Factor analysis with finite data

Factor analysis aims to describe high dimensional random vectors by means of a small number of unknown common factors. In mathematical terms, it is required to decompose the covariance matrix $\Sigma$ of the random vector as the sum of a diagonal matrix $D$ | accounting for the idiosyncratic noise in the data | and a low rank matrix $R$ | accounting for the variance of the common factors | in such a way that the rank of $R$ is as small as possible so that the number of common factors is minimal. In practice, however, the matrix $\Sigma$ is unknown and must be replaced by its estimate, i.e. the sample covariance, which comes from a finite amount of data. This paper provides a strategy to account for the uncertainty in the estimation of $\Sigma$ in the factor analysis problem.Comment: Draft, the final version will appear in the 56th IEEE Conference on Decision and Control, Melbourne, Australia, 201

Factor Models with Real Data: a Robust Estimation of the Number of Factors

Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in mathematical terms as follows. We are given the covariance matrix Sigma of the available data. Sigma must be additively decomposed as the sum of two positive semidefinite matrices D and L: D | that accounts for the idiosyncratic noise affecting the knowledge of each component of the available vector of data | must be diagonal and L must have the smallest possible rank in order to describe the available data in terms of the smallest possible number of independent factors. In practice, however, the matrix Sigma is never known and therefore it must be estimated from the data so that only an approximation of Sigma is actually available. This paper discusses the issues that arise from this uncertainty and provides a strategy to deal with the problem of robustly estimating the number of factors.Comment: arXiv admin note: text overlap with arXiv:1708.0040

Welfare issues of modern laying hen farming

This review starts with a brief outline of poultry behaviour and biology and a description of the present laying hen farming situation in Italy. Moreover, it points out the situation of EU legislation currently in effect for laying hen welfare. It then reviews the main welfare issues of layer farming. The following aspects are considered: rearing system (e.g. stocking density, light intensity and photoperiod, equipment and facilities) and some health aspects. All these aspects represent important issues for farmed species, but special attention should be paid when we deal with intensively farmed species like poultry, where a lot of potential stressors may impair the welfare with consequences on health and production. The adoption of suitable housing systems and of adequate management techniques, as well as the presence of well trained stockpersons with a sound knowledge of poultry physiology and behaviour, are particularly important in guaranteeing a sufficient welfare level to poultry. Therefore, the adoption of specific codes of recommendations is highly desirable

Robust Identification of "Sparse Plus Low-rank" Graphical Models: An Optimization Approach

Motivated by graphical models, we consider the "Sparse Plus Low-rank" decomposition of a positive definite concentration matrix -- the inverse of the covariance matrix. This is a classical problem for which a rich theory and numerical algorithms have been developed. It appears, however, that the results rapidly degrade when, as it happens in practice, the covariance matrix must be estimated from the observed data and is therefore affected by a certain degree of uncertainty. We discuss this problem and propose an alternative optimization approach that appears to be suitable to deal with robustness issues in the "Sparse Plus Low-rank" decomposition problem.The variational analysis of this optimization problem is carried over and discussed

RAPPORTO TECNICO SULL\u27ATTIVIT? DI ELABORAZIONE SISMICA DELLA LINEA CROP M-6A

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Effects of two different rearing systems (organic and barn) on production performance, animal welfare traits and egg quality characteristics in laying hens

Alternative housing systems for hen eggs production represents clear evidence of the trend in animal housing and husbandry towards extensive rearing methods. Consumer demand is oriented towards healthy foods controlled not only under a safety point of view, but also under a welfare assessment of the animals' living conditions. Among the different alternative systems deep litter and organic production in recent years have been improved in Italy. The aim of this study was to evaluate whether different housing systems (barn B and organic O) for laying hens may influence productive performance, fear responses and egg quality characteristics. A total of 4,745 birds were housed in the B system and 2,016 in the O system, both of which were commercial facilities. In each system the same strain (Hy-Line Brown) was housed and layer performance, external and internal egg characteristics, mortality and feed consumption were recorded weekly. Animal reactivity was recorded monthly with the approaching test. Moreover, the Tonic Immobility test was conducted at 70 weeks of age; feather and foot pad conditions were also investigated at the same time. The peak of laying was reached in both housing systems at 25 weeks of age and was higher in organic hens (94.5%) than in barn hens (93.0%). Feed conversion rate during the overall laying period was 2.36 vs 2.20, respectively, in O and B housing systems. There was a significant difference concerning the eggs classified as very dirty, dirty and cracked between the two systems. The dirty eggs were higher in O system probably due to laying eggs in a free range area, while the higher number of cracked eggs in B system may be due to a significantly less shell thickness in this system. Egg weight increased with layer age in both housing systems. Animals reared in O system showed less fearfulness than in B emphasised by the approaching and Tonic Immobility test results. Feather scoring did not evidence any severe plumage damage; statistical analysis showed some significant differences in comb and back areas between O and B systems. The hens reared on litter showed more aggressive pecking than the organic hens probably due to difference both in light intensity and in density

Individual and contextual determinants of inter-regional mobility in cancer patients

This paper will present an investigation of inter-regional mobility in patients with a diagnosis of cancer. By virtue of the availability of geocoded information relating to a patient's place of residence, the effect of socio-economic status and other individual characteristics regarding inter-regional mobility will be analysed by means of multilevel logit models. The results demonstrate the influence of age and comorbidity on mobility propensity, in addition to the treatment type, which plays a role in patient mobility. As contextual determinants, patients residing in less deprived areas show greater mobility than those who reside in materially deprived areas. The extent of patient mobility, and its dependence on their socio-economic status raises issues of equity, as well as regional policy considerations

Comparison of video and direct observation methods for measuring oral behaviour in veal calves

Measuring behaviour, especially oral behaviour, has always been a debated issue: therefore the aim of this paper is to closely examine the study of oral behaviour in calves and the approaching methodology. Behavioural observations were conducted by two media (direct observations by check sheets and indirect observations by videotapes recorded by cam- eras connected to a digital field switcher and a time-lapse video recorder) in order to compare data and assess the reli- ability and validity of the two methods in identifying some oral behavioural patterns in calves. The study was carried out on 54 Polish Friesian calves housed in group pens and in individual crates. The behaviour of the calves was investigated during the fattening period on the 2nd, 7th, 13th, 18th and 23rd week, one hour before and one hour after each of the two meals. Two experienced observers checked the behaviour of the calves, including oral behaviours on structures and buckets and oral stereotypies, by direct observations using a scan sampling every 2 min- utes. The calves' behaviour was also video recorded on the same days in which the direct observations were carried out and analysed by the same two observers. Percentages of time spent on each type of behaviour were calculated and anal- ysed by Chi-square test. Regardless of the housing system, the comparison between direct and indirect observations revealed significant differences in almost every behavioural category. Licking, biting and nibbling structures, nibbling and sucking the bucket, playing with the bucket and the teat, chewing and oral stereotypies were significantly higher in direct observations compared to indirect (P < 0.001), while inactivity was higher in video recorded observations (P < 0.001). In conclusion, regardless of the type of housing, our results revealed an objective difficulty in analysing videotapes with very detailed behavioural categories, like oral behaviours. Although video recording can certainly represent a useful and practical alternative to direct observations in many situations, the video recording system used in this study for investi- gating calves' oral behaviour, in spite of the use of multiple cameras, could not replace direct observations, probably due to the restricted field of view, the low depth of focus, the black and white vision, the lack of audio and the time-lapse feature

Parasitic worms in organic laying hens – relation with range use.

This abstract contains the results of Dutch farms 1-2