Category Sizes Research Articles

A stochastic ordering of multiple hypergeometric laws: Peakedness of category counts about half the population category sizes is symmetric unimodal in the sample size

Suppose X is a frequency vector that follows a central multiple hypergeometric distribution, such as arises in random sampling of an m-category attribute from a finite population without replacement. We call the event where X satisfies a prespecified set of symmetrical—but otherwise arbitrary—interval constraints in each component a symmetric core event. We show that the probability of any symmetric core event—in other words, the multivariate peakedness in the sense of Birnbaum (1948) and Tong (1988)—is symmetric unimodal as a function of the sample size. Two proofs are given. The shorter one relies on a convolution property of ultra-log-concave sequences, which implies that the sequence of peakedness values is log-concave (even for asymmetric rectangular events). The longer, though more elementary, proof does not rely on notions of log-concavity. To illustrate the use of symmetric core events, we analyze a simple yet interesting wager in a sequential card game. Finally, we indicate that the unimodality result for symmetric core events is pivotal in proving a certain variance reduction inequality involving multinomial frequencies subject to arbitrary interval censoring.

A model and solution approach for store-wide shelf space allocation

Store space is limited and one of the most costly resources of retailers. Retailers have to apportion available store space among the individual product categories of a store and therefore assign a certain share of shelf space to each category. Assigning more shelf space to one category requires reducing the number of shelves for another category as total space is limited. Reducing available shelf space in turn decreases assortment size and lessens the presentation quantity of products and vice versa. Both affect the demand of products and ultimately the profitability of the entire category such that the profit contribution of a category depends on its shelf size. This interrelation between category sizes and store profits needs to be taken into account for the shelf space assignment to categories and the space allocation for individual products.We introduce a store-wide shelf space model that optimizes shelf space assignment for categories based on the profit contribution of the corresponding product allocations. We decompose the problem into two hierarchically interlinked subproblems and show that the solution approach suggested works efficiently and provides solutions that are applicable to large problems in retail practice. In a case study with a major European retailer, we show that profits at stores can be improved by 3.2% using our approach. Further, we use simulated data to generalize the findings and derive managerial insights.

Category-length and category-strength effects using images of scenes.

Global matching models have provided an important theoretical framework for recognition memory. Key predictions of this class of models are that (1) increasing the number of occurrences in a study list of some items affects the performance on other items (list-strength effect) and that (2) adding new items results in a deterioration of performance on the other items (list-length effect). Experimental confirmation of these predictions has been difficult, and the results have been inconsistent. A review of the existing literature, however, suggests that robust length and strength effects do occur when sufficiently similar hard-to-label items are used. In an effort to investigate this further, we had participants study lists containing one or more members of visual scene categories (bathrooms, beaches, etc.). Experiments 1 and 2 replicated and extended previous findings showing that the study of additional category members decreased accuracy, providing confirmation of the category-length effect. Experiment 3 showed that repeating some category members decreased the accuracy of nonrepeated members, providing evidence for a category-strength effect. Experiment 4 eliminated a potential challenge to these results. Taken together, these findings provide robust support for global matching models of recognition memory. The overall list lengths, the category sizes, and the number of repetitions used demonstrated that scene categories are well-suited to testing the fundamental assumptions of global matching models. These include (A) interference from memories for similar items and contexts, (B) nondestructive interference, and (C) that conjunctive information is made available through a matching operation.

Multi-Category RFID Estimation

This paper concerns the practically important problem of multi-category radio frequency identification (RFID) estimation: given a set of RFID tags, we want to quickly and accurately estimate the number of tags in each category. However, almost all the existing RFID estimation protocols are dedicated to the estimation problem on a single set, regardless of tag categories. A feasible solution is to separately execute the existing estimation protocols on each category. The execution time of such a serial solution is proportional to the number of categories, and cannot satisfy the delay-stringent application scenarios. Simultaneous RIFD estimation over multiple categories is desirable, and hence, this paper proposes an approach called simultaneous estimation for multi-category RFID systems (SEM). SEM exploits the Manchester-coding mechanism, which is supported by the ISO 18000-6 RFID standard, to decode the combined signals, thereby simultaneously obtaining the reply status of tags from each category. As a result, multiple bit vectors are decoded from just one physical slotted frame. Built on our SEM, many existing excellent estimation protocols can be used to estimate the tag cardinality of each category in a simultaneous manner. To ensure the predefined accuracy, we calculate the variance of the estimate in one round, as well as the variance of the average estimate in multiple rounds. To find the optimal frame size, we propose an efficient binary search-based algorithm. To address significant variance in category sizes, we propose an adaptive partitioning (AP) strategy to group categories of similar sizes together and execute the estimation protocol for each group separately. Compared with the existing protocols, our approach is much faster, meanwhile satisfying the predefined estimation accuracy. For example, with 20 categories, the proposed SEM+AP is about seven times faster than prior estimation schemes. Moreover, our approach is the only one whose normalized estimation time (i.e., time per category) decreases as the number of categories increases.

New species ofClathria(Microciona) (Poecilosclerida: Microcionina: Microcionidae) from the Tropical South-western Atlantic Ocean (Sergipe State, north-eastern Brazil)

Clathriais one of the most species-rich genera among Demospongiae, but only nine species have been recorded so far from Brazil. Here we describe a new species ofClathria(Microciona) collected by trawling in waters of Sergipe State (north-eastern Brazil). The new species is differentiated from other encrustingClathriawith a hymedesmioid skeleton by the possession of a combination of long thin subectosomal subtylostyles, two category sizes of acanthostyles, both erect and echinating the basal spongin skeleton, long slightly curved choanosomal principal subtylostyles with tuberculate spine heads and wing-shaped toxas as microscleres.

Gametogenesis and Spawning Induction in Batissa violacea Lamarck, (1806) at Cagayan River, Philippines

Batissaviolacea Lamarck (l806) locally known as “cabibi” is considered endemic in Cagayan River at Lallo, Philippines and the most expensive freshwater bivalve in the region. This study described through monthly histological examination the cytological characteristics of gametogenesis and sexual dimorphism of the gonad of B. violacea collected from the wild, and determined spawning response using serotonin. Eight category sizes of the species were established, and 10 samples from each size were processed. Gonads were preserved, and subjected for histological processes to confirm gametogenesis. Using descriptive data analysis, confirmation of the identified mature stage at 31-35 mm was further tested through induction of serotonin. Results showed progressive stages of sperm formation in male follicles. Follicles could be seen in clusters and identified as to their sizes from spermatogonia, spermatocytes, spermatids and spermatozoa. Growing female follicles appeared attached to a cytoplasmic stalk in different sizes and shapes. Initially male germ cells appeared tiny and became concentrated at the lumen in radiating bands as they become mature. Likewise, mature oocytes with enlarged nucleus and tiny nucleolus fill the center of the lumen of the female gonad was observed. B. violacea successfully spawn using either 0.2 ml or 0.5 ml earlier (0.21 hour) compared to 36.70 hour when no injection was administered. This is a first time report in the country along the possibility of breeding the species in captivity.Keywords: Aquatic ecology, Batissa violacea, gametogenesis, Cagayan River, induced spawning,experimental design, Cagayan river

Effects of Shoot Clipping–Soil Disturbance Frequency and Tuber Size on Aboveground and Belowground Growth of Purple and Yellow Nutsedge (Cyperus rotundusandCyperus esculentus)

Purple and yellow nutsedges are two of the world's worst weeds, reproducing asexually by rhizomes that can develop into new shoots or tubers. These tubers are the storage organs for carbohydrate reserves that are replenished by growing shoots and exhausted by new shoot, root plus rhizome, and basal bulb production. Based on the biology of both species, we hypothesized that the regenerative potential of purple and yellow nutsedge would decrease, with increasing shoot clipping–soil disturbance (SCSD) frequency and decreasing tuber size. To test this hypothesis, greenhouse experiments were conducted in pots to determine the effect of SCSD frequency and tuber size on aboveground and belowground growth of purple and yellow nutsedges. Five viable tubers of two tuber category sizes (small, 0.40 ± 0.05; and large, 0.80 ± 0.05 g of tuber fresh weight) were subjected to four SCSD frequencies (weekly, biweekly, monthly, and none) for 12 wk. SCSD was performed by clipping the emerged nutsedge shoots followed by manually disturbing the soil. SCSD at biweekly or weekly intervals reduced purple nutsedge proliferation, regardless of initial tuber size. However, monthly SCSD did not suppress purple nutsedge as effectively as weekly or biweekly SCSD, and less proliferation occurred with small tubers than with large tubers. In contrast, yellow nutsedge proliferation was equally reduced with monthly or more-frequent SCSD, regardless of initial tuber size. Even weekly soil disturbance for 12 wk failed to eradicate all small or large tubers in either species. Thus, yellow nutsedge is managed more easily than purple nutsedge with less-frequent tillage or cultivation. However, tillage or cultivation alone during a 12-wk period will not likely eradicate either nutsedge species from infested soil.

Retail category management: State-of-the-art review of quantitative research and software applications in assortment and shelf space management

Retail requires efficient decision support to manage increasing product proliferation and various consumer choice effects with limited shelf space. Our goal is to identify, describe and compare decision support systems for category planning. This research analyzes quantitative models and software applications in assortment and shelf space management and contributes to a more integrated modeling approach. There are difficulties commonly involved in the use of commercial software and the implementation and transfer of scientific models. Scientific decision models either focus on space-dependent demand or substitution effects, whereas software applications use simplistic rules of thumb. We show that retail assortment planning models neglect space-elastic demand and largely also ignore constraints of limited shelf space. Shelf space management streams on the other hand, mostly omit substitution effects between products when products are delisted orout-of-stock, which is the focus of consumer choice models in assortment planning. Also, the problem sizes of the models are often not relevant for realistic category sizes. Addressing these issues, this paper provides a state-of-the-art overview and research framework for integrated assortment and shelf space planning.

Quantitative Models for Retail Category Management: A Review of Assortment and Shelf Space Planning in Practice, Software Applications and Science

Retail requires efficient decision support to manage increasing product proliferation and various consumer choice effects with limited shelf space. Our goal is to identify, describe and compare decision support systems for category planning. This research analyzes quantitative models and software applications in assortment and shelf space management and contributes to a more integrated modeling approach.There are difficulties commonly involved in the use of commercial software and the implementation and transfer of scientific models. Scientific decision models either focus on space-dependent demand or substitution effects, whereas software applications use simplistic rules of thumb. We show that retail assortment planning models neglect space-elastic demand and largely also ignore constraints of limited shelf space. Shelf space management streams on the one hand, mostly omit substitution effects between products when products are delisted or out of stock, which is the focus of consumer choice models in assortment planning. Also, the problem sizes of the models are often not relevant for realistic category sizes. Addressing these issues, this paper provides a state-of-the-art overview and research framework for integrated assortment and shelf space planning.Full paper is published in OMEGA

Determining the optimal size for posture categories used in video-based posture assessment methods

Currently, there are no standards for the development of posture classification systems used in observation-based ergonomic posture assessment methods. This study was conducted to determine if an optimal posture category size for different body segments and posture views could be established by examining the trade-off between magnitude of error and the number of posture category misclassification errors made. Three groups (trunk flexion/extension and lateral bend; shoulder flexion/extension and adduction/abduction; elbow flexion/extension) of 30 participants each selected postures they perceived to correctly represent the video image shown on a computer screen. For each view, 10 images were presented for five different posture category sizes, three times each. The optimal posture category sizes established were 30° for trunk, shoulder and elbow flexion/extension, 30° for shoulder adduction/abduction and 15° for trunk lateral bend, suggesting that posture category size should be based on the body segment and view of the image being assessed. Across all conditions, the posture category sizes were comparable to those used in published ergonomic tools.

Decrease in Performance on the Verbal Fluency Test as a Function of Time: Evaluation in a Young Healthy Sample

Participants were asked to generate as many words as possible using large and small category sizes with the initial letter and semantic category search strategies. The production of each participant for each 15-s time slice on each task was recorded. The results revealed that on all fluency tasks, the production in the initial time slice was highest and also of greatest frequency. As time on task increased the production decreased, as did the word frequency of the items produced. The results are consistent with the notion that there is a store of high-frequency words accessed during the early trials of the fluency tasks and as this store becomes exhausted the production and the word frequency decreases.

Individual Experience and the Fragmentation of Societies

We use computer simulations to show how social fragmentation and consequent social loss can result from six innocuous cognitive and behavioral assumptions. These assumptions govern individuals' choices with respect to each other and are independent of processes associated with fragmentation in various classical literatures. We model society as a set of individuals who encounter each other in circumstances that permit potentially productive but also risky relationships with each other Individuals (1) have the option of playing Prisoner's Dilemma games with others they encounter but they do not have to; (2) have preferences over mutual cooperation and free-riding outcomes; (3) have expectations about each other's play; (4) have observable category tags; (5) can modify their future responses to tagged individuals based on experience; (6) can search out partners they believe represent good prospects for productive relationships. In these terms, the only condition necessary for fragmentation to emerge is that some circumstance makes the probability of encounters across tagged categories unequal, and a difference in sizes of categories, however slight, is sufficient to do that. Some difference in category sizes is, for practical purposes, inevitable, and thus so are pressures toward fragmentation

Inadequacy of recall as a basis for frequency knowledge.

Subjects studied a word list comprising varying numbers of words from distinct semantic categories. The category names (trees, colors, etc.) were then re-presented, and for each name subjects either recalled as many exemplars as they could or estimated how many had been included in the list (Experiments 1 and 2). Recall was not sufficiently informative about actual category sizes to account for performance in the frequency estimation task. Moreover, it remained insufficiently informative when efforts were made to induce a recall-estimate strategy by requiring overt recall prior to estimation (Experiments 3-5), by using very small categories (Experiment 4), and by not showing the category name at study (Experiment 5), even though it did allow a partial account of estimation when the category exemplars were individually cued (Experiment 6). It is concluded that the role of recall in frequency estimation is much exaggerated.

Inadequacy of recall as a basis for frequency knowledge.

Subjects studied a word list comprising varying numbers of words from distinct semantic categories. The category names (trees, colors, etc.) were then re-presented, and for each name subjects either recalled as many exemplars as they could or estimated how many had been included in the list (Experiments 1 and 2). Recall was not sufficiently informative about actual category sizes to account for performance in the frequency estimation task. Moreover, it remained insufficiently informative when efforts were made to induce a recall-estimate strategy by requiring overt recall prior to estimation (Experiments 3-5), by using very small categories (Experiment 4), and by not showing the category name at study (Experiment 5), even though it did allow a partial account of estimation when the category exemplars were individually cued (Experiment 6). It is concluded that the role of recall in frequency estimation is much exaggerated.

Sentence Orientation and Semantic Processing Speed: Applicability to Label Design

Sentence orientation and category size were examined using a sentence verification task to determine whether the rotation of sentences would influence semantic processing. A total of 28 participants were asked to read sentences presented with five levels of rotation (−90, −45, 0, +45, +90) and two category sizes (small & large). A significant difference in the speed of sentence verification was found for sentence orientation. As the degree of rotation increased the time taken to process the sentences increased; this was especially true for vertically aligned sentences (oriented at ±90 degrees). The category size variable did not yield a significant main effect. The findings of this study may have direct implications for the positioning of labels on consumer products with varying orientations.

Word Fragments as Retrieval Cues: Letter Generation or Search through Nonsemantic Memory?

plored. Type of nonsemantic cue during study and test was factorially varied. Words were studied either (a) without modifying cues, (b) in the presence of context cues emphasizing initial letters, or (c) in the presence of contexts stressing endings. Regardless of study emphasis, test cues shared either beginnings or endings with their targets. Results showed that emphasizing either portion during study produced no benefit to recall. However, cue switches from study to test reduced recall. In addition to these manipulations, the category sizes defined by these cues were varied, as was cue embeddedness. In general, cues defining smaller categories were more effective. This result was generally linked to the use of specific cues, i.e., beginningcategory size effects were obtained with beginning but not with ending cues. Embedding the cue within a meaningful word substantially reduced recall. The findings were interpreted within a model of cued recall that assumes that nonsemantic cues operate by defining search sets of nonsemantic memory units. With one exception, the results were consistent with this model. In the exception, the results suggested that subjects used a lettergeneration strategy.

Monitoring Retrieval Processes by Children

Summary Six- and eight-year-old children were shown a list of categorized items representing three different category sizes. Half of the children were asked to estimate the number of items assigned to each category prior to being tested for recall of the list, while the other half did not receive such instructions. Recall was cued by pictorial category cues, but was terminated at children's own choice. For both age groups, children's estimates of category sizes became progressively larger as the actual category sizes became larger, indicating that even six-year-olds have the ability to acquire rather accurate knowledge about category size during the item presentation. The children were also found to terminate their memory search promptly when they had recalled all of the required items, but conducted an extended search when there were additional items unrecalled. These findings suggest that six-year-olds have the ability to monitor their search processes using their knowledge about the category size.

Search for Abstracted Information

ED INFORMATION 269 number of categories in the memory set, and (c) the typicality of the test probe. In scanning experiments, latency has been shown to increase with an increase in both the number and size of categories in the memory set (Homa, 1973; Naus, 1974); in semantic verification tasks, verification of statements is faster for typical (a robin is a bird) than for atypical (a raven is a bird) subordinates. In experiments on category abstraction, the degree of abstraction is enhanced as the size of the category (Homa et al., 1973) and the number of categories are increased (Homa & Chambliss, 1975). Furthermore, low-distortion patterns are classified more accurately than highlevel ones are classified (Homa, 1978), and low-distortion patterns are situated more centrally in a multidimensional space (Homa, Reed, & Curtis, Note 1). Thus, degree of distortion shares some similarity to the notion of typicality in semantic verification tasks. In the present study, the retrievability of abstracted information was investigated in two experiments. In Experiment 1, subjects initially acquired information about a number of different categories. On subsequent days, subsets from this population were selected to define memory sets composed of varying numbers of categories (N = 1, 2, 3) and category sizes (s = 1, 2, 3) in a manner analogous to high-speed scanning experiments for semantically categorized memory sets (Homa, 1973). Test probes included both positive and negative stimuli; negative stimuli were either familiar and categorically known stimuli (related negatives) or categorically inappropriate stimuli (unrelated negatives). A major concern was whether the abstracted categories, acquired during an earlier learning phase, would function to effectively short-circuit the search in a manner obtained for semantic categories (Homa, 1973). If so, then both the number of abstracted categories as well as their size should influence the latency function. In Experiment 2, the emphasis was shifted to the comparison process presumably involved in verification. Two manipulations were used to assess the comparison process: (a) the degree of prior category abstraction, and (b) the degree of distortion (typicality) of the test probe. Unlike Experiment 1, all test probes in Experiment 2 were novel, and the latencies reflected more a comparison process than a scan for specific memorial information. To the extent that category abstraction enhances the comparison process, it was predicted that manipulating category abstraction by increasing category size during acquisition would produce RT-functions of negative slope, i.e., the greater the category size, the smaller the latency. This content downloaded from 207.46.13.105 on Wed, 25 May 2016 06:31:59 UTC All use subject to http://about.jstor.org/terms 270 OMOHUNDRO AND HOMA