the provisions of “Specification for mix proportion design of masonry mortar” (JGJ 98-2000), In accordance with the principles of maximum using iron tailings and higher strength in 28d, recommended proportion of M5, M7.5, M10, M15, M20 iron tailings dry mortar has been determined. The test result will be used by actual production test.

A test of Allen’s rule in subterranean mammals: the genus Ctenomys (Caviomorpha, Ctenomyidae)

We tested the applicability of Allen's rule in 47 species and 32 unnamed forms (populations that are probably good species or undefined taxa within a superspecies or species group) of the South American subterranean Hystricomorph rodents of the genus Ctenomys (tuco-tucos) (Rodentia: Ctenomyidae) by analyzing tail length in relation with head and body length, and body mass. Tail length allometry was analyzed by Reduced Major Axis regression while the possible correlation of relative tail length with temperature, precipitation and evapotranspiration variables was explored through Simultaneous Autoregression to account for spatial autocorrelations. Our results indicate that tuco-tucos do not follow Allen's rule but its converse, tail proportion relative to body mass increasing with latitude while body size decreases in the same direction (the trend is similar for tail length relative to head and body length but not statistically significant). Regarding climatic variables, the main predictors of relative tail length were temperature and evapotranspiration variables with trends confirming the positive (non-Allenian) correlation of relative tail length with latitude. We conclude that tuco-tucos, being almost fully subterranean, thermoregulate behaviorally by maintaining constant temperatures within their burrows independent of geographic location. The former confirms previous results that indicated that Ctenomys follows the converse to Bergmann's rule. Relative tail length variation would be a result of simple allometric growth.

Bernieridae (Aves: Passeriformes): a family-group name for the Malagasy sylvioid radiation

The island of Madagascar is a renowned hotspot for adaptive radiations. Madagascar has been separated from mainland Africa since the end of the Jurassic, and from India since the Late Cretaceous. This long isolation, combined with the island’s large size and relatively few dispersal events has resulted in an avifauna characterized by a low species count and high endemism: for instance, 80% of the breeding Malagasy songbirds (Passeriformes) are endemic (Hawkins &amp; Goodman 2003). A first series of papers (Cibois et al. 1999, 2001; Fjeldsa et al. 1999) on the phylogeny of the Malagasy taxa traditionally classified as Timaliidae, Sylviidae and Pycnonotidae (all families included in the large sylvioid clade) showed that several of these passerines form an original radiation endemic to the island. Because these results were based solely on a single kind of molecular marker (mitochondrial DNA sequences), the authors refrained at that time from giving a name to this clade. More recently, other studies using nuclear markers as well (Beresford et al. 2005; Johansson et al. 2008a, 2008b) confirm the existence of this Malagasy sylvioid radiation. The species that comprise this group exhibit a great variety of bill shapes, wing and tail proportions, and tarsus lengths. This diversity in morphology is linked to varieties of habitat and prey favoured by these insectivorous forest dwellers (Schulenberg 2003). Thus the endemic Malagasy sylvioid clade rivals other island radiations, including the vangas of Madagascar and the finches of the Galapagos, in ecological and morphological diversity. Several authors were inclined to consider this group at the family level, using the name ‘Bernieridae’. To our knowledge the first study using this name was the book “The natural history of Madagascar”, edited by S. M. Goodman and J. Benstead in 2003, where the name ‘Bernieridae’ appeared in two chapters (in Tingle et al. (2003: p. 522) and Hawkins &amp; Goodman (2003: p. 1036), although Schulenberg (2003: p. 1131) referred to the Malagasy "warblers" in his chapter on the radiations of passerine birds on Madagascar). An alternative spelling for the family-group name, ‘Bernieriidae’, can be found in several personal pages on the internet, but we have not found an occurrence of this in any publication, as defined in the International Code of Zoological Nomenclature (4th edition, 1999). The name ‘Bernieridae’ was later used in several journal articles (Chouteau &amp; Fenosoa 2008; Fuchs et al. 2008; Johansson et al. 2008a, 2008b), however, none of these have introduced the family-group name ‘Bernieridae’ according to the provisions of the International Code of Zoological Nomenclature, i.e. the nominal taxon was not explicitly indicated as intentionally new (Article 16.1) and the type genus was not cited (Article 16.2). In the present paper, we therefore propose to rectify this situation by correctly introducing the family-group name for the Malagasy sylvioid radiation.

Hybrid Hydrogels: Macromolecular Assemblies through Inorganic Cross‐Linkers

AbstractThe adsorption process onto a silica surface of oligomers from three different monomers, N,N‐dimethylacrylamide (DMA), N‐isopropylacrylamide (NIPA) and ethylene oxide (EO), was studied. From the adsorption isotherms and calorimetric experiments, it was shown that N‐alkylacrylamide derivatives strongly interact with silica nanoparticles. At low coverage (Γ &lt; 0.5 mg m−2), the polymers were adsorbed in a flat conformation with a high proportion of trains, while for higher coverages (Γ = 0.5 – 1 mg m−2), the adsorption of new chains proceeded by chain displacement, forming an increasing proportion of loops and tails. Similarly, PEO chains readily interacted with silica nanoparticles but showed a lower affinity with an adsorbed amount (Γ ≅ 0.6 mg m−2) that was approximately half of the value obtained for both PDMA and PNIPA. When these oligomers were grafted onto a non‐adsorbing poly(acrylamide‐co‐sodium acrylate) backbone (PAMH), the binding process of these adsorbing side‐chains with silica nanoparticles proceeded very similarly and gave rise to the formation of hybrid hydrogels above critical copolymer and silica concentrations. The viscoelastic properties of these networks were controlled by the concentration of inorganic cross‐links and the fraction of adsorbing grafts that participated in the formation of bridges between particles, the others being involved in inelastic loops or pendant chains. For all the hybrid mixtures investigated, an optimum weight ratio between silica and grafts was found for the viscoelastic properties, which was in agreement with the saturation of silica beads by the graft precursors. Due to the temperature‐dependence of the solubility of the PNIPA side‐chains in aqueous solutions, the PAMH‐g‐PNIPA copolymer was also able to self‐assemble with temperature, giving rise to a hybrid conetwork in the presence of added silica.

Catalase supplementation on thawed bull spermatozoa abolishes the detrimental effect of oxidative stress on motility and DNA integrity

The potential protective effect of catalase supplementation during in vitro culture of frozen/thawed bull spermatozoa was investigated. Frozen/thawed semen collected from three fighting bulls was diluted in phosphate buffered saline (PBS) and incubated at 37 degrees C under different experimental conditions: Control, Catalase (CAT) (200 U/mL), Oxidant (OXI) (100 microm Fe(2+)/1 mm ascorbate), and Catalase + Oxidant (CAT/OXI). We assessed sperm motility, acrosomal integrity, viability and chromatin status (SCSA) at 0, 2 and 6 h of incubation. Our results showed that catalase abolished the effect of the oxidant, protecting spermatozoa against reactive oxygen species, and improving both sperm motility and chromatin status during incubation. The OXI treatment significantly reduced the percentage of motile sperm after 6 h of incubation. The statistical model also showed that there were differences in sperm motility between CAT/OXI (20.8 +/- 2.9%) and OXI (11.6 +/- 7.6%) (p < 0.001). There were no significant effects of OXI on sperm viability, acrosomal status or proportion of abnormal tails. %DFI (spermatozoa with moderate or high DNA Fragmentation Index) was significantly higher on OXI (p < 0.001). Catalase prevented DNA fragmentation even in the presence of the oxidant (%DFI: 30.3 +/- 0.8% OXI vs. 17.4 +/- 0.7% CAT/OXI). We conclude that catalase supplementation after thawing could protect bull spermatozoa against oxidative stress, and it could improve media used for processing thawed spermatozoa.

Ear and tail postures as indicators of emotional valence in sheep

To date, most studies on animal emotions have focused on the assessment of negative emotional states, and there is a lack of approaches to characterising positive emotional states. The aim of this investigation was to measure differences in ear and tail postures in sheep exposed to situations likely to induce states of negative, intermediate and positive emotional valence. Nineteen female sheep were observed in emotion-eliciting situations in two experiments. In the home-pen experiment, ear and tail postures were observed during separation from group members (negative situation), during rumination (intermediate), and while feeding on fresh hay (positive situation). In the fodder experiment, individual sheep were conditioned to anticipate the delivery of standard feed. Once familiar with this experimental condition, they were offered either the standard feed (control treatment), unpalatable wooden pellets (negative treatment), or energetically enriched feed mixed with preferred feed items (positive treatment). Ear and tail postures of sheep were recorded during the final 6 min preceding feed delivery (anticipation phase) and for 6 min during feed delivery (feeding phase). Data were analysed using linear mixed-effect models. In the home-pen experiment, sheep separated from group members showed a high number of ear-posture changes and a high proportion of forward ears compared to hay feeding, during which ears were mainly passive. In the fodder experiment, the total number of ear-posture changes was generally high during the anticipation phases, slightly lower during delivery of the wooden pellets, and clearly reduced during the delivery of standard and enriched feed. A higher proportion of passive ear postures occurred when standard feed and enriched feed were offered compared to the delivery of wooden pellets. The proportion of asymmetric and axial ear postures was influenced by the sequence of testing of the different feeding treatments, with a higher proportion of asymmetric and a lower proportion of axial ear postures during the first exposure to either the wooden pellets or the enriched feed. A high proportion of the sheep's tails being raised was only observed during separation from group members. In both experiments, frequent ear-posture changes were most clearly associated with situations inducing negative states, and a high proportion of passive ear postures with situations likely to induce positive emotional states. Unfamiliarity influenced emotional reactions towards a more negative appraisal. A raised tail only appears to occur in specific situations, and was not useful for distinguishing emotional valence. Apart from the need for further validation, observations of ear-posture changes seem to be a promising approach for assessing emotional reactions in sheep.

‘Catch-up’ numbers

It never ceases to amaze me how often an apparently innocent-looking problem can lead on to something altogether more deep and interesting. As an example of this, I had recently set one of my Lower Sixth classes, as part of a statistics revision lesson, the task of devising some original questions on probability when the following problem emerged:‘A person tosses a fair coin six times. Given that 4 heads and 2 tails result, what is the probability that the proportion of tails obtained at each point before the last toss is less than one third?’