Nearly sign-nonsingular matrices

AbstractA real matrix A is nearly sign-nonsingular if every term in the expansion of det A but one has the same sign. We show such matrices can be put into a normal form in which all diagonal entries are negative, all other nonzero entries are positive, and the directed graph of the matrix is intercyclic. With the help of recent results of Metzlar, McCuaig, and Thomassen on intercyclic digraphs, we are able to separate the nearly sign-nonsingular matrices into five classes and to characterize each of these classes. We also obtain two results showing where real matrices having intercyclic digraphs can or cannot be signed in such a way as to belong both to the class of sign-nonsingular matrices and the class of nearly sign-nonsingular matrices

Usefulness and expectations on skills development and entrepreneurship among women of low socioeconomic status in Ogun State, Nigeria

The acquisition of vocational training skills and entrepreneurial know-how is acknowledged as an added advantage and a safety net to navigate poverty, especially in dwindling economic recession time and massive unemployment. This study examined the factors influencing the usefulness and perceived realization of skills development/empowerment to encourage more women's involvement in small scale businesses and promote its effect on poverty alleviation in households across Nigeria. Data collection involved a structured questionnaire and in-depth interviews conducted post-the vocational skill/empowerment training. The training was organized among Campus Keepers in a private university in Ogun State, Nigeria. Forty Campus Keepers were selected using the systematic sampling technique from a total population of 224, and 37 of the 40 selected voluntarily participated in this study. The Campus Keepers were women with low socioeconomic status who worked as cleaners on the university campus. Five of the Campus Keepers were purposively selected as key informants for the study. Results showed that respondents who had earlier knowledge and vocational skills training reported that it leads to self-employment. This view was higher for respondents who had more people in their household than those with fewer people (OR = 22.7 [CI= .56, 921.31]). The perception that the training can lead to additional income was lower for respondents who reported that either they or their spouses were sole breadwinners in their household than for those who reported that both/others/none were breadwinners (OR = .05 [CI=0, 1.2]). The odds that the skills development/empowerment training will result in perceived improved business was higher for respondents who gained more knowledge/information from the training than those who did not (OR=29.19 [CI = 1.1, 777.48]). Findings from the qualitative study suggest that key informants who participated in past training were yet to establish a profitable business of their dream fully. Governmental policy and program intervention that incorporates these findings will lead to increased participation of the target population in similar training in the future, leading to poverty alleviation towards achieving the SDGs for Nigeria

Suono e Spettacolo. Athanasius Kircher, un percorso nelle Immagini sonore.

The Society of Jesus made great propaganda efforts throughout the seventeenth century and chose the images and the play as a privileged means to communicate and persuade. Athanasius Kircher, a key figure of the seventeenth century, he decided to dominate the wild nature of sound through Phonurgia Nova, which includes a gallery of powerful symbolic images for Baroque aesthetics. The essay, through the grant of the images from the Library of the Department of Mathematics "Guido Castelnuovo" Sapienza University of Rome, aims to understand, through the pictures offered by Kircher, the sound phenomenon and the spectacle that this produces. In Phonurgia Nova a process of dramatization sound effects takes place, often through machines and "visions" applied to the theatrical reality, as experimental and astonishing environment beloved in baroque. Kircher illustrates the sound through explanatory figures, so to dominate the sound through the eyes. Sound is seen, admired and represented: its spectacle not only takes place through the implementation of sound machines or the "wonders" applied to the theater, but even through images, creating create a sense of wonder in in the erudite person of the seventeenth century

Evaluating long term forecasts

The U.S. Department of Energy's Energy Information Administration (EIA), and its predecessor organizations, has published projections of U.S. energy production, consumption, distribution and prices annually for over 30 years. A natural issue to raise in evaluating the projections is an assessment of their accuracy compared to eventual outcomes. A related issue is the determination of the sources of "error" in the projections that are due to differences between the actual versus realized values of the associated assumptions. One way to do this would be to run the computer-based model from which the projections are derived at the time the projected values are realized, using actual rather than assumed values for model assumptions; and, compare these results to the original projections. For long term forecasts, this approach would require that the model's software and hardware configuration be archived and available for many years, possibly decades, into the future. Such archival creates many practical problems; and, in general, it is not being done. This paper reports on an alternative approach for evaluating the projections. In the alternative approach, the model is run many times for cases in which important assumptions are changed individually and in combinations. A database is assembled from the solutions and a regression analysis is conducted for each important projected variable with the associated assumptions chosen as exogenous variables. When actual data are eventually available, the regression results are then used to estimate the sources of the differences in the projections of the endogenous variables compared to their eventual outcomes. The results presented here are for residential and commercial sector natural gas and electricity consumption.Forecast evaluation Model approximation Pseudo data

A New Approach to Model Verification, Falsification and Selection

This paper shows that a qualitative analysis, i.e., an assessment of the consistency of a hypothesized sign pattern for structural arrays with the sign pattern of the estimated reduced form, can always provide decisive insight into a model’s validity both in general and compared to other models. Qualitative analysis can show that it is impossible for some models to have generated the data used to estimate the reduced form, even though standard specification tests might show the model to be adequate. A partially specified structural hypothesis can be falsified by estimating as few as one reduced form equation. Zero restrictions in the structure can themselves be falsified. It is further shown how the information content of the hypothesized structural sign patterns can be measured using a commonly applied concept of statistical entropy. The lower the hypothesized structural sign pattern’s entropy, the more a priori information it proposes about the sign pattern of the estimated reduced form. As an hypothesized structural sign pattern has a lower entropy, it is more subject to type 1 error and less subject to type 2 error. Three cases illustrate the approach taken here