A Conditional Approach for Modelling Patient Re-admissions in Hospital using a mixture of Coxian phase-type distributions incorporating Bayes Theorem

The number of elderly patients requiring hospitalisation in Europe is rising. With a greater proportion of elderly people in the population comes a greater demand for health services and, in particular, hospital care. Thus, with a growing number of elderly patients requiring hospitalisation competing with non-elderly patients for a fixed (and in some cases, decreasing) number of hospital beds, this results in much longer waiting times for patients, often with a less satisfactory hospital experience. However, if a better understanding of the recurring nature of elderly patient movements between the community and hospital can be developed, then it may be possible for alternative provisions of care in the community to be put in place and thus prevent readmission to hospital. The research in this paper aims to model the multiple patient transitions between hospital and community by utilising a mixture of conditional Coxian phase-type distributions that incorporates Bayes' theorem. For the purpose of demonstration, the results of a simulation study are presented and the model is applied to hospital readmission data from the Lombardy region of Italy.

On lattices from combinatorial game theory modularity and a representation theorem: Finite case

We show that a self-generated set of combinatorial games, S, may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question “Is there a set which will give an on-distributive but modular lattice?” appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented.

On lattices from combinatorial game theory modularity and a representation theorem: finite case

We show that a self-generated set of combinatorial games, S. may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question "Is there a set which will give a non-distributive but modular lattice?" appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented. (C) 2014 Elsevier B.V. All rights reserved.

Proving a market for a startup befor scaling using the hypothesis-driven entrepreneurship process

The year is 2015 and the startup and tech business ecosphere has never seen more activity. In New York City alone, the tech startup industry is on track to amass $8 billion dollars in total funding – the highest in 7 years (CB Insights, 2015). According to the Kauffman Index of Entrepreneurship (2015), this figure represents just 20% of the total funding in the United States. Thanks to platforms that link entrepreneurs with investors, there are simply more funding opportunities than ever, and funding can be initiated in a variety of ways (angel investors, venture capital firms, crowdfunding). And yet, in spite of all this, according to Forbes Magazine (2015), nine of ten startups will fail. Because of the unpredictable nature of the modern tech industry, it is difficult to pinpoint exactly why 90% of startups fail – but the general consensus amongst top tech executives is that “startups make products that no one wants” (Fortune, 2014). In 2011, author Eric Ries wrote a book called The Lean Startup in attempts to solve this all-too-familiar problem. It was in this book where he developed the framework for The Hypothesis-Driven Entrepreneurship Process, an iterative process that aims at proving a market before actually launching a product. Ries discusses concepts such as the Minimum Variable Product, the smallest set of activities necessary to disprove a hypothesis (or business model characteristic). Ries encourages acting briefly and often: if you are to fail, then fail fast. In today’s fast-moving economy, an entrepreneur cannot afford to waste his own time, nor his customer’s time. The purpose of this thesis is to conduct an in-depth of analysis of Hypothesis-Driven Entrepreneurship Process, in order to test market viability of a reallife startup idea, ShowMeAround. This analysis will follow the scientific Lean Startup approach; for the purpose of developing a functional business model and business plan. The objective is to conclude with an investment-ready startup idea, backed by rigorous entrepreneurial study.

The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships with fundamental theorems of convex analysis. The second part is about externality in sponsored search auctions. It shows that in these auctions, advertisers have externality effects on each other which influence their bidding behavior. It proposes Hal R.Varian model and shows how adding externality to this model will affect its properties. In order to have a better understanding of the interaction among advertisers in on-line auctions, it studies the structure of the Google advertisements networ.k and shows that it is a small-world scale-free network.

Backbone Colouring of Graphs

Consider an undirected graph G and a subgraph of G, H. A q-backbone k-colouring of (G,H) is a mapping f: V(G) {1, 2, ..., k} such that G is properly coloured and for each edge of H, the colours of its endpoints differ by at least q. The minimum number k for which there is a backbone k-colouring of (G,H) is the backbone chromatic number, BBCq(G,H). It has been proved that backbone k-colouring of (G,T) is at most 4 if G is a connected C4-free planar graph or non-bipartite C5-free planar graph or Cj-free, j∈{6,7,8} planar graph without adjacent triangles. In this thesis we improve the results mentioned above and prove that 2-backbone k-colouring of any connected planar graphs without adjacent triangles is at most 4 by using a discharging method. In the second part of this thesis we further improve these results by proving that for any graph G with χ(G) ≥ 4, BBC(G,T) = χ(G). In fact, we prove the stronger result that a backbone tree T in G exists, such that ∀ uv ∈ T, |f(u)-f(v)|=2 or |f(u)-f(v)| ≥ k-2, k = χ(G). For the case that G is a planar graph, according to Four Colour Theorem, χ(G) = 4; so, BBC(G,T) = 4.

A Representation Theorem for Domains with Discrete and Continuous Variables.

This paper proves a new representation theorem for domains with both discrete and continuous variables. The result generalizes Debreu's well-known representation theorem on connected domains. A strengthening of the standard continuity axiom is used in order to guarantee the existence of a representation. A generalization of the main theorem and an application of the more general result are also presented.

Arrow's Theorem in Spatial Environments

In spatial environments, we consider social welfare functions satisfying Arrow's requirements. i.e., weak Pareto and independence of irrelevant alternatives. When the policy space os a one-dimensional continuum, such a welfare function is determined by a collection of 2n strictly quasi-concave preferences and a tie-breaking rule. As a corrollary, we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave. When the policy space is multi-dimensional, we establish Arrow's impossibility theorem. Among others, we show that weak Pareto, independence of irrelevant alternatives, and non-dictatorship are inconsistent if the set of alternatives has a non-empty interior and it is compact and convex.

Harsanyi’s Social Aggregation Theorem : A Multi-Profile Approach with Variable-Population Extensions

This paper provides new versions of Harsanyi’s social aggregation theorem that are formulated in terms of prospects rather than lotteries. Strengthening an earlier result, fixed-population ex-ante utilitarianism is characterized in a multi-profile setting with fixed probabilities. In addition, we extend the social aggregation theorem to social-evaluation problems under uncertainty with a variable population and generalize our approach to uncertain alternatives, which consist of compound vectors of probability distributions and prospects.