Precision of the Nebra Disc in Astronomical and Geometric Aspect

The astronomical knowledge on the disc has been coded on two planes: horizontal and meridian. The range of sunrise and sunset directions during the year has been described on the horizontal plane. In turn, on the meridian (vertical) plane, the range of changes in the horizontal height and declination of the Sun in the upper culmination during the year and the Moon in its 18.61-year cycle were described. The relationships between the latitude of the place of observation, the horizontal height of the celestial body and its declination were described by means of geometric constructions. The presented article is a continuation of two publications [1] and [2], which describe the decryption of the Nebra disc. These publications were based on the interpretation of the results of angular measurements, made using a protractor with a scale of 0.5 degrees, without the use of a computer. The presented publication is based on a digital disc image obtained by means of its digitization. The obtained data was used for further calculations based on analytical geometry and graphic programs. This allowed to obtain results in a linear measure with a precision of less than 1 mm. PRECYZJA DYSKU Z NEBRY W ASPEKCIE ASTRONOMICZNYM I GEOMETRYCZNYM Wiedza astronomiczna na dysku została zakodowana na dwóch płaszczyznach: horyzontalnej i południkowej. Na płaszczyźnie horyzontalnej (poziomej) opisano zakres kierunków wschodu i zachodu Słońca w ciągu roku. Z kolei na płaszczyźnie południkowej (pionowej) opisano zakres zmiany wysokości horyzontalnej i deklinacji Słońca w kulminacji górnej w ciągu roku oraz Księżyca w jego 18,61-rocznym cyklu. Za pomocą konstrukcji geometrycznych opisano związki między szerokością geograficzną miejsca obserwacji, wysokością horyzontalną ciała niebieskiego i jego deklinacją. Prezentowany artykuł jest kontynuacją dwóch publikacji: [1], [2], w których opisano deszyfrację dysku z Nebry. Publikacje te były oparte na interpretacji wyników pomiarów kątowych, wykonanych za pomocą kątomierza o podziałce 0,5 stopnia, bez użycia komputera. Prezentowana publikacja bazuje na cyfrowym obrazie dysku, uzyskanym za pomocą jego digitalizacji. Uzyskane dane wykorzystano do dalszych obliczeń opartych na geometrii analitycznej oraz programach graficznych.

Summarized distributions of mass: a statistical approach to consumers’ consumption spaces

This paper focuses on logical aspects of choices being made by the consumer under conditions of uncertainty or certainty. Such logical aspects are found out to be the same. Choices being made by the consumer that should maximize her subjective utility are decisions studied by revealed preference theory. A finite number of possible alternatives is considered. They are mutually exclusive propositions identifying all quantitative states of nature of a consumption plan. Each proposition of it is expressed by a real number. This research work distinguishes it from its temporary truth value depending on the state of information and knowledge of the consumer. Since each point of the consumption space of the consumer belongs to a two-dimensional convex set, this article focuses on conjoint distributions of mass. Indeed, the consumption space of the consumer is generated by all coherent summaries of a conjoint distribution of mass. Each point of her consumption space is connected with a weighted average of states of nature of two consumption plans jointly studied. They give rise to a conjoint distribution of mass. The consumer chooses a point of a two-dimensional convex set representing that bundle of goods actually demanded by her inside of her consumption space. This paper innovatively shows that it is nothing but a bilinear and disaggregate measure. It is decomposed into two real numbers, where each real number is a linear measure. In this paper, different measures are obtained. They can be disaggregate or aggregate measures, where the latter are independent of the notion of ordered pair of consumption plans.

Daily Rhythm of Fractal Cardiac Dynamics Links to Weight Loss Resistance: Interaction with CLOCK 3111T/C Genetic Variant

The effectiveness of weight loss treatment displays dramatic inter-individual variabilities, even with well-controlled energy intake/expenditure. This study aimed to determine the association between daily rhythms of cardiac autonomic control and weight loss efficiency and to explore the potential relevance to weight loss resistance in humans carrying the genetic variant C at CLOCK 3111T/C. A total of 39 overweight/obese Caucasian women (20 CLOCK 3111C carriers and 19 non-carriers) completed a behaviour–dietary obesity treatment of ~20 weeks, during which body weight was assessed weekly. Ambulatory electrocardiographic data were continuously collected for up to 3.5 days and used to quantify the daily rhythm of fractal cardiac dynamics (FCD), a non-linear measure of autonomic function. FCD showed a 24 h rhythm (p < 0.001). Independent of energy intake and physical activity level, faster weight loss was observed in individuals with the phase (peak) of the rhythm between ~2–8 p.m. and with a larger amplitude. Interestingly, the phase effect was significant only in C carriers (p = 0.008), while the amplitude effect was only significant in TT carriers (p < 0.0001). The daily rhythm of FCD and CLOCK 3111T/C genotype is linked to weight loss response interactively, suggesting complex interactions between the genetics of the circadian clock, the daily rhythm of autonomic control, and energy balance control.

An Item Response Modeling Approach to Cognitive Load Measurement

The accurate measurement of the cognitive load a learner encounters in a given task is critical to the understanding and application of Cognitive Load Theory (CLT). However, as a covert psychological construct, cognitive load represents a challenging measurement issue. To date, this challenge has been met mostly by subjective self-reports of cognitive load experienced in a learning situation. In this paper, we find that a valid and reliable index of cognitive load can be obtained through item response modeling of student performance. Specifically, estimates derived from item response modeling of relative difficulty (i.e., the difference between item difficulty and person ability locations) can function as a linear measure that combines the key components of cognitive load (i.e., mental load, mental effort, and performance). This index of cognitive load (relative difficulty) was tested for criterion (concurrent) validity in Year 2 learners (N = 91) performance on standardized educational numeracy and literacy assessments. Learners’ working memory (WM) capacity significantly predicted our proposed cognitive load (relative difficulty) index across both numeracy and literacy domains. That is, higher levels of WM were related to lower levels of cognitive load (relative difficulty), in line with fundamental predictions of CLT. These results illustrate the validity, utility and potential of this objective item response modeling approach to capturing individual differences in cognitive load across discrete learning tasks.

Gastrointestinal tract morphometry and visceral organ weights of grower rabbit fed dried ginger (Zingiber officinale) root meal

Twenty-six grower rabbits of mixed sexes (12 males: 12 females) were used in the study to determine the effect of dietary dried ginger root meal (DGRM) on gastrointestinal tract morphometry and visceral organ weights. The rabbits were assigned by weight (average weight 557.09g) to four dietary treatments in a completely randomized design. Each treatment had six replicates. Four treatment diets; T1, T2, T3 and T4 were formulated to include 0%, 15%, 25% and 35% of DGRM respectively. Diets were offered ad-libitum to the rabbits. The experiment lasted for 8 weeks. Six rabbits were randomly selected from each treatment and sacrificed and eviscerated. Results showed that mean relative weights of the stomach, oesophagus and pancreas as well as the mean lengths of the oesophagus and intestines did not show any significant (p>0.05) variation. But significant (p<0.05) differences existed in the mean lengths of the proximal colon and caecum as well as the mean relative weights of the liver, kidneys, heart and lungs in rabbits fed DGRM. It can be concluded from this study that the inclusion of DGRM in the diets of growing rabbits significantly (p<0.05) increased the linear measure of the proximal colon and caecum and the mean weights of the visceral organs measured. Vingt-quatre lapins de croissance de sexes mixtes (12 mâles : 12 femelles) ont été utilisés dans l'étude pour déterminer l'effet de la farine de racine de gingembre séchée (le 'DGRM') sur la morphométrie du tractus gastro-intestinal et le poids des organes viscéraux. Les lapins ont été attribués en poids (poids moyen 557,09 g) à quatre traitements diététiques selon une conception complètement aléatoire. Chaque traitement comportait six répétitions. Quatre régimes de traitement ; T1, T2, T3 et T4 ont été formulés pour inclure respectivement 0%, 15%, 25% et 35% de 'DGRM'. Des régimes ont été offerts à volonté aux lapins. L'expérience a duré 8 semaines. Six lapins ont été choisis au hasard dans chaque traitement et sacrifiés et éviscérés. Les résultats ont montré que les poids relatifs moyens de l'estomac, de l'œsophage et du pancréas ainsi que les longueurs moyennes de l'œsophage et des intestins ne présentaient aucune variation significative (p> 0,05). Mais des différences significatives (p <0,05) existaient dans les longueurs moyennes du côlon proximal et du caecum ainsi que dans les poids relatifs moyens du foie, des reins, du cœur et des poumons chez les lapins nourris avec du 'DGRM'. On peut conclure de cette étude que l'inclusion de 'DGRM' dans l'alimentation des lapins en croissance de manière significative (p <0,05) a augmenté la mesure linéaire du côlon proximal et du caecum et les poids moyens des organes viscéraux mesurés.

The Effect of a Hidden Source on the Estimation of Connectivity Networks from Multivariate Time Series

Many methods of Granger causality, or broadly termed connectivity, have been developed to assess the causal relationships between the system variables based only on the information extracted from the time series. The power of these methods to capture the true underlying connectivity structure has been assessed using simulated dynamical systems where the ground truth is known. Here, we consider the presence of an unobserved variable that acts as a hidden source for the observed high-dimensional dynamical system and study the effect of the hidden source on the estimation of the connectivity structure. In particular, the focus is on estimating the direct causality effects in high-dimensional time series (not including the hidden source) of relatively short length. We examine the performance of a linear and a nonlinear connectivity measure using dimension reduction and compare them to a linear measure designed for latent variables. For the simulations, four systems are considered, the coupled Hénon maps system, the coupled Mackey–Glass system, the neural mass model and the vector autoregressive (VAR) process, each comprising 25 subsystems (variables for VAR) at close chain coupling structure and another subsystem (variable for VAR) driving all others acting as the hidden source. The results show that the direct causality measures estimate, in general terms, correctly the existing connectivity in the absence of the source when its driving is zero or weak, yet fail to detect the actual relationships when the driving is strong, with the nonlinear measure of dimension reduction performing best. An example from finance including and excluding the USA index in the global market indices highlights the different performance of the connectivity measures in the presence of hidden source.

QUANTIFYING SIZE AND SHAPE DIFFERENCES BETWEEN MUTURU AND N'DAMA BREEDS OF CATTLE

Body weight and eight linear body traits, namely heart girth, body and diagonal lengths, height at withers and at hip, width of loin and at pelvic bone, and depth at rear flank, were measured forthniylıtly on 32 Muturu bulls, 16 of which were born in the dry season (Muturu -D) and the remaining 16 in the rainy season (Muturu-R), and on 11 N'dama bulls. Correlations between all pairs of traits in all groups were high, positive and significant (r > 0.093). The first two principal components derived from the correlation matrix of the linear measurements, PCI and PC2 accounted for at least 98% of total variance in all cases and were regarded as, size' and 'shape' vectors, respectively. Whereas PC1 gave largest weight to heart girth, PC2 gave largest weight to two or more different other linear measurements in the three groups. N'dama had the best conformation, followed by Muturu -D and then Muturu - R. PC-based prediction models were more parsimonius than linear measure-based models and are considered preferable for selecting animals for "optimal" balance. Also, in addition to discriminating between the two different breeds, PC- based discriminant functions were able to discriminate among individuals within the same breed on the basis of putritional differences. These functions are therefore recommended for classifying animals according to different macro and micro criteria.

Manual ability in hand surgery patients: Validation of the ABILHAND scale in four diagnostic groups

Background Patients treated in hand surgery (HS) belong to different demographic groups and have varying impairments related to different pathologies. HS outcomes are measured to assess treatment results, complication risks and intervention reliability. A one-dimensional and linear measure would allow for unbiased comparisons of manual ability between patients and different treatment effects. Objective To adapt the ABILHAND questionnaire through Rasch analysis for specific use in HS patients and to examine its validity. Methods A preliminary 90-item questionnaire was presented to 216 patients representing the diagnoses most frequently encountered in HS, including distal radius fracture (n = 74), basal thumb arthritis (n = 66), carpal tunnel syndrome (n = 53), and heavy wrist surgery (n = 23). Patients were assessed during the early recovery and in the late follow-up period (0–3 months, 3–6 months and >6 months), leading to a total of 305 assessments. They rated their perceived difficulty with queried activities as impossible, difficult, or easy. Responses were analyzed using the RUMM2030 software. Items were refined based on item-patient targeting, fit statistics, differential item functioning, local independence and item redundancy. Patients also completed the QuickDASH, 12-item Short Form Survey (SF-12) and a numerical pain scale. Results The rating scale Rasch model was used to select 23 mostly bimanual items on a 3-level scale, which constitute a unidimensional, linear measure of manual ability with good reliability across all included diagnostic groups (Person-Separation Index = 0.90). The resulting scale was found to be invariant across demographic and clinical subgroups and over time. ABILHAND-HS patient measures correlated significantly (p<0.001) with the QuickDASH (r = -0.77), SF-12 Physical Component Summary (r = 0.56), SF-12 Mental Component Summary (r = 0.31), and pain scale (r = -0.49). Conclusion ABILHAND-HS is a robust person-centered measure of manual ability in HS patients.