A real-world comparison of circulating tumor cells in breast cancer from China: Novel device, CTC counts and its overall survival

Background

Both CellSearch and CellCollector have been accepted as the proper devices to capture CTC by domestic approval department. However, there is little article about the comparison between these two devices around the world. Herein, we conducted the real-world study to compare with these two devices and to re-verify the efficacy of CTC counts.

Methods

Patients who meet the following points should be included in the analysis. 1. Female, aged 18 years or older; 2. Eastern Cooperative Oncology Group (ECOG) score 0-2; 3. With at least one measurable tumor lesion; 4. Clear immunohistochemistry result; 5. Accept at least one CTC test. Patients were excluded in the analysis if they had a history of malignant tumors, incomplete follow-up information.

Results

536 metastatic breast cancer patients who had been detected for CTC at least once by CellSearch or CellCollector were included in the analysis. CellCollector in vivo CTC detection technology has a higher detection rate than the CellSearch system (69.2% vs 57.4%, P = 0.009). However, the proportion of CTC≥5 detected by CellSearch was higher than CellCollector (37.4% vs 16.3%, P < 0.001). There was a statistically significant difference in overall survival of patients with CTC negative and CTC positive (mOS:49.8 months vs 26.9 months). After 4 weeks of treatment, when CTC decreased by more than 50%, there was a significant difference in survival between the two groups (40.1 months vs 25.8 months, HR = 0.588, 95% CI: 0.350-0.933). In addition, for HER2-positive patients, Patients with CTC HER2 positive had longer overall survival than patients with CTC HER2 negative (median OS: 26.7 months vs 17.3 month, HR = 0.528, 95% CI: 0.269-0.887).

Conclusions

Real-world data indicate that CTC is an independent prognostic factor, and CellCollector and CellSearch have their own advantages in CTC detection.

Creating ad hoc graphical representations of number

The ability to communicate about exact number is critical to many modern human practices spanning science, industry, and politics. Although some early numeral systems used 1-to-1 correspondence (e.g., 'IIII' to represent 4), most systems provide compact representations via more arbitrary conventions (e.g., '7' and 'VII'). When people are unable to rely on conventional numerals, however, what strategies do they initially use to communicate number? Across three experiments, participants used pictures to communicate about visual arrays of objects containing 1-16 items, either by producing freehand drawings or combining sets of visual tokens. We analyzed how the pictures they produced varied as a function of communicative need (Experiment 1), spatial regularities in the arrays (Experiment 2), and visual properties of tokens (Experiment 3). In Experiment 1, we found that participants often expressed number in the form of 1-to-1 representations, but sometimes also exploited the configuration of sets. In Experiment 2, this strategy of using configural cues was exaggerated when sets were especially large, and when the cues were predictably correlated with number. Finally, in Experiment 3, participants readily adopted salient numerical features of objects (e.g., four-leaf clover) and generally combined them in a cumulative-additive manner. Taken together, these findings corroborate historical evidence that humans exploit correlates of number in the external environment - such as shape, configural cues, or 1-to-1 correspondence - as the basis for innovating more abstract number representations.

Counting many as one: Young children can understand sets as units except when counting

Young children frequently make a peculiar counting mistake. When asked to count units that are sets of multiple items, such as the number of families at a party, they often count discrete items (i.e., individual people) rather than the number of sets (i.e., families). One explanation concerns children's incomplete understanding of what constitutes a unit, resulting in a preference for discrete items. Here we demonstrate that children's incomplete understanding of counting also plays a role. In an experiment with 4- and 5-year-old children (N = 43), we found that even if children are able to name sets, group items into sets, and create one-to-one correspondences with sets, many children are nevertheless unable to count sets as units. We conclude that a nascent understanding of the abstraction principle of counting is also a cause of some children's counting errors.

An embedded toolset for human activity monitoring in critical environments

In many working and recreational activities, there are scenarios where both individual and collective safety have to be constantly checked and properly signaled, as occurring in dangerous workplaces or during pandemic events like the recent COVID-19 disease. From wearing personal protective equipment to filling physical spaces with an adequate number of people, it is clear that a possibly automatic solution would help to check compliance with the established rules. Based on an off-the-shelf compact and low-cost hardware, we present a deployed real use-case embedded system capable of perceiving people's behavior and aggregations and supervising the appliance of a set of rules relying on a configurable plug-in framework. Working on indoor and outdoor environments, we show that our implementation of counting people aggregations, measuring their reciprocal physical distances, and checking the proper usage of protective equipment is an effective yet open framework for monitoring human activities in critical conditions.

Banana plant counting and morphological parameters measurement based on terrestrial laser scanning

BACKGROUND

The number of banana plants is closely related to banana yield. The diameter and height of the pseudo-stem are important morphological parameters of banana plants, which can reflect the growth status and vitality. To address the problems of high labor intensity and subjectivity in traditional measurement methods, a fast measurement method for banana plant count, pseudo-stem diameter, and height based on terrestrial laser scanning (TLS) was proposed.

RESULTS

First, during the nutritional growth period of banana, three-dimensional (3D) point cloud data of two measured fields were obtained by TLS. Second, the point cloud data was preprocessed. And the single plant segmentation of the canopy closed banana plant point cloud was realized furtherly. Finally, the number of banana plants was obtained by counting the number of pseudo-stems, and the diameter of pseudo-stems was measured using a cylindrical segmentation algorithm. A sliding window recognition method was proposed to determine the junction position between leaves and pseudo-stems, and the height of the pseudo-stems was measured. Compared with the measured value of artificial point cloud, when counting the number of banana plants, the precision,recall and percentage error of field 1 were 93.51%, 94.02%, and 0.54% respectively; the precision,recall and percentage error of field 2 were 96.34%, 92.00%, and 4.5% respectively; In the measurement of pseudo-stem diameter and height of banana, the root mean square error (RMSE) of pseudo-stem diameter and height of banana plant in field 1 were 0.38 cm and 0.2014 m respectively, and the mean absolute percentage error (MAPE) were 1.30% and 5.11% respectively; the RMSE of pseudo-stem diameter and height of banana plant in field 2 were 0.39 cm and 0.2788 m respectively, and the MAPE were 1.04% and 9.40% respectively.

CONCLUSION

The results show that the method proposed in this paper is suitable for the field measurement of banana count, pseudo-stem diameter, and height and can provide a fast field measurement method for banana plantation management.

Assessing the performance of brushtail possums (Trichosurus vulpecula) on the Mechner counting procedure

This study assessed brushtail possums' performance on the Mechner counting procedure. Six brushtail possums were required to produce different Fixed-Ratio (FR) response targets by lever pressing. Their responses provided access to food reinforcement delivered either upon completing the target FR response requirement on a single lever or, in different conditions, on completing the target FR before producing an additional response on a second lever. The mean number of responses on the first lever before switching to the second lever typically occurred just above the target FR response requirement (FR: 4, 8, 16, 32 and 64). The variability in the number of switches between the levers around the target FR decreased from the first 10 days to the last 10 days, indicating an improvement in counting accuracy over sessions. The time to switch between the first and second lever was consistently variable across response requirements suggesting that it is unlikely the possums were using time to predict when to switch levers. This research further supports the use of the Mechner procedure as a method for measuring counting ability in animals and confirms the possibility of numerical competence in a marsupial species.

A biophysical counting mechanism for keeping time

The ability to estimate and produce appropriately timed responses is central to many behaviors including speaking, dancing, and playing a musical instrument. A classical framework for estimating or producing a time interval is the pacemaker-accumulator model in which pulses of a pacemaker are counted and compared to a stored representation. However, the neural mechanisms for how these pulses are counted remain an open question. The presence of noise and stochasticity further complicates the picture. We present a biophysical model of how to keep count of a pacemaker in the presence of various forms of stochasticity using a system of bistable Wilson-Cowan units asymmetrically connected in a one-dimensional array; all units receive the same input pulses from a central clock but only one unit is active at any point in time. With each pulse from the clock, the position of the activated unit changes thereby encoding the total number of pulses emitted by the clock. This neural architecture maps the counting problem into the spatial domain, which in turn translates count to a time estimate. We further extend the model to a hierarchical structure to be able to robustly achieve higher counts.

MGcount: a total RNA-seq quantification tool to address multi-mapping and multi-overlapping alignments ambiguity in non-coding transcripts

BACKGROUND

Total-RNA sequencing (total-RNA-seq) allows the simultaneous study of both the coding and the non-coding transcriptome. Yet, computational pipelines have traditionally focused on particular biotypes, making assumptions that are not fullfilled by total-RNA-seq datasets. Transcripts from distinct RNA biotypes vary in length, biogenesis, and function, can overlap in a genomic region, and may be present in the genome with a high copy number. Consequently, reads from total-RNA-seq libraries may cause ambiguous genomic alignments, demanding for flexible quantification approaches.

RESULTS

Here we present Multi-Graph count (MGcount), a total-RNA-seq quantification tool combining two strategies for handling ambiguous alignments. First, MGcount assigns reads hierarchically to small-RNA and long-RNA features to account for length disparity when transcripts overlap in the same genomic position. Next, MGcount aggregates RNA products with similar sequences where reads systematically multi-map using a graph-based approach. MGcount outputs a transcriptomic count matrix compatible with RNA-sequencing downstream analysis pipelines, with both bulk and single-cell resolution, and the graphs that model repeated transcript structures for different biotypes. The software can be used as a python module or as a single-file executable program.

CONCLUSIONS

MGcount is a flexible total-RNA-seq quantification tool that successfully integrates reads that align to multiple genomic locations or that overlap with multiple gene features. Its approach is suitable for the simultaneous estimation of protein-coding, long non-coding and small non-coding transcript concentration, in both precursor and processed forms. Both source code and compiled software are available at https://github.com/hitaandrea/MGcount .

Automatization through Practice: The Opportunistic-Stopping Phenomenon Called into Question

As a theory of skill acquisition, the instance theory of automatization posits that, after a period of training, algorithm‐based performance is replaced by retrieval‐based performance. This theory has been tested using alphabet‐arithmetic verification tasks (e.g., is A + 4  = E?), in which the equations are necessarily solved by counting at the beginning of practice but can be solved by memory retrieval after practice. A way to infer individuals’ strategies in this task was supposedly provided by the opportunistic‐stopping phenomenon, according to which, if individuals use counting, they can take the opportunity to stop counting when a false equation associated with a letter preceding the true answer has to be verified (e.g., A + 4  = D). In this case, such within‐count equations would be rejected faster than false equations associated with letters following the true answers (e.g., A + 4  = F, i.e., outside‐of‐count equations). Conversely, the absence of opportunistic stopping would be the sign of retrieval. However, through a training experiment involving 19 adults, we show that opportunistic stopping is not a phenomenon that can be observed in the context of an alphabet‐arithmetic verification task. Moreover, we provide an explanation of how and why it was wrongly inferred in the past. These results and conclusions have important implications for learning theories because they demonstrate that a shift from counting to retrieval over training cannot be deduced from verification time differences between outside and within‐count equations in an alphabet‐arithmetic task.

Counting and the ontogenetic origins of exact equality

Humans are unique in their capacity to both represent number exactly and to express these representations symbolically. This correlation has prompted debate regarding whether symbolic number systems are necessary to represent large exact number. Previous work addressing this question in innumerate adults and semi-numerate children has been limited by conflicting results and differing methodologies, and has not yielded a clear answer. We address this debate by adapting methods used with innumerate populations (a "set-matching" task) for 3- to 5-year-old US children at varying stages of symbolic number acquisition. In five studies we find that children's ability to match sets exactly is related not simply to knowing the meanings of a few number words, but also to understanding how counting is used to generate sets (i.e., the cardinal principle). However, while children were more likely to match sets after acquiring the cardinal principle, they nevertheless demonstrated failures, compatible with the hypothesis that the ability to reason about exact equality emerges sometime later. These findings provide important data on the origin of exact number concepts, and point to knowledge of a counting system, rather than number language in general, as a key ingredient in the ability to reason about large exact number.

Improved semi automatic approach to count the tracks on LR-115 film for monitoring of radioactive elements

An improved semi automatic technique for counting the tracks formed on LR-115 films with the advantages of simplicity and speed is reported. In this technique, a microscope with a Dino-Eye eyepiece camera is coupled to a PC equipped with a python compiler. After etching of the LR-115 film, 16 track images were taken to find the track density. The images generated were binarized before application of a Python algorithm. This process does not disfigure the original track and increase the spatial resolution. The batch process option in Jasc Paint Shop Pro was used to binarize the 16 images simultanously. The Python program automatically counts the total number of tracks formed on the 16 track images. This method was compared with manual counting and counting with the software program-Scion image to verify it. The results showed that the proposed method is reasonably good at counting the tracks. It is a faster and less time-consuming method, and will facilitate measurements of etched tracks in a variety of applications.

Children's understanding of the abstract logic of counting

When children learn to count, do they understand its logic independent of the number list that they learned to count with? Here we tested CP-knowers' (ages three to five) understanding of how counting reveals a set's cardinality, even when non-numerical lists are used to count. Participants watched an agent count unobservable objects in two boxes and were asked to identify the larger set. Participants successfully identified the box with more objects when the agent counted using their familiar number list (Experiment 1) and when the agent counted using a non-numeric ordered list, as long as the items in the list were not linguistically used as number words (Experiments 2-3). Additionally, children's performance was strongly influenced by visual cues that helped them link the list's order to representations of magnitude (Experiment 4). Our findings suggest that three- to six-year-olds who can count also understand how counting reveals a set's cardinality, but they require additional time to understand how symbols on any arbitrary ordered list can be used as numerals.

Exploring adults' awareness of and suggestions for early childhood numerical activities

This study focuses on adults who are neither preschool teachers nor professional caregivers and investigates their beliefs regarding the importance of engaging young children with numerical activities. It also examines the types of numerical activities adults report having observed children engaging with, as well as the types of activities they propose as a way for promoting counting, enumerating, recognizing number symbols, and number composition and decomposition. Findings showed that participants believed to a great extent that engaging young children with numerical activities is important. Most reported that they had observed children engaging with at least some numerical activity. In general, participants relayed more activities and more detailed activities when suggesting activities for each competency, than they did when reporting observed activities. Findings also suggested a need to enhance adults' knowledge regarding the necessity to promote verbal counting, separate from object counting, as well as to increase adults' awareness of number composition and decomposition. For mathematics educators wishing to plan workshops for adults, this study offers a method for investigating adults' knowledge of early numerical activities, as well as a starting point with which to plan appropriate workshops.

The neural basis of counting sequences

Sequence processing is critical for complex behavior, and counting sequences hold a unique place underlying human numerical development. Despite this, the neural bases of counting sequences remain unstudied. We hypothesized that counting sequences in adults would involve representations in sensory, order, magnitude, and linguistic codes that implicate regions in auditory, supplementary motor, posterior parietal, and inferior frontal areas, respectively. In an fMRI scanner, participants heard four-number sequences in a 2 × 2 × 2 design. The sequences were adjacent or not (e.g., 5, 6, 7, 8 vs. 5, 6, 7, 9), ordered or not (e.g., 5, 6, 7, 8 vs. 8, 5, 7, 6), and were spoken by a voice of consistent or variable identity. Then, neural substrates of counting sequences were identified by testing for the effect of consecutiveness (ordered nonadjacent versus ordered adjacent, e.g., 5, 6, 7, 9 > 5, 6, 7, 8) in the hypothesized brain regions. Violations to consecutiveness elicited brain activity in the right inferior frontal gyrus (IFG) and the supplementary motor area (SMA). In contrast, no such activation was observed in the auditory cortex, despite violations in voice identity recruiting strong activity in that region. Also, no activation was observed in the inferior parietal lobule, despite a robust effect of orderedness observed in that brain region. These findings indicate that listening to counting sequences do not automatically elicit sensory or magnitude codes but suggest that the precise increments in the sequence are tracked by the mechanism for processing ordered associations in the SMA and by the mechanism for binding individual lexical items into a cohesive whole in the IFG.

Verbal count sequence knowledge underpins numeral order processing in children

Recent research has suggested that numeral order processing - the speed and accuracy with which individuals can determine whether a set of digits is in numerical order or not - is related to arithmetic and mathematics outcomes. It has therefore been proposed that ordinal relations are a fundamental property of symbolic numeral representations. However, order information is also inherent in the verbal count sequence, and thus verbal count sequence knowledge may instead explain the relationship between performance on numeral order tasks and arithmetic. We explored this question with 62 children aged 6- to 8-years-old. We found that performance on a verbal count sequence knowledge task explained the relationship between numeral order processing and arithmetic. Moreover many children appeared to explicitly base their judgments of numerical order on count sequence information. This suggests that insufficient attention may have been paid to verbal number knowledge in understanding the sources of information that give meaning to numbers.

Metric error monitoring: Another generalized mechanism for magnitude representations?

Error monitoring refers to the ability to monitor one's own task performance without explicit feedback. This ability is studied typically in two-alternative forced-choice (2AFC) paradigms. Recent research showed that humans can also keep track of the magnitude and direction of errors in different magnitude domains (e.g., numerosity, duration, length). Based on the evidence that suggests a shared mechanism for magnitude representations, we aimed to investigate whether metric error monitoring ability is commonly governed across different magnitude domains. Participants reproduced/estimated temporal, numerical, and spatial magnitudes after which they rated their confidence regarding first order task performance and judged the direction of their reproduction/estimation errors. Participants were also tested in a 2AFC perceptual decision task and provided confidence ratings regarding their decisions. Results showed that variability in reproductions/estimations and metric error monitoring ability, as measured by combining confidence and error direction judgements, were positively related across temporal, spatial, and numerical domains. Metacognitive sensitivity in these metric domains was also positively associated with each other but not with metacognitive sensitivity in the 2AFC perceptual decision task. In conclusion, the current findings point at a general metric error monitoring ability that is shared across different metric domains with limited generalizability to perceptual decision-making.

Numerical averaging in mice

Rodents can be trained to associate different durations with different stimuli (e.g., light/sound). When the associated stimuli are presented together, maximal responding is observed around the average of individual durations (akin to averaging). The current study investigated whether mice can also average independently trained numerosities. Mice were initially trained to make 10 or 20 lever presses on a single (run) lever to obtain a reward and each fixed-ratio schedule was signaled either with an auditory or visual stimulus. Then, mice were trained to press another lever to obtain the reward after they responded on the run lever for the minimum number of presses [Fixed Consecutive Number (FCN)-10 or -20 trials] signaled by the corresponding discriminative stimulus. Following this training, FCN trials with the compound stimulus were introduced to test the counting behavior of mice when they encountered conflicting information regarding the number of responses required to obtain the reward. Our results showed that the numbers of responses on these compound test trials were around the average of the number of responses in FCN-10 and FCN-20 trials particularly when the auditory stimulus was associated with a fewer number of required responses. The counting strategy explained the behavior of the majority of the mice in the FCN-Compound test trials (as opposed to the timing strategy). The number of responses in FCN-Compound trials was accounted for equally well by the arithmetic, geometric, and Bayesian averages of the number of responses observed in FCN-10 and FCN-20 trials.

Does the standard search task predict performance in related tasks for Kanizsa-style illusory contours?

It is often assumed that results from standard visual search tasks will be replicated in related tasks but his idea is rarely tested. In a conceptual replication of Li, Cave, and Wolfe (2008), we investigated the attentional demands of Kanizsa-style illusory contours using orientation-based search, comparing performance for items defined by real- as compared to illusory contours. After confirming the initial findings in standard search, we tested the same manipulation in multiple-target search, Thornton and Gilden's (2007) hybrid standard/multiple-target search, and simple- and selective enumeration. The RT slope differences between real- and illusory contours did not replicate in Thornton and Gilden's task, though they did in multiple-target search and selective enumeration. In fact, absolute differences between real- and illusory contours in RT costs per distractor were 2 - 6 times larger than in standard search. To determine whether performance differences between real and illusory contours originated from shape-definition (necessary for distinguishing target shapes from distractors) or unit formation (grouping disconnected parts to define an item/unit), simple and selective enumeration were compared. The differences between real- and illusory-contours only emerged in selective enumeration (enumerating targets among distractors), which suggests the discrepancies between conditions originate from shape definition rather than unit formation processes. There was no evidence of subitizing in selective enumeration for illusory contour figures, but contrary to attention-based theories of enumeration, there was no subitizing for the real-contour controls either. This study contributes to research on illusory contours but it is especially important to the study of search and enumeration.

Counting phylogenetic networks of level 1 and 2

Phylogenetic networks generalize phylogenetic trees, and have been introduced in order to describe evolution in the case of transfer of genetic material between coexisting species. There are many classes of phylogenetic networks, which can all be modeled as families of graphs with labeled leaves. In this paper, we focus on rooted and unrooted level-k networks and provide enumeration formulas (exact and asymptotic) for rooted and unrooted level-1 and level-2 phylogenetic networks with a given number of leaves. We also prove that the distribution of some parameters of these networks (such as their number of cycles) are asymptotically normally distributed. These results are obtained by first providing a recursive description (also called combinatorial specification) of our networks, and by next applying classical methods of enumerative, symbolic and analytic combinatorics.

Finding patterns in objects and numbers: Repeating patterning in pre-K predicts kindergarten mathematics knowledge

Both recent evidence and research-based early mathematics curricula indicate that repeating patterns-predictable sequences that follow a rule-are a topic of major importance for mathematics development. The purpose of the current study was to help build a theory for how early repeating patterning knowledge contributes to early math development, focusing on development in children aged 4-6 years. The current study examined the relation between 65 preschool children's repeating patterning knowledge (via a fast, teacher-friendly measure) and their end-of-kindergarten broad math and numeracy knowledge, controlling for verbal and visual-spatial working memory (WM) skills as well as end-of-pre-K (pre-kindergarten) broad math knowledge. Relations were also examined between repeating patterning and specific aspects of numeracy knowledge-knowledge of the count sequence to 100 and the successor principle. Children's repeating patterning knowledge was significantly predictive of their broad math and general numeracy knowledge, as well as one specific aspect of their numeracy knowledge (counting to 100), even after controlling for verbal and visual-spatial WM skills. Further, repeating patterning knowledge remained a unique predictor of general numeracy knowledge and counting to 100 after controlling for end-of-pre-K broad math knowledge. The relation between repeating patterning and mathematics may be explained by the central role that identifying predictable sequences based on underlying rules plays in both. Theories of math development and early math instruction standards should thus give even greater attention to the role of children's repeating patterning knowledge.

Subitizing and counting impairments in children with developmental coordination disorder

Developmental coordination disorder (DCD) interferes with academic achievement and daily life, and is associated with persistent academic difficulties, in particular within mathematical learning. In the present study, we aimed to study numerical cognition using an approach that taps very basic numerical processes such as subitizing and counting abilities in DCD. We used a counting task and a subitizing task in forty 7-10 years-old children with or without DCD. In both tasks, children were presented with arrays of one to eight dots and asked to name aloud the number of dots as accurately and quickly as possible. In the subitizing task, dots were presented during 250 ms whereas in the counting task they stayed on the screen until the participants gave a verbal response. The results showed that children with DCD were less accurate and slower in the two enumeration tasks (with and without a time limit), providing evidence that DCD impairs both counting and subitizing. These impairments might have a deleterious impact on the ability to improve the acuity of the Approximate Number System through counting, and thus could play a role in the underachievement of children with DCD in mathematics.

Accuracy and efficiency of an artificial intelligence tool when counting breast mitoses

BACKGROUND

The mitotic count in breast carcinoma is an important prognostic marker. Unfortunately substantial inter- and intra-laboratory variation exists when pathologists manually count mitotic figures. Artificial intelligence (AI) coupled with whole slide imaging offers a potential solution to this problem. The aim of this study was to accordingly critique an AI tool developed to quantify mitotic figures in whole slide images of invasive breast ductal carcinoma.

METHODS

A representative H&E slide from 320 breast invasive ductal carcinoma cases was scanned at 40x magnification. Ten expert pathologists from two academic medical centers labeled mitotic figures in whole slide images to train and validate an AI algorithm to detect and count mitoses. Thereafter, 24 readers of varying expertise were asked to count mitotic figures with and without AI support in 140 high-power fields derived from a separate dataset. Their accuracy and efficiency of performing these tasks were calculated and statistical comparisons performed.

RESULTS

For each experience level the accuracy, precision and sensitivity of counting mitoses by users improved with AI support. There were 21 readers (87.5%) that identified more mitoses using AI support and 13 reviewers (54.2%) that decreased the quantity of falsely flagged mitoses with AI. More time was spent on this task for most participants when not provided with AI support. AI assistance resulted in an overall time savings of 27.8%.

CONCLUSIONS

This study demonstrates that pathology end-users were more accurate and efficient at quantifying mitotic figures in digital images of invasive breast carcinoma with the aid of AI. Higher inter-pathologist agreement with AI assistance suggests that such algorithms can also help standardize practice. Not surprisingly, there is much enthusiasm in pathology regarding the prospect of using AI in routine practice to perform mundane tasks such as counting mitoses.

Is thirty-two three tens and two ones? The embedded structure of cardinal numbers

The acquisition and representation of natural numbers have been a central topic in cognitive science. However, a key question in this topic about how humans acquire the capacity to understand that numbers make 'infinite use of finite means' (or that numbers are generative) has been left unanswered. While previous theories rely on the idea of the successor principle, we propose an alternative hypothesis that children's understanding of the syntactic rules for building complex numerals-or numerical syntax-is a crucial foundation for the acquisition of number concepts. In two independent studies, we assessed children's understanding of numerical syntax by probing their knowledge about the embedded structure of cardinal numbers using a novel task called Give-a-number Base-10 (Give-N10). In Give-N10, children were asked to give a large number of items (e.g., 32 items) from a pool that is organized in sets of ten items. Children's knowledge about the embedded structure of numbers (e.g., knowing that thirty-two items are composed of three tens and two ones) was assessed from their ability to use those sets. Study 1 tested English-speaking 4- to 10-year-olds and revealed that children's understanding of the embedded structure of numbers emerges relatively late in development (several months into kindergarten), beyond when they are capable of making a semantic induction over a local sequence of numbers. Moreover, performance in Give-N10 was predicted by other task measures that assessed children's knowledge about the syntactic rules that govern numerals (such as counting fluency), demonstrating the validity of the measure. In Study 2, this association was tested again in monolingual Korean kindergarteners (5-6 years), as we aimed to test the same effect in a language with a highly regular numeral system. It replicated the association between Give-N10 performance and counting fluency, and it also demonstrated that Korean-speaking children understand the embedded structure of cardinal numbers earlier in the acquisition path than English-speaking peers, suggesting that regularity in numerical syntax facilitates the acquisition of generative properties of numbers. Based on these observations and our theoretical analysis of the literature, we propose that the syntax for building complex numerals, not the successor principle, represents a structural platform for numerical thinking in young children.

Automatic kernel counting on maize ear using RGB images

BACKGROUND

The number of kernels per ear is one of the major agronomic yield indicators for maize. Manual assessment of kernel traits can be time consuming and laborious. Moreover, manually acquired data can be influenced by subjective bias of the observer. Existing methods for counting of kernel number are often unstable and costly. Machine vision technology allows objective extraction of features from image sensor data, offering high-throughput and low-cost advantages.

RESULTS

Here, we propose an automatic kernel recognition method which has been applied to count the kernel number based on digital colour photos of the maize ears. Images were acquired under both LED diffuse (indoors) and natural light (outdoor) conditions. Field trials were carried out at two sites in China using 8 maize varieties. This method comprises five steps: (1) a Gaussian Pyramid for image compression to improve the processing efficiency, (2) separating the maize fruit from the background by Mean Shift Filtering algorithm, (3) a Colour Deconvolution (CD) algorithm to enhance the kernel edges, (4) segmentation of kernel zones using a local adaptive threshold, (5) an improved Find-Local-Maxima to recognize the local grayscale peaks and determine the maize kernel number within the image. The results showed good agreement (> 93%) in terms of accuracy and precision between ground truth (manual counting) and the image-based counting.

CONCLUSIONS

The proposed algorithm has robust and superior performance in maize ear kernel counting under various illumination conditions. In addition, the approach is highly-efficient and low-cost. The performance of this method makes it applicable and satisfactory for real-world breeding programs.

Counting fast or slow, aloud or silently? A comparison of adult stutterers and non-stutterers

This study assesses factors influencing the capacity to maintain a steady rhythm during explicit counting activities. There are three counting paces (count every 800, 1200, or 1600 ms) and three experimental conditions (count silently, aloud and aloud in the presence of someone). The study also assesses the effect of a speech disorder, namely stuttering, on this counting ability by comparing the performance of a group of adult stutterers (n = 21) to that of a group of adult non-stutterers (n = 24). For temporal variability, in addition to replicating the fact that counting more slowly leads to lower performance, the results show that there are benefits to expect when participants count aloud instead of silently. There is no main effect of group, but the interaction between the experimental condition, the counting pace, and the group is significant. Adult non-stutterers are better than adult stutterers in the silent and long time-interval conditions (1600 ms). The significantly higher variability at 1600 ms indicates a loss of efficiency in the capacity to keep time constant when counting is slow, and it is in this condition that stutterers will gain the most benefits from counting aloud instead of silently.

The critical role of Arabic numeral knowledge as a longitudinal predictor of arithmetic development

Understanding the cognitive underpinnings of children's arithmetic development has great theoretical and educational importance. Recent research suggests symbolic and nonsymbolic representations of number influence arithmetic development before and after school entry. We assessed nonverbal ability and general language skills as well as nonsymbolic (numerosity) and symbolic (numeral) comparison skills, counting, and Arabic numeral knowledge (numeral reading, writing, and identification) in preschool children (4 years of age). At 6 years of age, we reassessed nonsymbolic (numerosity) and symbolic (numeral) comparison and arithmetic. A latent variable path model showed that Arabic numeral knowledge (defined by numeral reading, writing, and identification at 4 years of age) was the sole unique predictor of arithmetic at 6 years. We conclude that knowledge of the association between spoken and Arabic numerals is one critical foundation for the development of formal arithmetic.

Simple additions: Dissociation between retrieval and counting with electrophysiological indexes

There is current debate about the way adult individuals solve simple additions composed of one-digit operands. There are two opposing views. The first view assumes that people retrieve the result of additions from memory, whilst the second view states that individuals use automatized counting procedures. Our study aimed to dissociate between these two hypotheses. To this end, we analysed the type of problem effect when participants resolved simple additions by comparing additions with operands between 1 and 4 and control additions with at least one operand larger than 4. Brain-waves activity of a group of 30 adult individuals were recorded with 64 scalp electrodes mounted on an elastic cap, referenced against an electrode between Cz and CPz and re-referenced to an average reference offline. We considered two electrophysiological indexes, event-related potentials, ERPs, time-locked to the addition problems to distinguish between retrieval from memory and the use of procedures: A late positivity component (LP, 500-650 time window) over posterior regions associated to memory retrieval difficulty with higher LP positivity when participants resolve difficult vs. easy additions, and a negative component (N400, 250-450 ms time window) over fronto-central regions related to the use memory retrieval vs. procedures with more pronounced N400 amplitudes when the difficulty in the retrieval of semantic information increased. LP modulations were observed depending on the type of problem over posterior regions, P3 and Pz electrodes, whilst the N400 component was not affected. This pattern of results suggests that adult individuals use retrieval from memory to solve simple additions.

When one-two-three beats two-one-three: Tracking the acquisition of the verbal number sequence

Learning how to count is a crucial step in cognitive development, which progressively allows for more elaborate numerical processing. The existing body of research consistently reports how children associate the verbal code with exact quantity. However, the early acquisition of this code, when the verbal numbers are encoded in long-term memory as a sequence of words, has rarely been examined. Using an incidental assessment method based on serial recall of number words presented in ordered versus non-ordered sequences (e.g., one-two-three vs. two-one-three), we tracked the progressive acquisition of the verbal number sequence in children aged 3-6 years. Results revealed evidence for verbal number sequence knowledge in the youngest children even before counting is fully mastered. Verbal numerical knowledge thus starts to be organized as a sequence in long-term memory already at the age of 3 years, and this numerical sequence knowledge is assessed in a sensitive manner by incidental rather than explicit measures of number knowledge.

Nanoparticle Tracking Analysis for Multiparameter Characterization and Counting of Nanoparticle Suspensions

Nanoparticle tracking analysis (NTA) provides direct and real time visualization, sizing and counting of particulate materials between 10 nm and 1 μm in liquid suspension. The technique works on a particle by particle basis, relating the degree of movement under Brownian motion to the sphere equivalent hydrodynamic diameter particle size, allowing for high-resolution particle size distributions to be obtained within minutes. NTA has been used in studying protein complexes and protein aggregates, protein nanoparticles, metal nanoparticles, silica nanoparticles, viruses, cellular vesicles and exosomes to name just a few. Here we describe application of NTA to the analysis of model nanospheres of ~100 nm in liquid suspension, the size being representative of the middle of the NTA working range. The technique described can be adapted for use with nearly all particulate materials with sizes between approximately 10 nm and 1 μm, with appropriate adjustments to instrument settings.

GrCount: Counting method for uncertain data

We report a method for counting uncertain data, i.e. observations that cannot be precisely associated to referents. We model data uncertainty through Possibility Theory and we develop the counting method so as to take into account the possibility distributions attached to data. The result is a fuzzy interval on the domain of natural numbers, which can be obtained by two variants of the method: exact counting provides the true fuzzy interval in quadratic time complexity, while approximate counting carries out an estimate of the fuzzy interval in linear time. We give a step-by-step description of the method so that it can be replicated in any programming environment. We also provide a Python implementation and a use case in Bioinformatics. The method usage is the following: •The uncertain data are represented in form of matrix, one row for each observation. Each row is a possibility distribution;•The method variant must be selected. In the case of the approximate variant, the number of α-values of the resulting fuzzy interval must be provided;•For each referent, a fuzzy interval is determined and carried out by the method.

Visual search does not always predict performance in tasks that require finding targets among distractors: The case of line-ending illusory contours

The standard visual search task is integral to the study of selective attention and in search tasks target present slopes are the primary index of attentional demand. However, there are times when similarities in slopes may obscure important differences between conditions. To demonstrate this point, we used the case of line-ending illusory contours, building on a study by Li, Cave, and Wolfe (2008) where orientation-based search for figures defined by line-ending illusory contours was compared to that for the corresponding real-contour controls. Consistent with Li et al. (2008), we found search to be efficient for both illusory contour figures and the corresponding real-contour controls, with no significant differences between them. However, major differences between illusory contours and the real-contour controls emerged in selective enumeration, a task where participants enumerated targets in a display of distractors, with the number of targets and distractors manipulated. When looking at the distractor slopes, the increase in RT to enumerate a single target as a function of the number of distractors (a direct analogue to target present trials, with identical displays), we found distractor costs for illusory contour figures to be over 100 ms/distractor higher than for the corresponding real-contour controls. Furthermore, the discrepancies in RT slope between 1-3 and 6-8 targets associated with subitizing were only seen in the real-contour controls. These results show that similarities in RT slopes in search may mask important differences between conditions that emerge in other tasks.

Circular Estimate Method (CEM) - a Simple Method to Estimate Caenorhabditis elegans Culture Densities in Liquid Medium

Background

Nematodes are used in many different fields of science, including environmental and biomedical research. Counting and/or estimating nematode numbers is required during research. Although being one of the most common procedures, this apparently simple task is a time-consuming process, prone to errors and concerns regarding procedure, reliability, and accuracy. When an estimate is necessary, there is a traditional manual counting procedure that in this study it will be called as "drop method" (DM). This popular method that extrapolates an animal count from a small drop of fluid shows a high coefficient of variation. To solve this problem, the present study used the free-living nematode Caenorhabditis elegans to develop a new estimation procedure that was based on a relationship between area and volume of a larger sample.

Results

The new method showed a low coefficient of variation and a close relationship between estimated and real counts of the total number of nematodes in large C. elegans suspensions. Reactive oxygen concentration was measured as an example of method application and to allow comparison between methods.

Conclusion

The proposed method is accurate, facile and reproducible, requiring simple, inexpensive materials that make it an excellent alternative to the DM manual counting procedure. Although the DM is faster, its estimates are not as accurate or as precise as those of the new proposed method.

Image analysis-based recognition and quantification of grain number per panicle in rice

BACKGROUND

The number grain per panicle of rice is an important phenotypic trait and a significant index for variety screening and cultivation management. The methods that are currently used to count the number of grains per panicle are manually conducted, making them labor intensive and time consuming. Existing image-based grain counting methods had difficulty in separating overlapped grains.

RESULTS

In this study, we aimed to develop an image analysis-based method to quickly quantify the number of rice grains per panicle. We compared the counting accuracy of several methods among different image acquisition devices and multiple panicle shapes on both Indica and Japonica subspecies of rice. The linear regression model developed in this study had a grain counting accuracy greater than 96% and 97% for Japonica and Indica rice, respectively. Moreover, while the deep learning model that we used was more time consuming than the linear regression model, the average counting accuracy was greater than 99%.

CONCLUSIONS

We developed a rice grain counting method that accurately counts the number of grains on a detached panicle, and believe this method can be a huge asset for guiding the development of high throughput methods for counting the grain number per panicle in other crops.

Cytomorphology-based microchip with contour extraction processing for bioparticle analysis

In this paper, we demonstrated an integrated digital image processing framework that is training-free for high throughput beads or biological cells detection and enumeration by the bead aggregation splitting algorithm. By making contour extraction processing, the aggregated beads can be clearly split for precise counting. It can be potentially embedded on-chip in a miniaturized medical equipment to automatically adjust illumination condition and de-noise. This study demonstrates that the existing hematological analysis can be updated from manual classification and counting by high-speed and precise machine-based programs.

Fronto-parietal numerical networks in relation with early numeracy in young children

Early numeracy provides the foundation of acquiring mathematical skills that is essential for future academic success. This study examined numerical functional networks in relation to counting and number relational skills in preschoolers at 4 and 6 years of age. The counting and number relational skills were assessed using school readiness test (SRT). Resting-state fMRI (rs-fMRI) was acquired in 123 4-year-olds and 146 6-year-olds. Among them, 61 were scanned twice over the course of 2 years. Meta-analysis on existing task-based numeracy fMRI studies identified the left parietal-dominant network for both counting and number relational skills and the right parietal-dominant network only for number relational skills in adults. We showed that the fronto-parietal numerical networks, observed in adults, already exist in 4-year and 6-year-olds. The counting skills were associated with the bilateral fronto-parietal network in 4-year-olds and with the right parietal-dominant network in 6-year-olds. Moreover, the number relational skills were related to the bilateral fronto-parietal and right parietal-dominant networks in 4-year-olds and had a trend of the significant relationship with the right parietal-dominant network in 6-year-olds. Our findings suggested that neural fine-tuning of the fronto-parietal numerical networks may subserve the maturation of numeracy in early childhood.

Counting and Surveying Homeless Youth: Recommendations from YouthCount 2.0!, a Community-Academic Partnership

Communities across the United States are increasing efforts to find and count homeless youth. This paper presents findings and lessons learned from a community/academic partnership to count homeless youth and conduct an in depth research survey focused on the health needs of this population. Over a 4 week recruitment period, 632 youth were counted and 420 surveyed. Methodological successes included an extended counting period, broader inclusion criteria to capture those in unstable housing, use of student volunteers in health training programs, recruiting from magnet events for high risk youth, and partnering with community agencies to disseminate findings. Strategies that did not facilitate recruitment included respondent driven sampling, street canvassing beyond known hotspots, and having community agencies lead data collection. Surveying was successful in gathering data on reasons for homelessness, history in public systems of care, mental health history and needs, sexual risk behaviors, health status, and substance use. Youth were successfully surveyed across housing types including shelters or transitional housing (n = 205), those in unstable housing such as doubled up with friends or acquaintances (n = 75), and those who were literally on the streets or living in a place not meant for human habitation (n = 140). Most youth completed the self-report survey and provided detailed information about risk behaviors. Recommendations to combine research data collection with counting are presented.

Fundamentals of Counting Statistics in Digital PCR: I Just Measured Two Target Copies-What Does It Mean?

Current commercially available digital PCR (dPCR) systems and assays are capable of detecting individual target molecules with considerable reliability. As tests are developed and validated for use on clinical samples, the need to understand and develop robust statistical analysis routines increases. This chapter covers the fundamental processes and limitations of detecting and reporting on single molecule detection. We cover the basics of quantification of targets and sources of imprecision. We describe the basic test concepts: sensitivity, specificity, limit of blank, limit of detection, and limit of quantification in the context of dPCR. We provide basic guidelines how to determine those, how to choose and interpret the operating point, and what factors may influence overall test performance in practice.

Cleaner fish Labroides dimidiatus discriminate numbers but fail a mental number line test

Several species of primates, including humans, possess a spontaneous spatial mental arrangement (i.e. mental number line MNL) of increasing numbers or continuous quantities from left to right. This cognitive process has recently been documented in domestic chicken in a spatial-numerical task, opening the possibility that MNL is a cognitive capacity that has been conserved across vertebrate taxa. In this scenario, fish might possess the MNL as well. Here we investigated whether cleaner fish Labroides dimidiatus show evidence for MNL in two experiments. In Experiment I, we tested fish's abilities in number discrimination, presenting simultaneously either small (2 vs 5) or large (5 vs 8) continuous quantities where one quantity was systematically rewarded. Experiment II used a protocol of an MNL task similar to the study on chickens. We trained cleaners with a target number (i.e. 5 elements), then we presented them with an identical pair of panels depicting either 2 elements or 8 elements, and we recorded their spontaneous choice for the left or right panel on each presentation. Cleaner fish showed high abilities in discriminating small and large numbers in Experiment I. Importantly, cleaners achieved this discrimination using numerical cues instead of non-numerical cues such as the cumulative surface area, density, and overall space. In contrast, cleaners did not allocate continuous quantities to space in Experiment II. Our findings suggest that cleaner fish possess numbering skills but they do not have an MNL. While similar studies on animals from various clades are needed to trace the evolution of MNL within vertebrates, our results suggest that this cognitive process might not be a capacity conserved across all vertebrate taxa.

Automatic counting of trypanosomatid amastigotes in infected human cells

This article presents an automatic approach to counting amastigotes in human cells infected with Chagas. The approach is divided into four steps: first, morphological pretreatment removes the complex image background; sets are then segmented by unsupervised classification; the infected cells are then preserved using a thresholding process; and, finally, they undergo morphological granulometric processing and are filtered by the average. An experimental protocol was employed to compare the amastigotes nuclei labeled by a professional biochemist with the results obtained by the proposed approach. We observed that using the granulometric sieving conducted with square SE plus average size filtering is the best option to obtain the minor error and the best precision and using the granulometric sieving conducted with rhombus SE without average size filtering represents the best combination for obtaining the best F-measure and recall rates.

What counts in preschool number knowledge? A Bayes factor analytic approach toward theoretical model development

Preschool children vary tremendously in their numerical knowledge, and these individual differences strongly predict later mathematics achievement. To better understand the sources of these individual differences, we measured a variety of cognitive and linguistic abilities motivated by previous literature to be important and then analyzed which combination of these variables best explained individual differences in actual number knowledge. Through various data-driven Bayesian model comparison and selection strategies on competing multiple regression models, our analyses identified five variables of unique importance to explaining individual differences in preschool children's symbolic number knowledge: knowledge of the count list, nonverbal approximate numerical ability, working memory, executive conflict processing, and knowledge of letters and words. Furthermore, our analyses revealed that knowledge of the count list, likely a proxy for explicit practice or experience with numbers, and nonverbal approximate numerical ability were much more important to explaining individual differences in number knowledge than general cognitive and language abilities. These findings suggest that children use a diverse set of number-specific, general cognitive, and language abilities to learn about symbolic numbers, but the contribution of number-specific abilities may overshadow that of more general cognitive abilities in the learning process.

Transfer of training in alphabet arithmetic

In recent years, several researchers have proposed that skilled adults may solve single-digit addition problems (e.g., 3 + 1 = 4, 4 + 3 = 7) using a fast counting procedure. Practicing a procedure, however, often leads to transfer of learning to unpracticed items; consequently, the fast counting theory was potentially challenged by subsequent studies that found no generalization of practice for simple addition. In two experiments reported here (Ns = 48), we examined generalization in an alphabet arithmetic task (e.g., B + 5 = C D E F G) to determine that counting-based procedures do produce generalization. Both experiments showed robust generalization (i.e., faster response times relative to control problems) when a test problem's letter augend and answer letter sequence overlapped with practiced problems (e.g., practice B + 5 = C D E F G, test B + 3 = C D E ). In Experiment 2, test items with an unpracticed letter but whose answer was in a practiced letter sequence (e.g., practice C + 3 = DEF, test D + 2 = E F) also displayed generalization. Reanalysis of previously published addition generalization experiments (combined n = 172) found no evidence of facilitation when problems were preceded by problems with a matching augend and counting sequence. The clear presence of generalization in counting-based alphabet arithmetic, and the absence of generalization of practice effects in genuine addition, represent a challenge to fast counting theories of skilled adults' simple addition.

Cryptosporidium oocysts and Giardia cysts-A practical and sensitive method for counting and manipulating small numbers

A rapid and inexpensive method is described for accurate and reproducible counting and manipulating small numbers of Cryptosporidium oocysts and Giardia cysts. From a suspension of oocysts or cysts at concentration from 1000 to 5000/mL (1-5/μL), replicate 5μL droplets are micro pipetted onto the edge of a microscope slide. Unstained oocysts or cysts in each droplet can be counted in a few minutes and replicated for statistical strength. The concentration of the suspension can then be verified by pipetting desired volumes containing approximately desired numbers onto confined 13mm membranes for IFA staining and counting with replication as desired. Requiring only a micropipette, analytical balance, and a microscope, this provides a useful tool accessible to virtually any microbiology laboratory.

Why is number word learning hard? Evidence from bilingual learners

Young children typically take between 18 months and 2 years to learn the meanings of number words. In the present study, we investigated this developmental trajectory in bilingual preschoolers to examine the relative contributions of two factors in number word learning: (1) the construction of numerical concepts, and (2) the mapping of language specific words onto these concepts. We found that children learn the meanings of small number words (i.e., one, two, and three) independently in each language, indicating that observed delays in learning these words are attributable to difficulties in mapping words to concepts. In contrast, children generally learned to accurately count larger sets (i.e., five or greater) simultaneously in their two languages, suggesting that the difficulty in learning to count is not tied to a specific language. We also replicated previous studies that found that children learn the counting procedure before they learn its logic - i.e., that for any natural number, n, the successor of n in the count list denotes the cardinality n+1. Consistent with past studies, we found that children's knowledge of successors is first acquired incrementally. In bilinguals, we found that this knowledge exhibits item-specific transfer between languages, suggesting that the logic of the positive integers may not be stored in a language-specific format. We conclude that delays in learning the meanings of small number words are mainly due to language-specific processes of mapping words to concepts, whereas the logic and procedures of counting appear to be learned in a format that is independent of a particular language and thus transfers rapidly from one language to the other in development.

Identifying the cognitive predictors of early counting and calculation skills: Evidence from a longitudinal study

The extent to which phonological, visual-spatial short-term memory (STM), and nonsymbolic quantitative skills support the development of counting and calculation skills was examined in this 14-month longitudinal study of 125 children. Initial assessments were made when the children were 4 years 8 months old. Phonological awareness, visual-spatial STM, and nonsymbolic approximate discrimination predicted growth in early calculation skills.These results suggest that both the approximate number system and domain-general phonological and visual-spatial skills support early calculation. In contrast, only performance on a small nonsymbolic quantity discrimination task (where the presented quantities were always within the subitizing range) predicted growth in cardinal counting skills. These results suggest that the development of counting and the development of calculation are supported by different cognitive abilities.

The role of fingers in the development of counting and arithmetic skills

Interactions between fingers and numbers have been reported in the existing literature on numerical cognition. The aim of the present research was to test whether hand interference movements might have an impact on children performance in counting and basic arithmetic problem solving. In Experiment 1, 5-year-old children had to perform both a one-target and a two-target counting task in three different conditions: with no constraints, while making interfering hand movements or while making interfering foot movements. In Experiment 2, first and fourth graders were required to perform addition problems under the same control and sensori-motor interfering conditions. In both tasks, the hand movements caused more disruption than the foot movements, suggesting that finger-counting plays a functional role in the development of counting and arithmetic.

ImagePAD, a novel counting application for the Apple iPad, used to quantify axons in the mouse optic nerve

The present article introduces a new and easy to use counting application for the Apple iPad. The application "ImagePAD" takes advantage of the advanced user interface features offered by the Apple iOS platform, simplifying the rather tedious task of quantifying features in anatomical studies. For example, the image under analysis can be easily panned and zoomed using iOS-supported multi-touch gestures without losing the spatial context of the counting task, which is extremely important for ensuring count accuracy. This application allows one to quantify up to 5 different types of objects in a single field and output the data in a tab-delimited format for subsequent analysis. We describe two examples of the use of the application: quantifying axons in the optic nerve of the C57BL/6J mouse and determining the percentage of cells labeled with NeuN or ChAT in the retinal ganglion cell layer. For the optic nerve, contiguous images at 60× magnification were taken and transferred onto an Apple iPad. Axons were counted by tapping on the touch-sensitive screen using ImagePAD. Nine optic nerves were sampled and the number of axons in the nerves ranged from 38,872 axons to 50,196 axons with an average of 44,846 axons per nerve (SD = 3980 axons).

Determining absolute protein numbers by quantitative fluorescence microscopy

Biological questions are increasingly being addressed using a wide range of quantitative analytical tools to examine protein complex composition. Knowledge of the absolute number of proteins present provides insights into organization, function, and maintenance and is used in mathematical modeling of complex cellular dynamics. In this chapter, we outline and describe three microscopy-based methods for determining absolute protein numbers--fluorescence correlation spectroscopy, stepwise photobleaching, and ratiometric comparison of fluorescence intensity to known standards. In addition, we discuss the various fluorescently labeled proteins that have been used as standards for both stepwise photobleaching and ratiometric comparison analysis. A detailed procedure for determining absolute protein number by ratiometric comparison is outlined in the second half of this chapter. Counting proteins by quantitative microscopy is a relatively simple yet very powerful analytical tool that will increase our understanding of protein complex composition.

Enumeration skills in Down syndrome

Individuals with Down syndrome (DS) exhibit various math difficulties which can be ascribed both to global intelligence level and/or to their atypical cognitive profile. In this light, it is crucial to investigate whether DS display deficits in basic numerical skills. In the present study, individuals with DS and two groups of typically developing (TD) children matched for mental and chronological age completed two delayed match-to-sample tasks in order to evaluate the functioning of visual enumeration skills. Children with DS showed a specific deficit in the discrimination of small numerosities (within the subitizing range) with respect to both mental and chronological age matched TD children. In contrast, the discrimination of larger numerosities, though lower than that of chronological age matched controls, was comparable to that of mental age matched controls. Finally, counting was less fluent but the understanding of cardinality seemed to be preserved in DS. These results suggest a deficit of the object tracking system underlying the parallel individuation of small numerosities and a typical - but developmentally delayed - acuity of the approximate number system for discrimination of larger numerosities.

Fast determination of ⁹⁰Sr/⁹⁰Y activity in milk by Cherenkov counting

Cherenkov counting of the ⁹⁰Sr/⁹⁰Y pure beta emitters is an attractive method for ⁹⁰Sr activity determination, but the color quenching effect may be significant, especially for strongly colored or semi-opaque media. A quench correction method based on the external source of some liquid scintillation systems (named ESAR - external source area ratio) was proposed and checked for aqueous solutions and was proved to be effective also for urine samples. In the present work, the application of the ESAR method for fast determination of ⁹⁰Sr/⁹⁰Y activity in milk samples is described.

The idea of an exact number: children's understanding of cardinality and equinumerosity

Understanding what numbers are means knowing several things. It means knowing how counting relates to numbers (called the cardinal principle or cardinality); it means knowing that each number is generated by adding one to the previous number (called the successor function or succession), and it means knowing that all and only sets whose members can be placed in one-to-one correspondence have the same number of items (called exact equality or equinumerosity). A previous study (Sarnecka & Carey, 2008) linked children's understanding of cardinality to their understanding of succession for the numbers five and six. This study investigates the link between cardinality and equinumerosity for these numbers, finding that children either understand both cardinality and equinumerosity or they understand neither. This suggests that cardinality and equinumerosity (along with succession) are interrelated facets of the concepts five and six, the acquisition of which is an important conceptual achievement of early childhood.