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(2017)
A real matrix is called totally nonnegative if all of its minors are nonnegative. In this paper, the minors are determined from which the maximum allowable entry perturbation of a totally nonnegative matrix can be found, such that the perturbed matrix remains totally nonnegative. Also, the total nonnegativity of the first and second subdirect sum of two totally nonnegative matrices is considered.
Growth is a key indicator of the prosperity of an economy. In today's Germany the " Gründerzeit " still describes a period of enormous economic growth. Factors that lead to growth haven't been investigated in the context of the different life cycle stages of early-stage technology ventures so far. This paper proposes a model of early-stage ventures' growth based on factors. From a theoretical angle, we look at the business from the market-based view (MBV) and the resource-based view (RBV) on strategy in the longitudinal perspective of the business life cycle. With this view we get to know what are the stage specific needs and processes of new technology based ventures in order to provide appropriate support. We tested different potential growth indicators for the model with a questionnaire-based survey which was answered by 68 high-tech entrepreneurs. The results suggest that growth factors are stage specific in their relevance. While leading to growth in one stage, certain factors evince no or even negative influence on growth in other stages. Moreover, RBV factors as seen more relevant for the growth than the MBV factors. Further research requires a large and representative population to validate the results. Keywords:-growth factors, early-stage ventures, market-based view, resources based view.
Validity of the business model is a key indicator for buying into ventures in the early-stage. Business models of early-stage ventures decrease in validity when developing the business over the progressing stages of the business life-cycle. By doing so, the ventures are validating their business model when building transaction relationships to the surrounding value network. In prior research, we developed a research design based on existing business innovation proposals (onepager, pitch decks, business plans) that is assumed to evaluate the status of business model validation. The core hypothesis of the research design is that transaction relations represent a strong anchor between the business model and the business reality, thus providing information on the business model validity. In this research, we test this hypothesis by designing and analyzing a survey that was directed to founders taking part in a business plan competition. We compared the relationships described in the submitted business plans to the relations explicitely stated in the follow-up questionnaire. We identified that the described relations to customers, investors, and people (human resources) match the relationships expressed in questionnaires quite well. A significant disagreement, however, exists in the relationships to suppliers. We conclude that there is still a theoretical and empirical gap that leads to disagreement between business plans and reality in the group of suppliers.