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In many large testing programs, equipercentile equating has been widely used under a random groups design to adjust test difficulty between forms. However, one thorny issue occurs with equipercenti...

Given a graph $\Gamma$, its auxiliary \emph{square-graph} $\square(\Gamma)$ is the graph whose vertices are the non-edges of $\Gamma$ and whose edges are the pairs of non-edges which induce a square (i.e., a $4$-cycle) in $\Gamma$. We determine the threshold edge-probability $p=p_c(n)$ at which the Erd{\H o}s--Renyi random graph $\Gamma=\Gamma_{n,p}$ begins to asymptotically almost surely have a square-graph with a connected component whose squares together cover all the vertices of $\Gamma_{n,p}$. We show $p_c(n)=\sqrt{\sqrt{6}-2}/\sqrt{n}$, a polylogarithmic improvement on earlier bounds on $p_c(n)$ due to Hagen and the authors. As a corollary, we determine the threshold $p=p_c(n)$ at which the random right-angled Coxeter group $W_{\Gamma_{n,p}}$ asymptotically almost surely becomes strongly algebraically thick of order $1$ and has quadratic divergence.

The purpose of the Random group experimental study was to find out the influence of Simplified Kundalini Yoga on selected Body Mass Index and Resting Pulse Rate among Obese School Girls. It was hypothesized that there would be significant differences in Body Mass Index (BMI) and Resting Pulse Rate among Obese School Girls due to the influences of Simplified Kundalini Yoga. To achieve the purpose of the study, 30 Obese (BMI of 30 to 35) school girls from Alagappa Group of Educational Institutions, Karaikudi, Sivagangai District aged between 14 to 18 years were selected randomly into experimental and control groups of 15 subjects each. The selected subjects were divided into one experimental group and a control group with 15 subjects each in a group. Experimental group underwent Simplified Kundalini Yoga for the period of 12 weeks, six days per week of 1 hour basically, then slightly increased to 1.15 hours and 1.30 hours in the morning. The control group was not exposed to any specific training but they participated in their regular activities. The pre-test and post- tests were conducted before and after the training for both the groups. The Body Mass Index (BMI) was measured by Weighing machine, Meter Scale and Resting Pulse Rate was measured by BP Monitor machine. The data pertaining to the variables collected from the two groups before and after their training period were statistically analyzed by using Analysis of Covariance (ANCOVA) to determine the significant difference. The hypotheses were tested at 0.05 level of confidence. The results of the study showed that Body Mass Index (BMI) and Resting Pulse Rate were decreased significantly as a result of Simplified Kundalini Yoga. Hence, the hypothesis was accepted at 0.05 level of confidence. The conclusion was that the Simplified Kundalini Yoga was effective in decrease Body Mass Index (BMI) and Resting Pulse Rate among Obese School girls.

This paper explores the relationship between rating scales and response style using experimental data from a sample of 1500 households of the Innovation Panel (2008) which is part of the Understanding Society database. Two random groups of individuals are being asked about their level of job satisfaction using a self-assessment questionnaire through two (7 and 11 points) rating options. By comparing the two groups, we explore the effects of the different rating scales on Extreme Response Style (ERS). The experimental design of the data enables us to show that both high and low Extreme Response Style (ERS) are correlated with personal and demographic characteristics. In addition, when comparing the shorter to a longer scale, we show that the survey design may generates tendency to choose responses at the extreme values of the distribution.

OpticalGamification (OG) is an information and communication technology (ICT)-based gamification-application that applies the elements of game design in a serious context of optics. Through setting for the variations in pre-service physics teachers’ (PPTs) access to the topics presented in this application, two OG application models are generated, namely: 1) serial model; designed to facilitate PPTs who study sequentially, and 2) random models; designed to facilitate PPTs who study randomly depends on their choices. This research is quasi-experimental with pretest posttest nonequivalent multiple group design involving 48 PPTs enrolled in wave and optics course, specifically on the topics of interference and diffraction. The results of this research indicate that there is no significant difference in the improvement of PPTs’ concept mastery in the serial and random group. Both of these models can be used as references in designing ICT-based gamification-applications for a more effective and efficient learning in the future.

The purpose of this study is to address the necessity of subscore equating and to evaluate the performance of various equating methods for subtests. Assuming the random groups design and nu...

In this thesis, we study phase transitions in random groups at density. A random group at density d is defined by a presentation with m generators and 2m-1 powers dl random relations, where l is the maximal length of the relations. We have two main results: one on the free subgroup problem and the other on the existence of van Kampen 2-complexes. For any integer r between 1 and m-1, we find a phase transition at the density d(r) = min{1/2, 1-log(2r-1)/log(2m-1)}: If d>d(r), then the r first generators generate the whole group; if d, Dans cette thèse, nous étudions les transitions de phase dans les groupes aléatoires à densité. Un groupe aléatoire à densité d est défini par une présentation avec m générateurs et 2m-1 puissance dl relations aléatoires, où l est la longueur maximale des relations. Nous avons deux résultats principaux : un sur le problème des sous-groupes libres et l'autre sur l'existence des 2-complexes de van Kampen. Pour tout entier r entre 1 et m-1, nous trouvons une transition de phase à la densité d(r) = min{1/2, 1-log(2r-1)/log(2m-1)} : Si d>dr, alors les r premiers générateurs engendrent le groupe entier ; si d

Cross-Classroom Collaborative Project-Based Learning (C3PjBL) requires the formation of project-groups by pairing student-groups across classrooms. Unfortunately, due to the configuration of these groups, the group formation techniques found in the literature are unable to automatically create project-groups for C3PjBL. This paper describes an automatic project-group formation technique for C3PjBL which utilizes clustering to create homogeneous student-groups, based on the students’ perceived technological and higher-order thinking skills (student characteristics). Student-groups, from different classrooms, are then paired using an optimization technique to form project-groups. In our results, we present a comparison of the performance of a random group formation technique and our technique. We observed that automatic group formation using an n-dimensional space of student characteristics and k-means clustering is more effective than random group formation and, the strategy of forming homogeneous student-groups and heterogeneous project-group for C3PjBL creates more compatible group compositions than random grouping.

Equating is used to directly compare alternate forms of tests. We describe the equating of two alternative forms of a reading comprehension test for Brazilian children (2nd to 5th grade), Form A (n = 427) and Form B (n = 321). We employed non-equivalent random groups design with internal anchor items. Local independence was attested via standardized residual Pearson's bivariate correlation. First, from 176 items, we selected 42 in each form (33 unique and 9 in common) using 2PL model, a one-dimensional item response theory (IRT) model. Using the equateIRT package for R, the anchor items were used to link both forms. Linking coefficients were estimated under two different methods (Haebara and Stocking–Lord), resulting in scores equating by two methods: observed score equating (OSE) and true score equating (TSE). We provided reference-specific age-intervals for the sample. The final version was informative for a wide range of theta abilities. We concluded that the forms could be used interchangeably.

To contain COVID-19, most education institutions around the globe have been temporarily closed, impacting millions of students.Many medical universities have opted for online classes. Online teaching in medical universities is a novelty, and it poses different sets of challenges compared to regular classes. Since online teaching might persist for a longer time, this study was conducted to help students gain maximum out of these online classes. 150 First year medical students were selected for the study. Students were divided into two random groups (A &B) of 75 each. Group A were informed about the topic of the class and were encouraged to study prior to the class. Group B students attended the class without any preparation, but were instructed to study the topic immediately after completion of online lecture. Both the groups were compared for their involvement during the lecture class and their understanding of the topic were statistically analyzed. Group A scored better than group B with significant P value ( Group A, being aware of upcoming lecture class topic and had prepared, were more attentive in class, as well as interactive and performed better in the assessment. This study suggests to reduce the duration of online class, share the material of the class prior and encourage students to prepare on the topic for better results of online classes.

With the wide spread of large-scale e-learning environments such as MOOCs, peer assessment has been popularly used to measure learner ability. When the number of learners increases, peer assessment is often conducted by dividing learners into multiple groups to reduce the learner's assessment workload. However, in such cases, the peer assessment accuracy depends on the method of forming groups. To resolve that difficulty, this study proposes a group formation method to maximize peer assessment accuracy using item response theory and integer programming. Experimental results, however, have demonstrated that the proposed method does not present sufficiently higher accuracy than a random group formation method does. Therefore, this study further proposes an external rater assignment method that assigns a few outside-group raters to each learner after groups are formed using the proposed group formation method. Through results of simulation and actual data experiments, this study demonstrates that the proposed external rater assignment can substantially improve peer assessment accuracy.

We prove that if a finitely generated random group action is robustly expansive and has the shadowing property, then it is rigid. We apply this result to analyze the rigidity of certain iterated function systems or actions of the discrete Heisenberg group.

Background Early patterning competence has recently been identified as an important precursor of mathematical development. Whereas the focus of this research has been on children’s ability regarding repeating patterns, children might also differ in their spontaneous attention to patterns. Aims The present study aimed to explore 4‐ to 5‐year olds’ Spontaneous Focusing On Patterns (SFOP) and its association with their patterning and mathematical ability. Sample Participants were 378 children (Mage = 4 years 10 months; 191 boys) from 17 preschools. Methods Spontaneous Focusing On Patterns was measured with a construction task in which children had to build a tower with 15 blocks of three different colours. The constructions of the children were grouped into three categories (i.e., pattern, random, and sorting). We additionally administered tasks assessing their patterning ability, mathematical ability, spatial ability, and visuospatial working memory. Results When building a tower, 37% of the preschoolers spontaneously created a pattern, 49% made a random construction, and 14% sorted the blocks per colour. Preschoolers who spontaneously created a pattern had better patterning and mathematical ability than children in the random group. Group differences in patterning ability and spatial skills accounted for the difference in mathematical ability. Conclusions The current data suggest that children’s spontaneous attention to patterns is an important component of their mathematical ability. Children’s spontaneous pattern constructions may provide opportunities to discuss and practice patterns in preschool settings or at home, but more research is required to further analyse the role of SFOP in early mathematical development. ispartof: British Journal Of Educational Psychology vol:90 issue:3 pages:1-17 ispartof: location:England status: Published online

Group formation is one of the key processes in collaborative learning because having adequate members in the learning groups supports good collaborative interactions among members and is fundamental to ensuring satisfactory learning performance. Several previous studies have proposed genetic algorithm-based group formation scheme that considers multiple student characteristics to optimize collaborative learning groups. However, the fitness function used in the genetic algorithm (GA) for assessing the quality of group formation may determine collaborative learning groups with unbalanced learning characteristics. Additionally, few studies considered how learning roles and interactions among peers can be used to optimize collaborative learning groups and confirmed the effects of different group formation schemes on learning performance and peer interaction. Therefore, this work proposes a novel genetic algorithm-based group formation scheme with penalty function (GAGFS-PF) that considers the heterogeneous of students' knowledge levels and learning roles, and the homogeneity of social interactions measured by social network analysis among the members in the learning group, to generate collaborative learning groups with balanced learning characteristics for improving students' learning performance and facilitate students’ interactions in a collaborative problem-based learning (CPBL) environment. This work uses a quasi-experimental research method to collect quantitative data to assess the effects of three group formation schemes - the proposed GAGFS-PF, the random group formation scheme, and the self-selection group formation scheme - on the learning performance and effects of interaction in a CPBL environment and also adopts interview to enhance the results of qualitative data analysis. Namely, this study adopts a mixed study to examine the research findings. Eighty-three students from three Grade 6 classes at an elementary school in New Taipei City, Taiwan were invited to participate in the experiment. Three classes were randomly assigned to the three experimental groups that used different group formation schemes including the proposed GAGFS-PF, random group formation scheme, and self-selection group formation scheme for CPBL activities on the topic of “global warming.” The results reveal that the proposed GAGFS-PF is significantly superior to the random group formation scheme in the score of a completed report assessed by two teachers during the “action 2” learning stage, among the four CPBL stages. Analytical results also show that the proposed GAGFS-PF for group formation is significantly superior to the random and self-selection group formation schemes in the effects of peer interaction, as assessed using social network measures. The interview results also support that the proposed GAGFS-PF provides benefits in determining collaborative learning groups. This work contributes a novel and useful group formation scheme for enhancing collaborative learning performance and also helps in calling for future research in this field as well.

Variability in practice has been shown to enhance motor skill learning. Benefits of practice variability have been attributed to motor schema formation (variable versus constant practice), or more effortful information processing (random versus blocked practice). We hypothesized that, among other mechanisms, greater practice variability might promote an external focus of attention on the intended movement effect, while less variability would be more conducive to a less effective internal focus on body movements. In Experiment 1, the learning of a throwing task was enhanced by variable versus constant practice, and variable group participants reported focusing more on the distance to the target (external focus), while constant group participants focused more on their posture (internal focus). In Experiment 2, golf putting was learned more effectively with a random compared with a blocked practice schedule. Furthermore, random group learners reported using a more effective distal external focus (i.e., distance to the target) to a greater extent, whereas blocked group participants used a less effective proximal focus (i.e., putter) more often. While attentional focus was assessed through questionnaires in the first two experiments, learners in Experiment 3 were asked to report their current attentional focus at any time during practice. Again, the learning of a throwing task was more effective after random relative to blocked practice. Also, random practice learners reported using more external focus cues, while in blocked practice participants used more internal focus cues. The findings suggest that the attentional foci induced by different practice schedules might be at least partially responsible for the learning differences.

We consider a set of indivisible operations and a set of uniformly related agents, i.e., agents with different speeds. Our aim is to develop a task allocation algorithm that minimizes the makespan in a decentralized manner. To achieve this, we first present the Operation Trading Algorithm. We show that the algorithm guarantees a worst case approximation factor of 1.618 for the 2 agent case and $\frac{1+\sqrt{4n-3}}{2}$ for the general n agent case. Further, we prove that the algorithm guarantees a near-optimal makespan for real-life scenarios with large number of operations under the assumption of a fully connected network of agents. The algorithm also guarantees an approximation factor less than 2 for any number of identical agents. Following this, we present a Decentralized random Group Formation protocol which enables the agents to implement OTA(n) in a decentralized manner in presence of communication failures. Finally, using numerical results, we show that the algorithm generates near optimal allocations even in the presence of communication failures. Additionally, the algorithm is parameter free and allows fast re-planning, making it robust to machine failures and changes in the environment.

We introduce a model for random groups in varieties of $n$-periodic groups as $n$-periodic quotients of triangular random groups. We show that for an explicit $d_{\mathrm{crit}}\in(1/3,1/2)$, for densities $d\in(1/3,d_{\mathrm{crit}})$ and for $n$ large enough, the model produces \emph{infinite} $n$-periodic groups. As an application, we obtain, for every fixed large enough $n$, for every $p\in (1,\infty)$ an infinite $n$-periodic group with fixed points for all isometric actions on $L^p$-spaces. Our main contribution is to show that certain random triangular groups are uniformly acylindrically hyperbolic., Comment: v1: 9 pages, 1 figure; v2: 14 pages, 1 figure. Expanded exposition, final version

Objective: The purpose ofthis study was to examine the effect of high intensity and moderate intensityfootball specific circuit training on selected motor fitness variables among football players in Ethiopia.Method: For the purpose of this study random group design was implemented. To achieve this objective60 football players were taken as the subjects of the study. These subjects were distributed in to three highintensity football specific circuit training group (N1=20), moderate intensity football specific circuit traininggroup (N2=20) and control group (N=20) using random sampling technique. The high intensity footballspecific circuit training group and moderate intensity football specific circuit training group were engagedin high intensity football specific circuit training and moderate intensity football specific circuit trainingrespectively. The selected variables were agility, explosive strength and speed. The data was collected usingthe standardized tests such as zigzag run test for Agility, 30 meter speed test for Speed and Standing longjump test for Explosive strength.. The data was analyzed using ANCOVA and bonefferani post hoc test forpaired mean comparison when significant difference exists.Result: Our finding indicated that the HICT group increased significantly in agility, explosive strengthand speed than the control group with a mean difference made (-.743, P=.000), .(360, P=.000) and (-.725,P=.000) respectively. The MICT group also showed significant difference on speed, explosive strength andspeed than the control group with a mean difference made (-.562, P=.000), (.236, P=.000) and (-.367, P=.000)respectively. Moreover the difference made between the HICT group and MICT group on explosive strengthand speed was significant with a mean difference made (.125, P=.000) and (-.358, P=.000) respectively.Whereas the HICT group and MICT group didn’t show significant difference on their agility with a meandifference of (-.180, P = .099).Conclusion: From the finding we concluded that the intensity of circuit training is very crucial for themagnitude of adaptation in circuit training. Thus for the effectiveness of circuit training the plan of trainersor coaches should seriously consider the intensity to bring the intended or required changes.

The set of stable matchings induces a distributive lattice. The supremum of the stable matching lattice is the boy-optimal (girl-pessimal) stable matching and the infimum is the girl-optimal (boy-pessimal) stable matching. The classical boy-proposal deferred-acceptance algorithm returns the supremum of the lattice, that is, the boy-optimal stable matching. In this paper, we study the smallest group of girls, called the minimum winning coalition of girls, that can act strategically, but independently, to force the boy-proposal deferred-acceptance algorithm to output the girl-optimal stable matching. We characterize the minimum winning coalition in terms of stable matching rotations. Our two main results concern the random matching model. First, the expected cardinality of the minimum winning coalition is small, specifically \((\frac{1}{2}+o(1))\log {n}\). This resolves a conjecture of Kupfer [13]. Second, in contrast, a randomly selected coalition must contain nearly every girl to ensure it is a winning coalition asymptotically almost surely. Equivalently, for any \(\varepsilon >0\), the probability a random group of \((1-\varepsilon ) n\) girls is not a winning coalition is at least \(\delta (\varepsilon )>0\).

We present a theory for the composable security of sending-or-not-sending (SNS) protocol of twin field quantum key distribution (TF-QKD). We present methods to strictly calculate the finite-key effects in QKD with error rejection through two-way classical communication (TWCC) for SNS TF-QKD protocol. Unlike the normal QKD without TWCC, here the probability of tagging or untagging for each two-bit random group is not independent. We rigorously solve this problem by imagining a virtual set of bits where every bit is independent and identical. With explicit formulas, we show that simply applying Chernoff bound in the calculation gives correct key rate, but the failure probability changes a little bit. We calculate the key rate with strict bounds and security, and obtain key rates by far breaking the PLOB (Pirandola, Laurenza, Ottaviani, and Banchi) bound with composable security.

The purpose of this research was to find a grouping method that can instantly improve team productivity so that various organizations can use this grouping method to organize the team to achieve better performance. We conducted two experiments and evaluated the teams’ productivity of all groups and recorded conversation records and search behaviors of all subjects who were identified as one of the 4 categories: Execution, Influence, Relationship Building, and Strategic Thinking. For search behavior, the results show the Influence category has higher number of average different keyword searches than that of Relationship-Building category. Influence category has higher number of average different keywords than Execution category. For self-efficacy, although there is no significant difference in the confidence level between the talent categories, the Strategic Thinking category have a higher degree of confidence compared to other categories, while people belonging to the Influence category have lower confidence level than any of the other three categories. As for teamwork’s productivity, the group with the highest productivity is the heterogeneous talent group with one month time of collaboration or break-in, second is the immediate homogeneous talent group, third is the immediate random group, and the group with the lowest productivity is the immediate (with no time to break-in) heterogeneous talent group.

Cognitive biases shape our perception of the world and our interactions with other people. Information related to the self and our social ingroups is prioritised for cognitive processing and can therefore form some of these key biases. However, ingroup biases may be elicited not only for established social groups, but also for minimal groups assigned by novel or random social categorisation. Moreover, whether these ‘ingroup biases’ are related to self-processing is unknown. Across three experiments, we utilised a social associative matching paradigm to examine whether the cognitive mechanisms underpinning the effects of minimal groups overlapped with those that prioritise the self, and whether minimal group allocation causes early processing advantages. We found significant advantages in response time and sensitivity (dprime) for stimuli associated with newly-assigned ingroups. Further, self-biases and ingroup-biases were positively correlated across individuals (Experiments 1 and 3). However, when the task was such that ingroup and self associations competed, only the self-advantage was detected (Experiment 2). These results demonstrate that even random group allocation quickly captures attention and enhances processing. Positive correlations between the self- and ingroup-biases suggest a common cognitive mechanism across individuals. These findings have implications for understanding how social biases filter our perception of the world.

Area under expiratory flow-volume curve (AEX) has been proposed recently to be a useful spirometric tool for assessing ventilatory patterns and impairment severity. We derive here normative reference values for AEX, based on age, gender, race, height and weight, and by using artificial neural network (ANN) algorithms. We analyzed 3567 normal spirometry tests with available AEX values, performed on subjects from two countries (United States and Spain). Regular linear or optimized regression and ANN models were built using traditional predictors of lung function. The ANN-based models outperformed the de novo regression-based equations for AEXpredicted and AEX z scores using race, gender, age, height and weight as predictor factors. We compared these reference values with previously developed equations for AEX (by gender and race), and found that the ANN models led to the most accurate predictions. When we compared the performance of ANN-based models in derivation/training, internal validation/testing, and external validation random groups, we found that the models based on pooling samples from various geographic areas outperformed the other models (in both central tendency and dispersion of the residuals, ameliorating any cohort effects). In a geographically diverse cohort of subjects with normal spirometry, we computed by both regression and ANN models several predicted equations and z scores for AEX, an alternative measurement of respiratory function. We found that the dynamic nature of the ANN allows for continuous improvement of the predictive models’ performance, thus promising that the AEX could become an essential tool in assessing respiratory impairment.

Spinal cord injury research in experimental animals aims to define mechanisms of tissue damage and identify interventions that can be translated into effective clinical therapies. Highly reliable models of injury and outcome measurement are essential to achieve these aims and avoid problems with reproducibility. Functional scoring is a critical component of outcome assessment and is currently commonly focused on open field locomotion (the “BBB score”). Here we analyze variability of observed locomotor outcome after a highly regulated spinal cord contusion in a large group of rats that had not received any therapeutic intervention. Our data indicate that, despite tight regulation of the injury severity, there is considerable variability in open-field score of individual rats at 21 days after injury, when the group as a whole reaches a functional plateau. The bootstrapped reference interval (that defines boundaries that contain 95% scores in the population without regard for data distributional character) for the score at 21 days was calculated to range from 2.3 to 15.9 on the 22-point scale. Further analysis indicated that the mean day 21 score of random groups of 10 individuals drawn by bootstrap sampling from the whole study population varies between 9.5 and 13.5. Wide variability between individuals implies that detection of small magnitude group-level treatment effects will likely be unreliable, especially if using small experimental group sizes. To minimize this problem in intervention studies, consideration should be given to assessing treatment effects by comparing proportions of animals in comparator groups that attain pre-specified criterion scores.

For every dimension d, there is an infinite family of convex co-compact reflection groups of isometries of hyperbolic d-space --- the superideal (simplicial and cubical) reflection groups --- with the property that a random group at any density less than a half (or in the few relators model) contains quasiconvex subgroups commensurable with some member of the family, with overwhelming probability.

To analyze the quality of resuscitation (CPR) performed by individuals without training after receiving a set of instructions (structured and unstructured/intuitive) from an expert in a simulated context, the specific objective was to design a simple and structured CPR learning method on-site. An experimental study was designed, consisting of two random groups with a post-intervention measurement in which the experimental group (EG) received standardized instructions, and the control group (CG) received intuitive or non-standardized instructions, in a public area simulated scenario. Statistically significant differences were found (p &lt, 0.0001) between the EG and the CG for variables: time needed to give orders, pauses between chest compressions and ventilations, depth, overall score, chest compression score, and chest recoil. The average depth of the EG was 51.1 mm (SD 7.94) and 42.2 mm (SD 12.04) for the CG. The chest recoil median was 86.32% (IQR 62.36, 98.87) for the EG, and 58.3% (IQR 27.46, 84.33) in the CG. The use of a sequence of simple, short and specific orders, together with observation-based learning makes possible the execution of chest compression maneuvers that are very similar to those performed by rescuers, and allows the teaching of the basic notions of ventilation. The structured order method was shown to be an on-site learning opportunity when faced with the need to maintain high-quality CPR in the presence of an expert resuscitator until the arrival of emergency services.

A blackbox secret sharing (BBSS) scheme works in exactly the same way for all finite Abelian groups G; it can be instantiated for any such group G and only black-box access to its group operations and to random group elements is required. A secret is a single group element and each of the n players’ shares is a vector of such elements. Share-computation and secret-reconstruction is by integer linear combinations. These do not depend on G, and neither do the privacy and reconstruction parameters t, r. This classical, fundamental primitive was introduced by Desmedt and Frankel (CRYPTO 1989) in their context of “threshold cryptography.” The expansion factor is the total number of group elements in a full sharing divided by n. For threshold BBSS with t-privacy (Formula presented)-reconstruction and arbitrary n, constructions with minimal expansion (Formula presented) exist (CRYPTO 2002, 2005). These results are firmly rooted in number theory; each makes (different) judicious choices of orders in number fields admitting a vector of elements of very large length (in the number field degree) whose corresponding Vandermonde-determinant is sufficiently controlled so as to enable BBSS by a suitable adaptation of Shamir’s scheme. Alternative approaches generally lead to very large expansion. The state of the art of BBSS has not changed for the last 17 years. Our contributions are two-fold. (1) We introduce a novel, nontrivial, effective construction of BBSS based on coding theory instead of number theory. For threshold-BBSS we also achieve minimal expansion factor O(log n).(2) Our method is more versatile. Namely, we show, for the first time, BBSS that is near-threshold, i.e., r-t is an arbitrarily small constant fraction of n, and that has expansion factor O(1), i.e., individual share-vectors of constant length (“asymptotically expansionless”). Threshold can be concentrated essentially freely across full range. We also show expansion is minimal for near-threshold and that such BBSS cannot be attained by previous methods. Our general construction is based on a well-known mathematical principle, the local-global principle. More precisely, we first construct BBSS over local rings through either Reed-Solomon or algebraic geometry codes. We then “glue” these schemes together in a dedicated manner to obtain a global secret sharing scheme, i.e., defined over the integers, which, as we finally prove using novel insights, has the desired BBSS properties. Though our main purpose here is advancing BBSS for its own sake, we also briefly address possible protocol applications.

The body condition of does at the time of mating may affect feeding patterns and production performance during forthcoming lactation. For investigation, 40 Beetal does available for breeding were utilized, and their body condition score (BCS) was estimated using the visual-cum-palpation method with a 9-point scale (scale of 1=5 with increments of 0.5 point). The available goats were divided into 3 groups: higher BCS (T ≥ 3.0 " role="presentation"> ≥ 3.0 ≥ 3.0 _{≥3.0} ; n =11), moderate BCS (T 2.5 " role="presentation"> 2.5 2.5 _{2.5} ; n = 8), and lower BCS (T ≤ 2.0 " role="presentation"> ≤ 2.0 ≤ 2.0 _{≤2.0} ; n = 21) and maintained in 2 random groups (20 each). Beetal goats with higher BCS at breeding time spent significantly (P ≤ 2.0 ≤ 2.0 _{≤2.0} goats struggled (displacement and pushing) more at feeders, which included T ≤ 2.0 " role="presentation"> ≤ 2.0 ≤ 2.0 _{≤2.0} goats eating from the ground for more time (P ≥ 3.0 ≥ 3.0 _{≥3.0} goats had more agonistic interactions (threatening and hitting) toward moderate and lower BCS goats at feeders. Goats with higher BCS at mating had significantly (P ≥ 3.0 ≥ 3.0 _{≥3.0} group than other groups. It was concluded that Beetal goats should not have less than 3.0 BCS at the time of mating for better performance and health status.

Purpose: To compare the results of one-site versus two-site combined glaucoma filtration andphacoemulsification surgery with respect to visual acuity (VA) and intraocular pressure (IOP)control. Methodology: A prospective study was conducted on 40 patients with glaucoma andcataract. Cases will be divided into two random groups: Group A: 20 eyes were subjected to one sitePhacotrabeculectomy. Group B: 2o eyes were subjected to two-site Phacotrabeculectomy. Theresults were compared within one week, one month, three months and sex months postoperative as regards VA and IOP. Results: There was a statistically significant difference in VAand IOP in pre-operative and post-operative conditions in the whole patients. There was nostatistically significant difference in VA and IOP post-operatively between the two groups.Conclusion: The similar and excellent results achieved in the 2 groups imply that either techniquemight be used to handle the problem of concurrent cataract and glaucoma in many patients.